Wages, Risk Sharing and Economic Fluctuations. Enisse Kharroubi

Abstract This paper adresses risk sharing on the labor market. It …rst provides empirical evidence that, every thing else equal, real compensation per worker growth is more sensitive to changes in output growth in economies where the volatility of output growth is larger. Secondly the paper shows that this can be accounted for in a framework where …rms are confronted to imperfect capital markets. In this case, compensation insurance can have a negative e¤ect on …rm borrowing capacity. Then with risk averse workers, a trade-o¤ appears for …rms between the cost of labor and the intensity of borrowing constraints. Finally when embedded in a general equilibrium model, we show that the optimal labor contract displays fewer insurance, the larger the volatility of shocks on …rm production function.

Keywords: Wages, Insurance, Capital Market Imperfections, Volatility. JEL Codes: D21, E24, E25.

Banque de France - DELTA. Address: 1, rue de la Vrillière 75049 Paris cedex 01. e-mail: …rstname.surname(at)banquefrance.fr. I thank Philippe Ashkénazy, Hector Calvo, Gilbert Cette, Andrew Clark, Grégory Corcos, Christian P…ster, Xavier Ragot, Patrick Sevestre, Mathias Thoenig and seminar participants at AFSE, Banque de France, Vigo workshop on dynamic macroeconomics, DELTA and Eurequa. Usual disclaimers apply.

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1. Introduction. ”Observed real wages are not constant over the cycle but neither do they exhibit consistent pro- or countercyclical tendencies. This suggests that any attempt to assign systematic real wage movements a central role in an explanation of business cycle is doomed to failure.” Robert Lucas (1977, p. 226) It is a stylized fact that aggregate real compensation per worker does not vary with the cycle. In this paper I propose to challenge this view by providing both empirical evidence and theoretical reasons which support the idea that aggregate real compensation per worker growth does signi…cantly depend upon cyclical variationsis for why it may be much more dependent on the cycle than is usually considered1 . More speci…cally this paper shows that the sensitivity of worker real compensation growth to output growth ‡uctuations is signi…cantly and positively associated with the volatility of output growth. As a …rst piece of evidence, the simple correlation coe¢ cient between worker real compensation growth and real output growth happens to be increasing in the volatility of the output growth: economies with the largest output growth volatility are also, every thing else equal, economies with the largest correlation between workers real compensation growth and output growth2 . Insert …gure 1 here Secondly, running a formal regression with real compensation per worker growth on the left hand side, the …rst conclusion is con…rmed: every thing else equal, the correlation between real compensation per worker growth and output growth depends signi…cantly and positively on output growth volatility3 . Empirical evidence therefore shows that, every thing else equal, real compensation growth is more sensitive to output growth in economies where output growth volatility is larger. From this empirical result we raise two questions. First if it is reasonable to assume that workers are more risk averse than …rm 1 Although a number of papers have stressed that the a-cyclicity result may an aggregation artefact (cf. Solon, Barsky and Parker [1994] on composition e¤ects), we claim in this paper that under this so called aggregation artefact, there are both empirical evidence of real wage procyclicity and theoretical reasons which can account for aggregate real wage procyclicity. 2 As Easterly, Islam and Stiglitz [2001] put it ”Models based on price and wage rigidities become unpersuasive if countries have both more ‡exible wages and prices and still exhibit high volatility in growth output. We need to ask: whether this high level of volatility can be explained simply by the fact that the countries are exposed to more shocks (or have a less diversi…ed economy), or are there other aspects of their structure or policy regimes which explain this volatility or relative stability?” 3 For more details about the empirical analysis, c.f. appendix 7.1 data & plots.

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shareholders, then …rms should provide insurance to workers and the more so when the environment is more volatile. Then how possible it is to reconcile the empirical evidence with this theoretical framework. Second the empirical evidence implies that workers compensation growth volatility is lower in less volatile economies for two reasons. First because the variance of macroeconomic shocks is lower and second because for a given shock on output workers compensation is less impacted4 . We therefore ask how di¤erences in the volatility of output shocks can explain di¤erences in labor market risk sharing agreements.

