Université de Toulouse I – Sciences Sociales Midi-Pyrénées Sciences Economiques
Thèse pour le doctorat en Sciences Economiques Infrastructure and the Marginal Cost of Public Funds
Présentée et soutenue le 13 décembre 2004 par Michael WARLTERS sous la direction de Mme. Emmanuelle AURIOL
Membres du jury Mme. Emmanuelle AURIOL Professeur à l’Université de Toulouse I M. Helmuth CREMER Professeur à l’Université de Toulouse I M. Shantanayan DEVARAJAN Chief Economist, South Asia Region, Banque Mondiale M. Etienne DE VILLEMEUR Maître de Conférences à l’Université de Toulouse I M. Nicolas GRAVEL Chercheur au Centre de Sciences Humaines, Delhi M. Patrick REY Professeur à l’Université de Toulouse I
Infrastructure and the Marginal Cost of Public Funds Michael Warlters
L’Université n’entend ni approuver, ni désapprouver les opinions particulières du candidat.
Thanks I would like to thank my thesis and DEA supervisor, Mme. Emmanuelle Auriol, for her assistance throughout the course of the past four years. Her gentle direction has greatly improved the thesis, she was always available for discussion, and it was always a pleasure. I couldn’t have asked for more. I wish also to thank M. Devarajan and M. Gravel for accepting to be rapporteurs for the thesis. I appreciate the time and effort that has gone into their comments. My thanks are also due to M. Cremer, M. Rey and M. de Villemeur for their participation on the jury. I am very grateful for comments received from Stéphane Straub on Chapters 2 and 3 and Bertrand Villeneuve on Chapter 4. It’s difficult to think of any time of life that has provided me with such freedom and wealth, both intellectually and socially, as the doctorat. For those who became my French teachers, for those who invited me to their dinners, their parties and their weddings, for those who holidayed with me, for those who invited me to rugby matches and those who viewed my interest in cricket with amusement, for my fellow orienteers, for all the other friends who helped to make my time in Toulouse unforgettable, and for the ducks of the South-West, who sacrificed their lives for my pleasure, I thank you.
Contents 1 Introduction 1.1 Infrastructure, Growth and Poverty . . . . . . . . . . . . . . . 1.1.1 Productivity Effects of Infrastructure Investment . . . 1.1.2 Poverty and Inequality . . . . . . . . . . . . . . . . . . 1.1.3 Assessing the Adequacy of Infrastructure . . . . . . . . 1.2 The Marginal Cost of Public Funds . . . . . . . . . . . . . . . 1.3 Content of the Thesis . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 The Marginal Cost of Public Funds in Africa . . . . . . 1.3.2 Infrastructure Privatization and the Marginal Cost of Public Funds . . . . . . . . . . . . . . . . . . . . . . . 1.3.3 Regulating Natural Gas Transportation as an Exhaustible Resource . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.4 Nonlinear Pricing and the Rate of Extraction of an Exhaustible Resource . . . . . . . . . . . . . . . . . . .
1 2 3 7 8 9 12 12
2 MCF in Africa 2.1 The Marginal Cost of Public Funds . . . . . 2.2 The Model . . . . . . . . . . . . . . . . . . . 2.2.1 Data . . . . . . . . . . . . . . . . . . 2.2.2 Model Calibration . . . . . . . . . . 2.3 Results . . . . . . . . . . . . . . . . . . . . . 2.3.1 Base Case Estimates . . . . . . . . . 2.3.2 Robustness of Results . . . . . . . . 2.4 Informal Sectors and Administrative Costs . 2.4.1 The Informal Economy . . . . . . . . 2.4.2 Costs of Tax Administration . . . . . 2.5 MCF Dispersion & Tax System Inefficiency . 2.6 Conclusion . . . . . . . . . . . . . . . . . . . A.1 Model Specification . . . . . . . . . . . . . . A.2 Data . . . . . . . . . . . . . . . . . . . . . . A.3 Model Calibration . . . . . . . . . . . . . . .
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3 Privatization and the MCF 3.1 The Model . . . . . . . . . . . . . . . . . . . . . . 3.2 A Theory of Infrastructure Privatization . . . . . 3.2.1 Comparing Public and Private Ownership 3.2.2 The Change in Government Revenue . . . 3.2.3 The Privatization Decision . . . . . . . . . 3.3 Empirical Determinants of Privatization . . . . . 3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . B.1 Proof of Proposition 1 . . . . . . . . . . . . . . . B.2 Proof of Proposition 2 . . . . . . . . . . . . . . . B.3 Proof of Proposition 3 . . . . . . . . . . . . . . . B.4 Variable Descriptions . . . . . . . . . . . . . . . . B.5 Descriptive Statistics and Sources . . . . . . . . . 4 Regulating Gas Transportation 4.1 Assumptions and Notation . . . . . 4.2 Hotelling’s Rule . . . . . . . . . . . 4.3 Regulation with Linear Prices . . . 4.3.1 Welfare Maximization versus 4.3.2 Competing Producers . . . . 4.3.3 Production Monopoly . . . 4.4 Regulation with Non-Linear Prices 4.4.1 Welfare Maximization versus 4.4.2 Competing Producers . . . . 4.4.3 Production Monopoly . . . 4.5 Transmission and Distribution . . . 4.6 Conclusion . . . . . . . . . . . . . . 5 Nonlinear Pricing 5.1 Hotelling’s Rule . . . . . . . . . . . 5.2 Marginal Welfare . . . . . . . . . . 5.3 Marginal Profit . . . . . . . . . . . 5.4 Welfare versus Profit Maximization 5.5 Conclusion . . . . . . . . . . . . . .
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Chapter 1 Introduction This thesis concerns aspects of the delivery of infrastructure services: the cost-benefit analysis of public projects; when privatization is desirable; and potential improvements in the regulation of infrastructure services. The thesis also concerns the marginal cost of public funds which is of fundamental importance in any cost-benefit appraisal of public projects, and, it will be argued, an important determinant of the efficiency of infrastructure privatization. The emphasis of the thesis is on developing countries, but there is much that is relevant in rich countries as well. The 1994 World Development Report (World Bank 1994) reported that developing countries invested around $200 billion a year in infrastructure such as water, electricity, and natural gas transmission and distribution networks, telecommunications networks, ports, roads and railways. Around 90% of this was financed by government or foreign aid intermediated by governments. Foreign aid funded nearly $24 billion of infrastructure investment. Private investment accounted for the residual. On average, half of government investment spending went to infrastructure, while maintenance and operating expenditures represented large proportions of governments’ current expenditures. These figures on high finance and ostensible government concern with the provision of infrastructure services stand in stark contrast with the reality of service provision. In 2004, 1.1 billion people lack access to safe drinking water, 2.4 billion do not have adequate sanitation, 1.4 billion do not have access to electricity. Poor transport infrastructure in developing countries is a brake on growth and represents opportunities forgone for the alleviation of poverty. So the stylized facts motivating this thesis are: (i) lots of money is spent on infrastructure; (ii) lots of people do not receive adequate infrastructure services; and (iii) governments remain responsible for the majority of infras1
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CHAPTER 1. INTRODUCTION
tructure investment and service provision. The first two stylized facts suggest that either more money should be spent on infrastructure, or that existing expenditure is wastefully employed, or both. The third fact indicates that expenditures should be subject to public sector cost-benefit appraisal: that is marginal expenditures should yield returns at least as large as the marginal cost of public funds. Inherent in this analysis is a supposition that the services received in developing countries are less than ‘adequate.’ This supposition is examined in the next section, where the linkages between infrastructure, poverty and growth are reviewed. The following section presents the concept of the MCF and its use in public sector cost-benefit analysis. The final section introduces the articles that constitute the substance of the thesis, placing them in a broader context and discussing areas where further work is required.
1.1
Infrastructure, Growth and Poverty
In a prize-winning essay in the Economist (2002), Robert Guest described the development costs of poor roads (and corruption) in Cameroon. A voyage to deliver a lorry-load of Guinness a few hundred kilometres, that should ordinarily have taken one day, took four days because of washed-out roads, accidents and predatory police road blocks. The price of a bottle of beer was 50% higher in rural villages than at the point of bottling. This is a case where high returns can be imagined for investment in improved roads. In China, rapid output growth has outstripped investment in electricity production in recent years, resulting in impending capacity constraints. High returns for investment in electricity production and transmission could be imagined here. In contrast, in the Kyrgyz Republic, the electricity network was expanded to ensure almost universal coverage during the Soviet era, to the point of connections even for shepherds living at the top of remote mountains. The subsequent decline in national output and subsidies from the rest of the Soviet Union has left the network possibly over-sized given the current means of the population. Here, investment in network expansion may well be wasteful, although returns to maintenance are probably high as the network is deteriorating. These examples illustrate that the returns to infrastructure investment are very much case dependent. In some cases demand for infrastructure services exceeds existing capacity, so the returns to marginal projects are high. In other cases, existing capacity is sufficient, and the returns to investment are low. There can be no substitute for individual project cost benefit analysis. As an example of such analyses, the average rate of social return on
1.1. INFRASTRUCTURE, GROWTH AND POVERTY
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World Bank projects during 1983-1992 was 11% for electricity projects, and 29% for road building (World Bank 1994). Such rates suggest that on average the investments were worthwhile, but do not suggest great infrastructure shortages.
1.1.1
Productivity Effects of Infrastructure Investment
But there are problems with cost benefit analyses. Even if performed correctly, they are likely to miss certain externalities. Canning & Bennathan (2000) note, for example, that transport infrastructure may have an effect on market size, the ability to exploit economies of scale, the degree of competition, or the diffusion of knowledge and technology. The public provision of risky, large scale infrastructure used to provide energy services may provide a trigger for private sector investment, important in ‘big push’ models of development. In an effort to take account of such externalities, a small econometric industry has emerged measuring the consequences of infrastructure investment using macroeconomic data. Four methodologies have been used: aggregate production functions; cost or profit functions; regressions of the growth of output; and vector autoregressions (VARs), which avoid imposing assumptions about the direction of causality. Production Function Methodology The paper that launched the industry was that of Aschauer (1989), who sought to estimate the output effect of public investment in the United States. The basic idea is to estimate a Cobb-Douglas production function, of the form: ln(Y ) = ln(A) + a ln(K) + b ln(L) + c ln(G)
(1.1)
where Y is output, A is total factor productivity, K is private capital, L is the labour force and G is the government capital stock. Using time-series data, the estimated coefficient c, the elasticity of output with respect to government capital, had a value of 0.39. The marginal product of a unit of = c YG . Gramlich (1994) calculates that public capital can be estimated as dY dG in the United States in 1991, G was $1938 billion and Y was $4800 billion, implying a marginal product of almost one unit of output.1 The implication 1
A problem with this methodology is that it is very sensitive to the ratio Y/G, and the accuracy of measures of the capital stock. Moreover, when the capital stock is a small fraction of GDP (for example, the value of fixed telephone lines) the multiplier becomes huge, implying very high rates of return.
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CHAPTER 1. INTRODUCTION
from the time series data is that one unit of public capital pays for itself in one year. Many commentators found such rates of return implausibly high. Similar studies using different data sets found the output elasticity of public capital to be in the range 34-39% at the national level, 15-20% at the regional level and 3-8% at the metropolitan level (Munnell 1992). Some critics thought the range of estimates suggested fragile empirical linkages. But it can be argued that they simply show that as the geographic focus narrows, macroeconomic externalities are not captured. Another critique of Aschauer’s methodology was that reverse causation – higher output may lead to higher demand for infrastructure – could bias the results upward. Canning & Bennathan (2000) estimate a translog production function with panel data across countries, using econometric techniques to correct for the problem of reverse causality. For most countries they find rates of return to infrastructure that are similar to, or even below, the returns on other forms of physical capital. But for a group of middle income countries they find acute shortages of sealed roads: the ratios of the rate of return for paved roads to the rate of return for general capital was 37.09 in Bolivia, 17.53 in Colombia, 36.95 in South Korea and 17.99 in the Philippines. For a group of lower and lower-middle income countries they find evidence of high rates of return to electricity generating capacity: the ratio of returns on electricity to returns on general capital was 6.63 for Kenya, 4.74 for Bolivia, 4.58 for Congo, and 4.49 for Gambia. The results suggest there may be large macro-economic effects not detected by micro-economic cost benefit studies, but their existence depends on country and sector specific characteristics. An alternative interpretation of the production function approach is given by Calderón & Servén (2003). They find that the difference in infrastructure levels between Latin American countries and East Asian countries accounts for about one third of the gap in output per worker between these regions. Cost Function Methodology An alternative empirical approach is to use firm cost functions. Morrison & Schwartz (1996) estimate the potential cost savings from a decline in variable inputs required to produce a unit of output when infrastructure investment occurs. They use data for the 48 contiguous states of the United States for 1970–1987. The measure of public capital includes highways, water and sewer capital. Focusing on results for 1982, they find that a $1 million investment in infrastructure results in approximately $160,000-$180,000 cost saving for manufacturing firms in most regions, but almost twice that in southern states. It is not clear that additions to water or sewer capital would usually have major productivity effects for most manufacturing firms, so much of these
1.1. INFRASTRUCTURE, GROWTH AND POVERTY
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effects may come from transport investments. Growth Regressions Methodology Another strand of literature has used economic growth as the dependent variable, with infrastructure indicators on the right-hand side of a reduced form model. Barro & Sala-i-Martin (1995) perform one such analysis, with results suggesting that there is no significant difference in rates of return on public and private investment (i.e., rates of change of capital stocks). Similarly, Levine & Renelt (1992) performed regressions with a long list of variables potentially influencing growth rates, finding that the level of government capital stock never has significantly positive coefficients. Devarajan, Swaroop & Zou (1996) examine the determinants of growth of per capita real GDP in developing countries. Controlling for the level of total public expenditure, they find that the standard candidates for productive public expenditure – capital, transport and communication, health, and education – had either a negative or insignificant relationship with economic growth. The only broad category associated with higher economic growth was current expenditure. Performing similar regressions for rich countries they find opposite results, that increased capital expenditure is associated with higher growth. The results suggest that capital expenditures may have been excessive in developing countries, rendering them unproductive at the margin. Components of current expenditure such as operations and maintenance may have higher returns than capital expenditure. La Ferrara & Marcellino (2000) present a variant on the growth regressions using data on manufacturing output in regions of Italy in 1970-1994. They calculate the growth of total factor productivity (TFP) using a standard growth accounting framework, and then investigate the impact of the growth of capital, labour and public capital on the growth of TFP. They compare the results using this model with results obtained using the production function and the cost function methodologies. The growth accounting methodology suggested a significant elasticity of output with respect to public capital of 0.47. In contrast, using the production function technique, the elasticity is negative and significant. Using the cost function technique, increased public investment slightly increases firm costs, though the effect is close to zero. Esfahani & Ramírez (2003) develop a structural growth model that helps discern the mutual effects of infrastructure and the rest of the economy on each other, distinguishing how different policies and institutions affect steadystates and rates of convergence across countries. They find the elasticity of output with respect to the stock of telecommunications capital to be 0.08 and
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CHAPTER 1. INTRODUCTION
with respect to the stock of electricity capital to be 0.13. These estimates imply that if the growth rate of telephones per capita rose from about 5% as in Africa, to about 10% per year as in East Asia, the annual growth rate of GDP per capita would rise by about 0.4 percentage points. If the growth rate of electricity production increased from 2% in Africa, to 6% as in East Asia, annual GDP growth would increase by a further 0.5%.2 VAR Methodology A final technique for investigating the relationship between output and infrastructure investment is presented by Sturm, Jacobs & Groote (1999), using data on the Dutch economy in the 19th century. A Vector Auto-Regression (VAR) model seeks to explain a limited number of variables by their own lags and lags of the other variables. Infrastructure investment is said to ‘Grangercause’ an increase in GDP if the time-series prediction of GDP from its own past improves when lags of infrastructure investment are added to the equation. Using lags of GDP and investment in infrastructure and private capital, the authors find that infrastructure significantly Granger causes GDP to increase, while GDP growth has a significant, but lesser, negative effect on infrastructure investment. An advantage of this methodology is that it lets the data speak for themselves, without imposing assumptions of particular models. A disadvantage is that it cannot discriminate between infrastructure investments causing GDP to rise and infrastructure rising in anticipation of future GDP growth. Summary of Productivity Impact Estimates The different studies cited suggest ambiguous effects of infrastructure investment on output. Production function techniques commonly, but not always, give high estimates, at least at the national level. The cost function approach also gives significant and positive estimates although, in the paper cited, the rates of return are similar to the marginal cost of public funds, yielding a net return on investment that is close to zero. The growth regression technique gives widely diverging results, ranging from highly positive to negative effects of public infrastructure investment. The VAR technique suggests that in the Netherlands in the 19th century, infrastructure investment induced higher growth. 2
The authors do not report the implied marginal productivity of infrastructure investment. If we value Tanzania’s 862 MW of installed electricity capacity at $862 million, the ratio Y/G=26, so the implied marginal productivity of investment in electricity is 339%.
1.1. INFRASTRUCTURE, GROWTH AND POVERTY
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Part of the reasons for these different results is surely related to the estimation methodologies employed, as highlighted by La Ferrara & Marcellino (2000) who find different results using the same data but different methodologies. But part of the variation is probably also due to the fact that the productivity of infrastructure investment, even taking account of macroeconomic externalities, is likely to depend on whether the existing infrastructure is in short or excess supply. In interpreting the results of these macroeconomic studies it is also useful to bear in mind the standard warning message associated with all investment: past returns offer no guarantee of future performance. For example, construction of new infrastructure systems, such as railways in the 19th century or the US or European highway networks built in the 1950s to 1970s, may have had high returns. Extensions to the networks might have much lower returns. In developing countries, where the coverage of infrastructure networks is low, there are reasons to believe that investment in network expansion could have high returns, but if Devarajan et al. (1996) are right, maintenance of existing networks could have even higher returns.
1.1.2
Poverty and Inequality
Even if infrastructure investment does not yield output returns greater than other forms of physical capital, additional investment may be justified if it reduces poverty or inequality. Some of the strongest poverty links are found with investments in water services and rural roads. Access to clean water and adequate sanitation play an important role in health, one of the most important indicators of well-being. For example, Jalan & Ravallion (2000) find that the prevalence and duration of diarrhea for children under five in India is significantly lower for families with piped water than for equivalent families without access to piped water. Galiani, Gertler & Schargrodsky (2004) find that privatization of water services in Argentina led to increased connections to water and sanitation services for the poor, and higher quality services. As a result, child mortality fell by 8% on average in the areas that privatized their water services, and the effect was greatest (26%) in the poorest areas. Leipziger, Fay, Woden & Yepes (2003) find that a quarter of the difference in infant mortality between the rich and the poor is explained by their respective access to water services. Rural roads provide cheaper access to markets for agricultural outputs and for modern inputs, as well as improving the quality of life through improved access to modern consumer goods. They can thus lift the incomes of rural farmers. Jacoby (2000) finds that rural roads in Nepal substantially diminish rural poverty, but have only a limited effect on inequality within
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CHAPTER 1. INTRODUCTION
rural areas because the benefits tend to accrue more to landowners, who are not generally among the very poor. Other forms of infrastructure typically have an effect on poverty through their effects on output. But more direct effects are possible. For example, electricity allows more time for study (because of cheap lighting at night) and the use of computers, and so has an impact on educational attainment. Electric lighting can also have an effect on health, when it replaces kerosene lamps. Access to telecommunications services can lift incomes for rural farmers, by giving them better information about market prices, and so squeezing the margins of middle-men. A recent attempt to measure the effect of infrastructure provision on inequality found that income inequality declines with higher infrastructure quantity and quality. Calderón & Servén (2004) obtain this result with a database encompassing over 100 countries and covering 1960-2000, using the Gini coefficient as the dependent variable. A variety of tests supports the proposition that causation does indeed run from infrastructure to reduced inequality. Much of the interest in infrastructure’s effect on inequality has focused on the effects of privatization. Newly privatized firms may cut employment, but the impact on inequality depends on the income distribution of dismissed workers prior to being laid off, the monetary compensation they receive, and their probability of being re-employed. In some cases, notably telecommunications, privatization has been associated with reforms increasing competition, and an increase in total employment in the industry. The distributive impact of privatization can also depend on how transaction revenues are used. Privatization is often associated with pricing reforms, including the elimination of subsidies, which may limit affordability for low income groups. Overall, it seems that the effect of privatization on income distribution is very much a product of how the reforms are designed. Any adverse effects on inequality can be minimized by establishing a regulatory environment restraining prices and with obligations for increased service coverage for the poor; by cushioning the employment impact with adequate severance and retraining packages; and by using revenues for pro-poor expenditures.
1.1.3
Assessing the Adequacy of Infrastructure
On poverty or inequality grounds it can be argued that access to certain infrastructure services is a basic need, regardless of the cost. For example, the South African government has made it a priority to ensure that all households have access to safe water within 500 metres of the house. Such a policy automatically places high value on the benefits of water provision, and
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does away with the need for comparison of costs and benefits. (The policy does not, however, extinguish the need for comparison of least-cost means of providing safe water.) But outside such special cases there is a need for micro-economic cost benefit analyses. There is no blanket rule that infrastructure investment always has a high return. Since the returns to infrastructure investment are project specific, it is important that governments implement systems that ensure appropriate methodologies for decision-making. As argued in the next section, estimates of the benefits of public projects should be compared against the marginal cost of public funds. Privatization perhaps provides stronger incentives to make correct investment decisions (or at least to make the decisions more quickly)3 , but only to the extent that market demands reflect social benefits. It is likely that the wider economic benefits will not always be fully captured by micro-economic studies. The papers cited suggest that, at least in some cases, infrastructure investments can have important macroeconomic externalities, even to the point of lifting the rate of economic growth. When such externalities exist, there is a case for public subsidy. But it is not clear exactly how to identify the circumstances in which these external effects occur. It seems possible that a precondition for such externalities is an excess of private demand compared with infrastructure capacity. If so, standard cost-benefit studies should indicate high rates of return, sufficient to justify investment, any time when there are additional externalities. To avoid the possibility of white elephants built on the imagined possibility of great externalities, the safest course seems to be to rely on thorough cost-benefit analysis, comparing measurable benefits with the marginal cost of public funds.
1.2
The Marginal Cost of Public Funds
The marginal cost of one dollar of public funds is typically greater than one, because of the welfare costs induced by distortionary taxes. A commonly cited estimate of the MCF for the United States is 1.33, indicating that raising $1 by taxation induces a 33 cent welfare cost (Ballard, Shoven & Whalley 1985). In an efficient economy there is a single MCF, since the welfare cost of all tax instruments should be equalized at the margin. Moreover, in an efficient economy the MCF is equal to the marginal benefit of public funds (MBF). As illustrated in Figure 1.1, the intersection of the MCF and 3
Esfahani & Ramírez (2003) find that the rate of convergence to the steady state growth rate is higher when infrastructure is privatized.
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CHAPTER 1. INTRODUCTION
MCF
a MBF 1
b
Revenue/GDP
Figure 1.1: MCF and the Optimal Size of Government MBF functions determines the optimal MCF (a) and the efficient size of government (b). If a new public infrastructure project is proposed, it should have a return at least equal to the optimal MCF. This neat theoretical framework is disturbed by several considerations. In the first place there are multiple tax instruments, and in practice governments do not equate the MCF for different taxes. Thus, there are multiple MCFs, and in a non-optimized economy, it is not possible to draw a nice diagram such as Figure 1.1. Many practitioners side-step this problem by talking of a revenue-weighted average of MCFs for all tax instruments, supposing that governments needing additional revenue will increase all taxes proportionately. But the true marginal cost of funds will depend on which taxes are actually involved when governments marginally alter their revenues. It is thus important to know the marginal costs of each tax instrument. This is the subject of Chapter 2. Secondly, governments can raise funds by borrowing rather than by increasing taxation. Measures of the interest rate associated with government borrowing are frequently used in practical cost benefit analysis for public projects. If the true cost of debt were the interest rate, and if the interest
1.2. THE MARGINAL COST OF PUBLIC FUNDS
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rate were lower than the MCF of taxation, then governments should indeed increase debt. But there are various limits to the amount of debt governments can incur, and when these limits are reached any additional revenue must be raised by taxation. Moreover, the true cost of debt is not just the interest rate. In a draft paper, Dahlby (2004) uses a simple AK endogenous growth model to examine the relation between public debt, distortionary taxation and the growth rate. The net savings rate (public plus private savings) determines the growth rate. An increase in public debt of itself lowers the growth rate. But it also has an effect on private savings. Distortionary taxes must increase to meet the interest payments, reducing the return on saving, and so reducing private savings. And in a Ricardian equivalence effect, households anticipate higher taxes and so increase their savings. The Ricardian equivalence effect exactly offsets the decrease in public saving, so net savings decline because of the distortionary tax effect, resulting in lower growth, and thus lower welfare. Calibrating his model to the Canadian economy, Dahlby finds that government bonds with an interest rate of 8% have a marginal cost of public funds of 1.15.4 If the Ricardian equivalence effect is muted, the welfare cost of debt is higher. Finally, governments can fund marginal expenditure by cutting existing programs. The neat MBF function of Figure 1.1 implicitly supposes that governments analyze the returns on all their potential projects, and then perform the projects in descending order of return, until such a point that the revenue requirement increases the MCF to equate the MBF. In this setting, the MBF of a marginal project, would be equal to the MCF of raising funds through increased taxation. Cutting any other project would have a higher MCF than an increase in taxes. Thus, if governments make mistakes about the project with the lowest marginal benefit when choosing a program to be cut, the MCF of funds obtained by cutting an existing program will on average be higher than the MCF of funds obtained by increased taxes. In practice, there are likely to be implemented projects that yield marginal benefits less than the MCF, and the MCF of funds obtained by cutting existing programs will be program specific. But if governments have some tendencies towards choosing projects efficiently, the MCF of cutting programs should tend on average to be close to, but higher than the MCF of increased taxation. To summarize, governments can raise funds by different tax instruments, by borrowing, or by cutting existing programs. There is likely to be a different 4
The 8% interest rate is not mentioned by Dahlby (2004), but can be derived from his calibration figures.
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CHAPTER 1. INTRODUCTION
MCF associated with each of these mechanisms. The threshold rate of return to be used in public cost benefit analysis is different depending on how the government intends to raise the funds. Nevertheless, the argument that there are limits to borrowing suggests that, ultimately, if governments wish to increase total spending (i.e., without sacrificing existing programs) it must be paid for by increased taxes. Accordingly, the MCF associated with taxation is probably the best candidate as a threshold rate of return for public projects.
