Ebook Business Cycles in the Equilibrium Model of Labor Market Search and Self-Insurance
This paper has two main purposes. The first and the main purpose is to extend the standard labor search and matching model by incorporating capital and labor leisure choice and to re-examine the puzzle presented by Shimer (2005) in the extended model.
The Mortensen-Pissarides search and matching model has become the standard theory of equilibrium unemployment (Mortensen and Pissarides (1994), Pissarides (2001)). However, Shimer (2005) pointed out that the Mortensen-Pissarides model with labor productivity shocks cannot replicate the volatility of the unemployment and vacancies observed in the U.S. data. The volatilities of the unemployment and vacancies in Shimer’s (2005) model are about one-tenth of their volatilities in the U.S. data.
In the baseline model constructed below, workers can accumulate capital but the market is incomplete; workers cannot write a contract to completely insure away the unemployment risk, but they can self-insure by accumulating capital. In addition, workers in the model choose how many hours to work and how many hours to enjoy leisure. Comparing the properties of the baseline model and the model by Shimer (2005) is equivalent to exploring the role played by the two additional features, namely, precautionary saving and labor-leisure choice, in the baseline model economy.
Regarding the first purpose, there are two main findings. First, I find that if the model is calibrated in the standard way that a real business cycle model is calibrated, the model can generate a large volatility of unemployment and vacancies. In other words, the model has a strong amplifying mechanism. I also find that utility from leisure plays a key role in narrowing the gap between the value of being unemployed and that of being employed, even with the observed relatively low replacement ratio. The small gap of the two values is a key property for the model to exhibit a strong amplification, as Hagedorn and Manovskii (2005) argued using the standard Mortensen-Pissarides model.
Second, I find that the model’s strong amplification vanishes when the self-insurance channel is closed or utility from leisure is turned off. The reason is a combination of the following two: First, both have an effect of making unemployed suffer more, or, making the value of being unemployed lower compared with the value of being employed. Second, the model’s amplification property is sensitive to a change in the difference in the values, because the calibration of the baseline model implies that the difference is small, and thus can be affected substantially from a relatively small change in environment. The result is closely related to the sensitivity of unemployment of the labor search and matching model that is calibrated to have a strong amplification in response to a change in unemployment insurance benefit.
The second purpose of the paper is to compare the business cycle properties of the baseline model with those of the standard real business cycle model. The current model can also be considered the standard real business cycle model extended by incorporating search and matching in the labor market. Since the current model generates fluctuations in both employment (extensive margin) and average hours worked (intensive margin), the model has the capacity to match a variety of cyclical properties of U.S. business cycles, especially those associated with the labor market. With the capacity of the baseline model in mind, the cyclical properties of the model are explored and compared with those of the standard real business cycle model. I show that the model does a good job of replicating many cyclical properties of the U.S. labor market that the standard real business cycle model cannot produce. In particular, compared with the previous models that introduces labor search and matching to the standard real business cycle model, the current model is doing a better job in generating a large volatility in both unemployment and vacancies with a reasonable calibration.
On the other hand, the cyclical properties of the baseline model with respect to consumption and investment are similar to those of the standard real business cycle model. The similarity seems to indicate that, even though the baseline model features incomplete markets, agents self-insure well enough such that the incomplete market model behaves like a complete market counterpart at the aggregate level.
The rest of the paper is organized as follows. In Section 2, related literature is reviewed. Section 3 summarizes the cyclical properties of the U.S. economy. The model’s performance is measured by the extent to which the model can replicate the properties. In Section 4, the baseline model is presented. Section 5 discusses the calibration of the model, and Section 6 offers a brief discussion of the computational methods. Appendix A gives details of the computation. Section 7 presents the main results of the paper and discusses them. Section 8 uses the baseline model to evaluate the effect of the declining volatility of the productivity shock on the cyclical properties of macroeconomic aggregates. Section 9 concludes.
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