1.1. Mechanism of the model. Let us consider a risk neutral …rm which can hire workers, borrow capital and whose technology is subject to random shocks. Workers being risk averse, Pareto optimality implies that the …rm insures workers against ‡uctuations in labor productivity (Azariadis [1978] and Azariadis and Stiglitz [1983]). However this conclusion is modi…ed with imperfect capital markets. To illustrate it, let us consider a …rm subject to technological shocks. On average, its marginal productivity of capital is larger than the interest rate but when the …rm receives a bad shock the interest rate is larger5 . Moreover let us make the core assumption that there are ex post veri…cation costs for lenders to verify that a …rm is not able to pay back its debts when it does indeed declare so. Under these assumptions, the …rm is not able to borrow capital up to the point where the expected marginal productivity of capital would be equal to the risk free interest rate. By assumption, there are states of the world where the marginal productivity of capital is lower than the risk free interest rate and lenders have to pay for costs to verify that the …rm is e¤ectively in default. Put di¤erently, the …rm incurs ex ante the shadow price of veri…cation costs. To increase its borrowing capacity, the …rm needs to increase its pro…ts before debt repayments. One way to achieve that goal for the …rm consists in reducing its wage bill when a bad shock happens. The wage bill being lower, the …rm repayment capacity is larger. Lenders are less likely to spend veri…cation costs and the …rm is able to borrow a larger amount of capital6 . However reducing the wage bill in the case of bad shocks is costly because this implies introducing 4 Note

that this result hold, every thing lese equal, and employment in particular. shocks we consider are technological shocks. We therefore exclude any other type of shock such as demand shocks. However since the paper is about labor market long term structures, it is reasonable to focus on supply shocks. 6 This argument is based on the assumption that wages are senior to debt holder claims. If this priority structure were endogenous, that would come out to be the same since this structure is only relevant in as much as default is possible. In this 5 The

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variability in the compensation of risk averse workers. Therefore when a …rm proposes contingent wages contracts, it trades-o¤ an increase in its borrowing capacity against an increase in its average cost of labor7 . Based on this trade-o¤ and assuming that …rms face decreasing marginal returns to capital, we get two types of results. First, a …rm is more likely to propose contingent wage contracts to workers when its level of own capital and/or the risk free interest rate is low8 . These two …rst results are very intuitive. In both cases, the …rm demand for capital is large and it has large incentives to increase its borrowing capacity through contingent wage contracts. Secondly however, …rms are less likely to propose contingent wage contracts to workers when the volatility of shocks is large. In a partial equilibrium framework, a …rm facing shocks with a large volatility has a low borrowing capacity. If it decided to propose contingent wage contracts, it would increase its cost of labor, thus negatively a¤ecting its global productivity while little gain is expected on its borrowing capacity since shocks have a large volatility. Therefore when the volatility of shocks a¤ecting the …rm is large, the …rm is more likely to propose uncontingent wage contracts. To solve the apparent contradiction between the empirical evidence and the last result, we derive the general equilibrium of the economy. Then we show that the two …rst results still hold: at the equilibrium of the labor market, …rms are more likely to propose contingent wage contracts to workers when their level of own capital and/or the risk free interest rate on their loans is low. However we show that the last result is reversed and becomes coherent with the empirical evidence: …rms are more likely to propose contingent wage contracts to workers at the equilibrium of the labor market when the volatility of shocks is larger. Why is this last result reversed? While in the partial equilibrium case, the wage rate is exogenous, in the general equilibrium framework, the wage rate depends on the amount of capital …rms are able to invest. If the volatility of shocks is large, then, every thing else equal, …rms borrowing capacity is low and so is the amount of capital that …rms can invest. This means that the equilibrium wage rate is also low and so is the wage premium on contingent contracts. Providing contingent wage contracts then generates a …rst model …rms never default. 7 A possible illustration of the conclusions of the paper can lie in the di¤erences in the compensation structure between large and small …rms. The cost of capital is much lower for the former while insurance through labor contracts is much larger. Sometimes, large non …nancial corporations even have their own …nancial intermediary. 8 The model therefore gives an explanation to the stylized fact put forth by Rodrik [1998]: a decrease in the cost of capital increase, every thing else equal, the volatility of workers compensation.

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order increase in the …rm borrowing capacity but a second order increase in the cost of labor. As a result, at the equilibrium of the labor market, …rms are more likely to provide contingent wage contracts when the volatility of shocks is larger. Therefore, if di¤erences in growth volatility mainly come from di¤erences in the underlying shocks the economy faces, then a model based with imperfect credit markets can account for the positive correlation between real compensation growth sensitivity to output growth and output volatility.