1.3 1.3.1
Content of the Thesis The Marginal Cost of Public Funds in Africa
Despite the obvious importance of measures of the MCF for the cost-benefit appraisal of public infrastructure projects, in practice the MCF is rarely used. One of the principal reasons for this is that very few estimates exist, particularly in Africa. There is a need for a practical way to estimate the MCF of different taxes. The challenge taken up in Chapter 2 is to develop a means of estimating MCFs for the main classes of taxes, using data that is readily available. The paper uses a simple general equilibrium model, written in GAMS MPSGE, to estimate the MCFs of taxes on domestic goods, capital, labour, exports and imports in 38 sub-Saharan countries. The basic model is derived from the ‘1-2-3 model’ of Devarajan, Go, Lewis, Robinson, & Sinko (1994), a model that can be calibrated with little more than national accounts data. The 1-2-3 model has one country with two producing sectors and three goods: a domestic good, exports and imports. This model is extended to include production of an informal good, and four factors of production: formal capital, informal capital, formal labour and informal labour. The definition of an informal good or factor is simply one on which no tax is paid. The paper uses a very simple calibration method for calculating the size of informal parts of the economy. For example, the size of the formal domestic sector is calculated as VAT revenue divided by the VAT rate. Excluding export production, the residual part of GDP is the informal economy. Although crude, this methodology gives roughly the same estimates of the informal economy as are found for the two African countries mentioned by Schneider & Enste (2000) in their survey of informal economy estimates. The general equilibrium model is sufficiently simple that most of the results are entirely intuitive. But the estimates suggest an average African MCF of 1.17. This is lower than most estimates for rich countries, and runs counter to intuition for many people, who consider that inefficient taxation
1.3. CONTENT OF THE THESIS
13
MCF
MCF’
MBF’ a MBF
1
b
Revenue/GDP
Figure 1.2: MCFs in Rich and Poor Countries systems in poor countries should result in high MCFs. An inefficient tax system results in a higher MCF function. But it is also a fact that rich countries tax a larger proportion of GDP (25% to 50% in rich countries, compared with around 20% in Africa). So the apparent conundrum of a higher MCF function in poor countries, a higher observed MCF value and higher tax revenue in rich countries could be resolved by supposing that the MBF function is higher in rich countries. Thus, in Figure 1.2, rich countries are represented by MCF’ and MBF’, and the equilibrium MCF value is higher. In fact, it is not clear that the MCF function is higher in poor countries (when the MCF function is calculated as a revenue-weighted average of the MCFs of individual taxes). Chapter 2 suggests that the MCF function tends to be higher with greater reliance on capital, labour, or export taxes, and with higher administrative costs of collecting taxes or larger informal sectors. Rich countries tend to rely more on capital and labour taxes than poor countries, while poor countries tend to rely more on export taxes, have higher administrative costs and larger informal sectors. Where these effects balance is an empirical question that requires estimates of the MCFs for rich countries using a comparable model.
14
CHAPTER 1. INTRODUCTION
In the context of this thesis, the motivation for estimating MCFs is their use in infrastructure project appraisal. Using MCF estimates for cost-benefit analysis there is often a question whether the benefit side has been measured in a way that is appropriate given the MCF measurement methodology. In particular, benefits are often measured using consumer prices as the numeraire, while MCFs are often measured using producer prices as the numeraire. Such differences in methodology can render cost-benefit comparisons meaningless, since estimates of both MCFs and MBFs depend on the numeraire (Triest 1990). This may be further explanation for why MCF estimates are rarely used in cost-benefit analysis. MCF estimates requiring returns of between 17% and 30% sound like prohibitively high thresholds for analysts used to using thresholds such as an 8% rate of interest to justify public investment. But it seems possible that if benefits were measured in a fashion consistent with MCF estimates, the resulting rates of return on infrastructure would indeed be consistent with the high MCF thresholds. This is a case where greater theoretical work is required concerning the appropriate way to measure the marginal benefit of public expenditure. A more direct use of the MCF estimates generated by the paper is in tax reform. If the MCF of two taxes differ, welfare can be improved holding government revenue constant by lowering the tax with a high MCF and increasing the tax with a low MCF. Thus directions for partial tax reform can be derived from the MCF estimates, without any doubt about whether the estimates have been prepared using consistent methodologies. Much of the paper interprets the MCF estimates in terms of their implications for tax reform. For example, the paper suggests that taxes on factors and on exports are particularly costly, and suggests that greater reliance on VATs and imports taxes would improve welfare. Another of the findings of Chapter 2 is that the magnitude of the informal sector is an important determinant of the level of the MCF. At least for the African countries studied, the informal sector size seems to be more important than differences in tax structure. Auriol & Warlters (2004) suggest that developing country governments have a revenue incentive to limit the size of the formal sector, at least in the short term. Governments wish to create market power by limiting entry into the formal sector, in order to confiscate the rents. Barriers to entry are created using entry fees and other red tape obstructions. Reading the two papers together, governments that can reduce market entry fees are likely to enlarge their formal sectors, and thus increase their tax bases and tax revenue in the long term, and simultaneously reduce the marginal cost of public funds. As with many applied general equilibrium models, the results depend on
1.3. CONTENT OF THE THESIS
15
assumed elasticities. For the base case estimates all production and consumption elasticities of substitution are assumed to be Cobb-Douglas. For many of the elasticities this is a reasonable assumption. In any case, the ordering of results (important for tax reform) is little affected in sensitivity testing. Among the unknown elasticities, the results are most sensitive to the consumers’ elasticity of demand substitution between the informal good and the taxed domestic good. To tighten up the robustness of the model, empirical work to measure this elasticity would be particularly useful.
1.3.2
Infrastructure Privatization and the Marginal Cost of Public Funds
Since the 1980s governments have increasingly turned to the private sector to manage and to invest in infrastructure. There seem to have been two principal motivations for privatization. One is the conversion of a future flow of revenues into a capital sum, that can be used to resolve immediate cash flow difficulties. The other is a belief in the greater efficiency of the private sector. Chapter 3 examines the revenue and efficiency effects of privatization, finding that the benefits and costs vary with the MCF. Two forces operate: the private sector has stronger incentives to reduce costs, but also earns higher information rents under regulation than a public firm. When the cost of raising public funds through taxation is low, the welfare cost of paying information rents is low, and public sector managers have weak incentives to reduce costs because they know the government will bail them out in the event of a loss. When the MCF is high, the government can use a public firm as a low welfare cost source of funds, the welfare cost of a private firm’s information rents is high, and public sector managers have stronger incentives to reduce costs because bailouts are less likely. The paper supposes that the government is a welfare-maximizer. Whatever governments’ true motivations, privatization is presumably politically easier to implement if it enhances welfare, so that privatization is more likely to occur. Using the introduction of a VAT as a proxy for a reduction in the MCF (more efficient taxation lowers the MCF), the theory is empirically supported by data on infrastructure privatizations in developing countries. Various other arguments have been raised, for and against infrastructure privatization. Some politicians have mistakenly believed that privatization is a means of having the private sector fund infrastructure investment. Of course, private investors require a return on their investment, which must be achieved either through government payments or user fees. Citizens ulti-
16
CHAPTER 1. INTRODUCTION
mately pay for the services they receive, either as tax payers or as consumers. Privatization offers no free lunch. An argument opposing privatization is that governments have a lower cost of capital than private investors, so that it is cheaper for governments to finance investment. The interest rate on government borrowing is indeed typically lower than the rate offered to private firms in the same market. But Klein (1997) notes that this is because governments can have recourse to taxation to repay their debts in the event of project failure, so that taxpayers provide an unremunerated form of credit insurance or callable capital. If the insurance or callable capital were properly priced at the true cost to society, the government’s ostensible capital cost advantage would disappear. In any case, as argued above, the cost of government debt is not simply the interest rate, but also the additional distortionary cost of taxes necessary to meet the debt repayments. The theoretical section of Chapter 3 focuses on government motivations for privatization. It supposes that governments are able to obtain the full value of the privatized firm, by means of a competitive auction. But there have been many cases of governments that have sought to privatize but have been unable to find investors. In many cases this may be due to unrealistic expectations on the part of governments. A minimum requirement for profitability is that tariffs cover costs, but even this may not be possible when the population served is very poor. If the government is truly committed to providing infrastructure services to such a poor population, this problem can be overcome by so-called ‘negative concessions’, where the right to operate the business is auctioned to the private firm requiring the least subsidy. But such a mechanism requires investor confidence that the government will indeed pay the subsidy. Even when demand is sufficiently high to meet cost-covering tariffs, investors require credible government commitments concerning the durability of such tariffs. Governments face strong political pressures to reduce tariffs. Once investors have sunk their investments, governments can renege on commitments to keep prices sufficiently high to cover those fixed costs. Provided the regulated price covers marginal costs, the private operator could still be induced to continue operations. But investors know all this, so they will not invest unless the government can give credible commitments concerning the future trajectory of regulated prices. In many countries with weak governments it is simply impossible to give credible commitments. Private investors can compensate for some level of country risk by increasing the premium they require, but this has the effect of increasing consumer tariffs, and rendering the whole package even more unstable. It is for reasons such as these that infrastructure privatization practition-
1.3. CONTENT OF THE THESIS
17
ers have placed much emphasis on mechanisms which would help to increase the credibility of government commitments to cost-covering tariffs. Such mechanisms include the establishment of independent regulatory agencies with statutory duties to ensure cost-covering tariffs; transparent procedures for privatization transactions, to reduce the risk of subsequent legal challenges which would provide an excuse to subsequent governments to renege on the privatization contract; or the involvement of local investors in the privatization transaction to provide more effective political resistance to any subsequent government attempt to renege on privatization commitments. The empirical section of Chapter 3 finds that certain aspects of country risk do indeed have an effect on the probability of infrastructure privatization. For all these reasons, there is a need to supplement Chapter 3’s theory for when governments wish to privatize, with an additional theory of the conditions under which investors wish to participate in privatization transactions, and what proportion of the risk-free value of the transaction they are willing to pay.
1.3.3
Regulating Natural Gas Transportation as an Exhaustible Resource
A further possible critique of the analysis of Chapter 3 is that it supposes that infrastructure firms are regulated by classic mechanisms of the sort propounded by Baron & Myerson (1982) or Laffont & Tirole (1998), where the problem is to limit the market power of infrastructure monopolies. Historically, the problems of public infrastructure service provision in developing countries have frequently been low prices rather than monopoly prices. To curry political favour, politicians in many countries have resisted price increases or even the enforcement of consumer bills, resulting in the worst cases in inadequate firm revenues, and thus non-existent network expansion, inadequate maintenance and deteriorating services. Furthermore, the classic regulatory mechanisms have typically supposed strong institutions, including the ability to enforce contracts, assumptions that are not always relevant in developing countries. Accordingly, there is a developing literature on the adaptation of classic regulatory mechanisms to the constraints of developing countries. For example, Laffont (2004) examines how the choice between price cap and cost of service regulation is affected by developing country characteristics, and develops a theory of regulation with limited enforcement. Much work on regulation in developing countries addresses the incentives created by institutional arrangements.
18
CHAPTER 1. INTRODUCTION
Despite these advances there is still room for improvement in the classic forms of regulation developed for rich countries. Chapter 4 suggests a potential improvement in the way that natural gas pipelines are regulated. The name of the paper arises from the fact that pipelines are rendered useless when the gas resource is exhausted, so that pipelines are themselves exhaustible resources. The basic idea is that under Hotelling’s Rule for the optimal extraction of an exhaustible resource, prices on the welfare maximizing path should rise over time at a rate that ensures that marginal welfare rents (the difference between the price and the marginal cost of delivered gas) rise at the rate of interest. The existence of these positive rents means that regulators of the transportation price could cover the fixed costs of pipeline construction without any distortion of the first-best price path for delivered gas. In comparison, standard methods of regulation achieve at best an approximation of the optimal price path. The standard method of regulation is characterized in the paper as a fixed markup on the price of transportation over the marginal cost of transportation. The markup is designed to cover the fixed cost of pipeline construction. The markup could be determined by means such as cost of service or price cap regulation. The important point is that it stays fixed over time, so that marginal welfare rents do not rise over time as required by Hotelling’s Rule. If production is competitive, such a regulatory strategy would result in prices for delivered gas which are a little worse than optimal. If production is monopolized, the strategy would result in prices that are a little worse than an unregulated monopoly. Chapter 4 has obvious relevance in developing countries with natural gas resources. Pipelines already exist between and within Chile and Argentina; Bolivia and Brazil; Uzbekhistan, Kyrgyz Republic and Kazakhstan; Russia and Europe; North Africa and Europe; within Bangladesh; and a pipeline is planned along the coast of West Africa to take natural gas from Nigeria to the neighbouring countries as far as Côte d’Ivoire. The paper is useful for intra-country regulation, within the country of gas production. But one message of the paper is that access regulation is of little use for importing countries. Faced with a monopoly supplier of gas, regulation of the price of transportation can indeed achieve the optimal price of delivered gas, but only at the expense of very high rents being transferred to the supplier. To resolve such questions of market power, importing countries must participate in the larger game which is not addressed in the analysis of Chapter 4: the game in which the market structure is established. In this game, a natural gas pipeline is constructed only if the present value of the cost of delivered energy is less than the cost of energy delivered by other means – gas pipelines from other countries, or production of electricity by other means.
1.3. CONTENT OF THE THESIS
19
At the time of constructing the pipeline, the gas producer’s market power is constrained by the possibility of alternative energy sources. The importing country typically signs a contract to ensure that these constraints continue to operate over a long term, fixing the final consumer price for delivered gas, rather than just fixing the transportation price.
1.3.4
Nonlinear Pricing and the Rate of Extraction of an Exhaustible Resource
Chapter 5 presents a short technical note on nonlinear pricing, closely related to the analysis in Chapter 4. Existing analyses of extraction of exhaustible resources have entirely considered linear pricing. This is natural, since for the majority of exhaustible resources, of which oil is no doubt the most significant, the possibility of resale between consumers rules out the possibility of nonlinear prices. For natural gas, it is physically possible to liquefy natural gas and to resell it, but this is uneconomic for small quantities or for delivery distances shorter than about 3000 kilometres. For natural gas delivered by pipelines nonlinear prices are clearly feasible and indeed commonly observed: most consumers pay a fixed monthly fee and a per unit tariff. Hotelling’s Rule governs the optimal extraction of gas, fixing the quantities of gas to be extracted in each period. To maximize welfare, linear prices should be used in intra-period pricing, since this is the optimal fashion to ration a fixed quantity across heterogeneous consumers. But a monopolist, under the assumptions of the paper, would choose a price schedule that gives a lower marginal price to consumers who consume greater quantities of gas. In standard textbook expositions, where monopolists are constrained to use linear prices, monopolists extract gas too slowly, relative to the welfare maximizing rate. Allowing for the possibility of nonlinear prices, a monopolist extracts gas too slowly at periods far from the final exhaustion date, and too quickly at dates close to exhaustion.
Chapter 2 The Marginal Cost of Public Funds in Africa What social rate of return should public infrastructure projects be required to achieve in Africa? What is the next challenge in the reform of African tax structures? The answers to these questions require knowledge of the marginal cost of public funds (MCF). If a project does not yield a social return greater than the MCF, it is not worth having. Holding revenue constant, welfare can be increased by reducing taxes with high MCFs and increasing taxes with low MCFs, so estimates of MCFs provide directions for reform of tax structures. The central role of the MCF in these important public policy issues is well known. So it is surprising that there are few empirical estimates of MCFs. Table 2.1 summarizes existing estimates. We know of only three papers in which estimates of the MCF have been derived for developing countries. We know of only one African country, Cameroon, for which the MCF has been estimated. Moreover, for methodological reasons existing estimates are not all truly comparable. Perhaps the major reason for this relative paucity of MCF estimates has been the amount of data required and the time expense of creating and calibrating the computable general equilibrium (CGE) models used for estimation. CGEs are required because real tax systems are complex, and because it is necessary to take account of multiple interactions within tax systems.1 Thus, the challenge as we have conceived it is to develop a simple CGE model that can be calibrated with little more than national accounts data, and which can be used to provide consistent estimates comparable across 1
To provide the intuition for the effects of key parameters, analytical models with minimal data requirements were used in initial development of the theory (e.g. Stuart (1984), Mayshar (1991), Snow & Warren (1996)). But there are limits to the complexity of models that can be solved analytically.
21
22
CHAPTER 2. MCF IN AFRICA
countries. To be useful for tax policy analysis, the model should take account of the major classes of taxes in African countries: taxes on domestic goods, exports, imports, corporate income tax, and personal income tax. On average, in the sub-Saharan African countries that we examine, these taxes represent respectively 25%, 3%, 35%, 13%, and 14% of tax revenue, with the remaining 10% coming from other sources.2 A key requirement for realism is that the model should take account of the existence of informal sectors, which occupy a larger part of the economy in Africa than elsewhere. For example, Schneider & Enste (2000) report the shadow economy occupied on average 15% of GDP in OECD countries in 1990, but 27% in Botswana and 76% in Nigeria.3 We might suspect that in countries with larger informal sectors, it is easier for economic agents to shift from formal to informal activity. Greater substitutability would lead to higher marginal costs of taxation on formal activity. The presence of an informal sector has been shown to have a noticeable effect on MCF estimates in Canada.4 In addition to the economic effect of informal sectors, including informal sectors avoids a calibration problem. CGE models have sometimes applied ‘effective’ tax rates, calculated as tax revenues divided by sector size. This results in low modelled tax rates. Effective tax rates provide an average between taxpayers who pay tax at something like the legal rate, subject to some under-reporting, and informal producers or consumers who pay no tax. Effective tax rates underestimate the marginal tax rate incurred by those who actually pay tax. Models using effective tax rates are thus likely to underestimate MCFs.5 2
Eighteen countries in our sample do not use export taxes. Among the twenty countries that do use them export taxes constitute 7% of tax revenue. 3 These figures are estimated using physical input methods. 4 Fortin & Lacroix (1994) suggest the informal sector accounts for around 0.02-0.05 of their MCF estimates of 1.39-1.53 for labour taxation in Canada. They note that although small, the impact of the informal sector increases rapidly with the level of the marginal tax rate. The importance of the informal sector when analyzing taxation in developing countries is also emphasized in other settings in recent papers by García Peñalosa & Turnovsky (2003) and Emran & Stiglitz (2004). 5 It seems that the models used by Devarajan, Suthiwart-Narueput & Thierfelder (2001) apply ‘effective’ tax rates. For example their Cameroon model applies tax rates of 0.7% for food and forestry, 2.5% for intermediate goods, 3.4% for construction, 6% for services, 7.4% for food and consumption, and 19.1% for cash crops. We do not have access to the legal tax rates in force at the time the Cameroon model was created, but the current VAT rate (which has replaced the previous system of sales taxes) is 18%, suggesting that effective tax rates were indeed used in their model. The relatively high effective tax rate for cash crops may be explained by noting that cash crops are largely exported. Exports tend not to escape taxation, so the effective tax rate approximates a revenue-weighted
23
Country Australia Australia Australia Australia Bangladesh Bangladesh Cameroon Cameroon Canada Canada Canada China India India India Indonesia Indonesia New Zealand Sweden United States United States United States United States United States
Table 2.1: Tax type Labour Labour Capital Capital Sales Import Sales Import Commodity Labour Labour Sales Excise Sales Import Sales Import Labour All taxes All taxes Labour Labour All taxes Labour
Selected MCF Estimates Estimate Source 1.19-1.24 Campbell & Bond (1997) 1.28-1.55 Findlay & Jones (1982) 1.21-1.48 Diewert & Lawrence (1998) 1.15-1.51 Benge (1999) 0.95-1.07 Devarajan et al. (2001) 1.17-2.18 Devarajan et al. (2001) 0.48-0.96 Devarajan et al. (2001) 1.05-1.37 Devarajan et al. (2001) 1.25 Campbell (1975) 1.38 Dahlby (1994) 1.39-1.53 Fortin & Lacroix (1994) 2.31 Laffont & Senik-Leygonie (1997) 1.66-2.15 Ahmad & Stern (1987) 1.59-2.12 Ahmad & Stern (1987) 1.54-2.17 Ahmad & Stern (1987) 0.97-1.11 Devarajan et al. (2001) 0.99-1.18 Devarajan et al. (2001) 1.18 Diewert & Lawrence (1994) 1.69-2.29 Hansson & Stuart (1985) 1.17-1.33 Ballard et al. (1985) 1.21-1.24 Stuart (1984) 1.32-1.47 Browning (1987) 1.47 Jorgenson & Yun (1990) 1.08-1.14 Ahmed & Croushore (1994)
24
CHAPTER 2. MCF IN AFRICA
Our paper makes several contributions to the literature on MCFs. The first is the development of a simple general equilibrium model that can handle taxes on the five major tax classes, takes account of the existence of informal sectors, can be calibrated with little more than national accounts data, and can be easily reproduced by other researchers for other countries. After a brief review of the existing literature in section 2.1, we present the model in section 2.2. It is inspired by the minimal data requirements of the ‘1-2-3 model’ of Devarajan et al. (1994). The basic 1-2-3 model has one country with two producing sectors and three goods: a domestic good, exports and imports. This model is extended to include production of an informal good, and four factors of production: formal capital, informal capital, formal labour and informal labour. Our definition of an informal good or factor is simply one on which no tax is paid. Section 2.3 contains the paper’s second important contribution: application of the model to produce estimates of MCFs for taxes in 38 African countries, vastly increasing the number of developing countries for which MCF estimates exist. Sensitivity testing of the model reveals which elasticities are the most important in determining MCF magnitudes, and suggests that our base case estimates are reasonably robust for purposes of tax reform. The paper’s third innovation, presented in section 2.4 is an investigation of the marginal cost of raising funds in currently informal sectors, and the effect of administrative costs on MCF estimates. We find that quite high levels of administrative costs would be justified to extend taxation to currently exempt informal sectors. Finally, in section 2.5 we examine the relationship between dispersion of MCFs for different tax instruments and the scope for welfare improving tax reform. We conclude in section 2.6.
2.1
The Marginal Cost of Public Funds
The MCF measures the change in social welfare associated with raising an additional unit of tax revenue using a particular tax instrument: M CF = −
∆W ∆R
(2.1)
where ∆W is a monetary measure of the change in social welfare and ∆R is the change in tax revenue arising from a marginal change in a tax instrument. The change in social welfare is a measure such as the equivalent variation or change in consumer surplus, rather than the marginal excess burden. Useful average of legal tax rates.
2.1. THE MARGINAL COST OF PUBLIC FUNDS
25
Figure 2.1: Calculating the MCF @ @@ 1 @@D2 0 @ D2@ @@ @@ 1 + t2
@
@ D10 @ @
1 + t1
a
@ @
@
b @
1 c q11 q10
d@@ M C1
@ @
1 e
@ @
q20 q21
@@ M C2 @@ @@ @@
A marginal increase in the tax on good 1, reduces compensated demand for good 1 from q10 to q11 . The consumer’s reduction in spending on good 1 liberates income to be spent on good 2, shifting the compensated demand curve for good 2, and increasing compensated demand for good 2 from q20 to q21 . The marginal change in welfare is given by area a, the change in compensated tax revenue is given by areas a − b + d. So a measure of the MCF of the tax on good 1 is a/(a − b + d).
reviews of the theoretical and empirical literature on MCFs can be found in Ballard & Fullerton (1992) and Devarajan et al. (2001). One possible measure of the MCF in the presence of goods taxation is illustrated in Figure 2.1, in a simple two good partial equilibrium setting with fixed producer prices. Quantity units for the two goods are chosen so that producer prices for the two goods are equal to one. A marginal change in the tax on good 1 reduces consumer welfare by area a, and increases compensated tax revenue by a − b + d, giving an MCF of a/(a − b + d). If all the income released by the reduction in demand for good 1 is spent on good 2, the MCF can be approximated by M CF1 =
1 1+
t1 ε1 ( 1+t 1
−
t2 ) 1+t2
(2.2)
where ε1 < 0 is the compensated elasticity of demand for good 1.6 This simple formula highlights key determinants of the MCF, but it does not deal with the full complexity of the tax system. For example, it does not capture distortions arising from taxation of intermediate goods or factors, and it does not take into account how the marginal tax revenue is spent. 6
See Browning (1976) for the approximation methodology for areas a, b and c. The assumption that all income released from good 1 spending is spent on good 2 (eg. because t2 there are only 2 goods) enables area d to be measured as 1+t (b + c). 2
26
CHAPTER 2. MCF IN AFRICA
Nor is the methodology underlying this formula the only, or indeed the most common, way of calculating the MCF. Different measures of the MCF for the same tax instrument can be found according to: • The nature of the tax experiment conducted. Ballard & Fullerton (1992) identify two broad classes of theoretical analysis: ‘differential’ and ‘balanced budget.’ In differential analysis, one tax is marginally increased and another is decreased sufficiently to maintain the budget balance. The usual experiment is to increase a distortionary tax, and to reduce a lump-sum tax (return the revenue to consumers as a lump-sum). The income effects of the two tax changes cancel, leaving only substitution effects. Estimates of the welfare change, ∆W , depend on compensated elasticities, while the change in revenue, ∆R, can be equated with the actual lump-sum transfer. In balanced-budget analysis, one tax is marginally increased and the revenue is spent on a public project. Income effects are included in the analysis, and MCF estimates are derived using uncompensated elasticities. These are not the only possible measures. Wildasin (1984) proposed a measure in which the compensated change in welfare is divided by the compensated change in tax revenue rather than the actual change in tax revenue (the measure illustrated in Figure 2.1). • The choice of numeraire. Håkonsen (1998) has proposed an alternative measure derived from the dual of the government’s optimal tax problem (maximize revenue subject to a given level of social welfare) that is invariant to the choice of numeraire. • The attribution of some general equilibrium effects between benefit and cost. Consider a marginal tax increase that increases revenue by one dollar, before public spending occurs. Public spending could increase the tax base in a second round effect (for example, building highways increases petrol tax revenue). If this second round effect is attributed to the MCF, the increase in revenue is greater than one dollar, and the MCF is accordingly reduced. But the second round effect could equally well be attributed to a measure of the marginal benefit of public spending. Mayshar (1991) proposed that all revenue effects of public spending should be incorporated in the benefits measure (MBF), rather than the MCF. The consequence of this multiplicity of measures is that MCF estimates prepared using different methodologies are not comparable. Fortunately,
2.2. THE MODEL
27
Schöb (1994) has shown that standard MCF measures provide a valid basis for revenue-neutral tax reform, provided they are prepared using consistent methodologies (for example, with the same numeraire, with changes in welfare measured using the equivalent variation, and with public spending consisting only of lump sum transfers). For valid use in cost-benefit analysis, all revenue effects of public spending should be included in the MBF, and the MBF should be measured consistently with the MCF. For tax reform analysis, estimates of the MCF for different tax instruments in the same country will commonly be prepared using consistent methodologies. For tax reform, the MCF can loosely be thought of as ordinal, rather than a cardinal measure. The levels of MCF estimates will depend on the estimation methodology, but these levels are not important in deciding directions for reform. What is important is which tax instruments have high MCFs and which have low MCFs. Triest (1990) notes that MCF estimates are often made using producer prices as the numeraire, while benefits of public projects are usually calculated using consumer prices. Failure to adjust for the choice of numeraire could lead to wrong decisions. Care is required to ensure consistent comparisons when using the MCF in cost benefit analysis.
