Directed search with heterogeneous firms: an experimental study

Directed search models labor markets where workers observe wages before deciding where they will apply. This paper tests this model for the case of heterogeneous firms in a laboratory experiment. The theory predicts that more productive firms offer higher wages and workers apply more often to these higher wages. In consequence, more productive firms are more likely to match and the market is more efficient than the prediction of an alternative model where search is random. The main results of the experiment are that average firms offer wages that are close to or a little lower than the theoretical predictions but highly variable and workers apply more often to high offers but not to the extent predicted. The markets are no more efficient than random search predicts, because of the variation in wage offers.     

Holdups and Efficiency with Search Frictions

A natural holdup problem arises in a market with search frictions: Firms have to make a range of investments before finding their employees, and larger investments translate into higher wages. In particular, when wages are determined by ex post bargaining, the equilibrium is always inefficient: Recognizing that capital-intensive production relations have to pay higher wages, firms reduce their investments. This can only be prevented by removing all the bargaining power from the workers, but this, in turn, depresses wages below their social product and creates excessive entry of firms. In contrast to this benchmark, we show that efficiency is achieved when firms post wages and workers can direct their search toward more attractive offers. This efficiency result generalizes to an environment with imperfect information where workers only observe a few of the equilibrium wage offers. We show that the underlying reason for efficiency is not wage posting per se, but the ability of workers to direct their search toward more capital-intensive jobs.     

Wage and Technology Dispersion

This paper explains why firms with identical opportunities may use different technologies and offer different wages. Our key assumption is that workers must engage in costly search in order to gather information about jobs (Stigler (1961)). In equilibrium, some firms adopt high fixed cost, high productivity technologies, offer high wages, and fill job openings quickly. Other firms adopt less capital-intensive technologies and offer low wages, hiring mostly uninformed workers. In equilibrium, the amount of wage dispersion leaves workers indifferent about whether to gather information, and the fraction of informed workers leaves firms indifferent about their wage and technology choice. We show that worker search, which would appear to be a rent-seeking activity in partial equilibrium, may be efficiency-enhancing in general equilibrium.     

Equilibrium Wage Dispersion,Firm Size,and Growth

This paper analyzes a model of equilibrium wage dynamics and wage dispersion across firms. It considers a labor market where firms set wages and workers use on-the-job search to look for better paid work. It analyzes a perfect equilibrium where each firm can change its wage paid at any time, and workers use optimal quit strategies. Firms trade off higher wages against a lower quit rate, and large firms (those with more employees) always pay higher wages than small firms. Non-steady-state dispersed price equilibria are also analyzed, which describe how wages vary as each firm and the industry as a whole grow over time. Journal of Economic Literature Classification Numbers: D43, J41.     

COMPETITIVE SEARCH,EFFICIENCY, AND MULTIWORKER FIRMS*

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.     

RESIDUAL WAGE DISPERSION WITH EFFICIENCY WAGES

This article extends a classic on‐the‐job search model of homogeneous workers and firms by introducing a shirking problem. Workers choose their effort levels and search on the job. Firms elicit effort through wages and monitoring; an inverse relationship between wages and monitoring rates is derived. Wages play a dual role by allocating labor supply and motivating employee effort. This gives rise to an equilibrium wage distribution that contrasts with existing literature. In particular, I show that a hump‐shaped and positively skewed wage distribution, as observed empirically, can be derived even when firms and workers are, respectively, identical.     

Directed search with multi-vacancy firms

I construct a directed search model in which firms decide whether to enter a market and how many positions to create. Within this framework, the number of firms and the size of each firm are determined endogenously, wages play an allocative role in the matching process, and the frictions inherent in this process derive from the equilibrium behavior of workers and firms. I characterize the (unique) equilibrium. Comparative statics generate testable implications for cross-sectional variation in matching efficiency, as well as the dynamic behavior of vacancies and unemployment. Moreover, allowing for ex-ante heterogeneity across firms, the model can easily and naturally generate the observed relationship between firm size, wages, profitability, and hiring.     