1.2. Related literature. In a very stylized framework, this paper studies to the economics of risk allocation. Gomme and Greenwood [1995] study a similar question in order to assess how the cyclical allocation of risk between workers and entrepreneurs can help to understand cyclical variations of wages and the labor share in output. Danthine and Donaldson [1992] show that taking into account risk sharing considerations can help explain the wageemployment variability puzzle. Ichino [1994] also studies a similar question and asserts that when …rms increase the risks beard by workers, this can help them to reduce the cost of external capital9 . Chevalier and Scharfstein [1996] shows that the existence of credit market imperfections can help explain the cyclical behavior of mark-ups. More generally, a growing literature (Bronars and Deere [1991], Wasmer and Weil [2000]) studies the possible interactions between labor and capital markets. Contingent wages have also been studied as a mechanism to solve for moral hazard problems. When it is di¢ cult (costly) for a …rm to monitor the e¤ort delivered by workers, a labor contract with a contingent wage rate can give workers the incentives to deliver the optimal e¤ort. Contingent wage contracts are therefore generally considered as an incentive mechanism when there is asymmetric information (c.f. Gibbons [1998] for a survey). This paper is close. However contingent labor contracts arise here as the result of capital market imperfections while the labor market is perfectly competitive. 9 Ichino [1994] is based on a similar idea to this paper: that risk sharing agreements between an entrepreneur, its workers and its …nanciers can modify the value of the …rm. However this paper completes Ichino [1994] in two di¤erent ways. First, contrary to Ichino [1994] which claims that "[contingent] compensation schemes are introduced as risk sharing devices by …rms that perceive more uncertainty" we show that a partial equilibrium model is generates an opposite relation between the volatility of shocks a¤ecting the …rm and the degree of labor contracts contingency. Secondly we build the general equilibrium of the economy and we show that capital-labor complementarity in …rm production function is key to obtain the positive correlation between the volatility of shocks a¤ecting the …rm and the equilibrium degree of labor contracts contingency.

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1.3. Road map of the paper. The paper is organized as follows. The following section lays down the model and its main assumptions. Section 3 describes the di¤erent strategies …rms can adopt as regards the labor and capital demands. In section 4, we …rst examine individual and social optimality for the di¤erent strategies considered in the previous section. We also build the dynamics of the economy. The main results of the model can then be found in section 5 and section 6. Conclusion is eventually found in section 7.

2. The microeconomic framework. 2.1. Agents and markets. We consider a single good small open economy which lasts one period with three types of agents, entrepreneurs, workers and international investors. There is a continuum of unit mass of workers and a continuum of unit mass of entrepreneurs. Workers are risk averse, have a labor supply equal to one but no capital endowment. Their preference writes as uw = log (cw ) where cw is a worker’s end-of-life consumption. Entrepreneurs are risk neutral have a capital endowment k but no labor endowment. Their preference writes ue = ce where ce is an entrepreneur’s end-of-life consumption. They have access to a constant returns to scale technology which uses capital and labor. Entrepreneurs technology writes as ys;i = As ki li1

. It is subject

to a macroeconomic shock s, ki is the capital stock entrepreneur i invests and li is the number of workers he hires. There are two states of nature, a good s = h and a bad one s = l with Ah > Al . Both states of nature are equiprobable. We note EA the mean of As . We adopt the following notations: EA

Al = Ah

A= .

At the beginning of each period, there are two di¤erent markets which open one after the other. The …rst market on which transactions take place is the capital market. On this market, risk neutral entrepreneurs sign one period contracts with risk neutral investors and we assume ex post costly state veri…cation10 . 1 0 In the case of ex post costly state veri…cation, lenders need a mechanism to force borrowers to reveal their true repayment capacity. This can be achieved with a penalty system where borrower pay for a extra fee in case of untruthful report: If the borrower declares that he is able to pay for the face value of the contract, then he does so. If he declares to be unable to do so, then the lender pays for the ex post veri…cation costs. Then if the borrower’s declaration was truthful, the lender get the residual value of the …rm while if the borrower’s declaration was untruthful, then the lenders gets the total cash ‡ow of the …rm. Likewise, borrowers always make truthful reports.

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Investors have to undergo some cost to recover claims on defaulting …rms. Assuming that these costs are su¢ ciently large, there are no contingent debt contracts because the interest rate charged on such contracts would be too large. We therefore focus on risk free debt contracts11 . The risk free gross interest rate is exogenous12 noted r and …nancial capital supply is in…nitely elastic. The amount of capital lent to …rm i is di . Once …rms have signed contracts with …nancial investors, the labor market opens. The labor market is competitive. At the end of the period, …rms pay wages to workers and debt contracts to …nancial investors.

2.2. Workers insurance and …rms borrowing capacity: a micro model. Firms decisions about capital and labor are sequential. The program of a representative …rm can be solved with backward induction. First the strategy of the representative …rm as regards the labor market is determined. Then the capital demand of the representative …rm is solved. Let us consider a …rm i which has choosen a given compensation scheme fwl ; wh g when other …rms choose to propose an equivalent certain wage rate w. Then assuming that the compensation scheme fwl ; wh g veri…es workers participation constraint, E log (ws )

log (w), …rm i program …rst consists in choosing the number of worker li such that it solves

maxE (li ) = EA (ki + di ) li1 li

Ews li

(1 + r) di

The solution to this problem (…rm i optimal demand for labor) then writes as

(1

) EA (ki + di ) li

1 1 See

= Ews

(2.1)

appendix 7.4 for more details. The core assumption of the model is that default is costly. How costly it is does not modify the qualitative results of the model, in particular the fact that worker compensation is more sensitive to output ‡uctuations when the volatility of shocks is larger. Moreover this assumption helps to overcome the relative seniority issue of workers w.r.t. …nanciers’claims. Since …rms are always able to pay for all their liabilities, seniority analysis is irrelevant. 1 2 This is a small open economy. This hypothesis is not crucial to the results of the model, it simply simpli…es the resolution of the model and the exposition of its results.

