بیمه بیکاری ناقص و مجموع نوسانات

This paper develops a real business cycle model characterized by idiosyncratic employment shocks and quantitatively explores the behavior of aggregate variables under the assumptions of complete and incomplete insurance markets. The results show that the model with incomplete markets produces standard deviations and correlations of aggregate labor input and labor productivity close to the ones of the US economy for the post-war period.

In this paper I conduct a quantitative exploration of the implications of idiosyncratic shocks and incomplete markets in an otherwise standard real business cycle (RBC) model. In particular, I compare the predictions with respect to time series properties of the average productivity of labor and market hours of two model economies that differ only in their insurance technologies. The empirical observations from the US economy during the post- war period show that: (i) fluctuations in market hours are only slightly smaller than fluctuations in output; (ii) hours worked fluctuates more than labor productivity; (iii) hours per worker fluctuates less than the employment rate; and (iv) the correlation between average productivity and market hours is close to zero or even negative (the so-called Dunlop–Tarshis observation made by Sargent (1987) and Christiano and Eichenbaum (1992)). 1 The usual approach in the literature to explain these facts has been to model competitive economies where a continuum of agents live forever. In those economies, the basic impulses generating business cycles fluctuations come from a stochastic shock to technology and, in many studies, from additional sources of aggregate uncertainty such as shocks to government spending and tax rates. Furthermore, either because agents are identical beforehand or because of the existence of a complete set of insurance markets, in most model economies an aggregation theorem holds that permits the study of the economic system “as if ” it was inhabited by a single representative consumer. 2 One way to depart from the previous framework is to consider imperfectly competitive economies, as in, for instance, Galí (1996). Another alternative is to consider economies with incomplete insurance markets and idiosyncratic uncertainty. 3 This latter approach is the one I follow here. The model I develop below is related to that in Imrohoroglu (1989) and other aggregate models of incomplete markets such as Aiyagari (1994), Huggett (1997), and Krusell and Smith (1998). In these models agents live forever, individual labor productivity endowments follow an exogenously given stochastic process and labor supply is inelastic, i.e., productive agents work a fixed number of hours. I depart from this setup in that productivity endowments are interpreted as unemployment shocks and in that employed agents are allowed to choose their labor supply. Thus, while in previous models both the extensive and intensive margins are exogenously determined, in this paper the intensive margin is endogenous. 4 In line with the related literature, in the incomplete markets economy the existence of unemployment insurance markets is exogenously precluded. Also, I assume that agents are able to smooth consumption by holding differing amounts of the single asset in the economy. Following the RBC tradition, this asset is risky because it is used as an input in production, which is subject to technology shocks. In the model,therefore, there is both idiosyncratic and aggregate uncertainty. Finally, agents face a fixed bound on borrowing which may constrain their decisions in some periods. 5 I calibrate the artificial economy to mimic some key observations of the US economy and numerically solve the model under both complete and incomplete insurance markets. An important feature of the model is the complementarity between countercyclical employment risk and incomplete unemployment insurance. In particular, my results suggest that if idiosyncratic shocks are such that employment is constant over time, then the competitive allocations under complete and incomplete markets are nearly indistinguishable (in terms of volatility of aggregate series and correlations with output) and close to the results reported in other well known studies (e.g., Hansen, 1985). With acyclical idiosyncratic risk (when the employment rate displays some fluctuations but it is poorly correlated with output) both market arrangements produce slightly larger fluctuations (although the match with the data is better under incomplete markets). The main improvement of acyclical employment is that the correlation between hours worked and labor productivity reduces substantially under complete markets, and dramatically under incomplete markets. Finally, considering countercyclical employment risk with incomplete markets (when the employment rate is procyclical) output fluctuations are about 20% larger than with constant employment, and fluctuations in hours worked relative to output fluctuations are 60% larger. The same comparison in the complete markets model reveals a smaller improvement: output fluctuations are about 13% larger and those of relative hours are 38% larger. The correlation between hours worked and labor productivity tends to worsen with procyclical employment under both market arrangements, but this correlation under incomplete markets is still 50% smaller than under perfect insurance. Thus, countercyclical employment risk and incomplete markets effectively help to explain the high labor input variance and the small correlation between market hours and average productivity shown in the real data. In RBC models where impulses come from a shock to technology, agents work harder in good times not only to increase current consumption but also to increase their stock of capital. In bad times agents work less because the opportunity cost of leisure and the return to capital are both small. The usual finding in calibrated economies is that labor supply fluctuates too little relative to the data. This translates into small fluctuations of hours worked and into a large correlation between hours and labor productivity (because, essentially, only the demand curve shifts over a stable supply curve). As I mentioned before, a strategy to address this problem has been to enlarge the set of impulses generating the business cycle fluctuations by introducing additional sources of uncertainty. The way this additional uncertainty is introduced in general represents a distortion of the margins in operation. For instance, in models with home-production both the market technology and the technology to produce at home are subject to productivity shocks that perturb the marginal rate of substitution between working in the market and working at home. Similarly, in models with public expenditure shocks or stochastic taxes on income, the shocks distort the marginal rate of substitution between public–private consumption and/or the intertemporal decision between leisure today and leisure tomorrow. Thus additional uncertainty results in larger shifts of labor supply, increasing the volatility of hours worked in the market. This produces a smaller correlation between market hours and labor productivity, because both labor demand and supply curves simultaneously shift. The mechanisms explored in this paper provide similar results and are based on precautionary savings: incomplete insurance against idiosyncratic shocks induces agents to accumulate larger amounts of wealth. 6 Thus in good times, when the wage rate and the return to capital are high, agents work harder to build a buffer stock of savings not only to prevent dramatic reductions in their consumption when bad aggregate states are realized, but also to insure against unemployment in the future. This larger stock of saving allows a substantial reduction in an individual’s labor supply when bad times come, and thus labor supply fluctuates more than when the idiosyncratic risks are perfectly insured. Of course, with incomplete markets agents become heterogeneous in their wealth levels, and this represents an important qualitative difference with respect to the usual representative agent abstraction. However, if heterogeneity were the only difference between the complete and incomplete markets models, its effects would tend to wash out in the aggregate. The model I study in this paper has also predictions with respect to the differences between complete and incomplete markets economies. This relates my work to the studies by Ríos-Rull (1994) and Díaz-Giménez (1997). In both of these studies, the model economies are subject to both aggregate and idiosyncratic uncertainty. Ríos-Rull studies an overlapping-generations economy where the incompleteness of markets only appears across generations. Although he finds large differences in behavior across some cohorts, the aggregate statistics of his model are not noticeably different from those of a representative-agent model. In contrast, Díaz-Giménez’ assumptions differ from mine in that his framework has exogenous prices and does not allow hours worked to vary. He finds rather important contrasts with the representative-agent model, as I do here. Thus, it is encouraging that his results seem to be due to the importance of idiosyncratic risks and not to the modeling “shortcuts” used. An important element behind the results in this paper, and those obtained by Díaz- Giménez, is the assumption that idiosyncratic risk is countercyclical. I assume that unemployment risk is worse in bad times. 7 That having risk to be countercyclical increases the “welfare cost” of the risk is not a new observation—it was first pointed out by Mankiw (1986)—and the point here is simply that it is quantitatively important for understanding the fluctuations of hours worked. The rest of the paper is organized as follows: Section 2 develops the model, Section 3 describes the calibration, Section 4 presents the statistical properties of the results and Section 5 contains some concluding remarks. An explanation about the solution method is relegated to Appendix A, along with some additional results and tables from a sensitivity analysis.