Economists agree that labor contracts are a way of sharing idiosyncratic production risks between entrepreneurs and workers, especially when such risks are too complex for insurance contracts to be written on them and traded in organized markets. It is therefore important to understand how (economy wide) equilibrium employment and wages are influenced by risk related factors, in particular, risk aversion of entrepreneurs and workers and risk sharing opportunities elsewhere in the economy, such as in the asset markets.
The paper develops a general equilibrium model to address this issue. The model has several sectors of production which are subject to idiosyncratic productivity shocks, two inputs - labor and capital and stock markets which help diversify sectoral risks although not completely. We first prove the existence of equilibrium for this general model. Having parameterized the model by CRRA utility functions, we then prove that under certain conditions, the equilibrium employment levels vary inversely with the coefficient of relative risk aversion of agents a non obvious result in a general model with many risky assets of which labor is one.
The method that is proposed to prove this result is easily extendible to other types of utility functions from the HARA class, for which closed form solutions for demand functions are easy to find. We choose to present the result only for the CRRA type because of its wide applicability in Macroeconomics and Finance. We then compare results from numerical simulations of this parameterized model and those from a comparable benchmark model in which a complete set of Arrow securities are traded. It is seen that over a range of the risk aversion parameter, employment levels are higher when markets are complete. An explanation is provided for this.
The above results have a practical implication which may be regarded as one of the substantive motivation behind this paper. Workers in this model have an outside alternative to working for private entrepreneurs. This option is productively less efficient from the macro point of view and pays less than the latter. As the relative risk aversion goes up so does the use of this option. Also, over a certain range of the risk parameter, this option is less attractive when markets are complete than when they are not. The paper thus describes a role for a productively inefficient, low paying activity as an insurance instrument.
One can think of many examples of such outside options in real economies. Within the context of a developing economy, for example, household production (cottage industry) or self cultivation of land with the help of family labor can be such an alternative to wage labor in the manufacturing sector. Government financed unemployment doles, in developed economies also fits the description. A third example would be working in a less productive state owned firm in an erstwhile command/regulated economy which is trying to privatize. We choose the last example to think of the outside option in this paper, partly because of the current interest in privatization issues and partly because transition/deregulating economies are good examples of incomplete insurance markets. Thus the paper supplements other attempts to explain the slow pace of privatization3 by providing a rationale for state enterprises from a risk sharing point of view.
The Implicit Contract models were among the earliest attempts to point out the importance of labor contracts as risk sharing devices (see Rosen (1998) for a survey of this literature). The absence of asset markets however, make these essentially partial equilibrium approaches to the issue. Some later Real Business Cycle models with contractual labor (Boldrin and Horvath (1995), Gomme and Greenwood (1995)) remove this limitation. However, the assumption of a representative agent and market completeness simplifies many of the problems associated with risk sharing. The model in this paper is closer in spirit to Dreze’s (1991) CAPM model with labor contracts. The CAPM assumption, which for the purposes of this paper is restrictive, is removed and laborers are assumed to have sector specific skills (unlike in Dreze) which make them suitable for employment in only one sector at a time. We consider specificity of labor to be a more reasonable assumption as it explains why labor may be subject to idiosyncratic risks in the first place.
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Risk Sharing through Labor Contracts - Risk Aversion, Market Incompleteness and Employment
