William B. Hawkins’s research while affiliated with Yeshiva University and other places

We present a generalization of the standard random‐search model of unemployment in which firms hire multiple workers and in which the hiring process is time‐consuming as well as costly. We follow Stole and Zwiebel (1996a, 1996b) and assume that wages are determined by continuous bargaining between the firm and its employees. The model generates a nontrivial dispersion of firm sizes; when firms' production technologies exhibit decreasing returns to labor, it also generates wage dispersion, even when all firms and all workers are ex ante identical. We characterize the steady‐state equilibrium and show that, with a suitably chosen distribution of ex ante heterogeneity across firms, it is consistent with several important stylized facts about the joint distribution of firm size, firm growth, and wages in the U.S. economy. We also conduct a numerical investigation of the out‐of‐steady‐state dynamics of our model. We find that the responses of unemployment and of the vacancy‐to‐unemployment ratio to a shock to labor productivity can be somewhat more persistent than in the Mortensen–Pissarides benchmark where each firm employs a single worker.

Shimer (Mismatch, American Economic Review 97, 1074–1101 [2007]) introduced a model of mismatch in which limited mobility of vacant jobs and unemployed workers provides a microfoundation for their coexistence in equilibrium. He assumed that the short side of a local labor market receives all the gains from trade. In this note I show that modifying this assumption on wage-setting can deliver more reasonable predictions for wages at the level of the local market and in the aggregate.

I study competitive search equilibrium in an environment where firms operate a decreasing‐returns production technology and hire multiple workers simultaneously. Firms post wages, possibly several of them. The equilibrium can feature wage dispersion even though all firms and workers are ex ante identical. Unlike the benchmark where firms hire a single worker, hiring is constrained inefficient. Efficiency requires that firms commit to the number of hires, pay all applicants, or pay wages that depend on the number of applicants. Under wage‐posting, the inefficiency is highest at intermediate levels of labor market tightness.

We study the effects of financial market incompleteness on occupational mobility. Incomplete insurance not only generates an increase in consumption volatility, but also reduces occupational mobility. The correlation of labor supply with occupational productivity is lower than under complete markets. Low-asset workers remain in low-productivity occupations even when the expected value of switching is positive. Negative occupational productivity shocks therefore have larger effects on such workers' future earnings than they would for better insured workers. In a calibrated model, we find that the welfare costs of market incompleteness can be as large as 12 percent of lifetime consumption.

I study bargaining between workers and large firms when commitment to long-term contracts is feasible. The marginal surplus associated with a match is split in a pre-determined ratio, analogously to generalized Nash bargaining. Commitment avoids the over-hiring inefficiency identified by Stole and Zwiebel (1996a,b) and Smith (1999). However, even under the Hosios (1990) condition, the equilibrium is still not constrained efficient since large firms search too intensively relative to small firms. If workers can direct their search to firms by size, or if firms can hire workers instantaneously at constant marginal cost, the equilibrium is constrained efficient if the Hosios condition applies. The pattern of growth rates of firms by size can be used to identify how firms bargain with workers. JEL Codes: E24, J31, J64.

Benchmark labor search models abstract from the large cross-sectional heterogeneity in firm size and employment growth distributions present in US data; these models have also struggled to generate empirically-plausible amplification and propagation of productivity shocks. Does accounting for firm heterogeneity help in solving this problem? Recent work by several authors has argued that the slow adjustment of the firm size distribution following a shock to the economy might help generate more persistent or more volatile responses of key endogenous variables such as vacancies or unemployment than in the Mortensen-Pissarides benchmark. I study a model that allows for very rich microeconomic heterogeneity of firm productivity and productivity growth. I show that despite the ability of the model to replicate key cross-sectional features of the employment and employment growth distribution across firms, the equilibrium behavior of aggregate variables such as unemployment and the vacancy-to-unemployment ratio is practically indistinguishable from that in an appropriately-calibrated Mortensen-Pissarides model. In particular, unemployment is only volatile if the surplus from employment is small, and the vacancy-to-unemployment ratio is a jump variable. Despite allowing for both transitory and permanent idiosyncratic heterogeneity in firm productivity as well as for aggregate productivity shocks, the model is tractable enough to be solved without the need for approximate aggregation solution methods. for useful discussions and seminar participants at the Richmond Fed, Rochester, and Yale for helpful comments. The fault for the remaining imperfections is, of course, my own.

