Ebook Unemployment, Imperfect Risk Sharing, and the Monetary Business Cycle
Numerous empirical studies reflect a consensus among macroeconomists that monetary policy shocks have persistent effects on aggregate measures of real activity (e.g., Leeper, Sims, and Zha (1996) and Christiano, Eichenbaum, and vans (1999)). To explain such persistence within the context of a quantitative model of the economy, many believe that price-staggering along the lines of Taylor (1980) and Blanchard (1983) is essential. Models that graft this kind of friction into a general equilibrium framework, however, have had difficulty capturing the persistence evident in the data.
In a seminal contribution, Chari, Kehoe, and McGratten (2000) (henceforth, CKM) argue that equilibrium models with small nominal frictions alone possess weak internal propagation mechanisms. Specifically, the duration of output persistence following a monetary shock does not exceed the imposed length of price fixity in the model. An unappealing consequence of this finding is that significant persistence can only be obtained if one is willing to assume a high degree of exogenous rigidity. They go on to show that the inability to return longer episodes of endogenous persistence is a result of the procyclical nature of real marginal cost. With price staggering as the sole friction, changes in aggregate demand translate into considerable variation in marginal cost, particularly real wages. As a result, firms respond by making large price adjustments when they have an opportunity to do so, inducing smaller, less persistent movements in output.
This discovery led to the development of an extensive literature aimed at identifying various auxiliary frictions that enhance the propagation mechanism by dampening the sensitivity of marginal cost. In a model characterized by monopolistically competitive labor markets, Andersen (1998) and Huang and Liu (2002) demonstrate that staggered nominal wage-setting as an alternative to staggered price-setting enables the New Keynesian model to deliver persistent real effects of a monetary shock. Basu (1995) and Bergin and Feenstra (2000) incorporate a roundabout production structure in which all goods are material inputs for the production of other goods, implying that firm-level marginal cost depends on the prices charged by all other firms. Huang and Liu (2001) consider a vertical input-output structure in which finished goods go through multiple stages of production and firms encounter sticky prices at each phase of assembly. Neiss and Pappa (2005) and Dotsey and King (2006) emphasize the role of variable factor utilization in strengthening the propagation of nominal disturbances. Kiley (1997a) demonstrates that increasing returns to labor diminishes the elasticity of marginal cost with respect to output.
In this paper I add to the body of work referenced above by examining a different source of real persistence, namely, imperfect risk sharing between employed and unemployed workers. To provide a rationale for risk sharing behavior, I build on the model recently developed by Alexopoulos (2004) in which firms are unable to perfectly monitor labor effort, implying that workers face a temptation to shirk after negotiating employment contracts. To elicit the desired effort level, firms lift wages to the point where one’s utility from exerting effort is at least as great as the expected utility from shirking. Stated differently, equilibrium wage contracts must satisfy the workers’ incentive compatibility constraint. The outcome of this arrangement involves the payment of an efficiency wage that exceeds the Walrasian market clearing level, making unemployment a pervasive feature of the economy. Around this structural model of the labor market I add monopolistic competition with staggered price-setting in the spirit of Taylor (1980), money growth shocks as the exclusive source of exogenous fluctuation, and an unemployment insurance program that allows for varying degrees of risk sharing between agents in the model.
The scope of unemployment insurance affects persistence through its impact on the wagesetting process. Because effort is not perfectly observable, the feasible set of wages are restricted to those that satisfy the incentive compatibility constraint. It turns out that limiting the insurance opportunities available to workers reduces the sensitivity of real wages to changes in economic conditions that shift the incentive compatibility constraint. In particular, the wage increments needed to secure positive effort after a monetary expansion diminish as risk sharing activity declines. This is simply another way of stating that incomplete insurance interacts with unobservable effort to elevate the degree of endogenous wage rigidity present in the model. That is to say, firms choose to make smaller wage adjustments even though they are free to adjust every period. The presence of greater wage rigidity softens the response of marginal cost to demand shocks, encouraging firms to trim price adjustments when given the chance. More inertia in the price level, in turn, amplifies the persistence of real activity.
To assess the quantitative impact of partial insurance, I conduct dynamic simulations of the shirking model using structural parameters that are calibrated to match certain aspects of the U.S. data. In a version that abstracts from capital accumulation, I find that imperfect risk sharing generates output fluctuations that persist beyond the imposed duration of price rigidity. For the level of risk sharing permitted under the benchmark calibration, about 5 percent of the impact-period effect on output survives after all existing price contracts expire. When income pooling is scarce, however, persistence can be much higher with over 40 percent of the output effect remaining after the initial contract period ends. Under a full insurance arrangement, the model fails to deliver persistent real effects of a monetary shock, echoing the principle conclusion of CKM (2000). Simulation results also demonstrate that the persistence mechanism is not greatly impaired by the presence of capital, whereas previous studies have not always found this to be the case.
An interesting side effect of imperfect risk sharing is that it tends to create a trade off between two aspects of the business cycle: persistence and amplitude. Quantitative results indicate that as the amount of insurance coverage declines, the response profile of output becomes more persistent but the overall size of steady-state departures becomes smaller. Related studies find that amplitude either increases with or is mostly invariant to additional sources of persistence.
The paper is organized as follows. Section 2 develops the benchmark model and describes the calibration. Section 3 derives analytical solutions to a stripped-down version of the shirking model and then goes on to discuss simulation results from the full model. Section 4 examines the robustness of key findings to the presence of capital. Section 5 concludes.
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