Replicating Ricardian Equivalence Tests with Simulated Series Reports of Discussion

LI Xiaoxi, LIU Xingyi, WANG Yonglei

Replicating Ricardian Equivalence Tests with Simulated Series Review of the literature on Ricardian Equivalence The literature on Ricardian Equivalence starts with the classical paper of Barro 1974, “Are government debts net wealth” shows that if there is any kind of intergeneration bequest, as long as this bequest has an interior solution in the equilibrium, the government debts will have no effect on consumption. Even when tax is levied on more than two generations, i.e. the tax cut on the current generation is balanced by a tax of not only the direct descendent but also the following generations, as long as the bequest has an interior solution, the government debts won’t have any effect on consumption. However, if there is heteroskedasticity between consumers, there may be real effect of a tax cut or government debts, the scale of effect depends on the proportion of consumers who have a corner solution of intergeneration bequest. Barro also showed that even with finite life, the government debts B still may not change the consumption plans of consumers. But as to Barro’s reasoning, there are some cases in which the government debts or taxation can have real effects on consumption plans, such as the presence of transaction cost of government bonds, imperfect capital market, especially imperfect private capital market. Also, when we take government debts as some liquidity service, whether government debts have real effect on consumption depends on whether the liquidity market is competitive or monopolized by the government. Moreover, government debts may have some real effect when we take into consideration of the risk characteristics of tax liabilities, i.e. when we take into account uncertainty and expectations. Another topic Ricardian Equivalence concerns is the connection between budget deficits and current account deficits. Traditional view of budget deficits is that budget deficits usually lead to current account deficits in a small open economy. The substitution of budget deficit for current taxation leads to an expansion in aggregate demand, so private saving rises less than the tax cut, which means that the desired national saving decreases. In a closed economy, this decrease in desired saving will lead to an increase in interest rate, which tends to decrease the capital for future generations. However, in a small open economy, this decrease in desired national saving won’t have effect on the real interest rate, but ends in borrowing from the rest of the world, thus leads to current account deficits.

While Ricardian Equivalence suggests that the consumption will depends only on the present value of all future disposable incomes, as long as the present value of current tax cut and future tax increase are the same, the consumption won’t change, that is to say, the current budget deficits won’t lead to current account deficits. A lot of scholars have examined the relationship between government debts and consumption, and some of them have came up with results against Ricardian equivalence, the objection to Ricardian Equivalence came up from the following five aspects: 1. People do not live forever 2. Private capital market are imperfect, typical person’s real discounting rate exceeding that of the government 3. Future taxes and income are uncertain 4. Taxes are not lump-sum in general 5. The Ricardian results hinges on full employment Kormendi is one of the first who have tried to test the relationship between government behavior and private consumption, using the data of United States from 1930 to 1976, he estimated the following equation: ΔPCt=a0+a11ΔY+a12ΔYt+a2ΔGSt+a3ΔWt+a4ΔTRt+a5ΔTXt+a6ΔREt+a7ΔGINTt+ut He shows that the coefficient of TX, RE and GINT are insignificantly differently from zero, and generally of the wrong sign from that predicted by standard approach. And the F-test cannot reject the null hypothesis that the coefficient of TX, RE and GINT are zero. So, Kormendi’s work shows that the Ricardian Equivalence cannot be rejected, at least cannot in US during 1930-1976. However, Modigliani and Sterling got the opposite results using postwar data of US from 1949 to 1984, based on the life cycle paradigm, they estimate and test a different model from Kormendi’s: Ct=a+b0At+b1Gt+Σci(Yt-i-Tt-i)+ ΣdiDt-i And they show that consumption should be affected both by taxes and by government expenditure and by private claims on the government as well as the wealth. It was shown that the relative significance of taxes and government expenditure in the consumption function reflects mortality rates, the length of life, and both the personal discount rate and interest rate, but that as long as the representative planning horizon does not extend significantly beyond life, the role of taxes could be expected to be substantially larger than that of expenditure and the role of debt close to that of other wealth. Evans (1993) using the Blanchard model, he tests the Ricardian Hypothesis against the non-Ricardian alternative where the deviation from Ricardian alternative are