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Now one can solve the problem consisting for …rm i in determining its optimal amount of debt …nance di . This amounts to solve the following problem

maxE (di ) = EA (ki + di ) li1 Ews li (1 + r) di di 8 > > < (1 ) EA (ki + di ) li = Ews s.t. > > : 8s, As (ki + di ) li1 ws li + (1 + r) di Introducing …rm i optimal labor demand (2.1) in both the objective function E (di ) and the borrowing constraints As (ki + di ) li1

ws li + (1 + r) di we get to the following problem

i1 h [EA maxE (di ) = (1 Ew)EA s di h i1 h s.t. 8j, (1 Ew)EA Aj (1 s

(1

) EA] (ki + di ) (1 + r) di i w ) EA Ewjs (ki + di ) (1 + r) di

Then there are then two di¤erent cases: if raising debt is not pro…table for the …rm, i.e. 1 + r, then …rms expected pro…ts write as E

h

(1

)EA Ews

i1

EA

= (1 + r) k. As is clear the expected pro…ts of …rm i do not

depend upon on the type of the labor contract. On the contrary, if riasing debt is pro…table for the …rm, i.e. i1 h (1 )EA EA > 1 + r, then …rm i optimal expected pro…ts write as Ews E

wk ; Ews Ews

=h

Ews (1 )EA

EA i1

h

Ak

(1 + r)

(1 h

wk ) EA Ew s

Ak

(1

i

wk ) EA Ew s

i (1 + r) ki

where k is the state of nature for which the borrowing constraint is binding: "

k = arg min dj j j

1

(1

) EA Ews

Aj

(1

wj ) EA (ki + dj ) Ews

(1 + r) dj

#

The expected pro…ts of …rm i now do depend upon the type of the labor contract …rm i chooses to propose. We can then derive the following proposition. Proposition 1. When …rms cannot issue contingent debt, the optimal wage contract fwl ; wh g is such that

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wh > w > wl as long as …rms are credit constrained. Labor compensation contingency, i.e. the di¤erence wh

wl , decreases with the interest rate r and/or with the volatility

Proof. p

of macroeconomic shocks.

Let us consider that …rm i proposes a contingent compensation scheme fwl ; wh g such that wh =

w, w being the …xed wage proposed by other …rms. Then workers participation constraint implies that

wl =

p

1

w. Then the bad state of nature determines …rm i borrowing constraint if and only if

Al

(1

) EA

which under the assumption that (1

wl < Ah Ews

) EA

i

) EA

wh Ews

> 0 simpli…es as

(1 (1

Therefore expected pro…ts of …rm i E

(1

) EA + ) EA

can be written as

E ( ) = max [R ( ) ; 1] (1 + r) ki

where R( ) = h

w (1 )EA

i1

h EA Al h i1 1+ p 2

i ) EA 1+2 h (1 + r) Al (1 (1

) EA 1+2

i

and the optimal compensation scheme fwl ; wh g is the solution to the program maxR ( ) (1 (1

s.t.

)EA+ )EA

The …rst order condition to this problem writes as 1

1+r Ews EA (1 ) EA

1+

1 EA

2

1

4

9

EA

Al

(1

) EA

2 1+

=

Let us then note

the left hand side of the last condition. Taking the …rst derivative w.r.t.

1 2

@ @

where ' ( ; ) =

1 EA

h

1

Al

expression are positive since

"

2

#

3 2

+1

(1

1 2

1 +

) EA 1+2

2

i

1 ( 2

2

1) +

2

1

+1

[1

this yields

' ( ; )]

. As is clear both terms of the right hand side of the last

> 1. The expression 1

1+r Ews ( ; )= EA (1 ) EA

1+

1 EA

2

1

4

EA

Al

(1

) EA

2 1+

is therefore strictly increasing in . This implies that a necessary and su¢ cient condition for …rms to adopt contingent compensation schemes writes as

( = 1; )
wl if and only if the …rm is credit constraint. Then under the assumption that assuming that increasing function of both r. The ratio

=

wh wl

and r, the optimal wage contract

, due to the fact that

is a strictly

is a decreasing function of the interest rate

is therefore a decreasing function of the interest rate r. A larger interest rate reduces

optimal wage contingency. Finally since contract

( = 1; )
0), a necessary and su¢ cient condition for the left hand side to be increasing in , every thing lese equal writes as

@! l gy;l > 0 @

@! h gy;h @

which simpli…es as @! h @! l EB + > @ @ EB This condition is equivalent to " Given that