2.2
The Model
Our model is formally set out in Appendix A.1. Setting aside investment for the moment, three final goods are produced in the country: untaxed (U ), domestic (D), and exports (E ). Four goods are consumed: leisure (Z ), untaxed, domestic, and imports (M ). Exports are not consumed directly. Instead they are used to purchase foreign exchange (at a constant exchange rate), which is used to purchase imports from the rest of the world. The representative consumer has endowments of leisure (which may be converted into labour), capital, and foreign exchange.7 Investment occupies a large part of the economy in reality, so it needs to be incorporated somehow, although it serves no role in a static model. This is achieved in the model by creating an additional good, investment (I ). Consumers derive utility by purchasing investment, which can be thought of as deriving utility from future consumption. We set preferences as CobbDouglas over investment and all other goods, meaning that consumers devote a constant proportion of their incomes to investment. On the production side 7
The endowment of foreign exchange represents the trade balance. In Africa, this is financed by borrowing and foreign aid. In a static model borrowing has no purpose, so the endowment can be thought of as foreign aid.
28
CHAPTER 2. MCF IN AFRICA Figure 2.2: Utility and Production Functions U tility
W A A σW A A A
Z
C
I
A A σC A A A
U
D
M
Domestic D ID
Exports E IE
U ntaxed U IU
AA τ A D A A A σD A A A
AA τ A E A A A σE A A A
AA τ A U A A A σU A A A
KD
LD
KE
LE
KUi
C C σK C D C C
C C σL C D C C
C C σK C E C C
C C σL C E C C
LiU
f i KD KD LiD LfD KEi KEf LiE LfE
of the economy, firms receive funds from sales of their production and from investment. These funds are spent on factors of production. Thus the production sectors are modelled as using factor inputs, to produce jointly a final good (untaxed, domestic or export) together with investment. Sector output is divided between the good and investment according to a constant elasticity of transformation function. By setting this elasticity equal to one (Cobb-Douglas), a constant proportion of each production sector’s total income is derived from investment. The production goods use four factors of production: formal capital (K f ), informal capital (K i ), formal labour (Lf ) and informal labour (Li ).8 One consequence of including informal factors is that capital taxation results in a deadweight loss, even though the total supply of capital is fixed. Labour taxation also induces a deadweight loss as a result of substitution between formal and informal labour, in addition to the deadweight loss arising from substitution between labour and leisure. Constant elasticity of substitution (CES) functions are used in all production and utility functions. The structure of these functions is set out in Figure 2.2. The first panel is the utility function, where utility (W ) is a CES function of leisure, investment, and a consumption good C, and C is a composite good produced by a CES function of untaxed, domestic, and imports. The remaining panels are the production functions for domestic, export and untaxed. The bottom parts of these diagrams represent the 8
The informal good uses only informal capital and informal labour.
2.2. THE MODEL
29
nested CES functions over the factors of production, with the top levels representing capital/labour substitution, and the bottom levels representing formal/informal substitution. The top parts of the diagrams represent the CET functions between the final good and investment. The relevant elasticities, used in robustness testing of the model, are labelled by sigma and tau and appropriate sub- and super-scripts. Taxes are imposed on domestic, exports, imports, formal capital, and formal labour. There are no untaxed traded exports or imports. This is not meant to imply that no smuggling occurs in African countries. Rather, the official figures for trade are based on customs data, which typically reflects taxed goods. An implication is that the untaxed good is produced and consumed purely domestically. Tax revenue received by the Government is transferred lump-sum to consumers. The experiment of increasing a distortionary tax rate and returning the revenue lump-sum can be interpreted in terms of both ‘differential’ and ‘balanced-budget’ analysis. Treating government expenditure as transfers rather than spending on public goods may approximate the reality of much government spending in Africa.9 But as emphasized in section 2.1, for purposes of MCF estimates the realism of the modelled public expenditure is not as important as the fact that a consistent experiment is conducted across tax instruments. The economic relationships in the model can be represented by a rectangular social accounting matrix (SAM) such as Table 2.2. The entries in the SAM are expressed as percentages of GDP at market value. All rows and columns sum to zero, reflecting a Walrasian equilibrium in which incomes equal expenditures. In the consumer’s column positive entries are endowments or factor incomes, negative figures are expenditures on goods, including investment. In the production columns, positive entries are the receipt of sales revenue or investment, and negative entries are payments to factors or factor taxes. In the government’s column, positive figures are tax revenues, the negative figure is the transfer to consumers. The ‘Foreign’ column represents the purchase of exports and the sale of imports by the rest 9
In Uganda, Reinikka & Svensson (2002) found that schools received only 13% of the money paid by the central government for schools’ non-wage expenditures. Pritchett (1996) observes that growth accounting data can be reinterpreted supposing that total factor productivity growth is the same across all regions. Actual public investment in Africa could then be as little as 8.4% of the amount spent on capital. Rajkumar & Swaroop (2002) find that the effect on outcomes of marginal public spending on health and education is not significantly different from zero in countries rated as very corrupt or with ineffective bureaucracies. These studies suggest, by different means, that only a small portion of public spending in Africa arrives in projects with positive social rates of return.
30
CHAPTER 2. MCF IN AFRICA Table 2.2: SAM for Guinea-Bissau 2001 Consumer Untaxed Domestic Exports Imports Foreign Govt
Untaxed -48.20 Domestic -5.67 Exports Imports -57.71 Investment -18.92 Foreign Exchange 26.20 Formal Capital 2.36 Informal Capital 48.36 Formal Labour 9.45 Informal Labour 34.61 Capital Taxes Labour Taxes Transfers 9.51
48.20 4.93 24.60 11.73
1.20
0.74 -27.21 2.61 53.41 4.30
5.99 -53.40
-28.85 -31.08
-0.39 -2.93 -1.58 -0.92 -0.15 -0.16
-1.97 -16.58 -7.87 -2.61 -0.77 -0.79
27.20
0.92 0.95 -9.51
Figures represent a percentage of GDP at market value. Positive figures are revenues received by the column from the row. Negative figures are payments made by the column to the row. Figures in bold are taken directly from national accounts, all others are calculated using the calibration process.
of the world, using foreign exchange.
2.2.1
Data
The data are given in Appendix A.2. Country-specific data comprise values of exports, imports and investment as a percentage of GDP, tax revenues for each of the five taxes, and legal tax rates for domestic goods, capital and labour. These data were obtained from IMF country report statistical annexes, for the most recent years available. The data also include labouroutput ratios for untaxed, domestic and exports that are, by assumption, common for all countries. The labour-output ratios are the averages of ratios derived from SAMs prepared by IFPRI for Malawi 1998, South Africa 1999, Tanzania 2001, Zambia 1995, and Zimbabwe 1991. Data for tax revenue from sales of domestic are derived from tax revenues from domestic VATs. In the absence of a VAT, general sales tax revenues are used. Corporate income tax revenues are interpreted as tax revenues from formal capital. Personal income tax revenues are equated with revenues from formal labour. Data for tax revenues from exports and imports are taken directly from the national accounts.10 We ignore classes of tax revenue that 10
The countries of the Southern African Customs Union (Botswana, Lesotho, Namibia,
2.2. THE MODEL
31
do not fall into any of the five tax revenue classes of the model. For the countries in our sample, such other taxes represent on average 10% of total tax revenue. We suppose that these other tax revenues are unaffected by shocks to the model’s five tax rates, implicitly treating them as lump-sum taxes. Our model has only a single tax instrument for each good or factor. This rate is treated as both the average and the marginal tax rate. The inclusion of an untaxed domestic good and informal factors allows us to suppose that the average tax rates for domestic, formal capital and formal labour can be equated with the legal tax rates. We implicitly assume that either the legal tax bill is paid entirely or it is not paid at all. For domestic, the legal tax rate used is the standard VAT or sales tax rate on domestic goods. In countries without a VAT, tax rates on intermediate goods cascade in the taxed price of final output. In such cases, the tax rate applied in the model is likely to be an underestimate of the marginal tax rate on many domestic goods. Progressive personal income tax schedules provide multiple legal marginal tax rates for the tax on formal labour. Where the average public sector salary is known or can be calculated, this salary is treated as a proxy for the average wage paid to formal labour, and is used to determine the relevant marginal tax rate. If the average public sector salary is not known a marginal rate of income tax from the middle of the legally specified tax rates is chosen. To this rate is added the rate of any payroll tax. The standard rate of corporate income tax is used for the tax on formal capital. For taxes on exports and imports, there are usually multiple legal tax rates, and there is no simple method of choosing between them to provide a single tax rate for the model. Instead we used average tax rates calculated as tax revenue divided by the tax base. To the extent that informal traded goods are represented in the official statistics for exports and imports, this procedure underestimates the average of multiple marginal tax rates.
2.2.2
Model Calibration
The calibration process is formally described in Appendix A.3. All quantities in the SAM can be derived from the data described above. Using the quantities in the SAM, and the assumed elasticities, the production and utility functions can be calibrated. South Africa and Swaziland) share imports tax revenue according to a formula that gives a reduced share of the revenue to South Africa. Our calibration method is inaccurate to the extent that the formula differs from the share of regional imports that is consumed by each country.
32
CHAPTER 2. MCF IN AFRICA
The calibration process starts with a standard definition of GDP, the sum of consumption, investment and net exports: GDP = C + I + (E − M ). The figures for C and I incorporate government consumption and investment. This definition of GDP corresponds to the format usually given in IMF country reports. In our model the goods that are consumed (ignoring leisure), can be divided between imports and non-imports (N ), where non-imports comprise domestic and untaxed. Total consumption in the model is thus given by C = N + M . Using the definition of GDP we calculate the amount of nonimports consumed as N = GDP − I − E. Consumption of non-imports is equal to production of non-imports. Production of domestic, the taxed non-imported good in the model, is calculated by dividing VAT revenue by the tax rate, giving the tax base: D = RTDD . Consumer expenditure on the untaxed good (equal to the value of production) is thus the residual of non-imports: U = N − (1 + TD ) × D. Funds received by firms are spent on factors. Allocation of firm revenue between capital and labour is achieved using assumed labour-output ratios. The amount of formal factor usage is determined by dividing factor tax revenues by their tax rates. Informal factor usage is then the residual of total factor expenditure less formal factor expenditure. The calibration process can be illustrated with data from Guinea-Bissau and the SAM of Table 2.2. The value of investment, as a percentage of GDP at market prices, is available directly from the national accounts: I = 18.9. The producer value of exports is derived by subtracting export tax revenue from the market value of exports: E = 27.21 − 2.61 = 24.6. The producer value of domestic is determined by dividing tax revenue for domestic goods 0.74 = 4.93. (0.74% of GDP) by the standard sales tax rate (15%): D = 0.15 The value of untaxed is then the residual of GDP less investment and the taxed value of domestic and exports, all expressed as a percentage of GDP: U = 100 − (D + 0.74) − (E + 2.61) − I = 48.20. Total funds received by the firms in a sector is the sum of sales and investment. For example, firms producing exports receive E + IE = 24.60 + 5.99 = 30.59. It is assumed that production is competitive, so that all funds received by firms are paid out to factors. Capital and labour requirements for production are determined using the labour-output ratios. Thus, for example, with a labour-output ratio of 0.37 for exports, total capital used to produce exports is KE = (1 − 0.37) × (E + IE ) = 18.55. Since untaxed uses only informal capital and informal labour, this procedure is all that is required to determine the allocation of capital and labour to untaxed. For domestic and exports, factor usage must be divided between formal and informal factors. The amounts of formal capital and labour are deter-
2.2. THE MODEL
33
mined by dividing tax receipts by the legal tax rate. With a 39% corporations = 2.36. Applying a personal intax, total formal capital is K f = RTKK = 0.92 0.39 come tax rate of 10% implies total formal labour of Lf = 0.945 = 9.45. These 0.1 amounts are divided between domestic and exports in proportion to output. 24.60 E = 2.36× 24.60+4.93 = For example, formal capital in exports is KEf = K f × E+D 1.97. Informal capital and labour are then the residuals of total capital and labour for each industry less formal capital and labour and the taxes paid on these factors. For example informal capital used to produce exports is KEi = KE − KEf × (1 + tK ) = 18.55 − 1.97 × (1 + 0.39) = 16.58. The SAM of Table 2.2 does not show leisure. The quantity of leisure is determined by the representative consumer’s endowment of time less the sum of formal and informal labour. To enable simple calibration of the elasticity of labour supply, the utility function is specified with unitary (Cobb-Douglas) elasticity of substitution between leisure and all other goods. This implies a where T is the time endowment and L labour supply elasticity of η = T −L L is total labour supply. The value of L is fixed by the data – in the case of Guinea-Bissau L = Li +Lf = 9.45+34.61 = 44.06. The calibration approach is to choose a value for the labour supply elasticity, which then fixes the value of T . There appear to be very few published estimates of the elasticity of labour supply in developing countries. For rich countries, estimates of the elasticity of labour supply are close to zero, when estimated for those who are employed. Nevertheless at the extensive margin, the decision whether or not to take a job, the elasticity of labour supply is positive. For our developing countries, we felt that some small responsiveness of labour supply to changes in taxation was appropriate, and thus chose an elasticity of 0.05, implying that T = 1.05 × L. National accounts figures represent values: price × quantity. Following the Harberger convention, units of aggregate goods are chosen such that quantities equal values. This implies that for untaxed goods or factors, benchmark prices are equal to one. For taxed goods and factors, we choose quantity units such that either the net of tax price or the gross of tax price is equal to one at the benchmark equilibrium. Specification of the tax rates allows calculation of the missing prices. With all benchmark prices and quantities determined, calibration finishes with the selection of elasticities for the CES utility and production functions. Our base case uses unitary elasticities: constant returns to scale Cobb-Douglas functions. This appears to be reasonable for the elasticity of demand for imports (Senhadji 1998). But we do not have evidence on the empirical magnitude of other necessary elasticities. Faced with a data vacuum we preferred a simple functional specification, and performed sensitivity
34
CHAPTER 2. MCF IN AFRICA
checks by changing elasticities. While this account of the calibration process is straight-forward, it glosses over several problems with the calibration of informal sectors. It is likely that these problems affect all countries to some degree, but the issue is particularly acute in eight countries where, using the procedure described above, the calibrated values of sections of the informal economy are negative. The untaxed good is negative in Equatorial Guinea (-74% of GDP), Gabon (-2 %), Mauritania (-3%), Namibia (-22%), and Swaziland (-3%). In addition, the calibration process gives negative values for informal labour used to produce domestic and exports in Cape Verde (-5%), South Africa (-13%) and Zimbabwe (-13%). The first problem is a general question about the reliability of GDP data in small developing economies. In particular, statisticians dealing with developing economies make efforts to incorporate the informal economy, but to the extent that some informal activities escape the measure of GDP, our calibrated informal sectors are too small. Data reliability may affect results for all countries, but it does not give rise to negative calibrated values for untaxed goods. The second problem arises in countries with considerable re-exportation of imports. The problem can be seen when we consider the definition GDP = C + I + (E − M ). Suppose that initially there are no re-exports, and then an additional $100 of goods is imported and immediately re-exported without any value-added. The GDP figure, which is the sum of value-added, is unchanged. But the increase in measured exports reduces our measure of non-imports by $100, since N = GDP − I − E. With the size of domestic calibrated independently, any re-export of goods results in a corresponding diminution of the untaxed sector: U = N −D. With sufficient re-exportation, the untaxed sector becomes negative. An extreme case is Equatorial Guinea, where exports constitute 106% of GDP. For most countries it seems likely that re-exports constitute a sufficiently small part of total exports that the calibration method is not seriously compromised. Unfortunately we did not have the necessary data to eliminate the problem by separating total exports between those of domestic origin and those of foreign origin. The final problem in calibrating untaxed arises from the method of calculating domestic, by dividing sales tax revenue by the tax rate. Where the sales tax is a VAT, with full rebating of tax paid on inputs and a single rate, the calibration method probably gives a fairly accurate measure of the domestic tax base. But if sales taxes cascade, without rebates for taxes paid on inputs, the effective marginal tax rate can be much higher than the standard sales tax rate. In such cases, the tax rate used for calibration purposes is too low, so the estimated domestic tax base is too large. Then, noting that
2.3. RESULTS
35
U = N − D, when the estimated size of D is too large, the estimated size of the untaxed sector is too small. The fact that Namibia and Swaziland do not have VATs may help to understand the small calibrated values of their untaxed sectors. The further a country’s sales tax system departs from a ‘pure’ VAT (a single tax rate, no exemptions, and full refunds for taxed inputs), the less accurate is the calibration methodology for identifying the domestic tax base. Similar issues arise in calibrating informal factor supplies. If the assumed labour-output ratios are not sufficiently large, the total labour supply is less than the calibrated value of formal labour. If the personal income tax rate used for calibration is too small, the calibrated value of formal labour is too large. In principle the same problems could arise in calibrating informal capital, but in practice the problem did not arise. Our solution is pragmatic. The basic calibration methodology suggests ‘small’ values for the untaxed good and informal labour used to produce taxed goods. At the same time, strictly positive values are required for the experiments conducted in section 2.4.1. For the five countries with negative untaxed, we set the value of untaxed at 1% of GDP.11 For the three countries with negative informal labour requirements in exports and domestic, we adjusted the labour-output ratio to ensure that informal labour constituted 1% of formal labour. It should be emphasized that a process of adjustment of the values in the SAM is typical in the development of CGEs: real-world data rarely match the internal consistency requirements of a SAM. Nevertheless, our results should be interpreted with particular caution for the ‘problem’ countries, and for all countries lacking VATs (these are reported in the data appendix).
2.3
Results
We calculated the MCFs associated with six different shocks to tax rates. In the first five experiments we increased each tax rate individually by 1% of the existing tax rate.12 In the sixth experiment we increased all five tax rates simultaneously by 1%. In each case the additional tax revenue, ∆R, was redistributed to consumers as a lump sum transfer. The new equilibrium was established using a computable general equilibrium model written using GAMS MPSGE. 11
For these countries, the calibrated market value of the three produced goods thus exceeds 100% of GDP. 12 Where the tax rate was 0% we increased it to 1%.
36
CHAPTER 2. MCF IN AFRICA
The welfare change induced by the combined tax and spend experiment was measured in terms of the numeraire using the equivalent variation (EV ).13 The MCF of the experiment was calculated as M CF = −(EV − ∆R)/∆R. The value of the additional transfer was subtracted from the consumer’s new welfare level because the MCF measures the cost of taxation and not the benefit of public spending.
2.3.1
Base Case Estimates
The resulting MCF estimates are presented in Table 2.3. The estimates provide a basic blueprint for tax reform in each country. For any pair of tax instruments, the same total revenue could be achieved for lower deadweight loss by lowering tax rates associated with a high MCF and increasing lowMCF tax rates. On average, the MCF associated with a marginal increase in all five tax rates is 1.17, indicating a required rate of return of 17% for African public projects. Among individual tax instruments, on average the lowest MCFs are associated with taxes on the two taxed consumption goods (domestic and imports), and the highest MCFs are associated with the two taxed factors (formal capital and formal labour ). The exports MCFs exhibit the greatest variation. The high variance of exports MCFs requires comment. Much of the variation comes from two countries: Burkina Faso and Rwanda. The exports MCFs in these two countries are negative because the tax shock reduces tax revenue. The high absolute values occur because the exports tax rate shock induces a marginal change in total tax revenue that is close to zero.14 Excluding these two countries, the remaining countries can be divided into two groups. There are 16 countries with zero exports taxes (see the data in Appendix A.2), that as a group have a low average exports MCF of 1.07. The remaining 20 countries have positive exports taxes, and have an average exports MCF of 1.32. The relatively high MCF associated with positive exports taxes can be understood by noting that exports is effectively an input into imports, so that distortions introduced in the market for exports amplify 13
In theoretical papers on the MCF changes in utility are converted to a monetary measure by dividing by the marginal utility of income. When the utility function is linearly homogeneous (as is the case in our model) the equivalent variation gives the same measure of welfare change. 14 Although not apparent in the reported results, the exports tax shock also reduces total tax revenue in Burundi and Eritrea. In these countries, which have zero exports tax rates, the marginal reduction in tax revenue is associated with a positive exports MCF, because the marginal welfare change is positive.
2.3. RESULTS
37 Table 2.3: MCF Estimates
Country Benin Botswana Burkina Faso Burundi Cameroon Cape Verde Central African Rep. Chad Dem. Rep. of Congo Côte d’Ivoire Eq. Guinea Eritrea Ethiopia Gabon Gambia Ghana Guinea Guinea-Bissau Kenya Madagascar Malawi Mali Mauritania Mozambique Namibia Niger Nigeria Rwanda São Tomé Senegal South Africa Sudan Swaziland Tanzania Togo Uganda Zambia Zimbabwe Average Max Min Std. Dev.
Domestic 1.11 1.03 1.15 1.10 1.10 1.11 1.14 1.19 1.01 1.05 1.05 1.02 1.13 1.03 0.98 1.03 1.11 1.09 1.02 1.13 1.20 1.11 1.08 1.04 0.97 1.17 0.99 1.14 1.27 1.07 1.09 1.09 1.11 1.17 1.06 1.10 1.06 1.08 1.09 1.27 0.97 0.06
Exports 1.28 1.02 -10.82 0.76 1.08 1.96 1.31 1.26 1.02 1.06 1.00 0.63 3.14 1.02 1.12 1.17 1.01 1.35 1.20 1.16 1.04 1.27 0.97 1.17 1.10 1.29 1.02 -92.74 1.21 1.27 1.02 1.92 1.01 1.59 1.11 0.82 1.09 1.10 -1.58 3.14 -92.74 15.32
Imports 1.15 1.03 1.18 1.10 1.07 1.21 1.14 1.09 1.01 1.06 1.00 1.03 1.23 1.05 1.08 1.10 1.00 1.13 1.06 1.11 1.01 1.14 0.98 1.07 1.06 1.15 1.02 1.14 1.07 1.13 1.00 1.23 1.01 1.20 1.07 0.97 1.03 1.03 1.08 1.23 0.97 0.07
Capital 1.68 1.07 1.55 1.66 1.53 1.72 1.62 1.87 1.43 1.43 1.24 1.20 1.75 1.39 1.45 1.50 1.49 2.03 1.30 1.58 1.39 1.66 1.24 1.60 1.39 1.90 1.30 1.87 1.54 1.55 1.29 1.87 1.34 1.76 1.40 1.40 1.44 1.28 1.52 2.03 1.07 0.22
Labour 1.60 1.05 1.55 1.88 1.27 1.79 1.71 2.01 1.38 1.36 1.10 1.14 1.60 1.35 1.21 1.26 1.43 1.49 1.11 1.32 1.43 1.64 1.22 1.22 1.09 1.80 1.19 1.80 1.31 1.80 1.11 1.57 1.30 1.73 1.50 1.30 1.14 1.10 1.42 2.01 1.05 0.26
All 1.23 1.05 1.25 1.22 1.14 1.37 1.23 1.33 1.10 1.12 1.13 1.09 1.31 1.10 1.12 1.17 1.12 1.26 1.08 1.17 1.23 1.21 1.10 1.11 1.10 1.24 1.08 1.28 1.15 1.19 1.12 1.26 1.09 1.27 1.12 1.11 1.09 1.11 1.17 1.37 1.05 0.08
38
CHAPTER 2. MCF IN AFRICA
distortions in the market for imports. The general equilibrium interactions between tax instruments are illustrated in Figure 2.3 for the case of Guinea-Bissau. MCFs for different tax instruments are plotted as a function of the import tariff. The diagram provides various insights into the interactions within the system. • The imports MCF increases with the import tariff. • The MCFs for exports, capital and labour are greater than the imports and domestic MCFs, and they increase at a faster rate than the imports MCF. Exports, capital and labour are inputs into the production of the taxed consumption goods, imports and domestic, that enter directly into the consumer’s welfare function. Increases in taxation of these inputs causes increased distortion of the taxed prices of the outputs, in addition to substitution of informal factors for formal factors. • The domestic MCF decreases as TM increases. When TM ≥ 34% the domestic MCF is less than one, indicating that marginally increasing the domestic tax helps to correct the distortions induced by high import tariffs, thereby increasing welfare. Domestic and imports are substitutes in consumption, so as import tariffs increase, consumption of domestic increases, helping to offset the effect of existing domestic taxation. • Reflecting the conflicting effects of the individual taxes, the MCF obtained by simultaneously varying all tax rates decreases for values of TM < 4% and increases for TM > 4%. One implication is that this measure of the MCF does not necessarily increase with total tax revenue. (The illustrated values of TM are on the ‘good’ side of the Laffer curve: total revenue is increasing in TM .) The diagram also illustrates that over wide ranges of the import tariff rate the ordering of MCFs for individual taxes is unchanged.
2.3.2
Robustness of Results
Our results are dependent on the specified elasticity parameters. We experimented with alternative elasticities to see the effect on our estimates. The notation for the relevant elasticities is set out in Figure 2.2. In testing different elasticities we maintained the following values equal to one: σW , τD , τE , and τU . This ensures that the representative consumer invests a constant proportion of income, and that each production process receives a constant proportion of its total funds from investment.
2.3. RESULTS
39
3.5
3
MCFs
2.5 Capital Labour Exports All Imports Domestic
2
1.5
1
0.5 0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Import tariff rate
Figure 2.3: MCFs in Guinea-Bissau as a Function of the Import Tariff
40
CHAPTER 2. MCF IN AFRICA Table 2.4: Sensitivity Testing
Experiment D E M K L All (1) (2) (3) σC = 2 1.19 1.88 1.17 1.93 1.89 1.31 29 25 35 σ D = σ E = σU = 2 1.09 -0.26 1.08 1.50 1.45 1.17 33 33 38 σC = σD = σE = σU = 2 1.19 2.02 1.18 1.93 1.98 1.32 29 25 36 K L K L σD = σD = σE = σE =2 1.09 -1.58 1.08 2.53 1.89 1.24 35 34 37 L L σD = σE =2 1.09 -1.58 1.08 1.52 1.89 1.19 22 20 37 σC = 0.5 1.05 1.15 1.05 1.40 1.29 1.11 35 32 35 σD = σE = σU = 0.5 1.09 1.13 1.08 1.52 1.39 1.17 36 34 37 σC = σD = σE = σU = 0.5 1.05 1.14 1.04 1.41 1.28 1.11 34 32 35 K L K L σD = σD = σE = σE = 0.5 1.09 -1.58 1.08 1.29 1.28 1.14 31 28 37 L L σD = σE = 0.5 1.09 -1.58 1.08 1.52 1.28 1.16 31 27 38 Columns D, E, M, K, L, and All report average MCFs for the 38 countries. Columns (1), (2) and (3) indicate the number of countries that are ‘close’ to the base case estimates in the sense of giving the same recommendations for tax reform. In column (1) the tax instruments found to have the highest and lowest MCFs are the same as in the base case. In column (2) all five individual MCFs are ranked in the same order as in the base case. In column (3) at most one pairwise comparison of MCFs gives a different recommendation from the base case estimates.
