Minimum wages and compliance in markets with search frictions

We propose a framework to estimate the extent of compliance to minimum wage laws. Cases of non-compliance arise whenever the law enforcement is imperfect, and the share of the match rent offered by a firm to a worker falls below the minimum wage and above the worker’s reservation wage. This can be the case when the productivity of some job matches is lower than the minimum wage (but higher than both parties’ reservation values) or when employers’ monopsonistic power is relatively high. Data drawn from the National Longitudinal Survey of Youths provide evidence of imperfect compliance to the minimum wage in the U.S. In particular, 45% of white males with high school education are found to be working at least one month during the first 18 years since graduation in a job paying less than the federal minimum wage. Of course, observed wages below the minimum wage can result from both non-compliance and measurement error (as well as from some few well-identified cases of exemptions). But while measurement error should apply throughout the wage distribution, non-compliance by definition applies to wages below the minimum wage. This distinction will be the basis of our identification strategy. We will estimate a structural search model with measurement error in observed wages and imperfect compliance to the minimum wage. The extent of compliance will be identified by the truncation of the wage offer distribution at the minimum wage. Our job search model has three main ingredients: search on-the-job; wage growth on-the-job; and minimum wages. Individuals gradually move from unemployment into jobs when they receive a wage offer that at least matches their reservation wage. We allow for job offers below the minimum wage, whose arrival rate is α times the arrival rate of job offers above the minimum wage, with 0≤α≤1. In an economy without minimum wages α=1, and the resulting wage offer distribution is continuous at the minimum wage. With full minimum wage compliance α=0, and the wage distribution is truncated at the minimum wage. For values of α between 0 and 1 the wage distribution is not truncated, but discontinuous at the minimum wage. The rest of the model follows the standard job-search framework. Once employed, individuals enjoy some wage growth on-the-job, and receive offers from potential employers, which are accepted if they at least match the wage in their current job. Individuals lose their jobs and enter unemployment according to an exogenous job destruction process. This model will be estimated on NLSY data, using simulated GMM. Estimation allows for unobserved heterogeneity in the arrival rate of job offers and measurement error in observed wages.