@ @

EB +

2

(EB

) +

2

#

@ @

> (1 + ) EB

+

EB +

is a positive number and

@ @

2

= (1 + ) 4(1

h

4 ) EB

EB 1+r 2

(

1)

i 1

3

1

EB 5

the last condition simpli…es as

(EB

2

) +

2

2

EB +

> 4(1

h

4 ) EB

EB 1+r

1 2

(

1)

i

3

EB 5 EB

+

EB +

A su¢ cient condition which ensures that the last inequality is always correct writes as

(EB

2

2

) > 4(1

and EB +

2

2

> 4(1

h

4 ) EB

2

(

4 ) EB

i 1

EB 1+r

1)

h

(

EB 1+r 2

1)

3

EB 5 [EB

i 1

3

EB 5

]

EB +

The …rst of these su¢ cient conditions is trivially true. As to the second condition, it can be simpli…ed so that its LHS decreases with , while its LHS increases with . This condition is therefore always met if and 16

only if it is true for

(EB + )

=

(1 (1

(1 (1

)EB+ )EB

) EB ) EB +

which yields

> (1

) EB

4

EB 1+r

1

(1

) EB 2

2

EB

This simpli…es as (1

EB ) EB +

EB 1+r

>

and this is always correct since by de…nition

EB 1+r

1

(1

) EB

EB

> 1. Therefore ...

5. Main Results In the model we have built, labor contracts are endogenous as far as workers insurance is concerned. We have shown that the variability of workers compensation and economic ‡uctuations essentially depend upon three elements: the variance of TFP shocks, the cost of external capital for …rms, and the level of …rms own capital. Based on the previous discussion, we can observe that the variance of workers compensation increases with the variance of TFP shocks. At the steady state, workers compensation is more likely to be contingent when the volatility of technological shocks is large. The volatility of output is then large. On the contrary, compensation is more likely to be …xed, when the volatility of technological shocks is low. In this case, output volatility is low. Therefore the theoretical framework provides an explanation based on the existence of capital market imperfections for the empirical relation we described in the introduction (a positive correlation between the volatility of the economic ‡uctuations and real wages procyclicity). Two other remarks are possible. First the cost of external capital has a negative in‡uence on the degree of real wages procyclicity. A decrease in the gross risk free interest rate r increases real wage procyclicity. When it is less costly for …rms to borrow capital, (when economies become more integrated …nancially), …rms reduce the insurance they provide to workers through their wage contracts because a decrease in the cost of external capital increases …rms demand for capital. Since …rms are constrained in the amount of capital they can borrow, they more likely choose contingent labor contracts in order to reduce the intensity of the borrowing constraints they face and thereby increase their expected pro…ts. The theoretical frame-

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work therefore provides an explanation (based here on the existence of capital market imperfections) for the empirical relation described by Rodrik [1998] according to which the integration degree of economies plays a positive role in the volatility of workers compensation. Secondly this model helps to shed some light on how the volatility of shocks can a¤ect average economic growth. An increase in the volatility of technological shocks always reduces the speed at which the economy accumulates capital. When the volatility of technological shocks is larger, the bad shock Al is even worse. The borrowing capacity of …rms is then reduced and the amount of capital invested is lower. The model therefore predicts a negative relation between the average growth rate of the economy and the volatility of shocks the economy faces.

6. Conclusion. We have built a model in which the structure of workers compensation is endogenous. This has enabled us to build a theory of growth and macroeconomic ‡uctuations based on …rms choices as to the structure of workers compensation. The main of point of the paper consists in saying that …rms trade-o¤ the average cost of labor against the intensity of the borrowing constraints they face. When …rms increase the wage insurance they provide to workers this reduces the average cost of labor because workers are risk averse. This has therefore a positive impact on expected pro…ts. However when …rms increase the wage insurance they provide to workers, this tightens …rms borrowing constraints. This has a negative impact on expected pro…ts because fewer capital is invested. Then we have then shown that this mechanism embedded into a dynamic macroeconomic model can help explain the stylized fact raised in the introduction. Through a comparative statics exercise on the volatility of macroeconomic shocks and the cost of external capital for …rms, we have found a possible explanation for the stylized facts about the relation between the structure of workers compensation and the degree of macroeconomic volatility. Finally, we can make two other remarks. First it would be interesting to study wether introducing other contracts such as equities or short and long term debt would change or modify the results we have obtained. For instance, it is likely that …rms which can issue long term debt will also pay more frequently …xed wages. The second remark we can make concerns the supply of capital. In this model we have assumed

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that capital supply is exogenous. If it was endogenous, i.e. if workers were capital providers for …rms, then the compensation structure would in‡uence the amount of capital workers save. In particular, workers whose income is contingent will save more than those whose income is …xed. This could then generate multiple equilibria because the risk transferred to workers impacts positively the demand and the supply for capital. Put di¤erently, a negative relation could emerge between the quantity of capital …rms borrow and the cost of external capital for …rms.