We tested several combinations of elasticities, and the results are set out in Table 2.4. For each experiment, any unmentioned elasticity is equal to 1. The first five experiments increase elasticities. The first experiment increases the consumer’s elasticity of substitution between consumption goods. The second increases the elasticity of substitution between capital and labour in all goods. The third increases the elasticity of substitution between consumption goods and between capital and labour. The fourth increases substitution between formal and informal factors. The fifth increases substitution between formal and informal labour, but leaves unchanged the degree of substitution between formal and informal capital. The final five experiments perform corresponding reductions in the elasticities of substitution. Changing elasticities had the expected effect on the magnitude of our MCF estimates: higher substitutability results in higher MCFs. The MCF associated with a simultaneous shock of all five taxes, M CF (All), varied between 1.11 and 1.32. M CF (All) is more sensitive to variation in the consumer’s elasticity of substitution between consumption goods than the producers’ elasticity of substitution between capital and labour. On the production side, MCF estimates are more sensitive to changes in the elasticity of substitution between between formal and informal factors than the elasticity of substitution between capital and labour. It is clearly important to have a good estimate of the relevant elasticities if MCF estimates are to be used for cost-benefit analysis.
2.4. INFORMAL SECTORS AND ADMINISTRATIVE COSTS
41
But for partial revenue-neutral tax reform, it is the ordering of MCF estimates that is important, not their magnitudes. For such reform, the aim is to compare two tax instruments, increase the tax rate on the low MCF tax, and decrease the tax rate on the high MCF tax. Table 2.4 reports the number of countries in which the ordering of MCFs is robust to changes in elasticities. Three measures of robustness are used. The first measure supposes that reform is concentrated on the most extreme MCFs. The two tax instruments with the highest and lowest MCFs are identified. If these two instruments are the same as in the base case, the ordering is considered robust. Among the five tax instruments there are ten pairwise comparisons that are possible, identifying for each pair the high and low MCF instruments. The second measure of robustness requires that all ten such comparisons report the same pairwise ordering. This implies that all five instruments follow the same order as in the base case. The third measure of robustness permits just one pairwise comparison to give a different ordering from the base case. On the basis of the third measure the ordering of MCF estimates was robust to variations in elasticities in a minimum of 35 out of 38 countries. That is, we can be reasonably confident of the recommendations for tax reform that are implied by our base case estimates.
2.4
Informal Sectors and Administrative Costs
Analysis of African tax systems quickly confronts two salient features: the significance of informal sectors and the relatively high cost of tax administration: • Excluding countries in which our basic calibration method gave a negative untaxed good, the value of untaxed production represents on average 30% of GDP, with a maximum of 61% in Niger. Adding in the value of untaxed factors used to produce domestic and exports, the average informal economy in these countries represents 69% of GDP, with a maximum of 90% in the Democratic Republic of Congo. • Table 2.5 provides an international comparison of administrative costs, measured by dividing the expenses of tax collection agencies by the revenue collected. The average for rich countries is 1.36%, 1.88% for Latin American countries, and 2.35% for African countries.15 15
Not all of the tax agencies represented in these figures collect all types of taxes. Since the costs of collection vary by tax type, this may give a distorted impression of the efficiency of some agencies.
42
CHAPTER 2. MCF IN AFRICA Table 2.5: Tax Administration Costs Country Year(s) Cost/Collections Australia 2001-2002 1.2% Canada 2001-2002 2.3% New Zealand 2001-2002 1.2% UK 2001-2002 1.6% US 2002 0.5% Guatemala 1999-2001 1.9% Mexico 1995, 1997-98 1.7% Peru 1996-1998 1.9% Venezuela 1995-1998 2.0% Ghana 1993 2.8% Kenya 1995-2000 1.2% Namibia 2001-2002 1.3% South Africa 1998-2001 1.1% Tanzania 1996-1997 3.0% Uganda 1991-2000 3.6%
The cost/collections ratio reports the annual cost of tax collection agencies divided by the amount of money collected. For data sources, see Appendix A.2.
In this section we examine the impact of the informal economy on the MCF in the formal economy, and then measure MCFs of potential taxes in different parts of the informal economy, ignoring any administrative costs. We then examine how the presence of administrative costs affects our estimates for taxes in the formal economy, and we consider the level of administrative costs that could be justified to impose taxes in the informal economy.
2.4.1
The Informal Economy
The simple partial equilibrium formula 2.2 suggests that the magnitude of the MCF, and in particular whether the MCF is greater or less than one, is t1 t2 and 1+t . If we think of determined in part by the difference between 1+t 1 2 good 2 as a composite for all goods other than good 1, the average rate of taxation on good 2 falls as the proportion of untaxed goods in the economy increases. This suggests that economies with large informal sectors are likely to have high MCFs. Figure 2.4 plots our base case estimates of M CF (All) against the calibrated value of untaxed, suggesting the strength of this intuition. A simple regression of our 38 estimates of M CF (All) on untaxed and a constant has
2.4. INFORMAL SECTORS AND ADMINISTRATIVE COSTS
43
1.40
1.35
1.30
MCF(All)
1.25
1.20
1.15
1.10
1.05
1.00 0
10
20
30
40
50
60
70
Untaxed Output (% GDP)
Figure 2.4: MCF(All) as a Function of the Value of the Untaxed Good an adjusted R2 of 0.75. Some of the unexplained variation in MCF values in the diagram is due to variation in tax structures. To capture this in a simple way, we created a variable, structure, which measured the proportion of exports and factor tax revenue in total tax revenue (using the same figures used for calibration of the model). Adding this variable to the regression we 1.024 + 0.402 untaxed + 0.116 structure (0.024) (0.036) (0.049) 2 The adjusted R of this regression is 0.78. Standard errors are reported in brackets, with the coefficients on the constant and untaxed significant at 1% and the coefficient on structure significant at 2.5%. In contrast a regression of M CF (All) on just structure and a constant gives no statistically significant results. These results suggest that, at least for the African countries we have studied, the magnitude of an economy’s average MCF is dominated by the size of the informal economy, with the tax structure playing only a relatively small role. The logic of the simple partial equilibrium formula 2.2, suggests that if a good is more lightly taxed than goods in the rest of the economy, it will have a low MCF. Thus, taxes imposed on parts of the informal economy should have very low MCFs. We confirmed this intuition by imposing hypothetical
obtained: M CF (All) =
44
CHAPTER 2. MCF IN AFRICA
taxes on informal parts of the economy in our model. We supposed it was possible to impose a tax in these sectors, and marginally increased the tax from an initial rate of zero. We calculated MCFs when 1% taxes were imposed on: production of the untaxed good (U ); informal capital used anywhere in the economy (K i ); informal capital used to proi duce domestic or export goods (KDE ); informal labour used anywhere in i the economy (L ); and informal labour used to produce domestic or export goods(LiDE ). We distinguished between taxing a factor wherever it is used and taxing a factor when it is used to produce domestic or export goods because the latter seems more plausible. It seems more likely that the administration will be able to tax a firm’s accounting profits (returns to capital) and labour inputs in cases where the firm’s output is already taxed. The results of these experiments are reported in Table 2.6. In all countries the MCF of a tax on the untaxed good is less than 1. The negative welfare shock suffered by households (before the revenue is returned lump-sum) is smaller than the increase in government revenue. Once lump-sum redistribution of the revenue occurs, households are better off than before the tax shock. Increasing taxes in the informal sector helps to counteract existing taxes in other sectors, moving relative prices towards their undistorted levels. When taxation of informal factors is restricted to inputs to domestic and export goods, the MCF is higher than when informal factors are taxed i ) > M CF (K i ) and M CF (LiDE ) > wherever they are used: M CF (KDE i M CF (L ). Two effects operate. Taxing an untaxed factor helps to restore prices to their undistorted levels, tending to lower the MCF. When the untaxed factors are inputs to taxed goods, the relative costs of these goods rise, the distortion associated with goods taxation increases and the MCF tends to be higher. The second of these effects is relatively stronger when the tax shock is concentrated on inputs to domestic and export goods. Ignoring distributional issues, on average among the fictional tax instruments for taxing the informal sectors, the best way of raising money is by increasing taxes on untaxed goods. The average M CF (U ) is 0.87, lower than the average MCF elsewhere in the informal economy. But governments may hesitate to increase taxes of the informal sector if they care about distributional issues and poor households are concentrated in production of untaxed goods or they consume a lot of untaxed goods. When distributional issues are considered, a promising part of the informal economy i is informal capital used to produce taxed goods: average M CF (KDE ) is 1.05. That is, imposing taxes on companies that produce taxed goods but do not pay company tax generally offers a lower cost of public funds than increasing existing taxes elsewhere in the formal economy. In many cases
2.4. INFORMAL SECTORS AND ADMINISTRATIVE COSTS Table 2.6: MCFs in the Informal Sector Country Benin Botswana Burkina Faso Burundi Cameroon Cape Verde Central African Republic Chad Democratic Republic of Congo Côte d’Ivoire Equatorial Guinea Eritrea Ethiopia Gabon Gambia Ghana Guinea Guinea-Bissau Kenya Madagascar Malawi Mali Mauritania Mozambique Namibia Niger Nigeria Rwanda São Tomé Senegal South Africa Sudan Swaziland Tanzania Togo Uganda Zambia Zimbabwe Average Max Min Std. Dev.
U 0.87 0.86 0.89 0.83 0.89 0.81 0.92 0.93 0.97 0.83 0.98 0.87 0.87 0.85 0.84 0.87 0.93 0.89 0.81 0.91 0.96 0.89 0.89 0.86 0.79 0.94 0.92 0.90 0.84 0.83 0.78 0.95 0.78 0.91 0.89 0.92 0.82 0.76 0.87 0.98 0.76 0.06
Ki 0.95 0.90 0.94 0.95 0.97 0.79 0.98 0.97 0.99 0.95 0.98 0.88 0.89 0.97 0.95 0.95 1.00 0.97 0.92 0.97 0.98 0.96 0.96 0.98 0.92 0.98 0.98 0.94 0.95 0.95 0.89 0.97 0.96 0.98 0.96 0.98 0.97 0.88 0.95 1.00 0.79 0.04
i KDE 1.07 0.91 1.21 1.05 1.02 1.22 1.15 1.12 1.00 0.98 0.98 0.92 1.17 0.97 0.99 1.03 1.05 1.22 0.94 1.07 1.03 1.10 0.97 1.02 0.92 1.16 0.98 1.14 1.08 1.03 0.92 1.18 0.96 1.21 1.02 1.03 1.00 0.91 1.05 1.22 0.91 0.09
Li 0.94 0.92 0.92 0.87 0.97 0.80 0.97 0.97 0.99 0.95 1.00 0.93 0.92 0.99 0.93 0.92 0.98 0.92 0.87 0.96 0.98 0.96 0.94 0.95 0.85 0.98 0.97 0.96 0.80 0.93 0.71 1.00 0.89 0.93 0.98 0.98 0.81 0.69 0.92 1.00 0.69 0.07
LiDE 1.12 0.95 1.19 0.99 1.06 1.26 1.16 1.15 1.00 1.00 1.00 0.99 1.21 0.99 1.01 1.04 1.06 1.26 0.93 1.11 1.05 1.15 0.95 1.03 0.86 1.19 0.97 1.18 1.14 1.05 0.77 1.21 0.89 1.21 1.05 1.05 0.92 0.76 1.05 1.26 0.76 0.12
45
46
CHAPTER 2. MCF IN AFRICA
such companies have legal tax exemptions, which can be removed with low administrative expense.16 Removing such exemptions has the potential for a low marginal cost of taxation, without obvious major effects on the poorest households.17
2.4.2
Costs of Tax Administration
A taxpayer paying a dollar of taxes suffers the same loss of utility regardless of whether the administration has paid 2 cents or 50 cents to enforce the collection. Further, the administration costs are not lost to society. They are paid to civil servants and other providers of goods and services. Thus, tax administration costs do not alter ∆W in our MCF formula 2.1.18 Administration costs do, however, alter ∆R in our MCF formula, by reducing the net revenue available for government spending. If we suppose that administration costs constitute µ% of tax revenue collected, a tax shock ∆R %. Incorpothat changes gross revenue by ∆R changes net revenue by 1−µ rating administrative costs in our MCF estimates is thus a simple matter of 1 . multiplying by 1−µ Table 2.5 indicates that on average µ = 2.35% in Africa. On this evidence, our base case results should be multiplied by 1.024. Incorporating administration costs increases the average M CF (All) for African countries from 1.17 to 1.20. Although Africa has more costly tax administrations than other regions, this alone is unlikely to result in substantially higher marginal costs of public funds. One explanation for the failure to tax the informal sector may be large administrative costs associated with taxing the first marginal unit of the tax base. For example, there may be high lump sum costs associated with 16
In a survey of 197 businesses in Cameroon, Gauthier & Gersovitz (1997) report that 4 were legally exempt from sales tax, while 30 were legally exempt from the business profits tax. In Gauthier & Reinikka (2001) a similar survey of 158 businesses in Uganda reports 17 exemptions from sales tax and 41 exemptions from the corporate income tax. Both studies found that exemptions tended to be granted to large firms, while smaller firms were more likely to evade tax illegally. Legal tax exemptions may be the result of corruption. Fjeldstad (2002) reports that in the mid 1990s senior Tanzanian officials accepted bribes in return for tax exemptions: “within the Ministry of Finance, the Revenue Department went under the nickname of the ‘Tax Exemption Department.’ ” 17 An alternative means of increasing capital taxation may be to encourage firms to move from the informal to the formal sector by lowering licence fees and time costs for establishing formal enterprises (Auriol & Warlters 2004). 18 We treat as negligibly small the marginal change in consumer surplus forgone on goods that could have been produced using the factors of production involved in tax administration.
2.5. MCF DISPERSION & TAX SYSTEM INEFFICIENCY
47
identifying taxpayers. Thus µ may be higher for taxes on the informal sector than for taxes in other sectors. We do not have data on the magnitude of administrative costs for the informal sector (µi ). However, noting that in an optimized tax system the MCF of all tax instruments would be equal, we can calculate the µi that would equate the MCF of a tax in the informal sector, M CF i , with the base case M CF (All) when administrative costs are considered, according to the following formula: µi = 1 −
M CF i (1 − µ) M CF (All)
(2.3)
Using µ=0.0235, we calculated the threshold administrative costs, µi for the parts of the informal economy discussed in section 2.4.1. Table 2.7 reports the averages across our sample of countries. On average, increased efforts to enforce taxes on the untaxed good would be justified up to the point where administrative costs consume 27% of the revenue collected. Taxing currently untaxed profits of businesses that produce taxed goods would be justified with administrative costs of 13%. Table 2.7: Administrative Cost Thresholds i Li LiDE U K i KDE 0.27 0.21 0.13 0.23 0.12
2.5
MCF Dispersion & Tax System Inefficiency
When only distorting taxes are available, the MCFs of optimal taxes are all equal. This suggests that MCF dispersion could be used as a measure of tax system inefficiency. In fact, high variance of the MCFs does not necessarily indicate great scope for welfare-enhancing revenue-neutral tax reform. To assess the potential benefits of tax reform, we derived optimal taxes to achieve each country’s existing revenue. We iteratively reduced high MCF taxes and increased low MCF taxes until MCFs were equalized or remaining high MCF taxes had zero rates. The resulting tax structure involves zero taxes on exports, capital and labour. The only taxes are on the taxed goods that are consumed: domestic and imports. This is an illustration of the Diamond & Mirrlees (1971) production efficiency result. We calculated the welfare gain from moving to optimal taxes (subject to the limited set of distorting tax instruments), and calculated the resulting MCFs of the taxes on domestic and imports. For comparison, we also measured the welfare
48
CHAPTER 2. MCF IN AFRICA
gain from entirely removing all distorting taxes, or equivalently, only using lump-sum taxation. The results are reported in Table 2.8: • Countries are listed in order of the potential welfare gains from moving to optimal taxes to achieve the same tax revenue using only distorting taxes. The column ‘∆W (optimal)’ reports these welfare gains in percentage terms, where the change in welfare is measured using the equivalent variation. The average potential welfare gain is 0.44%. • The column ‘∆W (zero taxes)’ reports the total welfare cost of the tax system. On average, replacing all taxes by a lump sum tax (or equivalently in the model, eliminating all taxes), welfare could be increased by 0.8%. This suggests that more than half of the deadweight loss of African tax systems is due to the tax structure, rather than the revenue target. • The column ‘Std. Dev. MCFs’ reports the standard deviation of the base case MCF estimates for the five tax instruments. To examine the correlation between this measure of inefficiency and the potential welfare gains of optimal distortionary taxes we performed a simple regression of the form ∆Wi = aσi +b, where ∆Wi is the deadweight loss of current taxes relative to optimal taxation, σi is the standard deviation of base case MCFs, and a and b are coefficients to be estimated. The result was statistically insignificant. We conclude that the standard deviation of MCFs is not a good predictor of the potential benefits of tax reform. The reason is that the marginal cost of taxation can greatly exceed the average social cost.19 • The column ‘MCF’ reports the MCF associated with optimal taxation. The average figure is 1.07. This is well below the average figure for MCF(All) reported in the base case estimates (1.17). Tax reform can potentially lower the cost of public funds by a significant amount. If the MCF were actually used as a criterion for project approval, moving to optimal taxes would permit many more public projects to go ahead. • The ‘Revenue’ column reports tax revenue as a percentage of GDP. We explored the relationship between tax revenue and tax system inefficiency using simple regressions of the form Yi = aXi + b, with tax revenue as the single explanatory variable. We found tax revenue to be a significant determinant of the two deadweight loss measures, but 19
Note the convexity of the MCF functions for exports, capital and labour in Figure 2.3.
2.6. CONCLUSION
49
not significant in explaining the MCF measures nor the dispersion of MCFs.20 Revenue only explains part of the differences in the efficiency cost of taxation, even when the effects of tax structure are removed (by finding optimal imports and domestic taxes to achieve the given revenue), because differences remain in the structure of each economy.
2.6
Conclusion
Our results suggest that a reasonable estimate of the average MCF in Africa is 1.17 (the average of MCF(All) across the 38 countries). Among the various sensitivity tests that we conducted, this figure varied between 1.11 and 1.32. The estimate was most sensitive to changes in the consumer’s elasticity of substitution between imports, domestic and untaxed. Senhadji’s (1998) estimates of the elasticity of demand for imports supports our assumption of unitary elasticity of substitution between imports and other goods. So the major uncertainty concerning our base case estimates is the elasticity of substitution between domestic and untaxed. On average, taxes on factors have high MCFs and taxes on imports and domestic goods have low MCFs. This outcome follows from the Diamond & Mirrlees (1971) result for optimal taxation, that production decisions should not be distorted. A major focus of tax reform in recent years has been the introduction of VATs. Our results suggest that welfare could be improved by increased reliance on these VATs, and reduced reliance on exports and factor taxes. An important finding is the strong relationship between the size of the untaxed sector and the value of MCF(All). Auriol & Warlters (2004) suggest that governments could reduce the size of their informal sectors by reducing red tape barriers to business entry into the formal sector. The results here suggest that such a policy would not only help to enhance revenue by enlarging the tax base, but would also reduce the marginal cost of public funds. The existence of MCFs lower than one in the informal sector suggests scope for increasing welfare and tax revenue simultaneously. Measures to bring currently informal activities within the tax base would be justified even if a large proportion (up to 27%) of the additional revenue were consumed in enforcement and administration. Alternative measures to enlarge the tax Significant results are: ∆W (optimal) = 0.02(4.05)Revenue + 0.16(2.05), R2 = 0.31; and ∆W (zero taxes) = 0.04(4.26)Revenue+0.31(2.42), R2 = 0.34. Figures in parentheses are t-statistics. 20
50
CHAPTER 2. MCF IN AFRICA
Table 2.8: Measures of Tax System Inefficiency Country Botswana Eq. Guinea Dem. Rep. Congo Guinea Madagascar Uganda Nigeria Sudan Malawi Mozambique Eritrea Niger Cameroon Togo Gabon Mauritania C.A.R. Zambia Tanzania São Tomé Kenya Mali Gambia Zimbabwe Burkina Faso Ghana South Africa Côte d’Ivoire Guinea-Bissau Chad Benin Swaziland Rwanda Namibia Ethiopia Senegal Cape Verde Burundi Average
∆W (optimal) 0.02 0.11 0.12 0.19 0.25 0.26 0.28 0.28 0.29 0.29 0.29 0.30 0.33 0.34 0.36 0.36 0.37 0.38 0.41 0.43 0.43 0.43 0.44 0.45 0.47 0.48 0.50 0.52 0.56 0.58 0.59 0.60 0.63 0.72 0.75 0.76 1.12 1.13 0.44
∆W (zero taxes) 0.38 0.11 0.13 0.39 0.73 0.41 0.33 0.59 0.33 0.50 0.38 0.69 0.75 0.66 0.75 0.42 0.72 0.72 1.05 0.70 0.76 0.96 0.88 1.05 0.93 0.79 1.09 0.98 0.78 0.78 1.27 0.86 1.03 0.96 1.47 1.49 1.79 1.74 0.80
Std. Dev MCFs 0.02 0.10 0.21 0.23 0.20 0.24 0.13 0.37 0.19 0.22 0.22 0.36 0.20 0.21 0.19 0.13 0.27 0.17 0.28 0.17 0.11 0.27 0.18 0.10 5.45 0.18 0.11 0.19 0.38 0.42 0.26 0.15 42.14 0.16 0.81 0.31 0.38 0.46 1.48
MCF (optimal) 1.05 1.00 1.01 1.06 1.11 1.04 1.01 1.14 1.03 1.05 1.02 1.14 1.08 1.06 1.06 1.01 1.11 1.05 1.16 1.05 1.04 1.12 1.06 1.06 1.12 1.06 1.06 1.06 1.07 1.08 1.12 1.03 1.11 1.03 1.14 1.10 1.12 1.08 1.07
Revenue 12.50 3.42 2.57 6.96 9.40 8.88 6.45 5.23 3.78 11.18 13.96 6.69 10.43 11.30 10.20 10.52 7.75 17.30 9.40 15.18 19.48 11.19 16.57 23.34 10.00 11.86 21.17 15.74 9.51 6.22 12.90 22.69 9.66 25.19 13.28 17.23 18.32 18.04 12.25
base by reducing barriers to entry into the formal economy also seem like high priorities. An obvious question is whether MCFs in Africa are higher or lower than in rich countries. It is beyond the scope of this paper to estimate the MCF in rich countries,21 but we suggest that differences in the MCF are probably not strongly related to the wealth of the country. Our results suggest that M CF (All) tends to be greater with higher tax revenue, greater use of corporate and personal income taxes, higher administrative costs, larger informal sectors and greater use of export taxes. The first two of these factors tend to occur in rich countries, while the final three factors tend to occur in poor countries. The potential extensions of this paper are numerous. Extensions to take account of the dynamic effects of taxation on savings, investment and growth; or distributional considerations; or non-tax distortions such as labour-market rigidities or regulated prices22 would all be useful. We hope, however, that in the first instance the model we have presented can be applied to further countries and across time periods, to provide a panel of MCF estimates. These estimates would not only be useful for public policy analysis, but also for the testing of numerous economic theories in which the MCF plays a role.
21
There are several difficulties in adapting our model to rich countries. For example, the European customs union must be modelled to examine import tariffs, and in the United States, state level taxes vastly complicate the analysis. Social security taxes also need to be taken into account. These difficulties are not insurmountable, but we leave them for future research. 22 Devarajan et al. (2001) have empirically shown that tax and non-tax distortions are cumulative. Taxes in sectors with less total distortions tend to have lower MCFs because they push resources towards highly-distorted sectors. The relative importance of tax and non-tax distortions is a subject for further research.
Appendix A.1
Model Specification
The single representative consumer maximizes a CES utility function with five goods: leisure (Z ), untaxed (U ), domestic (D), imports (M ), and investment (I ) subject to the income constraint. M ax W = W (Z, U, D, M, I) subject to PL Z + p˜u U + P˜D D + P˜M M + P˜I I ≤ Y A tilde over a price indicates that it is tax-inclusive: f P˜j = (1 + Tj )Pj , ∀j ∈ {D, E, M, KD , KEf , LfD , LfE }
Consumer income is the value of the endowments of foreign exchange (¯ a), ¯ ¯ time (T ), and capital (K) plus the transfer received from the government (R). ¯ +R Y =a ¯ + PL T¯ + PK K Leisure plus labour supply equals the time endowment. Z + L = T¯ The consumer’s first order conditions are: ∂W/∂U ∂W/∂Z ∂W/∂D ∂W/∂M ∂W/∂I = = = = ˜ ˜ ˜ PL PI PU PD PM Factors are combined by CES production functions to produce intermediate goods for untaxed (ψU ), domestic (ψD ), and exports (ψE ). The factors used are capital and labour, each of which may be formal (taxed) or informal (untaxed). The notation for factors is sqr : the amount of factor s ∈ {K, L} used to produce good r ∈ {U, D, E}, where q ∈ {i, f } indicates whether the factor is informal or formal. 53
54
CHAPTER 2. MCF IN AFRICA
ψU = γU (KUi , LiU ) f i ψD = γD (KD , KD , LiD , LfD )
ψE = γE (KEi , KEf , LiE , LfE ) The 10 first order conditions determining factor usage in production are given by: P˜sqr ∂ψr = ∂sqr Pr The intermediate goods are divided between final goods and investment using CET production functions. ψU = δU (XU , IU ) ψD = δD (XD , ID ) ψE = δE (XE , IE ) The value of imports is equal to the value of exports plus the endowment of foreign exchange. P˜M XM = P˜E XE + A¯ Factor demand equals factor supply: f i ¯ KUi + KD + KEi + KD + KEf = K
LiU + LiD + LiE + LfD + LfE = L Factors receive the same after-tax return wherever employed: Psqr = Ps , ∀s ∈ {K, L}, ∀q ∈ {i, f }, ∀r ∈ {U, D, E} Taxes are zero for the informal good and factors: Tj = 0 ∀j ∈ {U, {sir }}, ∀s ∈ {K, L}, ∀r ∈ {U, D, E}. Formal factors face the same tax rates whether producing exports or formal goods. This permits simpler notation: TK ≡ TKrf , TL ≡ TLfr , ∀r ∈ {D, E} The numeraire is foreign exchange: w =1 PM
A.2. DATA
55
Goods supply equals demand. XU = U XD = D XM = M IU + ID + IE = I The transfer to the consumer is equal to tax revenue. f R = TE PE XE + TM PM XM + TD PD XD + TL PL (LfD + LfE ) + TK PK (KD + KEf )
Parameters in the model are: production and utility function parameters; endowments of time, capital and foreign exchange; and tax rates. Parameter values are determined by the calibration process.
