Why do wages differ across identical workers? Why do firm characteristics matter? What is the source of the wage dispersion that firm and worker characteristics cannot explain? To address these basic three questions, we construct and estimate an equilibrium model of the labor market with worker and firm heterogeneous match productivities and on the job search. Search frictions are indeed a cause of market imperfection which in theory resolves the three questions altogether: Wages differ across firms because search frictions are a source of inefficiency allowing less efficient firms to survive. Search frictions leave market power to employers whereby more efficient firms extract higher rents. On the job search forces employers to grant their employees wage raises randomly over time so that wages differ across identical employer employee pairs.
In our model, unemployed workers search for a job and employees search for a better job. Workers differ in ability and firms differ in the marginal productivity of efficient labor. Workers and firms are imperfectly informed about the location of worker and firm types, which precludes optimal assignments as in standard marriage models. Yet, when two agents meet, both are immediately informed about each others types. Employers have all the bargaining power and offer unemployed workers their reservation wage. The equilibrium nonetheless differs from Diamonds monopsony model as search on the job allows employees to locate alternative employers, whom they can bring into Bertrand price competition with their current employer. This competition either results in a wage rise or in job mobility, the poaching employer paying the worker a wage which can even be less than his/her current wage if the option value of turning down the best offer that the current employer can make the marginal productivity6, in exchange of a greater potential best offer the marginal productivity at the new job is large enough. Our model thus not only generates tenure effects but also job to job mobility with wage cuts.
The main prediction of the model however pertains to the cross sectional distribution of earnings. We show that log earnings are the sum of a worker specific contribution to match productivity and a firm specific component that closely interacts with a statistical summary of the last wage mobility that the worker enjoyed and which typically characterizes the effect of frictions. The worker effect is independent of the firm and the friction effects because employers do not sort workers by their characteristics thanks to the assumption of perfect substitutability of worker abilities. But it happens that the firm effect and the friction effect are not independent as more productive firms have stronger market power and thus suffer less from the Bertrand competition.
We use a rich panel of matched employer employee data to estimate our model semi non parametrically. By that we mean that the econometric model is only parametric when the theory requires specific parameters (discount rates, job offer arrival rates, etc.), and is non parametric as far as the distributions of firm and worker heterogeneities, exogenous to the model, are concerned.
Although the three components of the steady state earnings distribution are not independent, we proceed to a decomposition of the variance of earnings into three separate components by allocating the total within firm variance of earnings that is not explained by worker heterogeneity to market frictions and all the between firm variance to the firm effect. This wage variance decomposition is undoubtedly the main empirical result of this paper. We find that the share of the total log wage variance explained by person effects lies around 40% for managers, and quickly drops as the observed skill level decreases. The contribution of the person effect is estimated 0 for the three lower skilled worker categories, out of seven categories. Either there is no unobserved ability differences for low skilled workers, or some unmodelled institution, like collective agreements or minimum wages, forbids the individualization of wages.
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