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[20] Easterly, W.; R. Islam, and J.E. Stiglitz (2001): ”Shaken and Stirred: Explaining Growth Volatility,” Annual World Bank Conference on Development Economics, ed. by B. Pleskovic and N. Stern. [21] Gibbons (1998), ”Incentives in Organizations”, Journal of Economic Perspectives, vol.12 (4) pp.115-32. [22] Gomme, P. and J. Greenwood (1995), ”On the Cyclical Allocation of Risk,” Journal of Economic Dynamics and Control, vol. 19 (1), pp. 91-124. [23] Gottschalk, P. and R. Mo¢ tt (1994),”The Growth of earnings instability in the U.S. labor market,” Brookings Papers on Economic Activity, vol.2, pp.217-72. [24] Greenwald, B., J.E. Stiglitz, and A. Weiss (1984), ”Informational imperfections in the capital market and macroeconomic ‡uctuations,” American Economic Review, Papers and proceedings, vol.74(2), pp.19499. [25] Guiso, L., L. Pistaferri and F. Schivardi (2001), ”Insurance within the …rm,”Journal of Political Economy, vol. 113 (5), pp. 1054-87 [26] Ichino A. (1994), ”Flexible labor compensation, risk sharing and company leverage,”European economic Review, vol.38 (7), pp.1411-21. [27] Holmström, B. and P. Milgrom (1987), ”Aggregation and linearity in the provision of intertemporal incentives,” Econometrica, vol.55 (2), pp.303-28. [28] Jones D.C., T. Kato, and J. Pliskin (1997), ”Pro…t sharing and gain sharing: A review of theory, incidence and e¤ects,” in Lewin D. Mitchell D.J.B. and Zaidi M.A. (eds). [29] Keane, M., R. Mo¢ tt, and D. Runkle (1988) ”Real wages over the business cycle: Estimating the impact of heterogenity with micro data,” Journal of Political Economy, vol.96 (6), pp.1232-66. [30] Kruse, D. (1991), ”Pro…t sharing and employment variability: Microeconomic evidence on the weitzman theory,” Industrial and Labor Relations Review, vol.44, (3), pp. 437-453. [31] Lucas, R.E. (1977), ”Understanding Business Cycles,” In Brunner, K. and Meltzer, A., eds. 21

[32] Milgrom P. (1988), ”Employment contracts, in‡uence activities and e¢ cient organization design”, Journal of Political Economy, vol.96 (1), pp.42-60. [33] OECD (1995), ”Pro…t sharing in OECD countries,” Employment Outlook, Paris, OECD. [34] Rodrik, D. (1997), ”Has International Economic Integration Gone Too Far?”Institute for International Economics, Washington, DC. [35] Rodrik, D. (1998), ”Labor and capital Mobility,” Draft paper prepared for the NBER workshop on Trade, Technology, Education, and the U.S. Labor market. [36] Sachs, J. (1980), ”The changing cyclical behavior of wages and prices: 1890-1976,”American Economic Review, vol.70 (1), pp.78-90. [37] Solon, G., Barsky, R., and J. Parker (1994) ”Measuring the cylicality of real wages: How important is the composition bias,” Quarterly Journal of Economics, vol.109 (1), pp. 1-25. [38] Stiglitz J.E. (1994), ”Price rigidities and market Structure,” American Economic Review, (Papers and Proceedings), vol.74 (2), pp.350-55. [39] Stiglitz J.E. (1999), ”Toward a general theory of wage and price rigidities and economic ‡uctuations,” American Economic Review, (Papers and Proceedings), vol.89 (2), pp.75-80. [40] Tobin, J. (1993), ”Price Flexibility and Output Stability: An Old Keynesian View,”Journal of Economic Perspectives, vol.7 (1), pp. 45-65. [41] Wadhnani S. and S. Wall (1990), ”The e¤ects of pro…t sharing on employment, wages, stock returns and productivity: Evidence from U.K. miro-data,” Economic Journal, vol.100 (399), pp.1-17. [42] Wasmer, E. and P.Weil (2000), ”The Macroeconomics of Labor and Credit market Imperfections,”American Economic Review, vol.94 (4), pp. 944-63. [43] Weitzman M. (1985), ”The simple macroeconomics of pro…t sharing”, American Economic Review, vol.75 (5), pp. 937-53. 22

7. Appendix. 7.1. Data and plots. All the data used is taken from the OECD Economic Outlook database. We consider wi;t the real compensation index per worker in the business sector13 , de‡ated by consumption or GDP prices in country i at time t and yi;t is the value added in the business sector in country i at date t. There are 22 countries in the sample: Australia, Austria, Belgium, Canada, Danmark, Germany, Finland, France, Greece, Italy, Ireland, Japan, Korea, Mexico, Netherlands, Norway, Portugal, Sweden, Spain, Switzerland, United Kingdom and USA. The time period is 1983-2002. We run the following regression

ln

i

and

t

wi;t = wi;t 1

i

+

t

+

i

ln

yi;t yi;t

+ "i;t 1

are respecitvely country and time dummies. Real wage procyclicity in country i is

i.