uniquely due to the finiteness of horizons. He strongly rejects the null hypothesis but finds that the effects on consumption of the departure from Ricardian equivalence are relatively small. Since using real economic data, and using traditional method of estimation and test, different researchers got conflicting results; Cardia just used a different way from these authors above. Now that we cannot modify the real data, so we can construct an ideal model in which Ricardian Equivalence should be satisfied, then we simulate this model and check if the Ricardian Equivalence is indeed true in the simulation data. This is what exactly Cardia did in this paper. Cardia made some assumptions of the macroeconomic model, although the model is not the main point of this paper, but we still think that some key assumptions and some parameters may have a big influence on the simulated results. The main assumptions are: 1. Small open economy 2. One homogeneous tradable good 3. Perfectly integrated international financial capital market, so the domestic interest rate is pegged to the world real interest rate, which is exogenous 4. No aggregate uncertainty in the rest of the world and there are no common shocks to technology, all shocks are domestic 5. Domestic households cannot buy foreign assets that have a payoff contingent on the realization on domestic shocks 6. Perpetual youth assumption in the households, which indicates that consumers are homogenous, and people of different age have the same behavior Since in this paper, Cardia focuses on the role of distortionary taxes and finite life, she just made some perfect assumptions in the model like perfect financial market and homogenous individuals, which may have a significant impact on the credibility of Ricardian Equivalence. The model is simulated and the generated series for Consumption, Wealth, Government spending, Government debt, Tax revenue are used for the estimation of consumption equation. Cardia uses simulated series and shows that even in an ideal model where RE should hold, we can find a large proportion of simulated data that reject the hypothesis; on the contrary, in a model whether Ricardian Equivalence should not hold, a lot of simulated data cannot reject this hypothesis, moreover, these tests produce estimates of the effects of taxation and government debt on consumption that are not robust, which suggests that standard tests might not be capable of providing conclusive evidence about RE whether it is true or wrong. Moreover, the simulation reveals that the lack of a systematic relation between current

account and budget deficits is consistent with both RE and the non-RE alternatives and does not by itself provide evidence in favor of the RE hypothesis. Whether Simulation is Credible? This paper tried to replicate Ricardian Equivalence tests with simulated series from standard dynamic equilibrium models. The econometrics of R-E before this paper was mainly empirical tests of the consumption function on government debt and taxes. It starts from the theoretical model, which uses the dynamic general equilibrium context with infinite-living consumers. System of equations involving several economic variables are drew. Among them, several are adopted from the empirical data, others are simulated from some stochastic processes, and the simulation results from them are statistically analyzed. We argue that the simulation results are very much limited by the assumptions and function equations in the original theoretical models, and also the way that the random variables were generated from the stochastic processes. Usually the economic theory is not created to predict the reality as claimed in the theorem. Rather, we treat it as a benchmark within which, perfect assumptions are made to reach the nice results, and departing from it we check the significance of violated assumptions implied by the inconsistent empirical observations. For example, the existence of competitive market equilibrium is assured by the several assumptions, such as perfect information, no externalities, complete markets, perfect competitions and so on. We recognize the significance of the theory not lying in the beautiful proof or results, but the reasons of market failure.

The same arguments apply here in the Ricardian Equivalence theorem. As is stated, R-E is a validated or invalidated statement according to whether several assumptions are satisfied or not, such as the perfectness of capital market, the infiniteness of horizons, the non-distortion tax, and so on. Heterogeneity, and uncertainty of future income might also have huge impact on the results. Empirical test results that do not accept Ricardian Equivalence could help find which of the assumptions behind is not satisfied well, or have played quite important the role in real economy. However, in a simulation model, we are testing the theory with the assumptions needed. For example, even we could accept R-E in the simulation; we can not say more about the significance on the R-E of other conditions assumed in the model. For example, consumers' financial constraint, uncertainty of future income streams, and other factors on the result can not be tested from the simulation. Actually, the R-E is some generalization of the permanent income hypothesis. In reality, consumers' financial constrain and income uncertainty do matter much in consumption function.

