Equilibrium Wage Dispersion: Monopsony or Sorting?

Why are similar workers paid differently? I review and compare two lines of research that have recently witnessed great progress in addressing “unexplained” wage inequality: (i) worker unobserved heterogeneity in, and sorting by, human capital; (ii) firms’ monopsony power in labor markets characterized by job search frictions. Both lines share a view of wage differentials as an equilibrium phenomenon. Despite their profound conceptual and technical differences, they remain natural competitors in this investigation. Unlike other hypotheses, they provide natural and unifying explanations for job and worker flows, unemployment duration and incidence, job-to-job quits, and the shape of the wage distribution.

Aggregate worker reallocation and occupational mobility in the United States: 1971-2000

We investigate the evolution and the sources of aggregate employment reallocation in the United States in the 1971-2000 March files of the Current Population Survey. We focus on the annual flows of male workers across occupations at the Census 3-digit level, the finest disaggregation at which a moving worker changes career and relocates to an observationally different technology. We find that the total reallocation of employment across occupations has been strongly procyclical and sharply declining until the early 1990s, before remaining relatively constant in the last decade. To reveal the sources of these patterns, while correcting for possible worker selection into employment, we construct a synthetic panel based on birth cohorts, and estimate various models of worker occupational mobility. We obtain five main results. The cross-occupation dispersion in labor demand, as measured by an index of net employment reallocation, has a strong association with total worker mobility. The demographic composition of employment, more specifically the increasing average age and college attainment level, explains some of the vanishing size and procyclicality of worker flows. High unemployment weakens the effects of individual worker characteristics on their occupational mobility. Worker mobility has significant residual persistence over time, as predicted by job-matching theory. Finally, we detect important unobserved cohort-specific effects; in particular, later cohorts have increasingly low unexplained occupational mobility, which contributes considerably to the downward trend in total employment reallocation over the last three decades.

Occupational Mobility and the Business Cycle

Do workers sort more randomly across different job types when jobs are harder to find? To answer this question, we study the mobility of male workers among three-digit occupations in the matched files of the monthly Current Population Survey over the 1979-2004 period. We clean individual occupational transitions using the algorithm proposed by Moscarini and Thomsson (2008). We then construct a synthetic panel comprising annual birth cohorts, and we examine the respective roles of three potential determinants of career mobility: individual ex ante worker characteristics, both observable and unobservable, labor market prospects, and ex post job matching. We provide strong evidence that high unemployment somewhat offsets the role of individual worker considerations in the choice of changing career. Occupational mobility declines with age, family commitments and education, but when unemployment is high these negative effects are weaker, and reversed for college education. The cross-sectional dispersion of the monthly series of residuals is strongly countercyclical. As predicted by Moscarini (2001)’s frictional Roy model, the sorting of workers across occupations is noisier when unemployment is high. As predicted by job-matching theory, worker mobility has significant residual persistence over time. Finally, younger cohorts, among those in the sample for most of their working lives, exhibit increasingly low unexplained career mobility.occupational mobility, business cycle, synthetic cohorts

Rent Rigidity, Asymmetric Information, and Volatility Bounds in Labor Markets

Recent findings have revived interest in the link between real wage rigidity and employment fluctuations, in the context of frictional labor markets. The standard search and matching model fails to generate substantial labor market fluctuations if wages are set by Nash bargaining, while it can generate fluctuations in excess of what is observed if wages are completely rigid. This suggests that less severe rigidity may suffice. We study a weaker notion of real rigidity, which arises only in frictional labor markets, where the wage is the sum of the worker's opportunity cost (the value of unemployment) and a rent. With wage rigidity this sum is acyclical; we consider rent rigidity, where only the rent is acyclical. We offer two contributions. First, we derive upper bounds on labor market volatility that apply if the model of wage determination generates weakly procyclical worker rents, and that are attained by rent rigidity. Quantitatively, the bounds are tight: rent rigidity generates no more than a third of observed volatility, an outcome that is closer to Nash bargaining than to wage rigidity. Second, we show that the bounds apply to a sequence of famous solutions to the bargaining problem under asymmetric information: at best they generate rigid rents but not rigid wages.