In …gure 1

the standard deviation of value added growth is on the x-axis and real wage procyclicity per country

i

is

on the y-axis. 70%

MEX 60% PRT KOR

50%

SWE 40% GRC NOR 30%

CHE GBR JPN

FIN

DNK

20% AUT

USA BEL

10%

DEU

AUS CAN

ITA 0% 0%

1%

IRE

ESP FRA

2%

3%

4%

5%

NLD -10%

1 3 The business sector as it is de…ned by OECD is the whole economy minus the public sector. c.f. OECD Economic Outlook: Sources and methods, (http://www.oecd.org/eco/sources-and-methods).

23

Figure 1 : Standard deviation of GDP growth vs. real wage per worker procyclicity1 4 .

Then, the following equation are estimated

ln

wi;t = wi;t 1

i

+

t

+ xi;t +

Control variables are gathered in vector xi;t ,

yi

0

ln

yi;t + yi;t 1

1 yi

ln

yi;t + "i;t yi;t 1

is the variance for country i of the growth rate of yi;t , and

other notations are the same as previously.

Table 1. Dependent variable: Real compensation per worker growth rate in bus. sector de‡ated by GDP prices. yi

(=100)

-0,15a

-0,07c

y

-0,09

0,48a

0,49a

0,38a

4,16a

1,72b

1,59b

1,93b

ln yi;ti;t 1 y

yi

ln yi;ti;t 1 (=100)

ei

(=100) e

-0,59a

ln ei;ti;t 1

-0,60a

-0,59a

e

ei

ln ei;ti;t 1 (=100)

0,66a

0,63a

0,54a

0,32a 2,41a

0,04b

0,01

0,19b

-0,40a

-0,30a

-0,41a

-0,37c

-2,31a

-1,23a

-1,45a

-1,02a

-1,21a

R2

18%

30%

30%

37%

7%

30%

33%

46%

48%

controls

no

yes

yes

yes

no

yes

yes

yes

yes

Fixed e¤ects

no

no

yes

yes

no

no

yes

yes

yes

Heteroscedasticity

no

no

no

yes

no

no

no

yes

yes

N T

22 20

22 18

22 15

22 15

22 18

22 15

22 15

22 15

22 15

Note: Signi…cance levels 1%, 5% and 10% are indicated respectively with superscript a, b and c. Control variables are the following: ratio of imports in goods and services to total GDP, unemployment rate in total economy, share of business sector employment in total employment, share of business sector added value in total added value. All the samples used are balanced and all estimations include time e¤ects. Estimation periods are the following 1982-2001 with 20 periods, 1984-2001 with 18 periods, 1987-2001 with 15 periods. 1 4 In this diagram, real wage procyclicity has been estimated pulling out of the sample the data for Germany in year 1990 since large changes in output and wages have occured due to the political uni…cation of the country. Output has risen by almost 15% while real wages have decreased by 10% this year.

24

All the estimations display the same result: every thing else equal, real wages procyclicity is larger in economies where the volatility of the business cycle is larger. Table 2. Dependent variable: Real compensation per worker growth rate in bus. sector de‡ated by cons. prices. yi

(=100)

-0,17a

-0,08b

y

-0,06

0,33c

0,37a

0,27a

5,24a

2,09a

1,94a

2,03a

ln yi;ti;t 1 y

yi

ln yi;ti;t 1 (=100)

ei

(=100) e

-0,42a

ln ei;ti;t 1

-0,42a

-0,37a

e

ei

ln ei;ti;t 1 (=100)

0,52a

0,55a

0,43a

0,18b 2,87a

0,04b

0,01

0,25a

-0,17c

-0,12

-0,18b

-0,14c

-2,03a

-1,28a

-1,47a

1,17a

-1,43a

R2

21%

23%

24%

25%

05%

24%

26%

31%

34%

control variables

no

yes

yes

yes

no

yes

yes

yes

yes

Fixed e¤ects

no

no

yes

yes

no

no

yes

yes

yes

Heteroscedasticity

no

no

no

yes

no

no

no

yes

yes

N T

22 21

22 15

22 15

22 15

22 18

22 15

22 15

22 15

22 15

Note: Signi…cance levels 1%, 5% and 10% are indicated respectively with superscript a, b and c. Control variables are the following: ratio of imports in goods and services to total GDP, unemployment rate in total economy, share of business sector employment in total employment, share of business sector added value in total added value. All the samples used are balanced and all estimations include time e¤ects. Estimation periods are the following 1982-2001 with 20 periods, 1984-2001 with 18 periods, 1987-2001 with 15 periods.