We could also make some extensions of this simulation, 1. Adopt more complex or realistic process other than AR(1) to describe the government policy. 2. Model consumers' Financial Constraint 3. Heterogeneous Agent. We could divide agents into two types, the poor and wealthy. Poor ones are more liquid constrained and have more own substitute effects of puclic projects, such as education, health insurance etc. 4. Model agents' utility as function of government expenditure, i.e., u(c, g) (it makes sense since research on R-E is mainly about the relationship of g and c). The conflicting, or inconclusive results from the simulation may be due to the inappropriate or incomplete empirical data adopted. For example, measure of wealth is quite difficult, and endogeneity might arise. Using OLS regressions as done in the paper cannot explore the full information inside, or might even yield conflicting results. The random shocks in this model could also be discussed . It is assumed an AR(1) process of the random variables, which might imply the hight insistence of the government policy. In reality, it is more complex than is expressed here. Our opinions on this simulation test are that simulations do have some innovations in testing R-E compared with the empirical tests before. Simulations have been extensively used in economic equilibrium models since introduced. It makes a good connection between theoretical models and empirical data. Properly used, we could test in somehow the insistence of the theoretical models. However, it should be very careful for us to deal with the theoretical basis of the modeling, taking into account the relevant conditions that might have significant impact on the result. Also, the data gathering should be well fitted with the theoretical requirements. Are the reported results reasonable? (1) Simulation In the AR(1) process the author assumes the coefficients of the model are set at 0.95. In that case, “changes in taxes, fiscal spending, and productivity are assumed to be highly persistent.” However, this assumption does not include the consideration of the temporal change of the policy. It can not account the situation when government policy might be not stable. Besides, under this assumption the shocks will decrease slowly, and may lead some problems especially in the finite life horizon as we will see later. (2) Results Analysis To start with this part, we claim that the simulation may affect the results of the Ricardian equivalence test.

In the analysis of table 5 (distortion taxation case), “when changes in the labor taxes only are included (i.e., both fiscal spending and productivity are kept constant), Ricardian equivalence is always rejected and the estimates are robust and consistent with the non-Ricardian view.” As we know the productivity shock plays the most important part in affecting the consumption-- “productivity shocks have very important effects on consumption; they explain at least 77 percent of the unconditional forecast error variance of the consumption.” And the shocks term is random under the simulation’s data generation process; a positive shock of the production will increase the consumption, while the negative one will decrease the consumption. So it is nature that the distortion tax has an uncertain affection on the consumption making the consumption more variable if it is accounted. There is the possibility that the non-clear conclusion from the test given in the table 5 lies in this huge randomly effect of the productivity shock. At the same time, the result of rejecting Ricardian equivalence when only including the shock of tax, as we are concerned, is just consistent with economy theory underneath. The second point we want to discuss is that interpreting the correlation parameters as the indication of the Ricardian equivalence may be kind of oversimplified and it seems that by making some deeper discussions we can also get the consistent conclusion to some extend. For example, under the finite horizon situation (table 6),

The regression rejects Ricardian equivalence in most cases. Only with a relative large value of  could not the test reject the Ricardian equivalence. However, once we review the reason why Ricardian equivalence does not hold under the finite horizon, this seemingly misleading result would be reasonable. As we know when the life time is finite the consumer will take the government debt as his net wealth. As a result the reducing of the tax will increase the consumption Ricardian equivalence will not hold. When we increase the value of  , “increase in taxation are made increasingly temporary and it is therefore more likely that the benefits will fall on the same individuals who saw their taxes increase”. Expecting this, the consumption of this finite individual will of course not change. Thus, the result in which Ricardian equivalence cannot be rejected is reasonable, and it seems that this would not cause any misleading conclusion in our opinions. Moreover, the t-statistics of estimators in Table 6, i.e.,-7.21, -10.66 for tax revenue and 8.15, 2.40 for government debt, shows that the test is relatively robust. This supports our above discussion. (3) The endogeneity problem of the regression model The last point in our discussion is related with the endogeneity problem of the regression. It is easy to notice that in the four cases, the estimations of the coefficients of the tax revenue and government debt are not stable; the results strongly depend on the regression model the author chooses. This suggests that the regression itself may involve some problems. It is known that the efficiency of OLS estimation relies on the assumption of exogenous regreesers. However, it is clear that this uni-equational consumption model easily causes endogeneity problems because the income, the financial wealth is generally correlated with the economic policy--As Lucas Critique mentions that in a model with rational agents, a change in the economic policy

conducts expectations thus changing the agent behavior. Thus, with this endogeneity problem, the analysis on the correlation parameters of the consumption function is not clear enough to give any robust conclusion. Thus the OLS model is not a good one to use in this estimation. But can we find a proper instrument variable? Or maybe this consumption function estimation approach is useless, other methodology is needed. In a word, in this paper, Cardia nests the Ricardian Equivalence Hypothesis with non-Ricardian alternatives, and used simulated data but not real data to estimate the consumption function, and she showed that there may be some problem with the statistical method used in estimating no matter whether Ricardian Equivalence is right or wrong. Although this simulating method has its own merits, there are also other problems with the assumption in the model and the regression equation, which may lead to this misleading result.