A.2 The data E M RD RE RM RK RL TD TK TL αU αD αE
Data required for the model are: exports (% of GDP) imports (% of GDP) tax revenue from VATs and sales taxes (%GDP) tax revenue from export taxes (% GDP) tax revenue from import taxes (% GDP) tax revenue from capital taxes (% GDP) tax revenue from labour taxes (% GDP) tax rate on domestic goods and services tax rate on capital (corporate tax rate) tax rate on labour labour-output ratio in production of untaxed labour-output ratio in production of domestic labour-output ratio in production of exports
Country-specific data are set out in Table A.9. All country-specific data were obtained from IMF Statistical Annexes to country reports, available on the internet at www.imf.org. Table A.9 also reports the year for which the data apply, and whether the country had a VAT in that year. In the absence of data on labour-output ratios for all countries, the model uses the average ratios for the five countries of Table A.10, supposing that the ratios are constant across all countries. These data are derived from social accounting matrices prepared by the International Food Policy Research
56
CHAPTER 2. MCF IN AFRICA Table A.9: Country-Specific Data
Country Benin Botswana Burkina Faso Burundi Cameroon Cape Verde CAR Chad Congo Côte d’Ivoire Eq. Guinea Eritrea Ethiopia Gabon Gambia Ghana Guinea Guinea-Bissau Kenya Madagascar Malawi Mali Mauritania Mozambique Namibia Niger Nigeria Rwanda São Tomé Senegal South Africa Sudan Swaziland Tanzania Togo Uganda Zambia Zimbabwe
year 2001 2001 2001 2000 2001 2001 1999 2000 1999 1999 2001 2000 2001 2000 1998 1998 1998 2001 2000 2001 1999 2000 2002 2001 1997 2000 2000 2001 2000 2000 1999 1999 2001 2002 1998 1998 1998 2000
E 27.69 56.20 9.34 7.79 31.80 30.82 16.78 16.58 21.90 44.33 106.02 5.26 15.36 66.96 50.53 34.27 21.60 27.21 26.47 28.59 27.04 25.50 38.54 21.90 52.62 17.80 53.27 9.30 35.32 30.50 25.70 8.11 70.20 15.90 33.72 11.78 29.30 29.81
M 35.40 33.20 23.38 21.23 29.20 65.35 23.83 32.03 25.59 37.46 125.60 67.37 31.18 32.65 61.32 46.66 23.40 57.71 36.39 31.75 49.32 37.50 66.93 38.50 58.17 25.33 37.54 25.80 82.44 39.60 24.40 15.13 83.30 24.50 40.39 28.48 38.40 31.00
I 19.18 15.70 19.50 8.39 17.80 17.36 14.41 17.02 24.10 16.30 56.79 18.50 18.04 21.84 18.30 24.67 17.10 18.92 15.55 15.50 17.08 20.60 33.04 41.64 19.75 10.78 17.70 18.40 43.49 19.10 16.50 16.70 18.10 17.00 14.20 17.65 14.40 15.55
RD 2.76 2.07 3.66 9.16 3.96 0.58 2.76 1.88 1.03 4.82 0.63 2.77 2.66 1.99 1.46 1.62 4.65 0.74 6.62 2.65 1.61 2.32 3.87 3.99 4.54 1.61 1.37 3.16 0.41 4.64 5.87 1.29 3.55 2.51 3.20 6.56 6.60 6.00
RE 0.14 0.00 0.42 0.00 0.08 0.78 1.12 0.22 0.05 2.56 0.45 0.00 0.18 0.79 0.00 2.32 0.02 2.61 0.00 0.00 0.00 0.22 0.00 1.98 0.00 0.18 0.00 0.00 0.05 0.00 0.00 0.07 0.00 0.00 0.00 0.01 0.00 0.00
RM 6.54 2.95 3.32 3.40 3.91 9.78 2.36 1.85 0.74 4.60 0.28 4.37 6.22 5.16 11.18 4.30 1.45 4.30 5.96 4.79 0.61 6.22 2.34 3.22 9.62 3.61 2.77 3.41 10.20 8.48 1.00 2.85 13.20 4.67 5.60 1.00 4.60 2.59
RK 1.90 5.00 1.28 1.57 1.46 3.59 0.52 1.13 0.27 2.08 1.67 4.84 2.90 1.54 2.09 1.85 0.20 0.92 3.45 0.99 0.71 1.31 2.01 0.73 5.03 0.56 1.22 1.91 1.81 1.91 3.60 0.90 2.15 0.66 1.60 0.66 1.40 3.89
RL 1.57 2.48 1.32 3.91 1.03 3.59 1.00 1.15 0.49 1.68 0.39 1.98 1.32 0.72 1.85 1.77 0.65 0.95 3.45 0.97 0.86 1.12 2.30 1.27 6.00 0.73 1.09 1.19 2.71 2.20 10.70 0.12 3.78 1.55 0.90 0.66 4.70 10.86
TD 0.18 0.10 0.18 0.20 0.19 0.10 0.18 0.18 0.03 0.20 0.06 0.05 0.15 0.18 0.10 0.10 0.18 0.15 0.15 0.20 0.20 0.18 0.14 0.17 0.10 0.19 0.05 0.15 0.35 0.20 0.14 0.10 0.32 0.20 0.14 0.17 0.18 0.15
TK 0.38 0.15 0.20 0.40 0.39 0.20 0.30 0.45 0.40 0.35 0.25 0.25 0.30 0.35 0.35 0.35 0.35 0.39 0.30 0.35 0.30 0.35 0.25 0.45 0.40 0.43 0.30 0.40 0.30 0.35 0.30 0.40 0.30 0.30 0.30 0.30 0.35 0.30
TL 0.28 0.10 0.15 0.50 0.17 0.20 0.31 0.48 0.35 0.27 0.10 0.12 0.15 0.30 0.15 0.15 0.29 0.10 0.15 0.15 0.32 0.29 0.26 0.15 0.20 0.34 0.20 0.30 0.13 0.44 0.30 0.20 0.33 0.25 0.33 0.20 0.20 0.30
VAT X X X X X X X X X X X X X X X X X X X X X -
Table A.10: Labour-Output Ratios (%) export domestic untaxed
Malawi 38.08 48.34 58.66
South Africa 56.14 48.28 53.99
Tanzania 33.58 33.59 43.79
Zambia 19.39 39.37 53.15
Zimbabwe 37.09 46.82 49.70
Average 36.86 43.28 51.86
Institute. Among other data, the SAMs provide for each commodity: the value-added by each factor; exports of each commodity; domestic demand for the commodity; and goods taxes paid. Let Li denote the labour share of value added for each commodity i. Let Ei denote exports of each commodity. The P (Li ×Ei ) iP . first row in the table, the labour-output ratio for exports is then i Ei Commodities are classified as untaxed if the taxes paid on the commodity constitute less than 5% of the value of domestic output of the commodity, and domestic if more than 5% is taxed. Let Uj be the value-added ofPuntaxed (Lj ×Uj ) goods. The labour-output ratio for untaxed is then calculated as jP Uj . j The same procedure is used to calculate the labour-output ratio for domestic. The administrative costs of tax collection presented in Table 2.5 are derived from various sources. For the United States: IRS Data Book, FY2002,
A.3. MODEL CALIBRATION
57
available at: www.irs.gov/pub/irs-soi/02db30cs.xls; For other OECD countries – authors’ calculations based on the following tax agency annual reports: Australia – ATO Annual Report 2002, available at www.ato.gov.au; United Kingdom – Inland Revenue, Annual Report for the year ending 31st March 2002, available at www.inlandrevenue.gov.uk/pdfs/report2002.pdf; New Zealand – Inland Revenue Annual Report 2001-2002, available at: www.ird.govt. nz/aboutir/reports/annual-02.pdf; and Canada: Canada Customs and Revenue Agency, 2001-2002 Annual Report to Parliament, Financial Statements, available at www.cra-arc.gc.ca/agency/ annual/2001-2002/. For Guatemala: simple average of adjusted figures from Mann (2002). Ghana: revenueweighted average of figures cited by Terkper (1995). Namibia: statistics provided by Klaus Schade of the Namibian Economic Policy Research Unit. Tanzania: statistics provided by Odd-Helge Fjeldstad of the Chr. Michelsen Institute. Remaining countries: Taliercio (2004). We are very grateful to Klaus Schade, Odd-Helge Fjeldstad and Robert Taliercio for their assistance in obtaining these data.
A.3
Model Calibration
Benchmark quantities of goods and factors (entries in the SAM) are calculated using the following equations: XD = RTDD XU = 100 − E − I − XD − RD XE = E − RE XM = M − RM A¯ = XM − E XU IU = I XU +X D +XE XD ID = I XU +X D +XE XE IE = I XU +X D +XE f +ID RK KD = XD +IXDD+X E +IE TK KEf =
XE +IE RK XD +ID +XE +IE TK
LfD =
XD +ID RL XD +ID +XE +IE TL
LfE =
XE +IE RL XD +ID +XE +IE TL
production of domestic production of untaxed production of exports quantity of imports endowment of foreign exchange investment in untaxed investment in domestic investment in exports formal capital used to produce domestic formal capital used to produce exports formal labour used to produce domestic formal labour used to produce exports
58 LiD = αD (XD + ID ) − (1 + TL )LfD LiE = αE (XE + IE ) − (1 + TL )LfE LiU = αU (XU + IU ) f i KD = (1−αD )(XD +ID )−(1+TK )KD
KEi = (1−αE )(XE +IE )−(1+TK )KEf KUi = (1 − αU )(XU + IU ) ¯ = Kf + Kf + Ki + Ki + Ki K E D U E D L = LfE + LfD + LiE + LiD + LiU T¯ = 1.05L
CHAPTER 2. MCF IN AFRICA informal labour used to domestic informal labour used to exports informal labour used to untaxed informal capital used to domestic informal capital used to exports informal capital used to untaxed total capital endowment total labour supply endowment of time
produce produce produce produce produce produce
Tax rates on exports and imports are calibrated, rather than being drawn directly from the legal tax rates: RE TE = X E RM TM = X M
tax rate on exports tax rate on imports
We do not observe price or quantities of goods, but we do observe the total amount of money spent on each good (values as a percentage of GDP). Following the Harberger convention we choose units of the aggregate goods such that quantities equal values. This implies that initial prices equal one. Where goods are taxed, goods units can be chosen such that either the gross of tax or net of tax price equals one. We chose units such that the agent supplying the good or factor received a price of one, with remaining prices implied by tax rates: w PM =1
PI = 1 PU = 1 PL = 1
PK = 1
world price of imports (and foreign exchange) price of investment price of untaxed wage received by labour (formal or informal); also the wage paid by producers for informal labour wage received by capital (formal or informal); also the wage paid by producers for informal capital
A.3. MODEL CALIBRATION PD = 1 PE = 1
59 producer price of domestic producer price of exports
P 1 An n-factor CES production function, F = A( nj=1 θj Xjρ ) ρ , with factors Xj , share parameters θj , scale parameter A, and elasticity of substitution 1 , can be rewritten in calibrated form as σ = 1−ρ " F = F¯
n X i=1
¯ p¯ X Pn i i ¯ ¯j Xj j=1 p
Xi ¯i X
ρ # ρ1
where a bar over a variable indicates the observed benchmark level. The benchmark factor demands, factor prices and product outputs, combined with the elasticities of substitution fully specify the three production functions. The same methodology can be used for the CES utility function, where the Xi s represent goods consumed, the pi s are goods prices, and the benchmark utility level is normalized to unity. The calibration process is completed with the selection of substitution elasticities for production and utility functions. In the absence of reliable evidence on the magnitude of these elasticities for Africa we chose a base case of σ = 1 for all four functions, and then ran sensitivity checks with different values for σ.
Chapter 3 Infrastructure Privatization and the Marginal Cost of Public Funds It is commonplace to talk of a wave of infrastructure privatization, spreading out across the world from the initial stones cast by Maggie Thatcher. What is a little less appreciated is that some countries have been drenched by the wave, while others have stayed entirely dry. Exploring an efficiency-based motivation for privatization, the paper offers a possible explanation for why the wave has hit some countries and not others. The theory is tested using data from the World Bank’s Private Participation in Infrastructure (PPI) database.1 The PPI database deals with private investment in electricity, water, telecommunications, railroads, toll-roads, and ports, in developing countries. It records money paid to the government for purchase or use of government assets, and money invested by private firms in expanding or modernizing these facilities. The annual sum of money invested around the world rose from US$0.074 billion in 1984, to a peak just before the financial crises in 1997 of US$115 billion, and has more recently declined to a still considerable annual level of US$48 billion in 2002. Infrastructure privatization is a global phenomenon. The PPI database lists 135 developing countries that have had at least one PPI transaction.2 1
http://rru.worldbank.org/PPI/ Among countries included in the World Bank’s World Development Indicators CDROM (World Bank 2001), the only countries not to have privatized at least one infrastructure firm during 1984-2002 were American Samoa, Antigua and Barbuda, Bahrain, Bhutan, Ethiopia, Iraq, Isle of Man, Democratic Republic of Korea, Republic of Korea, Liberia, Libya, Marshall Islands, Mayotte, Federated States of Micronesia, Palau, Puerto 2
61
62
CHAPTER 3. PRIVATIZATION AND THE MCF
But this figure masks tremendous concentration of transactions. Ranked by the number of privatization transactions, the top ten countries account for 60% of transactions.3 Ranked by the amount invested, the top ten countries account for 67% of all PPI in developing countries.4 Brazil alone accounts for almost 20% of total funds invested between 1984 and 2002. In trying to understand why some countries have undertaken considerable infrastructure privatization, while others have not, a useful starting point is the existing literature on general privatization. Bortolotti, Fantini & Siniscalco (2003) have recently examined panel data for privatization around the world, highlighting four groups of determinants of privatization: political ideology, fiscal pressures on a liquidity constrained government, legal origin and stock market liquidity. They find privatization is more likely in wealthy democracies with right wing governments, high debt, liquid stock markets and a legal system that better protects shareholders. They do not consider the possibility that governments privatize depending on whether or not privatization enhances welfare. They start from the premise that privatization enhances efficiency. So if governments do not privatize, it must be for reasons other than efficiency. In fact, theory is ambiguous about whether privatization enhances welfare. Laffont & Tirole (1991) highlight the theoretical ambiguity, listing a number of arguments which suggest privatization could either improve, worsen or make no difference to total welfare. Empirically, however, there is evidence of the superior performance of private firms in competitive industries. Megginson & Netter (2001) survey empirical evidence from 38 studies of privatization. It seems that privatization provides stronger incentives to improve productivity and lower costs, which in a competitive industry translates into higher welfare. So for purposes of Bortolotti et al. (2003), who address privatization across all industries, it is reasonable to suppose that privatization always enhances efficiency. But in natural monopoly infrastructure markets the empirical welfare effect of privatization is less clear. Studies that permit large samples for econometric analysis involve comparison of pre- and post-privatization enterprise performance as measured by accounting data.5 Among these studies, only D’Souza & Megginson (2000) address an infrastructure industry – telecommunications – finding operational and financial improvements in Rico, St. Vincent and the Grenadines, Suriname, Syria, and Turkmenistan. 3 The top ten are: China, Russian Federation, Brazil, Argentina, India, Mexico, Chile, Thailand, Malaysia, and Colombia. 4 In descending order of total investment, the countries are: Brazil, Argentina, China, Mexico, Malaysia, Chile, Philippines, India, Indonesia and Thailand. 5 Table 4, Megginson & Netter (2001)
63 firm performance. For skeptics of infrastructure privatization, however, such performance improvements could be accompanied by welfare-reducing exploitation of market power. Another group of studies compares post-privatization changes with a comparison group of firms or a counterfactual.6 Many of these studies address telecommunications. When the effects of telecommunications competition are distinguished from those of privatization, there is not unanimity that privatization makes a difference to welfare. In any case, telecommunications is arguably becoming a normal competitive industry, without implications for the effect of privatizing a natural monopoly in other infrastructure industries. There remain some careful case studies, notably Galal, Jones, Tandon & Vogelsang (1994) and Newbery & Pollitt (1997), that find net welfare gains in other infrastructure privatizations.7 But again, the determined skeptic could argue that a handful of case studies hardly proves the thesis that privatization invariably improves welfare. Even if all empirical studies of infrastructure privatization showed unambiguous improvements in welfare, this would not prove that all governments should privatize all their infrastructure services. Such evidence would be entirely consistent with a theory of privatization in which governments are motivated by efficiency, and privatize only when they expect to increase welfare. It thus seems warranted to enquire more closely into the determinants of infrastructure privatization, focusing on an efficiency motivation. An important recent contribution in this domain is the paper of Auriol & Picard (2002). They find that whether privatization improves welfare depends on the shadow cost of public funds and on the extent to which the privatization transaction transfers expected profit of the privatized firm to the government. If the transaction fully transfers expected profits through a franchise fee, then privatization improves welfare for high values of the shadow cost of public funds and reduces welfare for low values of the shadow cost of public funds. When the government does not fully capture expected profit, privatization improves welfare for intermediate values of the shadow cost of public funds, but public ownership is preferable for high or low values. The paper thus offers a potential explanation for privatization. Governments privatize when the shadow cost of public funds changes, moving from a situation in which public ownership is optimal to one where privatization is optimal. An important qualification on the paper of Auriol & Picard (2002) is 6
Table 3, Megginson & Netter (2001) A further paper, Chisari, Estache & Romero (1999), was not considered by Megginson & Netter (2001). The study uses a computable general equilibrium model of Argentina, to find net welfare gains from privatization. 7
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CHAPTER 3. PRIVATIZATION AND THE MCF
that it supposes that privatization involves a shift from a regulated public monopoly to an unregulated private monopoly. The trade-off in their model is between information rents of a regulated public firm, and market power rents of an unregulated private firm. They argue that it is difficult to establish credible regulatory agencies in developing countries, so that privatization is effectively a move to laissez-faire, including the deregulation of prices. This view of infrastructure privatization in developing countries seems too extreme. It is very rare, if not impossible, to find an infrastructure privatization that is not subject to regulatory control. Governments are highly conscious of the political impact of increases in prices of water, electricity, telecommunications, and rail and road tolls. This political sensitivity makes investors wary of infrastructure privatization. They know that once investments are sunk, governments have short term political incentives to renege on price commitments, lowering regulated prices and profitability. In Latin America, where there has been the most progress in privatizing retail distribution systems that interact directly with consumers, some of the regulatory agencies are among the most sophisticated in the world. The African country leading in terms of the number of deals and total investment, South Africa, has similarly established effective regulatory agencies. In Asia, infrastructure privatization has more frequently involved wholesale purchases, such as independent power plants.8 Here a typical model is an auction of the right to sell power to the government purchaser, with the winner being the firm that promises the lowest price. The final terms and conditions are written into a binding contract, frequently subject to international arbitration in the event of a dispute. In transactions such as these, the absence or weakness of an explicit regulatory agency does not mean that the private firm has freedom to set price and quality. It seems more appropriate to model privatized firms as being subject to regulation. But if both public and private firms are regulated, an efficiencybased theory of privatization must find an alternative explanation for differences in performance. An answer can be found in the literature on soft budget constraints. When social surplus exceeds profit, it can be optimal for a benevolent 8
In East Asia and the Pacific, 58% of PPI transactions have been greenfield developments, of which electricity deals have amounted to 46%. The most popular business model for these transactions has been the independent power plant: see Gray & Schuster (1998). Among non-greenfield projects, toll-roads have been the most frequent PPI transactions (38% of non-greenfield projects). Both of these types of transactions typically involve a regulatory framework implemented in terms of an explicit contract with performance incentives, and with little scope for intervention of specialist regulatory agencies. Source for statistics: PPI database.
65 government to support a loss-making firm, to avoid closure of the firm. When the possibility of such bail-outs exists, the firm’s budget constraint is ‘soft’. The manager knows that if the firm makes a loss the government will provide a subsidy. Segal (1998) illustrates how this possibility can create incentives for a firm’s manager to increase costs, in order to obtain such support. He further shows how this problem is likely to be more extreme in monopoly industries than competitive industries. For purposes of this paper, Schmidt (1996) provides the most relevant analysis of the soft budget constraint affecting a regulated firm. Schmidt argues that the government is better informed about the firm’s costs and profits if it owns and directly controls the firm than if the firm is privatized. He considers the right to detailed cost and profit information to be a residual right of control, which cannot be contractually allocated. To make the point clear for modelling purposes, Schmidt supposes that when a firm is in public ownership the government has perfect information about the firm’s costs, but knows only the potential distribution of the firm’s costs when it is privatized. Schmidt further supposes that the manager receives a higher benefit from a higher level of output, and can make a personally costly investment to reduce costs. Accordingly, the government wishes to cut back production when costs are high, in order to punish the under-performing manager. But if realized costs are high, in public ownership with perfect information about costs, the government has an ex post incentive to set prices at the efficient level, where marginal benefit equals the inflated marginal cost. Thus, with public ownership it is not credible for the government to threaten to cut back production to punish the manager. Accordingly the manager has an incentive to under-invest in cost reduction. In contrast, with asymmetric information and private ownership, the optimal regulatory scheme involves cutting production below the ex post efficient level when high costs are realized. Thus, privatization acts as a commitment device by the government not to acquire detailed cost information, and provides a stronger incentive to the firm’s manager to invest in cost reduction. To summarize, Schmidt (1996) provides a theory suggesting that public regulated firms have higher costs than private regulated firms. The theory of soft budget constraints can be criticized on the grounds that governments bail out private firms as well as public firms. This is especially likely to occur for essential public services, which are judged to be too socially important to be allowed to fail. Arguably, however, bail-outs are less likely to occur with private firms. The argument of Schmidt (1996) suggests that the severity of the problem could be related to the degree to which government information about the firm’s costs differs under public and private ownership. Even if the theory of soft budget constraints is not
66
CHAPTER 3. PRIVATIZATION AND THE MCF
the explanation, privatization appears empirically effective in reducing costs, notwithstanding the unclear evidence concerning total welfare. The model presented in section 2 uses the demand and technology assumptions and the notation of Auriol & Picard (2002), with modifications to embrace the setting of Schmidt (1996). In particular, the inefficiency of public ownership arises from the soft budget constraint problem, while the inefficiency of private ownership is the ex post inefficient production level that arises with a regulated firm under information asymmetry. Section 3 explores theoretically how the relative efficiency of the two ownership regimes differs for different values of the shadow cost of public funds, and suggests that a decrease in the shadow cost of public funds may trigger privatization. Section 4 tests this theory using the PPI database for developing countries, applying the methodology of Bortolotti et al. (2003). Section 5 concludes.
3.1
The Model
It is assumed that the government privatizes if privatization increases expected welfare. The game’s timing is: 1. The government constructs an infrastructure facility that has fixed cost sufficiently large that no other firm can survive in the market. The fixed cost is sunk and thus plays no further role. 2. Nature reveals to all parties the values of all parameters except the value of β, the firm’s type. 3. The government decides whether or not to privatize. If the firm is privatized, a private investor pays a lump sum transaction fee, F , to the government to purchase the regulated firm; and the firm is transferred to the investor. 4. The actual value of β is realized. If the firm is public the value of β is revealed to the firm and the government. If the firm is private, the value of β is revealed to the firm only. 5. The government announces the regulatory mechanism, fixing the quantity, Q, and the transfer, t, to the regulated firm as a function of the firm’s type, using the actual type for a public firm, and the reported type for a private firm.9 9
When regulating the private firm under information asymmetry, the ‘Revelation Principle’ ensures that there is no loss of generality in restricting the government to use ‘truthful
3.1. THE MODEL
67
6. Production occurs. Decisions are made in periods 3, 5 and 6. In period 6, inverse demand is given by P (Q) = a − bQ (3.1) where P is the price, Q is the quantity, and a > 0 and b > 0 are parameters. The implied gross consumer surplus is: b S(Q) = aQ − Q2 . 2
(3.2)
The firm uses linear pricing, giving firm revenue: R(Q) = P (Q)Q
(3.3)
Whether the firm is public or private it incurs fixed cost K in period 6. The firm’s marginal cost is dependent on the firm’s type, β > 0, which ¯ with probability g(β), where g(·) has a is drawn from the support [β, β] cumulative density function G(β). Expectations over β are denoted by E[·] = R β¯ (·)g(β)dβ. β If the firm is private, its cost function is given by: C = βQ + K
(3.4)
Two technical assumptions ensure no corner solutions, and no ‘bunching’ in the period 5 regulatory decision under asymmetric information. a ≥ β¯ +
¯ G(β) ¯ g(β)
G(β) is non decreasing g(β)
(3.5) (3.6)
When the firm is publicly owned, the firm incurs costs in period 6 equal to: C = (β + x(λ))Q + K
(3.7)
The addition of the marginal cost penalty, x(λ), due to public ownership should be thought of as a reduced form representation of Schmidt’s (1996) analysis. That is, although x is exogenous here, there is an endogenous direct’ regulatory mechanisms. Mechanisms are ‘direct’ when the firm tells the government its type. Mechanisms are ‘truthful’ when the firm has no incentive to lie about its type. See Laffont & Martimort (2002).