All the estimations display the same result: every thing else equal, real wages procyclicity is larger in economies where the volatility of the business cycle is larger.

7.2. Optimal labor contracts in general equilibrium. First part of the proof: the derivative wrt to . The condition determining the optimal labor contract in the general equilibrium of the economy can be

25

written as 1+r 1 k EA Noting

=

2

4

1

@F @

' ( ; )]

=

2

1+

4

h

1

2

1

1

4

[1

i1 '( ; )

' ( ; )]

and F the right hand side of the last expression we have

@F @

Then

1

[1

@F @'

(1

) [1 +

2 '] [1 +

(1

')]

[1

'] [1

']

is a positive number if and only if

[1

'] [1

'] < (1

) [1 +

(1

')] [1

'+

(1

')]

A su¢ cient condition which ensures that this last inequality is always correct then writes as

[1

given that 1

'] [1

h ) [1

'] < (1

2

'] +

[1

i ']

' is a positive number, this condition simpli…es as

(1

)
0 1+

which itself writes as

1+

2

> 1+

2

Al EA

2 (1 1+

)

+ 2 (1

)

(

1) 1+

We then …nally end up with the following condition

2 (1 1+

) 2

>

Al EA

1

which is always true since the left hand side is always positive and the right hand side always negative. Therefore this means that the right hand side of (??) is a decreasing function of .

27

Finally given that the general equilibrium optimal labot contract

is such that F ( ; ) =

1+r 1 EA k

we can

write from this condition d = d

@F=@ @F=@

which is positive given the conclusions reached upwards. At the general equilibrium of the economy the optimal labor contract is such that is decreasing function of the volatility of shocks . Firms provide fewer insurance to workers when they face more volatile shocks.

7.3. Contingent debts and wage contract insurance. We extend here the micro model to the case where …rms can issue contingent debt. As previously …rms decisions about capital and labor are sequential. Debt contracts are contingent in the sense that there is at least one state of the world where …rms are not able to pay for the face value of their …nancial liabilities. Since there are two states of the world, let us soppose that …rms are not able to pay for the face value of their …nancial debts in the bad state of nature. Therefore The program of …rm i …rst consists in choosing the number of worker li such that it solves

maxE (li ) = li

1 2

Ah (ki + di ) li1

s.t. E log (ws )

wh li

rdi

log (w)

The solution to this problem (…rm i optimal demand for labor) then writes as

(1

) Ah (ki + di ) li

= wh

Now the problem consisting for …rm i in determining its optimal amount of debt …nance di . If …rm i chooses to issue risk free contracts only then its program and the solution are identical to those derived in the micro

28

model. On the contrary if …rm i chooses to issue contingent contracts then the program of …rm i is

s.t.

8 > > > > > >
> > > > > : Al (ki + di ) li1 wl li < (1 + r) di

The …rst condition represent …rm i optimal labor demand, the second condition reprsents the no arbitrage condition with which …nanciers price the interest rate on contingent …nancial contracts. The term 2c (ki + di ) represents the ex post veri…cation cost …nancier pay for when the …rm declares that it cannot pay for the face value of debt. The assumption that this cost is lenar in the amount of capital invested in the …rm is simply made to simplify the analysis. Finally the last condition (inequality) states that when the bad state of nature happens, …rms are not able to pay for their debts even with the lowest interest rate possible (the risk free one in fact). Simplifying this program then amounts to

max 21 di

h

(1

)Ah wh

s.t. (1 + r) di = 12 rdi +

1 2

i1

h

(1

[Ah )Ah wh

i

(1 1

) Ah ] (ki + di ) h

wl wh

Al

(1

) Ah

(1

) Ah

rdi i

2c (ki + di )

Firms demand for capital is then optimal if and only if 1

(1 + r) + c = EA

Ews (1 wh

) Ah

wh

Then the optimal expected pro…ts of …rm i depend only upon the compensation scheme fwl ; wh g. Therefore the optimal wage contract is such that

max

fwl ;wh g

h

EA

Ews wh

(1

) Ah

ih

(1

)Ah wh

s.t. log wl + log wh = 2 log w

29

i1

Introducing the individual rationality constraint into the expected pro…t expression, we end up with a function of wh only. Then taking the value of the derivative of this expression w.r.t. wh for wh = w we get an expression ( 1

Ah EA ) w

which is always positive. In other words, the possibility for …rms to issue

contingent debt does not modify the result: When …rms are credit constrained, they optimally choose to provide workers with contingent compensation schemes.

30