AN EQUILIBRIUM SEARCH MODEL WHEN FIRMS OBSERVE WORKERS' EMPLOYMENT STATUS*

This article considers an equilibrium search model, where firms post wages using information on workers' employment status. Earnings differentials between workers of different employment statuses are driven by firms' ability to discriminate workers' reservation wages. I study how these wage policies depend on firms' and workers' characteristics, and how these policies affect the wage distribution. The model delivers new predictions for the amount of wage dispersion that can be generated with search models and provides a better representation of the left tail of the wage distribution in the presence of a legal minimum wage than standard equilibrium search models.     

Unobserved Heterogeneity,Exit Rates,and Re‐Employment Wages

Exit rates from unemployment and re‐employment wages decline over a period of unemployment, after controlling for worker observable characteristics. We study the role of unobserved heterogeneity in an economy with asymmetric information and directed search. We show that the unique equilibrium is separating and that skilled workers have more job opportunities and higher wages. The composition of the unemployed varies with the duration of unemployment, so average exit rates and wages fall with time. The separating equilibrium relies on performance‐related pay schemes and the ability of firms to commit to renting an input that is complementary to worker skills.     

On-the-job search and strategic bargaining

This paper studies wage bargaining in a simple economy in which both employed and unemployed workers search for better jobs. The axiomatic Nash bargaining solution and standard strategic bargaining solutions are inapplicable because the set of feasible payoffs is nonconvex. I instead develop a strategic model of wage bargaining between a single worker and firm that is applicable to such an environment. I show that if workers and firms are homogeneous, there are market equilibria with a continuous wage distribution in which identical firms bargain to different wages, each of which is a subgame perfect equilibrium of the bargaining game. If firms are heterogeneous, I characterize market equilibria in which more productive firms pay higher wages. I compare the quantitative predictions of this model with Burdett and Mortensen's [1998. Wage differentials, employer size and unemployment. International Economic Review 39, 257-273.] wage posting model and argue that the bargaining model is theoretically more appealing along important dimensions.     

How does FDI affect domestic firms’ wages? theory and evidence from Vietnam

This paper explores the role of inward foreign direct investment (FDI) as a determinant of domestic firms’ wages, namely wage spillovers. We first construct a theoretical model to demonstrate that the presence of FDI firms affects domestic firms’ expected average wages via productivity spillovers and a cut-off capability. We then estimate FDI-induced wage spillovers by employing IV-GMM estimator with a five-year panel dataset of a growing service industry in Vietnam. Despite FDI firms on average pay 2.25 times that of domestic firms, they put a downward pressure on domestic firms’ wages. A one percent increase in FDI presence causes domestic firms to cut average wages by 2.03 percent. The estimations also find that firm-specific features are attributable to significant differences in their wages as well as FDI-linked wage spillovers.     

Wages and the Size of Firms in Dynamic Matching Models

This paper studies the joint distribution of wages and employment levels in simple matching models of job creation and destruction with costly search and firm-specific labor demand shocks. Existing evidence on the relationship between employer size, the mean and variance of employees' wages, and the character of gross job creation and destruction by continuing firms is broadly consistent with decreasing returns in firm-level production and hiring technologies. Journal of Economic Literature Classification Numbers: J31, J63.     

The Role of Expectation on Job Search and the Firm Size Effect on Wages

We formulate dynamic games which give a rationale to the firm size–wage effect that the sheer firm size increases wages. We postulate that past wages of large firms are known to new employees, while those of small firms are not. Large firms can credibly induce workers to expect high future wages and reduce turnover, while small firms have no choice but to be myopic and pay low wages. The equilibrium wage differential obtains under the same worker characteristics and production function. We provide empirical evidence that workers' expectations depend on firm size and affect wages as predicted by our model.     