68
CHAPTER 3. PRIVATIZATION AND THE MCF
explanation for why costs are higher under public ownership than private ownership. The shadow cost of public funds, λ > 0, measures the deadweight loss induced when taxation revenue is increased marginally. A dollar of tax revenue has a welfare cost of (1 + λ) dollars. It is assumed that x is a decreasing function of λ. Segal (1998) observes that as the cost of public funds becomes very high, bail-outs of underperforming public firms become prohibitively expensive. Knowing that subsidies will not be forthcoming, managers do not have an incentive to underinvest. Thus x tends to zero as the cost of public funds tends to infinity:10 x > 0;
dx lim < 0; x=0 λ→∞ dλ
(3.8)
A technical assumption ensures no corner solutions under public ownership: a ≥ β¯ + x(0)
(3.9)
In each period the firm seeks to maximize profit, which in period 6 is given by its information rent: π = R(Q) − C(Q; β) + t
(3.10)
where t is the net transfer received from the government. In period 5, the government chooses a regulatory scheme to maximize welfare. The control variables are quantity, Q, and the transfer, t. The objective function is net social welfare, being gross consumer surplus less the cost of production and the social cost of any transfer to the firm: W = S(Q) − C(Q; β) − λt
(3.11)
Transfers may be positive (subsidy) or negative (taxation) in either public ownership or privatized settings.11 10
The important feature is that for high (low) values of λ the marginal cost penalty of public ownership is smaller (greater) than the information rent under regulated private monopoly. The results are qualitatively unchanged if, for example, the cost penalty is modelled as interacting multiplicatively with β, C = K + (1 + x(λ))βQ, or if x is modelled as a constant. In the latter case an additional assumption is required that x not be too large (x < E[G/g]), to ensure that a public firm is more efficient than a private firm for at least some values of λ. This is necessary to explain why public firms are observed in the first place. 11 The possibility of positive or negative transfers to a regulated firm is a staple of the theory of regulation under asymmetric information. It might, however, seem at odds with
3.1. THE MODEL
69
If the firm is public, the government maximizes welfare subject to the firm’s participation constraint, π ≥ 0. Since the government has full information, the public firm can be constrained to have zero rents in period 6. If the firm is private, the government regulates under asymmetric information and incentive compatibility constraints must be added to the government’s period 5 problem. The regulated private firm earns information rents which are strictly positive in expectation. In period 3, the private investor is assumed to be risk neutral and so pays a transaction fee equal to the information rents expected in period 6: F = E[π].12 The transaction fee is sunk in subsequent periods and so affects neither the firm’s participation constraint nor the government’s objective function in period 5. In making the privatization decision at period 3, the government compares expected welfare under privatization and continued public ownership. If the government privatizes, it must take account of the transaction fee, F . Total welfare is reduced by F when the investor pays the fee, but is increased by (1 + λ)F when the government spends the fee on public services. The net effect, λF , is added to the period 6 measure of ‘ownership welfare’ to give a measure of period 4 ‘total welfare’ under privatization: ˜T = W ˜ + λE[π] W
(3.12)
The government’s assessment at time 3 of expected ‘total welfare’ under continued public ownership is simply: WT = W
(3.13)
The difference in the government’s objective functions in periods 3 and 5 arises because of the game’s timing: F is sunk at time 5. Higher welfare the real world that governments would subsidize a privatized firm. It could be argued that the hardening of a privatized firm’s budget constraint occurs because it is politically unacceptable to transfer public funds to a private firm that would be loss-making without the transfer. As the Schmidt (1996) paper demonstrates, ‘hardening’ of the budget constraint can occur without such a political economy explanation. Perhaps more significantly, the different forms of private participation create various opportunities to make transfers to the private firm. For example, a lease of infrastructure facilities leaves the government responsible for large fixed cost investments, while making the private operator responsible for the operating costs. And of course tax concessions are not unknown in infrastructure privatizations. 12 As the game is structured, F is necessarily positive. There is no change to the results of the paper if the firm incurs an additional fixed cost in period 4. In this case, F is equal to the expected period 6 information rents less the period 4 fixed cost, and could be positive or negative. This change embraces the possibility of a ‘negative concession’, where an infrastructure firm is franchised to the bidder who demands the lowest subsidy.
70
CHAPTER 3. PRIVATIZATION AND THE MCF
could be achieved if the timing of the game were different, so that there were consistent objectives at the time of privatization and the time of regulation. In particular, it would seem possible for the government to write its regulatory decision into the privatization contract at time 3. With no asymmetry of information at time 3, the privatization contract would yield first-best regulation in expected terms. Since the privatized firm does not suffer from the soft budget constraint problem, privatization would always be preferable to public ownership, and the model could not explain why public firms are observed. But it seems unrealistic to deny asymmetric information in regulatory decisions concerning long-lived infrastructure. Initial privatization contracts may indeed contain regulatory provisions but, empirically, government regulatory decisions evolve subsequently in conditions of asymmetric information. Further, with the amended timing, the firm would have zero expected profit, so the investor would pay a zero transaction fee. This would be inconsistent with frequently observed positive transaction fees. The timing presented at the beginning of this section seems more closely to represent the observed timing of privatization and regulatory decisions.
3.2
A Theory of Infrastructure Privatization
Privatization can be viewed as a public finance instrument. Privatization is efficient if the marginal welfare cost of privatization revenue is less than the marginal welfare cost of other sources of funds, λ. That is, privatization may increase total welfare (period 3) even if it reduces ownership welfare (period 5), provided that it raises sufficient government revenue.13 It is thus interesting to explore the determinants of ownership welfare and government revenue, before investigating the determinants of total welfare. The privatization decision is made on the basis of total welfare.
3.2.1
Comparing Public and Private Ownership
The first step is to compare welfare expected in period 5 under private and public ownership. When the firm is publicly owned the government observes β and chooses 13
The tension between ownership efficiency and government revenue is often observed within teams responsible for organizing privatization transactions. ‘Reformers’ would like to increase efficiency; government budget officers and advisers working for a transactionbased premium would happily sell an unregulated private monopoly if it would raise greater revenue.
3.2. A THEORY OF INFRASTRUCTURE PRIVATIZATION
71
Q and t to solve: max W subject to π ≥ 0
(3.14)
Solving this problem, expected welfare is given by: i h 1+λ V2 −K W (λ) = E (1 + λ) 1 + 2λ 2b
(3.15)
where V is defined by: V =a−β−x
(3.16)
When the firm is privatized, the government cannot observe the firm’s marginal cost. Incentive compatibility constraints are added to problem (3.14). The resulting expected welfare is given by:14 i h ˜2 ˜ (λ) = E (1 + λ) 1 + λ V − K W 1 + 2λ 2b
(3.17)
where V˜ is defined by: V˜ = a − β −
λ G(β) 1 + λ g(β)
(3.18)
The increase in welfare from a change of ownership can thus be defined as: ∆W =
(1 + λ)2 E[V˜ 2 − V 2 ] 2b(1 + 2λ)
(3.19)
The relative efficiency of public and private ownership depends on the shadow cost of public funds. Proposition 1 summarizes the circumstances under which private ownership yields higher period 5 expected welfare. The proofs of all propositions are in the Appendices. Proposition 1 There exists a critical value of the shadow cost of public funds, λ1 > 0 such that ∆W > 0 if and only if λ < λ1 . For low values of λ private ownership yields higher expected welfare than public ownership, while the situation is reversed for high values of λ. The welfare cost of information asymmetry under private ownership increases with λ. For sufficiently high values of λ this effect outweighs the marginal cost disadvantage of public ownership. 14
The methodology for deriving this result is well known. See, e.g., Laffont & Martimort (2002).
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CHAPTER 3. PRIVATIZATION AND THE MCF
Comparing (3.16) with (3.18), the critical value λ1 satisfies: G λ1 E[ ] (3.20) x= 1 + λ1 g The critical value is independent of the demand parameters, a and b, and the fixed cost, K, but increases as β decreases.15 Thus, shifts in demand do not alter the balance between public and private ownership, but technological progress that lowers marginal cost, β, does. In particular as β falls, it becomes more likely that the actual shadow cost of public funds is less than the critical value, and that private ownership is preferable to public ownership. A re-interpretation of (3.20) also reveals something of the magnitude of the soft budget constraint problem. For example, if β is uniformly distributed β−β and λ = 31 then private ownership is preferable if x ≥ 14 2 . Thus, if β can vary by ±10% around its mean value, private ownership is preferable if the soft budget constraint inflates average marginal cost by 2.5% or more.
3.2.2
The Change in Government Revenue
The next step is to discover when privatization increases government revenue expected at time 3. The expected government revenue raised by a public firm is the negative of the transfer to the firm:16 λ (1 + λ) 2 V − K] (3.21) b (1 + 2λ)2 The government revenue generated by a privately owned firm is the transaction fee F = E[π], less the expected transfer to the firm, which in this case includes an element of information rent: t = π −R(·)+C(·). The information rents are netted out, yielding expected government revenue:17 # " λ 1 G λ(1 + λ) ˜ − C(·) ˜ − K] = E V˜ 2 + V˜ − K (3.22) T˜ = E[R(·) b(1 + 2λ)2 (1 + 2λ) b g T = E[−t] = E[R(·) − C(·)] = E[
Comparison of equations (3.21) and (3.22) yields the expected increase in government revenue resulting from privatization: " ( )# λ 1 + λ G ∆T ≡ T˜ − T = E (V˜ 2 − V 2 ) + V˜ (3.23) b(1 + 2λ) 1 + 2λ g 15
Totally differentiating (3.20) yields
dλ1 dβ = dx dλ < 0.
. λ 1 dx − 1+λ E[ d(G/g) ] E[G/g]− dβ (1+λ)2 dλ ≤
0 since by assumption d(G/g) ≥ 0 and dβ 1+λ a−ω 16 Public firm revenue and cost can be calculated using Q = 1+2λ with ω = β + x. b 17 ˜ = 1+λ a−˜ω with ω Private firm revenue and cost can be calculated using Q ˜ =β+ 1+2λ b λ G 1+λ g .
3.2. A THEORY OF INFRASTRUCTURE PRIVATIZATION
73
Using this result, Proposition 2 summarizes the conditions under which privatization increases expected government revenue. Proposition 2 There exists a critical value λ2 > λ1 such that ∆T > 0 if and only if λ < λ2 . Privatization may not always reduce the government’s budget deficit. For high values of the shadow cost of public funds (λ > λ2 ) privatization increases the deficit, while for low values (λ < λ2 ) privatization reduces the deficit. An implication of Proposition 2 is that whenever private ownership is more efficient than public ownership (λ < λ1 ), privatization increases expected government revenue.
3.2.3
The Privatization Decision
The privatization decision in period 3 is based on a comparison of expected welfare under public ownership or after privatization, taking account of the expected transaction fee. Using expressions (3.12) and (3.13), the increase in total welfare from privatization expected in period 3 is: ∆WT = ∆W + λE[π] =
1 λ ˜G (1 + λ)2 E[ (V˜ 2 − V 2 ) + V ] b(1 + 2λ) 2 (1 + λ) g
(3.24)
Privatization increases total welfare if λ ≤ λ1 , since it increases ownership welfare and government revenue. Privatization decreases total welfare if λ ≥ λ2 , since it lowers ownership welfare and government revenue. The interesting ˆ 2 , where privatization increases government revenue case is when λ1 ≤ λ ≤ λ but reduces ownership welfare. The conditions under which the government decides to privatize are summarized in Proposition 3. Proposition 3 There exists a critical value λ3 in (λ1 , λ2 ) such that ∆WT > 0 if and only if λ < λ3 . The government decides to privatize only if the shadow cost of public funds is sufficiently small (λ < λ3 ). Since λ3 < λ2 , expected government revenue increases whenever it is efficient to privatize. Proposition 3 yields a possible explanation for privatization. Privatization may be triggered if the shadow cost of public funds falls, shifting from greater than λ3 to less than λ3 . Not all falls in λ trigger privatization, only those that move beyond the critical value. Nevertheless, the critical value is determined by demand and technology parameters, so a reduction in a country’s shadow cost of public funds may trigger privatization of some industries but not others.
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A government may also decide to privatize when λ stays unchanged, but shifts in demand or technology increase the critical value λ3 . It can be shown that λ3 increases in response to an increase in a or a decrease in β.18 Privatization becomes more likely as a country becomes richer (higher a) or adopts new technology (lower β). The theory helps to understand the difficulty for empirical studies to demonstrate that privatization improves total welfare,19 while there has been stronger evidence of improvements in indicators of firm performance. The switching point between the two ownership regimes occurs when expected welfare under each regime is equal. The firm’s marginal cost should fall after privatization because the public firm’s cost disadvantage is eliminated. Profitability should rise after privatization because a regulated private firm earns information rents that a public firm does not. The theory may also help to understand difficulties with public acceptance of privatization. At time 5, a marginal privatization occurring when λ = λ3 reduces ownership efficiency: λ > λ1 ⇒ ∆W < 0. If the public does not take account of the additional public services purchased with the (sunk) transaction fee, privatization may be perceived as lowering welfare.
3.3
Empirical Determinants of Privatization
The theory predicts that reductions in the marginal cost of public funds can induce privatization. To examine the relevance of this prediction, the empirical determinants of infrastructure privatization are examined using probit regressions with panel data from the PPI database. The data cover 155 developing countries as defined by the World Bank (2001), for the years 1984-1998. The variables used are described in Appendices B.4 and B.5. The results are presented in Table 2.3. The dependent variable, P rivit , is set equal to one if country i privatizes at least one infrastructure firm in year t, and zero otherwise. The transactions include management contracts, leases, concessions and divestitures. Greenfield projects (i.e., entirely new infrastructure facilities) are excluded since they do not represent a transition of a facility from public to private operation. The mean value of P rivit indicates that infrastructure privatizations occurred in 8.8% of the country-year observations, from 1984 to 1998. Forty From the proof of Proposition 3, the critical value λ3 satisfies E[a − β]x − 12 x2 − dλ3 3 = 0. Totally differentiating this expression yields dλ da > 0 and dβ < 0. Data availability, and assessing the counterfactual, are probably the greatest difficulties in assessing welfare changes after privatization. 18
λ3 G 2 1 2 2 ( 1+λ3 ) E[( g ) ] 19
3.3. EMPIRICAL DETERMINANTS OF PRIVATIZATION
75
percent of the countries (62 countries) did not privatize any infrastructure during 1984-1998. An ideal empirical examination of the theory would compare data on changes in the cost of public funds with the incidence of privatization. Unfortunately very few estimates of the marginal cost of public funds in developing countries have been made, certainly nothing like the necessary panel data corresponding to the PPI database. Moreover, there seems to be no suitable proxy for the level of the shadow cost of public funds. The shadow cost of public funds is the result of a complex general equilibrium interaction between multiple tax instruments, and cannot be simply computed from widely observed macroeconomic indicators such as summary taxation statistics.20 But the variable of interest here is the effect of shifts in the shadow cost of public funds. For this we do, arguably, have two potential proxies. The first possibly proxy for a decrease in λ is a decrease in public debt. When a government’s debt level increases, for example because foreign denominated debt increases with a currency devaluation, the government must meet increased repayments by borrowing more, possibly at a higher interest rate, or by increasing taxation, or a combination of the two measures. Although the linkage deserves a thorough theoretical and empirical examination, it seems probable that a decrease in the level of public debt leads to a decrease in the marginal cost of public funds.21 Since it takes time for 20
Some authors have suggested that λ is inversely related to the level of development. This is unclear on several grounds. First, for a given level of revenue, a rich country with a more efficient tax system will have a lower cost of public funds than a poor country. But for a given tax system, λ is an increasing function of revenue, and rich countries tax a higher proportion of GDP than poor countries. Second, some poor countries may have some highly inefficient individual tax instruments, with high marginal costs of public funds (MCF). But the existence of great inefficiency in one sector often means that increasing an existing tax in another sector will help to restore relative prices, reducing the inefficiency in the first sector, and resulting in a low MCF for the second tax instrument. Inefficient tax systems may thus exhibit wider variance of MCFs of individual tax instruments, but have similar revenue-weighted average MCFs to those of more efficient systems. Third, empirical MCF estimates for developing countries do not seem very different from those in rich countries (see Chapter 2 and Devarajan et al. (2001)). Finally, some think of λ as the opportunity cost of public funds, the marginal benefit of public spending that must be foregone in order to finance a new project. If all governments had the same concave welfare function, the marginal benefits of expenditure would be greater in countries with low levels of expenditure, that is, poor countries. But inefficiency in public expenditure in poor countries is likely to reduce such marginal benefits significantly. For example, Reinikka & Svensson (2002) present evidence from Uganda, where only 13% of a class of public funds reached the intended destination. 21 This suggestion should not be taken to imply that countries with higher debt necessarily have higher values of λ. The level of λ is determined by a country’s tax system, but for a given tax system an increase in debt is likely to increase the government’s revenue
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an decrease in debt to have an effect on the tax system and the shadow cost of public funds, and it takes time for privatization transactions to be implemented, lagged values of changes in public debt are used. The second possible proxy for a shift in the shadow cost of public funds is the introduction of a VAT. VATs have been widely introduced around the world in recent decades, usually replacing less efficient systems of cascading sales taxes (see Ebrill, Keen, Bodin & Summers (2002)). The introduction of a VAT is thus likely to reduce the shadow cost of public funds. Again, because it takes time for a VAT to be settled into place,22 and because privatization transactions take time, lagged values of the year of introduction of a VAT are used. Column (1) of Table 3.1 considers the effects of lagged values of these two explanatory variables on the probability of privatization. Column (1) is the outcome of an iterative variable selection process. Initially, values of the change in debt, lagged from two to six years prior to the privatization, were regressed against ‘Priv’, giving significant results only for ∆Debtt−5 . A regression with values for the introduction of a VAT gave significant results for all lags from two to six years prior to privatization. Combining ∆Debtt−5 with the lagged VAT values, the only significant coefficients were those used in the regression of Column (1). Column (1) provides some support for the hypothesis that a reduction in the cost of public funds may induce infrastructure privatization. The five to six year lag can be understood noting that it takes time for shocks to the cost of public funds to filter through to implementation of privatization transactions. The existence of this lag suggests that the introduction of a VAT is not simply an indicator of a reforming government. While reforming governments might desire both privatization and VATs, there is no particular reason to suppose that they would on average wait for five to six years after the introduction of a VAT to implement their privatization program. To test the robustness of the results in Column (1) a range of additional control variables were added to the regression. Variables that were not significant at the 10% level were not included in the regression reported in Column (2). These additional variables are GNP per capita, the growth rate of GDP, an index of the extent of regulatory intervention in the economy as a whole, and an index measuring respect for the rule of law. For the latter two measures, higher scores reflect better governance. The first point to note is that the inclusion of these additional variables requirement, and thus to increase λ. 22 For example, in the first year or so many businesses entitled to VAT refunds do not claim them, so initial VAT revenues may be higher than in subsequent years.
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Table 3.1: Panel Probit Equations for the Probability of Privatization (1) (2) (3) Constant -1.32 -1.97 -2.30 (0.10) (0.15) (0.25) ∆Debtt−5 -0.69* (0.32) VATt−5 0.64* 0.72 (0.27) (0.23) VATt−6 0.88 1.10 1.20 (0.26) (0.24) (0.35) GNP per capita 0.22 0.34 (0.04) (0.08) Growth 0.03 0.04 (0.01) (0.02) Regulation 0.72 1.16 (0.19) (0.39) Rule of Law -0.50 -1.52 (0.19) (0.36) Capitalisation 1.82 (0.39) Turnover 0.76 (0.19) No. Obs. 1397 1917 634 No. Countries 125 120 62 Log likelihood -519 -606 -293 Standard errors in parentheses. All coefficients are significant at the 1% level, except those marked with an asterisk, which are significant at 5%.
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renders the coefficient on ∆Debtt−5 statistically insignificant. A possible explanation for why changes in debt explain privatization less well then the introduction of a VAT is that debt levels fluctuate, so that a reduction in debt is not a guarantee of lower λ in the future. In contrast, there have been very few instances of the repeal of a VAT, so a VAT’s effect on λ is likely to be permanent.23 Turning attention to the newly included variables, the results suggest that richer countries and faster growing countries are more likely to privatize infrastructure.24 These results could be accommodated in terms of the theoretical model. As noted in the previous section, if richer countries have higher a, privatization is more likely. Growth could be correlated with adoption of new technologies, lowering β and rendering privatization more likely. But too much should not be made of these interpretations. The assumed demand function is not well adapted for analysis of income effects, and it is not clear that new technology is diffused more quickly to faster growing countries. Moreover there are probably some transmission mechanisms that are not readily embraced by the theoretical model. For example, a country’s wealth and growth may affect risk-averse investors’ demand for privatization transactions. The theoretical model addresses only the supply of privatizations. Considerations of investor demand for privatizations led to the inclusion of measures of country risk. Column (2) suggests that infrastructure privatization is more likely in countries with more market-friendly regulation (e.g., fewer price controls, adequate bank supervision, and lower perceptions of excessive regulation in foreign trade and business development). Surprisingly the results also suggest that privatization is more likely in countries with less respect for the rule of law (the index aggregates measures such as perceptions of the incidence of crime, the effectiveness and predictability of the judiciary, and the enforceability of contracts). It is difficult to explain this latter result. A number of other variables were tested for Column (2), but found not to be statistically significant. A surprising result was that the level of debt, measured as a proportion of GDP was not a significant determinant of privatization. Bortolotti et al. (2003) suggest that general privatizations are more likely with higher levels of debt. But when attention is confined to infrastructure privatizations the level of debt is not a significant determinant, indeed Column (1) suggests that privatization is more likely after a decrease 23
In April 2001, 123 countries had VATs. Only five countries have ever removed a VAT (Belize, Grenada, Ghana, Malta and Vietnam), and the last three subsequently reintroduced their VATs: Ebrill et al. (2002). 24 It is interesting that Bortolotti et al. (2003) do not find growth to be a significant determinant of general privatizations.
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79
in debt. This difference of outcomes confirms that infrastructure monopolies cannot be analyzed in the same way as competitive industries. Privatization is often seen as being ideologically driven, an analysis that is supported by Bortolotti et al. (2003). But using measures of government ideology (whether a government was left-wing, right-wing, centrist or nondemocratic) we found no significant role for ideology in the decision to privatize infrastructure. The hypothesis that privatization is associated with new governments, able to use their political capital to push through unpopular reforms, was tested using a dummy variable for an election year, as well as one- and twoyear lags of the dummy. No significant effects were found. Additional variables measuring other aspects of country risk and governance were also tested. These included: ‘Voice and Accountability’, an index of various aspects of the political process, civil liberties and political rights; ‘Political Stability and Absence of Violence’, an index measuring perceptions of the likelihood that the government will be overthrown by violence; ‘Government Effectiveness’ a measure of the quality of public service provision, the competence of civil servants and the credibility of governments’ commitments to policies; and ‘Control of Corruption’, measuring perceptions of corruption. These data were drawn from Kaufmann, Kraay & Mastruzzi (2004), for the year 1996. No significant effects were found on the probability of privatization. In Column (3) two additional variables suggested by Bortolotti et al. (2003) are included. These were not included in the testing for Column (2) because their inclusion significantly reduces the sample size. The variables are measures of stock market liquidity drawn from Beck, Demirgüç-Kunt & Levine (1999). Stock market liquidity reduces constraints on raising large amounts of capital necessary for infrastructure investment, and also favours the participation of local investors, which may enhance the sustainability of the privatisation. The variables used are the ratio of stock market capitalisation to GDP and the ratio of stock market total value traded to total market capitalisation. These two variables were found to have the expected positive effects on the likelihood of privatization. Their inclusion also renders the coefficient on VATt−5 statistically insignificant. Nevertheless VATt−6 remains statistically significant. That is, controlling for the country’s wealth, growth rate, aspects of country risk and stock market liquidity, the results suggest that the introduction of a VAT significantly increases the probability of infrastructure privatization six years later.
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3.4
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Conclusion
The theoretical section of the paper suggests that a reduction in the shadow cost of public funds may induce infrastructure privatization. When the cost of raising public funds through taxation is high, the government prefers to keep the firm in the public sector as a relatively cheap (in welfare terms) source of revenue. When the cost of raising public funds through taxation is low, the information rents earned by a privatized firm are cheap in terms of welfare cost, and the government prefers to privatize to take advantage of the private sector’s stronger incentives to lower operating costs. The empirical section lends support to this hypothesis, finding that the introduction of a VAT (a proxy for a reduction in the shadow cost of public funds) significantly increases the probability of infrastructure privatization. The empirical support for the theory suggests that infrastructure privatization is not always welfare enhancing and that governments are more likely to privatize when conditions occur under which privatization does increase welfare.25 Even if welfare maximization were not the government’s motivation, it seems likely that privatization would be politically easier to implement when it enhanced welfare (at least in theory permitting losers to be compensated) than when it reduces overall welfare. One possible motivation for privatization that was not examined in the empirical section is donor conditionality. The literature on the effectiveness of aid conditionality suggests that international institutions and bilateral donors are unlikely to be successful in pushing for privatization when the government does not want to privatize. Ghosh Banerjee & Rondinelli (2003) support this conclusion in the case of general privatizations, although they do not separately consider infrastructure privatizations. Nevertheless, foreign aid has presumably low welfare cost for a recipient government,26 so additional aid could lower the government’s marginal cost of public funds, and thereby induce privatization. The causation envisaged is via the cost of public funds, rather than via donor conditionality. Among the assumptions used to obtain the theoretical results, one in particular could be examined in more detail. The model supposes that the government extracts the full expected value of the firm from a risk neutral 25
Another interpretation of the empirical evidence arises if the theory is simply accepted as correct. The data then support the proposition that the introduction of VATs has lowered the marginal cost of public funds in many developing countries. 26 But even grant funds have a welfare cost, because administering them consumes considerable amounts of bureaucrats’ time. Given the extreme shortage of skilled civil servants in many developing countries, this administration time represents reform opportunities forgone.
3.4. CONCLUSION
81
investor. Under this assumption, the model of Auriol & Picard (2002) suggests that privatization improves welfare for high values of the shadow cost of public funds (the opposite result from this paper). But Auriol & Picard (2002) go further and allow for the government to extract varying proportions of the firm’s expected value. This change introduces a range of low values of λ for which privatization enhances welfare. Thus, the proportion of value captured by the government plays an important role in a model very similar to that of the present paper. This idea receives further support in the empirical results, where factors which could affect investors’ perceptions of risk were found to play a role in the likelihood of privatization. Other extensions could also be envisaged. The paper has stressed the role of uncertainty over marginal cost, but for infrastructure firms uncertainty over the size of post-privatization capital investments is probably at least as important. Foreign ownership of the privatized firm means that some of the welfare benefits of privatization leak out of the country when the transaction fee is less than the realized profit. Empirically, it would be interesting to test the theory with a direct measure of the shadow cost of public funds. In this, as in other fields of public policy assessment, there is a need for more information about the shadow cost of public funds in different countries, and how it shifts across time.
Appendix B.1
Proof of Proposition 1
Private ownership yields higher welfare if ∆W > 0, or equivalently, if V˜ 2 − V 2 > 0. When λ = 0, V˜ 2 − V 2 > 0. When λ → ∞, V˜ 2 − V 2 → E[(a − β − G(β) 2 ) ]−E[(a−β)2 ] 0 if and only if λ < λ1 .
B.2
Proof of Proposition 2
(1+λ) ˜ 2 Define X ≡ (1+2λ) (V − V 2 ) + Gg V˜ . Then ∆T > 0 ⇔ E[X(λ)] > 0. For λ ≤ λ1 , V˜ 2 − V 2 ≥ 0 ⇒ X(λ) > 0. As λ → ∞, X → − 12 ( Gg )2 < 0. By continuity, there exists an odd number of values of λ such that E[X(λ)] = 0. Denote one such value λ2 . Define Y ≡ (1 + 2λ)(1 + λ)E[X]. Then, E[X] > 0 ⇔ Y > 0. Now, Y = 2 E (1+λ)2 (a−β)2 −V 2 − 2(a−β)λ−(1+2λ) (1+λ) Gg −2λ2 Gg . Define Z as expression Y with the variable V replaced by the constant a−β −x(λ2 ), that is, by V evaluated at λ2 . Z is quadratic in λ, implying there are at most two values of λ > 0 for which Z = 0. Since there is an odd number of roots, λ2 is the unique value for which Z = 0. Since V (λ) is increasing in λ, if λ < λ2 then Y > Z; if λ > λ2 then Y < Z. Since Z > 0 if and only if λ < λ2 it follows that Y > 0 if and only if λ < λ2 ; and thus ∆T > 0 if and only if λ < λ2 .
