چرخه های کسب و کار، بیمه بیکاری و درجه بندی مدل های تطبیقی

This paper theoretically and empirically documents a puzzle that arises when an RBC economy with a job matching function is used to model unemployment. The standard model can generate sufficiently large cyclical fluctuations in unemployment, or a sufficiently small response of unemployment to labor market policies, but it cannot do both. Variable search and separation, finite UI benefit duration, efficiency wages, and capital all fail to resolve this puzzle. However, either sticky wages or match-specific productivity shocks can improve the model's performance by making the firm's flow of surplus more procyclical, which makes hiring more procyclical too.

A model of real business cycles with matching (RBCM) is a natural candidate for exploring many dynamic policy issues. Postulating a job matching function helps us give a coherent analysis of unemployment and its response to labor market policies (see Rogerson et al., 2005 for a recent survey of matching models). Moreover, Merz (1995), Andolfatto (1996), and den Haan et al. (2000) have claimed that endogenizing unemployment by means of a matching function improves the fit of real business cycle models. Thus it is tempting to use the RBCM framework to measure the costs of business cycles or the purported benefits of output stabilization, or to ask whether unemployment benefits should vary with the cycle, among other issues. These questions interest us. But when we tried to build a model to address them, we quickly encountered problems with the RBCM framework which existing literature had not pointed out. For our purposes, we needed a model consistent both with business cycle facts and with the effects of labor market policies. We found it easy to choose parameters to make the cyclical variation in unemployment as large in the model as it is in the data, or to make the response of unemployment to a change in the unemployment insurance (UI) benefit as small in the model as it is in the data. But no calibration permits the standard RBCM model to reproduce both these features: improving the fit over the cycle makes the fit worse with respect to policy, and vice versa. Similar problems occur with employment, vacancies, tightness, and the probability of job finding. These findings are related to a prominent recent controversy. Shimer, 2004 and Shimer, 2005 and Hall, 2003, Hall, 2005a and Hall, 2005b studied the cyclical dynamics of calibrated RBCM models and obtained fluctuations of unemployment and vacancies an order of magnitude smaller than those in the data.1 The reason is that in their models, productivity shocks cause strong wage movements that offset the incentive to vary hiring, thus eliminating most fluctuations in unemployment and vacancies. As a corollary, they also found that a model with sticky wages, instead of the more traditional Nash wage bargaining framework, does a better job of reproducing labor market fluctuations. While our observations are related to those of Shimer and Hall, we feel that an important element is missing in their argument, because their claim that unemployment is insufficiently variable in the RBCM model is not true in general. In fact, it is specific to their particular calibration: Shimer and Hall both assume that workers’ cost of working is low compared to their productivity, so that the match surplus is large. When this restriction is removed, it is easy to make unemployment volatile. If the surplus is small on average, then a small fall in labor productivity may eat up a large proportion of the surplus, so that realistic productivity fluctuations generate arbitrarily high variability in vacancies, unemployment, and tightness. Stated differently, if the cost of working is acyclical, and is on average only slightly less than after-tax labor productivity, then wages will be relatively rigid and profits and hiring incentives will be strongly procyclical. The observation that employment is volatile in the RBCM model if the surplus is small has been made again more recently by Hagedorn and Manovskii (2006) in a sharp critique of Shimer and Hall's claims. However, our main point here is that such a calibration only creates another problem. The hiring margin is affected by productivity, taxes, and workers’ disutility costs and opportunity costs of labor. If we blow up the impact of productivity by making the surplus small on average, then hiring becomes extremely sensitive to taxes and labor market policies too. We demonstrate analytically in a simple benchmark RBCM model that the responses of unemployment to productivity shocks and to policy variables cannot be simultaneously reconciled with the data. We go on to show numerically that this problem remains when the model is extended in several ways not considered by Shimer and Hall, and is also present but undiagnosed in previous papers. The recent survey of Hornstein et al. (2005a) concludes, like us, that solving the unemployment fluctuation problem by making the surplus small is likely to exaggerate the model's policy effects. However, while cyclical labor market dynamics have been extensively documented in recent papers, the policy effects that underlie the other half of our argument are more controversial. Therefore, we also perform a detailed robustness analysis of the best-known cross-country policy regressions. We conclude that the effects of UI benefits and taxes are quite robustly identified by both cross-sectional and time series evidence, and are approximately equal, as our model implies. Our coefficients are around twice as large as those of Nickell and Layard (1999), and imply that benefits and taxes have economically important effects, but are still much too small to be reconciled with the cyclical volatility of unemployment in the standard RBCM model. Finally, our paper also discusses two possible solutions of our ‘puzzle’. Shimer (2004) and Hall, 2005a and Hall, 2005b argument that sticky wages help by making firms’ share of surplus more procyclical also helps resolve our puzzle, as long as wages eventually adjust to long run policy changes. However, we also identify a real mechanism that can reconcile the cyclical and policy-related variation in unemployment. Embodied (that is, match-specific) technological change also increases the cyclicality of the match surplus, especially for the firm, without changing long run policy impacts. While we focus on one particular puzzle for the RBCM model, and propose one new solution, several other recent papers make related points. Other empirical criticisms of the RBCM model include Cole and Rogerson (1999), Fujita (2004), and Ravn (2006). Other papers offering ways of improving the model's fit include Mortensen and Nagypál (2006), Silva and Toledo (2005), and Hall and Milgrom (2005). The next section states our general model. In Section 3, we analytically calculate the relationship between the cyclical variability of unemployment and the effects of UI on unemployment in a tractable special case. In Section 4, we briefly discuss cyclical stylized facts and then carefully study the robustness of cross-country evidence on policy effects, concluding that these two sets of evidence jointly reject our baseline model. Section 5 shows that neither variable search, variable separation, finite UI benefit duration, nor efficiency wages suffice to make the model fit the data, but that sticky wages or match-specific productivity shocks might. In Section 6, we discuss some earlier RBCM papers that are not nested in our analysis (mainly because they allow for physical capital), and show that they are subject to the same critique. Section 7 concludes.