Asymmetric Information and Employment Fluctuations

Shimer (2005) showed that a standard search and matching model of the labor market fails to generate fluctuations of unemployment and vacancies of the magnitude observed in US data in response to shocks to average labor productivity of plausible magnitude. He also suggested that wage determination through Nash bargaining may be the culprit. In this paper we pursue two objectives. First, we identify those properties of Nash bargaining that limit the ability of the model to generate a large response of unemployment and vacancies to a shock to average labor productivity. In light of these properties, cast in terms of a general model of wage determination, we reinterpret some of the specific solutions proposed so far to this problem. Second, we examine whether asymmetric information may help to violate those properties and to provide amplification. We assume that the firm has private information about the job's productivity, the worker about the amenity of the job, and aggregate labor productivity shocks do not change the distribution of private information around their mean. In this environment, we consider the monopoly (or monopsony) solution, namely a take-it-or-leave-it offer, and the constrained efficient allocation. We find that our key properties are satisfied for the first model essentially under all circumstances. They frequently (for commonly used specific distributions of beliefs) also apply to the constrained efficient allocationUnemployment, Vacancies, Business Cycle, Asymmetric Information

Large Employers Are More Cyclically Sensitive

We provide new evidence that large firms or establishments are more sensitive than small ones to business cycle conditions. Larger employers shed proportionally more jobs in recessions and create more of their new jobs late in expansions, both in gross and net terms. The differential growth rate of employment between large and small firms varies by about 5% over the business cycle. Omitting cyclical indicators may lead to conclude that, on average, these cyclical effects wash out and size does not predict subsequent growth (Gibrat's law). We employ a variety of measures of relative employment growth, employer size and classification by size. We revisit two statistical fallacies, the Regression and Reclas- sification biases, that can affect our results, and we show empirically that they are quantitatively modest given our focus on relative cyclical behavior. We exploit a va- riety of (mostly novel) U.S. datasets, both repeated cross-sections and job flows with employer longitudinal information, starting in the mid 1970’s and now spanning four business cycles. The pattern that we uncover is robust to different treatments of entry and exit of firms and establishments, and occurs within, not across broad industries, regions and states. Evidence on worker flows suggests that the pattern is driven at least in part by excess layoffs by large employers in and just after recessions, and by excess poaching by large employers late in expansions. We find the same pattern in similar datasets in four other countries, including full longitudinal censuses of employers from Denmark and Brazil. Finally, we sketch a simple firm-ladder model of turnover that can shed light on these facts, and that we analyze in detail in companion papers.business cycle , employment, firm size.

Stochastic Search Equilibrium

We analyze a stochastic equilibrium contract-posting model. Firms post employment contracts, wages contingent on all payoff-relevant states. Aggregate productivity is subject to persistent shocks. Both employed and unemployed workers search randomly for these contracts, and are free to quit at any time. An equilibrium of this contract-posting game is Rank-Preserving [RP] if larger firms offer a larger value to their workers in all states of the world. We show that every equilibrium is RP, and equilibrium is unique, if firms differ either only in their initial size, or also in their fixed idiosyncratic productivity but more productive firms are initially larger, in which case turnover is always efficient, as workers always move from less to more productive firms. The RP equilibrium stochastic dynamics of firm size provide an explanation for the empirical finding that large employers are more cyclically sensitive (Moscarini and Postel-Vinay, 2009). RP equilibrium computation is tractable, and we simulate calibrated examples.Equilibrium job search, Dynamic contracts, Stochastic dynamics

The Demand for Information: More Heat than Light

This paper produces a comprehensive theory of the value of Bayesian information and its static demand. Our key insight is to assume 'natural units' corresponding to the sample size of conditionally i.i.d. signals -- focusing on the smooth nearby model of the precision of an observation of a Brownian motion with uncertain drift. In a two state world, this produces the heat equation from physics, and leads to a tractable theory. We derive explicit formulas that harmonize the known small and large sample properties of information, and reveal some fundamental properties of demand: (a) Value 'non-concavity': The marginal value of information is initially zero; (b) The marginal value is convex/rising, concave/peaking, then convex/falling; (c) 'Lumpiness': As prices rise, demand suddenly chokes off (drops to 0); (d) The minimum information costs on average exceed 2.5% of the payoff stakes; (e) Information demand is hill-shaped in beliefs, highest when most uncertain; (f) Information demand is initially elastic at interior beliefs; (g) Demand elasticity is globally falling in price, and approaches 0 as prices vanish; and (h) The marginal value vanishes exponentially fast in price, yielding log demand. Our results are exact for the Brownian case, and approximately true for weak discrete informative signals. We prove this with a new Bayesian approximation result.Value of information, Non-concavity, Heat equation, Demand, Bayesian analysis