B.3
Proof of Proposition 3
λ G˜ Define φ ≡ 21 (V˜ 2 − V 2 ) + 1+λ V . Then ∆WT > 0 ⇔ E[φ] > 0. When g λ ≤ λ1 , (V˜ 2 − V 2 ) ≥ 0, so φ > 0. Using the proof of Proposition 2, when (1+λ) ˜ 2 (V − V 2 ) + Gg V˜ ≤ 0. It follows that when λ ≥ λ2 , φ < 0. λ ≥ λ2 , X = (1+2λ)
83
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λ 2 G 2 ) ( g ) . Thus, Expanding the expression, φ = (a − β)x − 12 x2 − 12 ( 1+λ dφ dx λ G 2 = (a − β − x) dλ − (1+λ)3 ( g ) < 0. Since φ is monotone decreasing, there dλ is a unique value λ3 in (λ1 , λ2 ) for which φ = 0.
B.4
Variable Descriptions
Privit
Debtit
∆Debtit VATit GNP per capitait Growthit Rightit
Leftit Centerit Election Yearit Capitalisationit Turnoverit Accountabilityi Stabilityi Effectivenessi
Regulationi Rule of Lawi Corruptioni
Dummy variable equal to 1 if country i privatizes at least one infrastructure firm in year t, 0 otherwise. All transactions except greenfield investments are considered. Data for 1984-1998 Public debt divided by GDP at current market prices in US dollars. Data for 1980-1998 to allow for lags corresponding to the first privatization observations The change in Debtit between years t − 1 and t, positive for an increase in debt Dummy variable equal to 1 if a VAT was introduced in year t 1,000 current USD, Atlas method, 1984-1998 GDP growth, annual percent, 1984-1998 Dummy variable equal to 1 if the government is classified as right-wing in the Politics database, 0 otherwise. Governments are classified as right, left, center, or non-democratic. 1984-1998. As for ‘Right’. As for ‘Right’. Dummy variable equal to 1 if an election took place in year t. Ratio of stock market capitalisation to GDP Ratio of stock market total value traded to total market capitalisation Index of aspects of civil liberties and political rights. Index of political stability and absence of violence Index of government effectiveness, including quality of service provision, quality of the bureaucracy and the credibility of governments’ commitments Index measuring market-unfriendly policies such as price controls and perceptions of excessive regulation Index combining the incidence of crime, predictability of the judiciary and the enforceability of contracts Index of perceptions of corruption
B.5
Descriptive Statistics and Sources
Variable Mean S.D. N Source Privit 0.088 0.286 2945 PPI Debtit 0.586 0.655 2189 WDI ∆Debtit 0.024 0.209 2054 WDI VATit 0.024 0.154 2945 VAT GNP per capitait 1.661 1.873 2266 WDI Growthit 2.598 6.656 2441 WDI Rightit 0.172 0.377 2610 Politics Leftit 0.315 0.464 2610 Politics Centerit 0.041 0.198 2610 Politics Election Yearit 0.140 0.347 2610 Politics Capitalisationit 0.059 0.167 711 Finance Turnoverit 0.282 0.443 662 Finance Accountabilityi -0.276 0.811 2850 Governance Stabilityi -0.235 0.836 2451 Governance Effectivenessi -0.390 0.538 2736 Governance Regulationi -0.313 0.726 2774 Governance Rule of Lawi -0.364 0.632 2185 Governance Corruptioni -0.390 0.587 2185 Governance Sources: PPI–PPI database; WDI–World Bank (2001); VAT–Ebrill et al. (2002); Politics–Beck, Clarke, Groff, Keefer & Walsh (2001); Finance–Beck et al. (1999); Governance–Kaufmann et al. (2004). Indices in the Governance data set are constructed with mean 0 and standard deviation 1. Higher values correspond to improvements in governance. The means and standard deviations reported here differ from 0 and 1 because only those countries for which PPI data were available were selected. The Governance data are for 1996.
Chapter 4 Regulating Natural Gas Transportation as an Exhaustible Resource The thrust of infrastructure reform in recent decades has been to separate competitive elements and to regulate remaining natural monopolies. In the natural gas industry ‘open access’ regimes have been operative since the 1990s. Natural monopoly transporters are separated from other elements of the industry (producers, traders, retailers) and are compelled to provide their services at regulated prices. The objective is to promote competition outside the transportation sector, and to ensure that the benefits of this competition are passed to consumers. Where there was once a single market for delivered gas, access regulation creates separate markets for gas and for transportation services. Pioneers of access regulation have included Argentina,1 Australia,2
1
In 1992 the state-owned monopoly Gas del Estado was divided into two transmission and eight distribution companies. An independent regulator, Enargas was established to regulate transmission and distribution. Energas uses price cap regulation. The cap is reset each five years to cover operating costs, maintenance, expansion and a reasonable return on invested capital. (Gomez-Lobo & Foster 1999). 2 In 1997 the national and state governments adopted the ‘National Third Party Access Code for Natural Gas Pipeline Systems.’ If a transporter and access seeker do not agree on terms of access either party may seek binding arbitration under terms consistent with the Code. The construction of major new pipelines in recent years has simultaneously increased the possibilities for competition between producers. Regulated prices under the Code are based on the cost of service, including a reasonable return on invested capital.
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Canada,3 New Zealand,4 the United Kingdom5 and the United States.6 The European Union’s 1998 gas directive marks a step towards liberalization although implementation across all countries will take time. Academic analysis of access regulation in the gas industry is a relatively new field, developing largely in response to these observed new policies. There are obvious similarities with access regulation in other infrastructure industries, but a significant difference is exhaustibility of gas reserves. Since Hotelling’s (1931) classic paper, it has been well known that exhaustible resources have special properties. In particular, maximizing profits or welfare requires that fixed stocks be rationed across time such that marginal rents rise over time at the rate of interest. This implies different pricing strategies from intra-period profit or welfare maximization. Despite the long pedigree of literature on exhaustible resources, it seems not to have been incorporated into the literature on access regulation of gas transportation. For example, Cremer & Laffont (2002), Cremer, Gasmi & Laffont (2003) and Oviedo Arango (2000) do not discuss exhaustibility. It may be that analysts have considered that taking account of exhaustibility imposes excessive informational requirements on the regulator. We return to this argument in the conclusion. Alternatively, it might be thought that the issue of exhaustibility has minimal consequences for analysis of access regulation. There is some strength to this argument. As we shall see, when gas production is workably competitive, setting transportation prices close 3
The 1985 Agreement on Natural Gas Prices between the Federal government, Alberta, British Columbia and Saskatchewan deregulated natural gas commodity prices. Pipeline prices are generally determined by the National Energy Board, and distribution prices are determined by provincial authorities. Regulated prices are based on the cost of providing service. 4 Open access to one of the major pipeline systems and the distribution networks is provided by asset owners pursuant to the Pipeline Access Code. The Code was developed voluntarily by a group of industry participants as a means of ensuring compliance with New Zealand competition laws prohibiting misuse of a dominant position. The Code has been operating since 1998. It provides that access must be provided on a non-discriminatory basis, but does not provide any principles for pricing of pipeline services. No access arrangements apply to the major Maui pipeline system, but the government is encouraging industry-wide access arrangements and has indicated that it may regulate if necessary. See www.med.gov.nz/ers/gas/review. 5 In 1986 British Gas was privatized as a vertically integrated producer, transporter and retailer. At the same time large consumers or independent shippers and traders were permitted to contract directly with producers. New competition was slow to emerge, however, until the 1997 structural separation of British Gas’s transportation and storage business from its production and retail business. Natural gas markets are now substantially deregulated, while gas transportation remains heavily regulated. 6 The 1992 FERC Order 636 separated gas sales from transportation services and created open access to pipeline capacity for both producers and consumers.
89 to marginal cost results in approximately optimal prices for delivered gas. Nevertheless, there are important reasons for bringing exhaustibility into the analysis of access regulation. One reason is that practical regulation almost never uses marginal cost pricing. Using terminology such as ‘long-run incremental cost’ or ‘reasonable rate of return on capital’, regulators allow fixed costs to be incorporated into the regulated price, to provide incentives for ongoing investment and maintenance. Once price is above marginal cost, there are positive rents. The Hotelling logic suggests that these rents should rise over time. In fact, we will see that the existence of these rents even in competitive markets provides a means for regulators to cover fixed costs that may be superior to standard regulatory strategies. The second reason is that there are many countries where gas production is monopolized. From Hotelling we know that the behavior of a monopolist of an exhaustible resource cannot be analyzed in the same way as that of a conventional monopolist. To understand the consequences of access regulation in the presence of a production monopoly, we need to take account of exhaustibility. It might be thought that if production is monopolized there is little point in introducing access regulation. But countries may introduce access regulation in the hope that it will stimulate the entrance of new producers. In at least some markets in Australia and Britain, access regulation was introduced before there were possibilities for strong competition between producers. Moreover, there are several examples of countries that receive gas from a foreign producer with market power. These countries cannot hope to influence the market structure of production. Relevant examples include the Argentina-Chile pipeline, the Bolivia-Brazil pipeline, Europe’s increasing dependence on Russia and North Africa, or the proposed pipeline using gas from Nigeria to supply countries as distant as Côte d’Ivoire. In these cases it seems important to understand the effects and limitations of pipeline regulation. This paper is concerned only with access regulation. We do not consider regulation of the final consumer price, or of producers’ well-head prices. In section 4.1 we set out assumptions and notation that are common across subsequent sections. We use a simple model, with constant marginal costs of transportation. In section 4.2 we briefly review Hotelling’s rule. In section 4.3 we present the regulator’s strategy for maximizing welfare, under the assumption that firms and the regulator use only linear prices.7 When 7
Following standard terminology, linear pricing is any price structure p(x) = j with j constant. Nonlinear pricing is any price structure where the price of a marginal x-th unit is a function of x. Affine functions of the form p(x) = r + sx with r and s constant thus belong to the class of nonlinear prices. See Wilson (1997).
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production is competitive, a simple rule for the regulated transport price allows the transporter’s fixed costs to be covered, and yields optimal depletion of the resource stock over time. When production is monopolized, a similar rule yields optimal depletion of the resource stock, but the limited (possibly negative) rents earned by the transporter limit the practical usefulness of this rule. In section 4.4 the analysis is extended to the case where firms and the regulator may use non-linear prices. In section 4.5 we briefly consider the case when transportation consists of separate transmission and distribution monopolies. We conclude in section 4.6.
4.1
Assumptions and Notation
We consider a stylized natural gas industry in which gas flows from a single gas field (perhaps having multiple competing producers) to a single transmission pipeline to a single city’s distribution network and then to consumers. The transportation infrastructure, like the gas field itself, is an exhaustible resource: the more gas that is transported the earlier the infrastructure will be rendered valueless. For simplicity we suppose that pipelines have no scrap value, and rights of way have no resale value. The premise of access regulation is that transmission pipelines and distribution networks constitute bottleneck facilities, with the potential to extract monopoly rents from consumers. In the absence of regulation we suppose that gas transporters purchase gas from producers and sell delivered gas to consumers. We focus on consumer access, which permits consumers to purchase gas directly from gas producers and to purchase delivery through the transportation system separately and at regulated prices. We take industry structure as fixed, and consider the optimal regulatory response. The model can be considered part of a larger game between investors and the regulator. In the larger game, investors develop gas fields and build transportation facilities depending on the rents they expect to gain. Once the infrastructure is built, the regulator can treat the industry structure as fixed. In our model, we do not consider the dynamic effects on investment of anticipated regulation. We make several assumptions about industry technology. We generally treat transmission pipelines and distribution networks as a single business, called transportation. Transportation is characterized by large fixed costs, K, associated with establishment of the infrastructure, and low marginal costs for delivering gas, assumed constant and equal to c. We do not consider fixed costs of transportation incurred each period. Because the focus is on regulation of transportation, we assume there are no fixed costs in production.
4.1. ASSUMPTIONS AND NOTATION
91
Production has constant marginal costs equal to d. Under both profit and welfare maximizing strategies price is above social marginal cost. We assume that the present value of the fixed costs are ‘not too large’ in the sense that the present value of rents under the welfaremaximizing strategy is greater than the value of fixed costs, so that gas extraction increases total welfare. We assume that transportation facilities are not subject to capacity constraints. Whereas transportation is a natural monopoly, production (i.e. extraction) may be competitive or monopolized. In our stylized market, where a single pipeline connects a single gas field with a single distribution network, the development of each element of the infrastructure is dependent on the other. It is thus natural to suppose that construction of the infrastructure will be subject to bargaining, with long-term contracts sharing the rents before any construction begins. Given this background, we assume that situations of bilateral monopoly can be analyzed using Nash bargaining and the maximization of joint profits. To keep the analysis simple we focus on linear consumer demands and we suppose that demand does not change over time. Competition between gas and other energy sources is reflected in the slope and intercept of demand for gas. At a sufficiently high price, consumers abandon gas and move to other energy sources. Linear demand curves reflect quasi-linear utility, with no income effects arising from price changes. When we consider inter-period allocations we can measure time forward from the present (t = 0), or backward from the date that reserves are exhausted, E. When necessary to refer to time-periods we express variables as a function of t to indicate that time is measured from the present (e.g. Q(t) is the quantity of gas t time periods from the present) or with subscript E − τ to indicate time measured relative to the exhaustion date (e.g. QE−τ is the quantity of gas τ periods before the exhaustion date). We assume a one-to-one correspondence between units of gas produced, transported and delivered, implying no wastage of gas in transportation. The production price of gas (well-head price) is denoted PG , the price of transportation services is PT , and the price of delivered gas is the sum of the well-head and the transportation prices: PD = PG + PT . We define ‘marginal welfare’ as the sum of consumer and producer surplus W W obtained on sale of a marginal unit of gas. We denote by λW D , λT and λG marginal welfare in the markets for delivered gas, transportation services and well-head gas respectively. We define ‘marginal profit’ as the producer surplus obtained on sale of a marginal unit of gas, and denote by λπD , λπT and λπG marginal profit in the markets for delivered gas, transport services and well-head gas respectively. The social optimum maximizes total welfare in
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the market for delivered gas. We denote the social optimum with an asterisk superscript. Thus, λ∗D (t) is the optimal value of λW D at time t. At points in the analysis we contrast our proposed regulatory strategy with a crude caricature of a ‘standard’ regulatory strategy. The standard strategy is to set a fixed price of transportation equal to marginal cost plus a fixed markup to cover fixed costs, PT = c + g. The method of calculating g is left deliberately vague. It can be thought of as cost-plus pricing, or price cap regulation for a single product. The important point is that g is constant over time. In reality regulated prices rise with inflation and fall with technological progress, but in our model both of these effects are assumed to be zero.
4.2
Hotelling’s Rule
The characterization of problems of exhaustible resources has been wellknown since Hotelling (1931). The problem can be expressed as finding RE the extraction path Q(t) so as to maximize V = 0 R(Q)e−rt dt subject to RE Qdt = Z where R is the optimizer’s intra-period reward function, Q(t) is 0 the quantity of gas extracted in period t, E is the (unfixed) time of exhaustion, r is the interest rate, and Z is the known total stock of gas reserves. R(Q) can be interpreted as either firm profit or social welfare, depending on the maximizer’s objective. Provided R is concave in Q, the absolute maximum of V can be identified using the first order condition, R0 (Q) = φert where φ is the multiplier on the gas stocks constraint. Define λ ≡ R0 (Q) and let a hat over a variable denote the inter-temporal rate of change of the variable. The first order condition implies Hotelling’s Rule, that intra-period marginal rewards increase over time at the rate of interest: b ≡ ∂λ/∂t = r λ λ
4.3
(4.1)
Regulation with Linear Prices
In this section we assume that firms and the regulator can only use linear prices. We contrast access regulation when production is competitive and when it is monopolized. In each period aggregate demand for delivered gas is given, in inverse form, by PD = a − bQ, with a > c + d and b > 0. The marginal welfare obtained on sales of delivered gas is λW D = PD − (c + d). The marginal welfare obtained on sales of transportation services is λW T = PT − c. The W marginal welfare obtained on well-head gas sales is λG = PG − d.
4.3. REGULATION WITH LINEAR PRICES
4.3.1
93
Welfare Maximization versus Monopoly
To provide benchmarks for comparison with regulated outcomes we first contrast welfare maximization with monopolistic profit maximization in a vertically integrated industry. Under our assumptions monopolistic profit maximization results in excessive conservation of gas reserves, a result that has been familiar since Hotelling’s (1931) paper. Along the optimal time path λ∗D = λW D = PD − (c + d). Applying Hotelling’s Rule, along the optimal path the price of delivered gas rises at the rate (PD∗ (t) − c − d)r ∗ Pc = D PD∗ (t)
(4.2)
In contrast, in a monopolized industry, marginal profits are given by: λπD = PD +
∂PD Q − (c + d) ∂Q
(4.3)
which for any given Q > 0 is less than marginal social welfare. Using the assumed demand curve and Hotelling’s Rule, the implied monopoly price path for delivered gas rises at a slower rate than optimal: (2PDπ − a − c − d)r ∗ π < Pc Pc = D D 2PDπ
(4.4)
Since marginal rewards increase monotonically at the rate of interest, they reach a maximum value when reserves are exhausted at time E. Under both welfare maximization and monopoly the maximum marginal rewards are identical: a − (c + d) when Q = 0. Consequently, the marginal rewards are the same under profit and welfare maximization at all periods E − τ , i.e. λπ (QπE−τ ) = λW (QW E−τ ). But within any period, for any given Q > 0, λπ (Q) < λW (Q). So in each period the monopolist sells less than is socially optimal: QπE−τ < Q∗E−τ . With fixed total stocks, the monopolist’s exhaustion date is further from the present than optimal, E π > E ∗ .
4.3.2
Competing Producers
An unregulated transporter has complete market power when dealing with perfectly competitive producers. By making a take-it-or-leave-it offer to purchase a desired quantity from competing gas producers, the transporter can reduce the demand curve facing producers to a single point in each period. The transporter exerts monopsony power to set PG = d in each period. Producers earn zero rents (λπG = 0) in all periods. The problem
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then facing the unregulated transporter is to choose the quantity in each period which ensures that marginal profits rise at the rate of interest. The transporter has marginal costs of c plus the well-head price of gas PG = d and sells delivered gas at price PD , as defined by the consumers’ aggregate demand curve. The transporter’s intra-period marginal profit is given by: D (Q) Q − (c + d). Comparison with (4.3) reveals that the λπT (Q) = PD (Q) + ∂P∂Q unregulated transporter chooses the same quantities as a vertically integrated monopolist, selling less gas in each period than is socially optimal. Access regulation of transportation changes the bargaining relationships in the industry. Consumers purchase gas from producers and transportation services from the transporter, rather than buying delivered gas from the transporter. Since the transport price is regulated, producers are no longer constrained by the transporter’s monopoly power. By (4.1), competitive producers set prices such that their marginal profit rises at the rate of interest: π λc G = r. Competitive producers are price takers so their marginal profits are equal to marginal welfare in the production sector: λπG = λW G. Marginal welfare in the market for delivered gas is the sum of marginal welfare in the markets for transportation services and well-head gas: λW T = W . Knowing that marginal welfare in the well-head market rises at − λ λW G D the rate of interest, the regulator should ensure that marginal welfare in the transportation services market rises at the rate of interest, to ensure that marginal welfare in the market for delivered gas rises at the rate of interest. W ∗ c That is, to achieve λc D = λD = r the regulator should set transport prices W such that λc T = r. This implies the price of transport should rise at the rate cT = (PT − c)r (4.5) P PT The regulator may choose any final period price for transportation that lies on the interval [c, a − d]. Which price path the regulator chooses determines the division of rents between producers and the transporter. Under marginal cost pricing, PT = c in all periods and the well-head price of gas rises to a maximum of PG = a − c, at which time demand for delivered gas is driven to zero. This achieves the socially optimal depletion of gas reserves, with all rents flowing to gas producers rather than the transporter. An alternative means of achieving the socially optimal price path for delivered gas is to have the price of transportation rise over time at the rate specified by (4.5) to achieve a price of PT = a − d at time E ∗ , the optimal depletion time. The maximum price producers can achieve at time E ∗ is d, implying that producers’ marginal profits are zero in the final period. Thus, by (4.1) producers’ marginal profits are zero in all periods, PG = d. All rents flow to the transporter.
4.3. REGULATION WITH LINEAR PRICES
95
There is a unique price path that satisfies (4.5) and that exactly covers the transporter’s fixed costs. In the initial period the regulator provides a markup over marginal cost equal to the fixed establishment costs divided by the optimal number of periods: PT (0) = c + EK∗ . The regulator increases price over time at the rate (4.5), or equivalently increases the transporter’s marginal profit at the rate of interest. The present value at time t = 0 of the markup (marginal profit) in each period t ≥ 0 is thus equal to EK∗ . Summed across all periods fixed costs are exactly reimbursed. Within limits, this strategy forgives regulatory error. If the regulator overestimates E ∗ the transporter’s fixed costs are not fully covered, but the price-path of delivered gas remains optimal. If the regulator underestimates E ∗ , but increases price at the rate (4.5), the transporter’s share of rents is higher, but the price-path of delivered gas is optimal. An important limit on the ‘forgiveness’ of the strategy is that if the regulator underestimates E ∗ by too much the starting price of transportation is too high, and reaches PT > a − d before time E ∗ . If this occurs there are unconsumed gas reserves at E ∗ , a sub-optimal result. We may contrast these regulatory strategies with ‘standard’ regulatory practice, under which PT = c + g. The residual inverse demand curve facing producers is PG = PD − PT = a − bQ − c − g so that marginal welfare in the well-head market is λW G = a − bQ − c − d − g. Competitive production ensures that marginal welfare in the market for well-head gas rises at the rate of interest. The resulting price path for delivered gas rises at the rate (PD −c−d−g)r ∗ < Pc Pc D = D . Standard practice results in excessive conservation PD of gas relative to the social optimum. The smaller is g the closer standard practice approximates the optimal regulatory strategy. If g < a−c−d then 2 π c Pc D > PD , and standard practice is an improvement on the unregulated outcome.
4.3.3
Production Monopoly
Figure 4.1 sets out the price paths for delivered gas with a production monopoly under different regulatory regimes. In the absence of regulation, a bilateral monopoly arises. The joint profit maximization problem involves demand for delivered gas, PD = a − bQ, and joint marginal cost, c + d. The resulting price path for delivered gas is thus the same as the monopoly price path used by the unregulated transporter when faced with competing producers: the price for delivered gas rises at the rate (4.3). In this instance, however, profits are shared between the producer and the transporter.
CHAPTER 4. REGULATING GAS TRANSPORTATION
Price for Delivered Gas
96
Standard regulation Unregulated monopoly Constrained regulation Optimal regulation
Time to exhaustion
Figure 4.1: Transport Regulation with a Production Monopoly
With regulated consumer access, the producer is freed from the bilateral monopoly relationship and may exercise unrestrained monopoly power subject to the well-head demand for gas. Inverse well-head demand, however, is the residual of inverse demand for delivered gas less the regulated price of transportation: PG (Q) = PD (Q) − PT . The regulator’s problem is to manipulate the transportation price to constrain the producer’s market power. It might seem that the regulator could use the transporter’s market power to reduce the well-head demand to a single price and quantity in each period. Thus, the regulator might set PT = PD∗ − d at all times. If the producer responded by setting PG = d in all periods, marginal profits would be zero in all periods and condition (4.1) would be satisfied. The price for delivered gas would then be optimal in all periods and reserves would be exactly exhausted at time E ∗ . But if the producer sets price PG > d the producer makes a positive profit in each period, less gas is consumed in each period than optimal, and reserves are not exhausted at time E ∗ . Given the regulator’s strategy, the producer does not wish to extract gas after time E ∗ , so the producer is freed from the resource constraint and may set prices to maximize profits in each period. Prices for delivered gas are higher than optimal in all periods and there are unconsumed reserves at time E ∗ . Thus, the regulator must take the bilateral monopoly into account when
4.3. REGULATION WITH LINEAR PRICES
97
setting transport prices. For the producer, the transport price is fixed in any period, so the producer’s intra-period marginal profit is λπG (Q) = PD + ∂λπ ∂PD G T Q − P − d = 2P − P − a − d. This implies that = 2 ∂P∂tD − ∂P . If T D T ∂Q ∂t ∂t the price of delivered gas is optimal in each period, then by (4.2) we have ∂λπ G T = 2(PD∗ −c−d)r − ∂P . Applying (4.1), the monopolist’s pricing strategy ∂t ∂t ∂λπ π ∗ G sets ∂t = rλG = r(2PD − PT − a − d). Equating expressions we obtain the rate of change of the regulated price of transport that achieves the optimal price path for delivered gas: cT = (PT + a − 2c − d)r P PT
(4.6)
To compensate for the monopolist’s tendency to increase prices too slowly over time, the regulator sets transport prices that rise faster than the rate used when production is competitive: equation (4.6) implies a faster rate of price change than equation (4.5). Any transportation price path that satisfies (4.6) with PD (E ∗ ) ≤ a − d results in the optimal price path for delivered gas. The price path giving the highest possible stream of rents to the transporter has a final period price of PT (E ∗ ) = a − d. Under this regulatory strategy, the marginal profit earned by the producer in the final period is zero. By (4.1) the producer’s marginal profit is zero in every period. That is, the producer sets the intraperiod profit-maximizing price in each period, as if there were no resource constraint. If reserves are sufficiently great, the transportation price in periods far from exhaustion is less than marginal cost, or even negative. For example, with an annual interest rate of 5%, and values a = 5, c = 1, and d = 1, the implied regulated transport price equals zero 22 years before exhaustion and reaches the marginal cost of transportation 14 years before exhaustion.8 Although the regulatory strategy gives high rents to the transporter in the final periods before exhaustion, these may not be sufficient to cover losses incurred in early periods and/or fixed costs. Even if the regulatory strategy generates an overall profit for the transporter after fixed costs are included, it is possible that a regulatory strategy that sets price below marginal cost in some periods is not politically feasible. We may wish to introduce an additional constraint that PT ≥ k, where k is some positive number, greater than or equal to marginal cost. Introducing this constraint results in a regulatory policy of PT = k for early periods, prior k+a−2c−d ∗ . Knowing that λW PT = 2PD − a − d = k implies λW D = D increases at the 2 k+a−2c−d rτ rate of interest to a final value of a − c − d we have ( )e = a − c − d. This implies 2 2(a−c−d) 1 PT = k when τ = r ln k+a−2c−d . 8
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to some time t˜, and the unconstrained regulatory policy PT = 2PD∗ − a − d for final periods after time t˜.9 After time t˜, the regulatory policy achieves the first-best price-path for delivered gas. Prior to time t˜, if k = c the price path for delivered gas rises at the vertically integrated monopolist’s π rate, Pc D defined by (4.4), albeit at a lower price level. If k > c, prior to π 10 time t˜ the price path for delivered gas rises at a slower rate than Pc D. The constrained regulatory policy unambiguously improves welfare if the price path for delivered gas under regulation never exceeds the unregulated vertically integrated monopolist’s price path. We can again examine ‘standard’ regulatory practice, in which the regulator fixes the transportation price at PT = c + g in all periods. Standard regulatory practice causes the price of delivered gas to rise more slowly than the price of an unregulated monopolist, over-conserving gas relative to the monopoly position. Standard regulation actually diminishes welfare when there is a production monopoly.
