The Anatomy of Sorting—Evidence From Danish Data

In this paper, we formulate and estimate a flexible model of job mobility and wages with two-sided heterogeneity. The analysis extends the finite mixture approach of Bonhomme, Lamadon, and Manresa (2019) and Abowd, McKinney, and Schmutte (2019) to develop a new Classification Expectation-Maximization algorithm that ensures both worker and firm latent-type identification using wage and mobility variations in the data. Workers receive job offers in worker-type segmented labor markets. Offers are accepted according to a logit form that compares the value of the current job with that of the new job. In combination with flexibly estimated layoff and job finding rates, the analysis quantifies the four different sources of sorting: job preferences, segmentation, layoffs, and job finding. Job preferences are identified through job-to-job moves in a revealed preference argument. They are in the model structurally independent of the identified job wages, possibly as a reflection of the presence of amenities. We find evidence of a strong pecuniary motive in job preferences. While the correlation between preferences and current job wages is positive, the net present value of the future earnings stream given the current job correlates much more strongly with preferences for it. This is more so for short- than long-tenure workers. In the analysis, we distinguish between type sorting and wage sorting. Type sorting is quantified by means of the mutual information index. Wage sorting is captured through correlation between identified wage types. While layoffs are less important than the other channels, we find all channels to contribute substantially to sorting. As workers age, job arrival processes are the key determinant of wage sorting, whereas the role of job preferences dictate type sorting. Over the life cycle, job preferences intensify, type sorting increases, and pecuniary considerations wane.