It is convenient to think about the coexistence of unemployed workers alongside unfilled jobs in terms of heterogeneities and imperfect information. In the presence of heterogeneous workers and jobs, some workers are offered employment because they are sufficiently profitable; others remain unemployed because they are insufficiently profitable. These differences may arise since workers differ in terms of their productivities at various jobs, their costs of being identified as searching and employable, their relocation and training costs, etc. In the same vein, some job offers are accepted because they offer sufficient remuneration; others are rejected because they are not sufficiently remunerative. These differences may exist because jobs differ in terms of job productivities associated with various workers, costs of being identified as vacant, etc.
In the presence of imperfect information, jobs that are in fact heterogeneous may look ho- mogeneous to a searching worker, who then may choose randomly among these jobs. Similarly, workers that are in fact heterogeneous may look homogeneous to a searching firm, leading the firm to make a random choice among these workers. (In addition, of course, there is also random choice among jobs and workers that are in fact homogeneous.)
The matching function is an analytic device that is meant to capture both the heterogeneities and the imperfect information. As aptly noted by Petrongolo and Pissarides (2001, p. 390): “The attraction of the matching function is that it enables the modeling of frictions in otherwise conventional models, with a minimum of added complexity. Frictions derive from information imperfections about potential trading partners, heterogeneities..."
The heterogeneities are particularly important in accounting for unemployed workers along-
173The “standard” calibration of the model excludes rigid wages and small surplus calibrations. Although the
rigid wage version of the search and matching model can also generate higher volatilities (Hall, 2005), it implies that counterfactual prediction that wages are acyclical. Thus we do not make this assumption here. We also do not rely on Hagedorn and Manvoskii’s (2008) small surplus calibration, in which the average unemployed worker is basically indifferent between working and not working. In the calibrated version of our model, the current period’s utility of an average unemployed is only about 60% of the utility of an employed.
174The search and matching model with exogenous job destruction actually has a strong negative correlation
between the job finding rate and the unemployment (see Shimer, 2005). However, there is an intensive debate in the literature whether separations are exogenous or not (see, for example, Hall, 2006, and Fujita and Ramey, 2009, for opposing views). Separations are endogenous in our analysis.
side unfilled jobs. In practice, workers are rarely indistinguishable in terms of all the character- istics relevant for job acquisition and thus firms are rarely in a position of choosing randomly among interchangeable workers. Similarly, workers are rarely in a position of choosing randomly among interchangeable jobs. Often firms and workers draw on a store of prior information, so that their objects of choice are heterogeneous. Of course firms and workers also assemble op- portunities blindly — as when they place and read advertisements — but these activities are usually far less costly than the subsequent ones of choosing among heterogeneous options. So if the matching function is to capture the costly process of labour market choice "without the need to make the heterogeneities ... explicit" (Pissarides, 2000, p.4), then it is important that it be able to capture matching behaviour among heterogeneous agents.
This chapter focuses on these heterogeneities. We examine whether a stable matching function can reproduce the behaviour of optimizing agents among heterogeneous options. We do not dispute that a matching function may be appropriate in describing the outcome of choices among options that look homogeneous, due to imperfect information. What is at issue is whether it can describe heterogeneous choice. On this account, we present choice-theoretic models of hiring and job acceptance, as well as firing and quits, for heterogeneous workers and jobs.175
Shimer (2007, p. 1074) makes an insightful distinction between search and mismatch: “Ac- cording to search theory, unemployed workers have left their old jobs and are actively searching for a new employer. In contrast, this dynamic model of mismatch emphasizes that unemployed workers are attached to an occupation and a geographic location in which jobs are currently scarce. Mismatch is a theory of former steel workers remaining near a closed plant in the hope that it reopens. Search ... is a theory of former steel workers moving to a new city to look for positions as nurses.” While this distinction is undoubtedly important, it is worth emphasiz- ing that adjustment costs are responsible for both mismatch and search. The reason that the former steel workers remain near the closed plant is that the cost of adjusting to another job (net of the expected benefits) is greater than the cost of waiting for the plant to open (again net of the expected benefits). Moreover, if the former steel workers can’t find jobs as nurses despite the existence of nursing vacancies, then the reason is that either it was too costly for the workers to find the available vacancies or it was too costly for the employers to find the available workers. So, under both mismatch and search, unemployed workers and vacancies coexist because it is too costly to fill the vacancies with the unemployed workers. Otherwise, obviously, the match would have been made. Under mismatch, the costs are frequently large and persistent, whereas under search they are often small and transient; but the fact remains that adjustment costs are responsible for the friction in both cases.
We investigate the role of these adjustment costs as a source of labour market frictions. The adjustment costs of course come in many guises. Some are costs of geographic and occupational mobility (as in Shimer’s analysis); others are costs of obtaining the relevant information (the
175In the Appendix 5.A.1, we present a model of both heterogeneous choice as well as choice among agents who
appear homogeneous, combining our analysis (dealing with heterogeneities) with a matching function analysis (dealing with random choice among homogeneous agents).
standard search costs, e.g. costs of advertising, monitoring, screening).
While various other authors have modeled the matching process without resorting to a matching function (e.g. Hall, 1977, Lagos, 2000, Shimer, 2007, and others), our analysis explic- itly focuses on two-sided search (i.e. search by both workers and firms at the same time) and an optimizing framework that replaces the matching function. Due to our focus on heterogeneities and adjustment costs, it is not necessary for our analysis to make a sharp distinction between search and mismatch. Our analysis is meant to cover both phenomena, depending on how we choose to interpret the nature of the heterogeneities and adjustment costs. In this context, as noted above, we show that our analysis can explain various stylized facts that are not accounted for in the convential search and matching literature.