4.4
Regulation with Non-Linear Prices
The model of gas markets with linear prices is useful for understanding relationships between various agents in the gas markets, but actual pricing practices are clearly richer. In this section monopoly firms in gas markets and the regulator are able to set different marginal prices for different quantities. As previously, a profit-maximizer wishes intra-period marginal profit to increase at the rate of interest, and the regulator wishes intra-period marginal welfare to increase at the rate of interest. The inter-period problem is thus essentially the same as before: quantities of gas are allocated across time so as to satisfy (4.1). The difference arises in the nature of the intra-period pricing structure: how given quantities should be allocated across consumers within each period. 9
If the unconstrained problem has a Hamiltonian equation H(PT , PG ), addition of the constraint gives a Lagrangean equation L = H(PT , PG )+φ(PT −k). If φ > 0 the constraint is binding, and we immediately know that PT = k. If PT > k then φ = 0 and the problem reduces to the original Hamiltonian, giving the same first order condition concerning the rate of change of PT as in the unconstrained problem. 10 The monopoly producer faces inverse demand PG = a − bQ − PT . The producer’s ∂λπ G marginal profit can be expressed as λπG = 2PG − a − d + PT , from which ∂tG = 2 ∂P ∂t . ∂λπ ∂PG π G From (4.1) ∂t = rλG . Equating these expressions we find ∂t = (2PG + PT − a − d) 2r . r Using PD = PG + PT we find that Pc D = (2PD − PT − a − d) 2PD .
4.4. REGULATION WITH NON-LINEAR PRICES
4.4.1
99
Welfare Maximization versus Monopoly
To contrast access regulation of an industry with competitive production versus an industry with a production monopoly it is useful first to characterize the within period non-linear pricing structures under welfare maximization and monopoly. Within each period, the firm or the regulator’s problem is to find a pricing structure that sells the period’s allocation of gas for the maximum reward. We suppose that in each period heterogeneous consumers of type θ are willing to pay m(x, θ) = θ − bx for an x-th marginal unit of delivered gas, where b > 0 is a parameter. We suppose that consumer types, θ, are dis¯ Only consumers know their own types.11 All tributed continuously on [0, θ]. parameters are assumed time-invariant. The non-linear pricing structures adopted for a vertically integrated industry under welfare maximization and under profit maximization are examined in Chapter 5. Under our assumptions, the welfare-maximizing intraperiod pricing structure is linear: PD (x) = j with j constant. This is true more generally, as can be seen with a little reflection. If the prices at the m-th and n-th increments are different, say PD (m) > PD (n), total welfare can be increased by lowering PD (m) sufficiently to induce one more unit to be sold at the m-th increment, and by correspondingly increasing PD (n) sufficiently to reduce sales at the n-th increment by one unit. This process of transferring individual units of the fixed Q from consumers with lower marginal valuations to consumers with higher marginal valuations can be continued until the price schedule is linear, i.e. constant for all x. Although non-linear prices are feasible, the welfare-maximizing pricing structure for delivered gas is, in fact, linear in each period. In contrast, a vertically-integrated profit maximizer chooses a non-linear price structure in each period. Hotelling’s Rule implies that the monopolist chooses to have marginal profit rising at the rate of interest. Once the maximum marginal rent is known, the interest rate fixes the marginal rent at any time. The marginal rent is a function of quantity, so the monopolist’s desired quantity is fixed at any time. Chapter 5 shows that to maximize intra-period profit subject to the constraint of selling a specific quantity, Q, q 2 k(b−1) ¯ − b k + bθQ, the monopolist’s pricing structure is P (x) = θ¯ − bx + 2
2
2
4
where k is the vertically-integrated monopolist’s marginal cost. The fact that 11
These conditions are sufficient to give a well-structured problem in the standard literature on non-linear pricing (see Goldman, Leland & Sibley (1984)). We present a variation on this literature by considering optimal non-linear pricing in the presence of a quantity constraint. The constraint does not, however, alter the concavity of the problem, so the maximization problem remains well structured.
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this pricing structure is downward sloping in x is sufficient to show that it is not welfare-maximizing.
4.4.2
Competing Producers
In a market with competitive producers, competition ensures linear pricing. The welfare maximizing price schedule for delivered gas is linear in each period. Thus in a market with competitive production, the regulator’s problem and the optimal regulatory strategy are the same as in section 4.3. The price of transport should rise at the rate specified by (4.5), and to cover fixed costs exactly, the price in the initial period should be PT = c + EK∗ . To ensure a linear price for delivered gas, the regulated transport price should be linear in each period. This contrasts with many observed regulatory policies where the price for transportation is non-linear: a fixed ‘capacity’ fee and a price per unit of gas transported.
4.4.3
Production Monopoly
Analysis of a production monopoly using non-linear prices proceeds in the same fashion as the analysis when only linear prices are used. In the absence of regulation there is a bilateral monopoly that behaves like a vertically integrated monopolist. Introducing regulation of the transport price breaks the bilateral monopoly. As with the analysis where only linear prices were used, marginal cost pricing in the transport market does not induce the producer to behave optimally. Setting the price of transport at PT = c in all periods shifts the demand curves facing the producer down by the constant c (i.e. the producer faces derived inverse demand PG = PD − c. Since the producer is interested in marginal profit this is analytically equivalent to increasing the producer’s marginal cost to k = c + d. The producer’s intra-period non-linear pricing problem is then the same as the vertically integrated profit maximizer’s problem analyzed above. The producer uses non-linear pricing for well-head gas that results in the same inter-temporal prices as an unregulated vertically integrated monopolist. Following the same logic as in section 4.3.3 the regulator can target the optimal price of delivered gas in each period, supposing that the producer maximizes intra-period profits in each period. A difference arises from section 4.3.3, however, because the intra-period profit maximizing price schedule used by the producer is non-linear. If the regulator sets a non-linear price for transport, PT (x), the residual demand facing a monopoly producer for each consumer of type θ is m(x, θ) =
4.5. TRANSMISSION AND DISTRIBUTION
101
θ − bx − PT (x). As seen by the producer, the marginal consumer at each x-th unit is defined by θˆ = PG (x) + bx + PT (x). The number of consumers who purchase an x-th unit of gas when the producer price is PG (x) is given R θ¯ ¯ θ¯ − PG (x) − bx − PT (x)}. by n(x, PG (x)) = θˆ f (θ)dθ = (1/θ){ If the producer maximizes intra-period profit R x¯ without regard to resource constraints, the problem is Max Π(PG (x)) = 0 (PG (x)−d)n(x, PG (x))dx−K subject to PG (¯ x) = θ¯ − b¯ x − PT (¯ x). The producer’s first order condition provides the profit maximizing price schedule: PG (x) = 12 (θ¯+d−bx−PT (x)). To achieve a target linear price for delivered gas, the regulator must set the transportation schedule PT (x) such that PT (x) + PG (x) = PD . Setting PT (x) = (2PD − θ¯ − d + bx) causes the producer to choose the price schedule: PG = (θ¯ + d − bx − PD ), and results in the target price for delivered gas, PD constant for all x. The price for transport increases with x, just sufficiently to offset the downward slope of the monopoly producer’s price schedule. Again, as in section 4.3.3, if reserves are sufficiently large, regulated transport prices in early periods may be less than marginal cost or even negative. We may again be concerned to add an additional constraint concerning politically feasible pricing structures for transportation. For example, we could introduce constraints such as PT (x) ≥ c for all x, or a requirement that the transporter not make an intra-period loss. In early periods the constraint will bind the regulator, and only in periods closer to exhaustion can the regulator achieve the optimal price for delivered gas. Whether standard regulatory practice, (i.e. setting PT = c + g) improves or worsens welfare (relative to no regulation) is ambiguous in this setting. As the markup allowed for fixed costs (i.e. g) diminishes, interand intra-temporal prices tend toward the prices of the vertically integrated monopolist.
4.5
Transmission and Distribution
We have so far assumed a single gas transportation firm. In practice, the transmission pipeline and the distribution network are often separately owned monopolies. In the absence of regulation, the distributor and the pipeline form a bilateral monopoly, and under Nash bargaining pursue a joint profit maximization strategy. In the case of competitive producers, the distributor and the pipeline will exercise monopsony power to hold the well-head price of gas down to marginal cost. In the case of a monopoly producer, a trilateral monopoly exists in which all three firms may pursue the joint profit maximization strategy, dividing profits according to Nash bargaining.
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If just one of the distributor or pipeline is regulated, the remaining sector, acting with the production sector, takes the place in the earlier analysis of a monopolized production sector. If all firms and the regulator are constrained to use linear prices, the analysis of section 4.3.3 can be applied. When non-linear pricing is used, it is important that the regulator is able to influence the price structure for delivered gas. This is the case, for example when (i) only distribution is regulated; or (ii) only transmission is regulated and consumers purchase the transmission service separately from distribution and well-head gas. In these cases the analysis of section 4.4.3 can be applied, treating the unregulated sectors as a single profit maximizing monopolist. But the regulator is unable to influence the price structure of delivered gas if the only regulated sector is the pipeline, and the distributor purchases transmission services and sells delivered gas to consumers. In this setting the regulator can determines the total amount that the distributor pays for transmission services. The regulator cannot alter the form of consumer demand faced by the distributor for different ‘x’-th increments. The regulator can cause marginal welfare to rise at the rate of interest, but cannot induce the optimal rationing between consumers within each period. This is a case where regulation should be extended to either the price of distribution services, or the price of delivered gas. We can apply the same logic when comparing consumer access and producer access. Throughout we have assumed that it is consumers who purchase regulated transportation services, and purchase gas directly from producers. It is also possible that producers purchase regulated transportation services and sell delivered gas directly to consumers. If production is competitive, the regulator can achieve the optimal inter-temporal and intra-temporal rationing. If production is monopolized, the regulator can achieve the optimal inter-temporal rationing, but cannot offset the nonlinearity of the producer’s intra-temporal prices for delivered gas. Either consumer access or regulation of the price of delivered gas would be preferable to producer access when production is monopolized.
4.6
Conclusion
When production is competitive, ‘standard’ regulation is likely to be better than no regulation. As fixed costs diminish, standard regulation approaches the social optimum. We have suggested, however, an alternative regulatory strategy that will actually achieve the social optimum and exactly cover the transporter’s fixed costs. When production is monopolized we have also
4.6. CONCLUSION
103
found a regulatory strategy that will deliver optimal prices for delivered gas. This strategy will be of little comfort, however, to countries that are dependent on foreign monopoly suppliers, since it depends on large rent transfers to the monopoly producer. Independently of the implications for access regulation, the analysis of the monopoly situation carries important implications concerning non-linear pricing by gas utilities. Gas regulators have typically drawn upon experience from electricity or telecommunications pricing when reviewing non-linear pricing. Our analysis suggests that exhaustibility of gas reserves implies quite different pricing strategies. In particular, exhaustibility implies that to maximize social welfare the price of delivered gas should be linear in each period: a linear price is the most efficient means of rationing a fixed quantity. This contrasts with most observed regulatory policies that permit non-linear pricing as a supposedly efficient (or least inefficient) means of covering fixed costs. The information required to implement optimal regulatory strategies is information that would be required for standard regulation. For the case of competitive production, the transporter’s marginal cost and the interest rate are the only information needed to ensure that the transport price rises at the rate given by (4.5). The value of fixed costs and the estimated date of exhaustion are additionally required if fixed costs are to be covered exactly. All of these data are commonly used in standard regulation, where a markup over marginal cost is given to amortize fixed costs over the life of the gas reserves. Moreover, the proposed regulatory strategy is forgiving, in the sense that if the regulator is mistaken about the optimal exhaustion date, the socially optimal prices of delivered gas may still be achieved. When production is monopolized, achieving optimal prices for delivered gas is more information-intensive for the transportation regulator. In addition to information required for the competitive case, the regulator needs information concerning the producer’s cost structure in order to calculate the optimal price path for delivered gas. Further, the regulator needs as much information about demand conditions as the firm itself in order to offset the producer’s intra-period non-linear pricing. If these informational requirements seem prohibitive, the alternative of standard regulation is even less attractive. Standard regulation may actually diminish welfare relative to an unregulated industry. If fixed costs are relatively small standard regulation merely approximates the outcome of an unregulated industry. Our analysis can be extended in many directions. The literature on exhaustible resources incorporates many features such as marginal cost or demand that evolves over time, uncertainty over the extent of reserves, the effect of discovery of new reserves and more thorough analyses of market
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power than the two extremes (monopoly and perfect competition) considered here. Incorporating such features can have substantial consequences for the optimal path of delivered gas – for example, repeated discoveries of additional reserves may result in a downward price path. The literature on access regulation incorporates features such as more complicated pipeline networks, capacity constraints on pipelines, private information concerning costs and more complicated regulatory games in which the market structure responds to the regulatory strategy. Clearly more work is required to integrate these branches of the literature.
Chapter 5 Nonlinear Pricing and the Rate of Extraction of an Exhaustible Resource There are established bodies of literature that deal with exhaustible resources and with nonlinear pricing. But the two fields appear never to have been united. There is an obvious reason for this. For most exhaustible resources nonlinear pricing is not possible: it requires both market power and the ability to prevent resale. While there are exhaustible resources extracted by producers with market power (OPEC comes to mind), there are very few such resources where sellers can prevent resale. Natural gas delivered by pipelines is an exception, however. Sellers of piped gas control the pipe network by which resale could most easily be implemented physically. Consequently, nonlinear pricing of natural gas is not only possible, it is frequently observed. Consumers usually pay a monthly fixed fee and a separate tariff per unit of gas consumed. Important articles in the development of the theory of nonlinear pricing include those of Mirrlees (1971), Mirrlees (1976), Spence (1977), Roberts (1979), and Goldman et al. (1984). While Mirrlees was interested in taxation, the inspiration for much subsequent analysis was the pricing of utility services, such as telecommunications or electricity. At first blush it might seem reasonable to apply the standard analysis to another utility service: natural gas. In fact the exhaustibility of natural gas reserves considerably alters the analysis. A decision-maker dealing with a non-exhaustible resource, such as telecommunications or electricity, would like in every time-period to maximize total rents (profit or social surplus depending on the decision-maker). In contrast, a decision-maker dealing with an exhaustible resource seeks to equate the 105
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present value of marginal rents across periods. To deal with exhaustible resources, the literature concerning nonlinear prices must be adapted to examine the behavior of intra-period marginal rents. An application of this new analysis is to revisit the literature on whether a monopolist extracts an exhaustible resource too quickly or too slowly relative to the social optimum. This question was first studied by Hotelling (1931). He found a case in which monopolists excessively conserve resources. Stiglitz (1976) showed that with zero marginal costs and constant elasticity of demand the optimal and monopoly price paths coincide. Others, including Lewis, Matthews & Burness (1979) and Dasgupta & Heal (1979), found cases where, depending on the evolution of the elasticity of demand, a monopolist may extract resources more quickly than optimal. All of these analyses assumed that prices were linear, and gave the result that over the life of the resource a monopolist always extracted resources too quickly or too slowly, but never both. When nonlinear pricing is brought into the analysis we find a case in which a monopolist may extract the resource too slowly when far from the exhaustion date, and too quickly when close to the exhaustion date. We begin the analysis with a brief review of Hotelling’s Rule for optimal extraction of an exhaustible resource. In section 3 we examine the pricing strategy used at a particular instant in time when the decision-maker maximizes social welfare while selling a fixed quantity of the resource. In section 4 we repeat the analysis for the case where the decision-maker uses nonlinear prices to maximize profit. In section 5 we bring together results from the previous sections to compare a monopolist’s rate of extraction with optimal extraction. We conclude in section 6 with some observations on potential extensions. Because natural gas is the most obvious example we will interchangeably refer to an abstract ‘exhaustible resource’ and ‘gas’. The analysis of course applies to any exhaustible resource for which nonlinear pricing is possible.
5.1
Hotelling’s Rule
The use of nonlinear pricing does not affect the basic insight of Hotelling (1931), that optimal extraction of an exhaustible resource equates the present value of marginal rents in different periods. The control instrument is a price schedule, P (x, t), which specifies the marginal price for an x-th unit of gas, sold at time t. Given this price schedule, a particular quantity of gas, Q(P (x, t)), is sold in each period. The decision-maker’s problem is to choose RE RE P (x, t) so as to maximize V = 0 R(Q(·))e−rt dt subject to 0 Q(·)dt = S where R is the optimizer’s intra-period reward function, E is the (unfixed)
5.2. MARGINAL WELFARE
107
time of exhaustion, r is the interest rate, and S is the known total stock of gas reserves. R(Q(·)) can be interpreted as either firm profit or social welfare, depending on the maximizer’s objective. Provided this problem is concave, the absolute maximum of V can be identified using the first order condition, R0 (Q) = φert , where φ is the multiplier on the gas stocks constraint. Define µ(Q) ≡ R0 (Q) and let a hat over a variable denote the inter-temporal rate of change of the variable. The first order condition implies Hotelling’s Rule, that intra-period marginal rewards increase over time at the rate of interest. µ b≡
∂µ/∂t =r µ
(5.1)
If we know the form of µ(Q), the marginal reward function, Hotelling’s Rule tells us how the stock of reserves should be allocated across time. To examine the marginal reward function under nonlinear pricing we can consider the nonlinear price schedule that would be used to sell a given quantity, Q, at a particular instance in time. When Q is shocked marginally, a new nonlinear price schedule is implied, with a resulting change in the optimizer’s reward at time t.
5.2
Marginal Welfare
We make the following assumptions, in order to analyze the price structure used when the decision-maker maximizes social welfare while selling a specific quantity of gas at a particular point in time. Consumers have marginal valuations for gas given by m(x, θ), where x is the number of units consumed, ¯ with density 1/θ. ¯1 and θ is the consumer’s type, uniformly distributed on [0, θ] Consumers’ demands for gas are unaffected by changes in income. Individual consumers’ demand curves are decreasing in quantity: ∂m < 0. Demand ∂x ∂m curves are ordered by consumer type: ∂θ > 0. The mass of consumers is normalized to unity. The firm has a constant marginal cost of gas extraction, c. We suppose that second-order conditions for maximization are satisfied, giving an internal solution to our problem.2 Finally we suppose that the demand and technology parameters remain constant over time. We suppress ‘t’ in our notation as we are concerned with the price structure at a given instant in time. 1
By re-scaling units of θ, any other distribution may be transformed into the uniform distribution, so we lose no generality with this assumption. 2 Cases of bunching and gaps in the price schedules, due to failure of second order conditions, are considered by Goldman et al. (1984) in the context of non-exhaustible resources.
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Consumers of type θ who buy an x-th unit of gas at price P (x), have marginal valuations of the x-th unit that equals or exceeds the marginal price: ˆ P (x)), m(x, θ) ≥ P (x). At the x-th unit, the marginal consumer type, θ(x, is the consumer type for which marginal valuation is exactly equal to the ˆ = P (x). marginal price: m(x, θ) The number of consumers who purchase an x-th unit of gas at price P (x) ˆ θ. ¯ The total quantity sold is obtained by is given by n(x, P (x)) = (θ¯ − θ)/ R x¯ integrating across the individual x-th units sold: Q(P (x)) = 0 n(x, P (x))dx. The terminal point of the marginal price schedule is given by P (¯ x) = θ¯ − b¯ x, where x¯, is the highest number of units of gas purchased by an individual ¯ consumer (of type θ). The net social welfare obtained at the x-th increment given price schedule R θ¯ ˆ P (x) is given by w(x, P (x)) = θˆ (m(x, θ) − c)/θdθ. Total welfare is given R x¯ by W (P (x)) = 0 w(x, P (x))dx. The welfare maximization problem is: Max R x¯ W (P (x)) subject to Q = 0 n(x, P (x))dx Define F ≡ w(x, P (x)) − µW n(x, P (x)), with µW the Lagrange multiplier on the quantity constraint. At the optimum, the interpretation of µW is the change in social welfare achieved when the quantity constraint is relaxed marginally. That is, µW is the variable we are interested in for purposes of Hotelling’s Rule. Using the calculus of variations, the first order condition of the problem is FP = 0. By the first order condition P (x) = c + µW . In order to sell any given quantity Q, the welfare maximizing price schedule is constant for all x. The efficient way to ration a fixed quantity of a good is with a linear price. The intuition is simple. If the prices at the m-th and n-th increments are different, say PD (m) > PD (n), total welfare can be increased by lowering PD (m) sufficiently to induce one more unit to be sold at the m-th increment, and by correspondingly increasing PD (n) sufficiently to reduce sales at the n-th increment by one unit. This process of transferring individual units of the fixed Q from consumers with lower marginal valuations to consumers with higher marginal valuations can be continued until the price schedule is linear, i.e. constant for all x. To proceed further we need a specific functional form for consumers’ demands. To keep the analysis simple we assume linear demands: consumers have inverse demand curves given by m(x, θ) = θ − bx. The marginal conˆ P (x)) = P (x)+bx. The number of consumers sumer type is thus given by θ(x, ¯ consuming an x-th unit of gas is given by n(x, P (x)) = (θ¯ − P (x) − bx)/θ. Recognizing that price is constant (P (x) = P for all x) allows the terminal ¯ . Substituting this value into the point condition to be expressed as x¯ = θ−P b p ¯ quantity constraint and performing the integration yields P = θ¯ − 2bθQ.
5.3. MARGINAL PROFIT
109
Marginal welfare is then given by µW (Q) = θ¯ − c −
5.3
p
¯ 2bθQ.
Marginal Profit
We may proceed in a similar fashion to examine the form of the marginal profit function when the decision-maker wishes to set a nonlinear price structure to maximize profit while selling a fixed quantity of gas. We continue with the same assumptions about demand and technology, including the specific functional form for consumers’ demands. R x¯ The firm’s profit is given by: Π(P (x)) = 0 (P (x) − c)n(x, P (x))dx. The R x¯ problem to be examined is thus: Max Π(P (x)) subject to Q = 0 n(x, P (x))dx. Define G(x, P (x)) ≡ (P (x) − c − µπ )n(x, P (x)), where µπ is the Lagrange multiplier on the quantity constraint. Then the solution is characterized by the first order condition, GP = 0, the transversality condition, G|x=¯x = 0, and the quantity constraint. Differentiating G with respect to P (x) to obtain the first order condition, we find P (x) = (θ¯ − bx + c + µπ )/2. Substituting this expression into G and evaluating at x = x¯, we obtain from the transversality condition µπ = θ¯ − b¯ x R− c. Using these two results, the quantity constraint becomes Q = p 2 + 4bθQ ¯ − c. The ¯ x¯ b¯ c (1/2θ) x + c − bx)dx which in turn implies x ¯ = 0 marginal price function expressed q in terms of an arbitrary quantity, Q, is 2 c(b−1) ¯ an affine function with slope − b thus P (x) = θ¯ − bx + − b c + bθQ, 2
2
2
4
2
and an intercept that declines as Q increases. Marginal profit is given by p ¯ µπ (Q) = θ¯ + c(b − 1) − b c2 + 4bθQ.
5.4
Welfare versus Profit Maximization
Figure 5.1 compares the marginal welfare and marginal profit functions derived in sections 5.2 and 5.3, for a specific set of parameter values. Defining ˜ ≡ c¯2 22b 2 , in general there are four cases: the critical value Q θ (2b −1) • for Q = 0, λW (Q) = λπ (Q) ˜ λW (Q) < λπ (Q) • for 0 < Q < Q, ˜ λW (Q) = λπ (Q) • for Q = Q, ˜ λW (Q) > λπ (Q) • for Q > Q,
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Marginal Profit
Marginal Welfare
0
QW Q
~ Q
Figure 5.1: Marginal Rents under Nonlinear Pricing
Depending on parameter values, there are two special cases occurring at ˜ When Q ˜ = 0, that is, when there are zero marginal extreme values of Q. costs, marginal welfare is always greater than marginal profit: λW (Q) > ˜ is larger than any feasible quantity. λπ (Q), ∀Q > 0. It is also possible that Q ˜ occurs where marginal welfare and marginal profit are less than That is, Q zero. In such cases, marginal welfare is less than marginal welfare for all feasible quantities. For all parameter values marginal welfare and marginal profit are equal at Q = 0. That is, when the stock of resources is finally exhausted, the marginal reward earned on the final unit of gas stocks will be the same under welfare and profit maximization. Under Hotelling’s Rule marginal rewards increase over time at the rate of interest. Marginal welfare under welfare maximization and marginal profit under profit maximization have the same values at the exhaustion date, E. It follows that at any time τ periods before exhaustion, E − τ , marginal welfare under welfare maximization should have the same value as marginal π π profit under profit maximization: λW (QW E−τ ) = λ (QE−τ ). ˜ Thus, close to exhaustion, when τ , QW and Qπ are small (i.e. less than Q), the quantity sold under welfare maximization is smaller than the quantity
5.5. CONCLUSION
111
π sold under profit maximization: QW E−τ < QE−τ for τ small. This case is illustrated in Figure 5.1. Far from the exhaustion date, when τ , QW and Qπ are large, the quantity sold under welfare maximization is greater than the π quantity sold under profit maximization: QW E−τ > QE−τ for τ large.
5.5
Conclusion
To determine the optimal rate of extraction of an exhaustible resource it is necessary to know the form of the decision-maker’s intra-period marginal reward function. Hotelling’s Rule then determines the allocations of quantities across time. The intra-period problem is to take this allocated quantity and derive the maximum reward. The application of this quantity constraint alters the standard calculation of optimal nonlinear pricing. Using a specific functional form for heterogeneous consumer demands we have found a case in which far from exhaustion, a monopolist using non-linear pricing over-conserves reserves. Close to the exhaustion date the monopolist under-conserves reserves. There are many possible extensions of this analysis. Different functional forms of demand could be explored, and consideration could be given to the case where demand and technology parameters evolve with time. Following the literature on exhaustible resources the analysis could be extended to cases where the extent of reserves are uncertain, or new reserves are discovered. The extension with perhaps the most practical interest, however, is to see how exhaustibility of natural gas reserves affects optimal regulation. Gas regulators have typically drawn upon experience from electricity or telecommunications pricing when establishing non-linear pricing schedules. Our analysis suggests that exhaustibility of gas reserves implies quite different pricing strategies. In particular, exhaustibility implies that to maximize social welfare the price of delivered gas should be linear in each period. Most observed regulatory policies permit nonlinear pricing as the supposedly least inefficient means of covering fixed costs, particularly the fixed costs of transportation pipelines. But under Hotelling’s Rule, even under welfare maximization, the firm extracting the resource earns positive rents. It seems possible that these rents could be exploited to cover fixed costs, leaving no requirement for regulators to use nonlinear pricing in the intra-period problem.
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