In the labour market many things happen simultaneously: a large amount of job seekers find employment while, at the same time, many employed workers lose their jobs (either through voluntary quits or through layoffs). Some firms grow in size, while others shrink, and many workers move from one employer to another. Many of these flows correlate with each other and vary over the business cycle: for example, job separations increase rapidly in the early parts of a recession, and job switches are more common in booms. This paper develops a model economy which allows us to explain and analyse many of these empirical regularities.
The model is of the “search and matching” class, which means that vacancy posting firms match with job applicants stochastically. Relative to the canonical search and matching model developed by Mortensen and Pissarides (1994) a number of additional ingredients are added: (i) firms at random receive shocks to their productivity, which means that sometimes they wish to grow in size (after a positive shock) and sometimes they wish to decrease in size (after a negative shock), (ii) workers can search for new jobs both when they are unemployed, but also when they are employed, which is how the model generates employer switches, and (iii) firms have decreasing returns to scale, which means that, for a given baseline productivity, a firm’s marginal output gain from adding an additional worker falls as the firm grows in size. Despite the addition of these extra mechanisms making the model difficult to solve, the paper shows how it is possible to derive an analytical solution to the model equilibrium.
Several new insights can be drawn from the model. One particularly interesting finding is that the interplay between the firms’ decreasing returns to scale and workers searching for new jobs while employed means that firms may not grow to the societally efficient size (the one that maximizes overall production). The intuition behind this result is as follows: in the efficient outcome, the marginal productivity of each firm should be the same. Were this not the case society could produce more by moving a worker from a firm with low marginal productivity to one with high. Since firms’ marginal productivities are decreasing in their size, this means that the most productive firms should be the largest. However, when workers are allowed to search for new jobs while working, firms may not want to grow to their societally efficient size. Instead they may choose to employ fewer workers, who they pay a slightly higher wage in order to reduce the risk of them leaving, as workers leaving mean that firms have to undertake another round of costly recruitment. Indeed, this mechanism is shown to be active in the equilibrium solution to the model, with firms allowing their marginal productivities to disperse over an interval and only gradually revert to a common value – an outcome which is shown not to occur in a model without the combination of decreasing returns to scale and workers looking to switch jobs while employed. This means that the model generates a misallocation of workers to firms without adding any additional assumptions or market imperfections apart from the search frictions, which is a novel finding.
The paper also tests whether the model can be used to explain some of the key cross-sectional data regularities that labour economists have established. A parameterized version of the model is shown to be able to replicate a host of empirical facts; in particular the model can match the observed negative correlation between wages and quit rates, and the observed rent-sharing rate between firms and workers following an innovation (an idiosyncratic productivity boost). It also replicates observed worker flows at the firm level, with expanding firms not only hiring more workers, but also laying off fewer workers and facing fewer worker quits. Finally the paper looks at aggregate shocks (economy-wide booms and busts), and finds that the model economy matches the data well over the business cycle. In particular, it can explain 60% of the observed volatility of unemployment over the business cycle, a moment which is famously difficult for search and matching models to match (Shimer, 2005). The model also implies a level of pro-cyclicality of wages that matches empirical observations, predicts a spike in job separations at the onset of a recession in line with the data, and matches well the positive correlation between the job switching rate and economic booms.
Mortensen, Dale T., and Christopher A. Pissarides. 1994. “Job creation and job destruction in the theory of unemployment.” Review of Economic Studies 61(3): 397- 41
Shimer, Robert. 2005. “The Cyclical Behavior of Equilibrium Unemployment and Vacancies.” American Economic Review 95(1): 25-49