We present a generalization of the standard Diamond-Mortensen-Pissaridessearch model of unemployment in which there is both an intensive and extensive margin of employment creation. In our model, each firm can invest to gain access to a production technology with diminishing returns to labor and then post vacancies in order to recruit workers. Entry by new firms corresponds to the extensive margin of employment creation, while job creation by existing firms captures the intensive margin. As in the baseline Diamond-Mortensen- Pissarides search model and theories of the firm developed by Stole and Zwiebel (1996a,b) and Wolinsky (2000), wages are determined by continuous bargaining between the firm and its employees. We characterize the steady-state equilibrium in this class of models and dis- cuss the implications of various different types of shocks on the equilibrium unemployment rate.

For the equilibrium of a frictional labor market to be efficient, firms and workers must face the socially optimal incentives for entry and hiring decisions. One important approach to modeling search frictions in decentralized labor markets is competitive search equilibrium, in which workers direct their search towards wages that firms commit to pay them if hired. In an environment in which each firm wishes to hire precisely one worker, it is known that the competitive search equilibrium is efficient. In this paper, I show that if firms wish to employ more than one worker, then hiring will not generally be efficient if firms can post only a single wage. Efficiency requi res that firms be able to commit to hire a fixed number of workers at a given wage, to pay all applicants, or to make wages contingent on the number of applicants. I show that if firms post only a wage, the amount of inefficiency is highest at intermediate levels of labor market tightness. Efficiency under wage posting is restored in a dynamic model if the duration for which firms commit to posted contracts becomes small. The model also provides a framework for investigating the interaction of wages, labor market conditions, within- firm wage policies, and the growth of firms.

We present a generalization of the standard random-search model of unemployment in which firms hire multiple workers and in which the hiring process is time-consuming as well as costly. We follow Stole and Zwiebel (1996a,b) and assume that wages are determined by continuous bargaining between the firm and its employees. This gener-ates a non-trivial dispersion of firm sizes; when firms' production technologies exhibit decreasing returns to labor, it also generates wage dispersion, even though all firms and all workers are ex ante identical. We characterize the steady-state equilibrium of the model; some important special cases are characterized in closed form. We also characterize the out-of-steady state dynamics of employment and wages in response to productivity shocks. Firms can respond to shocks on both an intensive margin (a change in the intensity of vacancy posting of incumbent firms) and extensive margin (a change in the number of active firms); we show that both margins, as well as whether there are decreasing returns to labor at the firm level, are important for the qualitative behavior of the unemployment rate and of the distribution of employment and wages across firms. When there are decreasing returns to labor and free entry of firms, the responses of unemployment and of the vacancy to unemployment ratio to a shock to labor productivity are significantly more persistent than in the Mortensen-Pissarides benchmark. The persistence is caused by a novel mechanism arising from an inter-action of two key elements of our model: new entrant firms are small for some time because hiring is time-consuming and they pay high wages because of bargaining; this drives up wages for other firms and slows down job creation.

Shimer (2007) introduced a model of mismatch, in which limited mobility of vacant jobs and unemployed workers provides a microfoundation for their coexistence in equilibrium. Shimer assumed that the short side of a local labor market receives all the gains from trade, and argues that the model helps to explain the volatility of unemployment and the vacancy-unemployment ratio in response to productivity shocks. I show that the assumption on wages is essential for this conclusion by considering alternative assumptions. When wages are de-termined according to the Shapley (1953b) value, they depend more smoothly on local labor market conditions, but unemployment and the vacancy-unemployment ratio are even more volatile. However, in both cases amplification relative to the Mortensen-Pissarides benchmark arises only because the implied process for wages is more volatile. JEL Codes: E24, J41, J63, J64.