Wage differentials, discrimination and efficiency

I analyze a large labor market where homogeneous firms post wages to direct the search of workers who differ in productivity. I show that the model has a unique equilibrium. The wage differential depends positively on the workers’ productivity differential only when the latter is large. When the productivity differential is small, high-productivity workers get a lower wage than low-productivity workers. This reverse wage differential remains even when the productivity differential shrinks to zero. However, the equilibrium is socially efficient. High-productivity workers always get the employment priority and higher expected wages than low-productivity workers. Although discrimination in terms of expected wages does not exist, conventional measures are likely to incorrectly find discrimination in the model.     

EFFICIENCY OF WAGE BARGAINING WITH ON-THE-JOB SEARCH

This article studies efficiency in a general class of search models where both unemployed and employed workers search for better jobs and can meet multiple firms simultaneously. Employers can respond to outside offers and wages are a weighted average of the productivities of the current employer and a credible poaching firm. I derive a condition that balances firms' bargaining power and their meeting externality. This condition ensures efficiency of both worker turnover and firm entry. Finally, the efficiency condition unifies and extends many of the results on the efficiency of equilibrium search models.     

Directed search with multiple job applications

We develop an equilibrium directed search model of the labor market where workers can simultaneously apply for multiple jobs. Our main theoretical contribution is to integrate the portfolio choice problem faced by workers into an equilibrium framework. All equilibria of our model exhibit wage dispersion. Consistent with stylized facts, the density of wages is decreasing and higher wage firms receive more applications per vacancy. Unlike most models of directed search, the equilibria are not constrained efficient.     

Wage posting without full commitment

Wage posting models of job search typically assume that firms can commit to paying workers exactly the posted wage. We relax this assumption and impose “downward” commitment; firms can commit only to paying at least their advertised wage. As each firm can only commit to pay at least their advertised wage, workers may demand that the firm pay more than the advertised wage. In labor markets with a finite number of workers and firms, the strategic interaction between firms makes it costly for firms to provide applicants the incentive not to demand wages in excess of the advertised wage. In equilibrium, firms may settle for running job auctions at the cost of losing control of the number of applicants that they can attract. When this strategic interaction between firms vanishes, workers never choose to demand more than the advertised wage.     

Pareto-improving firing costs?

We examine self-enforcing contracts between risk-averse workers and risk-neutral firms (the ‘invisible handshake’) in a labor market with search frictions. Employers promise as much wage-smoothing as they can, consistent with incentive conditions that ensure they will not renege during low-profitability times. Equilibrium is inefficient if these incentive constraints bind, with risky wages for workers and a risk premium that employers must pay. Mandatory firing costs can help, by making it easier for employers to promise credibly not to cut wages in low-profitability periods. We show that firing costs are more likely to be Pareto-improving if they are not severance payments.     

DIRECTED SEARCH AND FIRM SIZE*

Standard directed search models predict that larger firms pay lower wages than smaller firms, contrary to the data. This article proposes one way to obtain this positive size–wage differential in a directed search setting. I posit that there is an optimal size associated with a firm: A firm suffers a penalty by not operating at its optimal size. I show that if this penalty is sufficiently large the size–wage differential will be obtained. My model also gives a new way to look at the data because it highlights the importance of the distinction between intended and realized firm sizes.     

What did China’s labor contract law do to its private manufacturing firms?

Well-intended employment protection legislation may have adverse consequences. This paper uses Chinese firm-level data to assess the impacts of China’s Labor Contract Law, effective on January 1, 2008. My results show that, relative to public firms, private firms as a whole were negatively affected in terms of firm-level year-to-year employment changes. The law had negligible effects on employment and wages in firms with high wages. At the same time, employment fell and wages rose in firms with low wages. Moreover, firms who did not train workers intensively to acquire firm-specific skills had more job turnover than firms who did. Finally, I study how labor demand responded to the law along the extensive margin. For regions that experienced abrupt declines in labor mobility, possibly due to stricter labor regulation enforcement following the enactment of the Labor Contract Law, firm exit rose significantly, suggesting large incidence of mass layoff.