A model of real business cycles and matching implies that job creation depends on the surplus available to the matched pair. Procyclical employment fluctuations occur if surplus rises in booms, and raising UI benefits drives down employment by decreasing the surplus. The standard RBCM model implies a close relationship between these two aspects of employment variability, which is strongly at odds with data. To fit business cycle data, the surplus must be small enough so that productivity shocks have a big effect on vacancies; but to reproduce the observed effects of policies, the surplus must be large enough so that UI benefits have a small effect on vacancies. We have shown analytically that these two requirements cannot be reconciled in a baseline version of the model. We have shown numerically that this result is robust to endogenous search, endogenous separation, finite benefit duration, and efficiency wages; we have also argued that capital, variable benefits, and variable hiring costs are unlikely to resolve the puzzle; and we have argued that the HP filter is not crucial for our results. Match-embodied technological change can help reconcile these two implications of the model (see also Hornstein et al., 2005a), because it makes the surplus accruing to the firm substantially more procyclical, so that hiring, unemployment, and the worker's job-finding probability all fluctuate more. Sticky wages have a similar effect on the firm's surplus, so they also help increase cyclical variability without exaggerating the impact of labor market policy (see also Shimer, 2004, Hall, 2005b, Gertler and Trigari, 2006 and Menzio, 2005). Our findings suggest that modeling labor market fluctuations by calibrating a very small match surplus, as Hagedorn and Manovskii (2006) advocate, is unhelpful because it is inconsistent with robust observations about labor market policy effects. There is endless scope for debating cross-country regressions, but we find that the small surplus calibration needs to stray far from any available evidence on policy effects in order to reproduce cyclical fluctuations. While sticky wages or embodied productivity shocks may prove to be fruitful explanations of labor market dynamics, many other ways of improving the fit of the matching model have also been suggested recently, including alternative specifications of the bargaining game, hiring and training costs, and shocks to job destruction (Hall and Milgrom, 2005, Silva and Toledo, 2005 and Mortensen and Nagypál, 2006). In the long run we expect economists to learn a lot about labor markets and business cycles by asking which of these alternatives are consistent with a wide range of empirical facts. More generally, we believe policy studies may often provide useful tests for business cycle models: measuring the impact of observable policy shocks may help impose discipline on business cycle models where shocks might otherwise have to be treated as unobservables. This sort of discipline seems especially important if the models in question are intended for use in policy analysis.