The time trend in the matching function

We revisit the puzzling finding that labour market performance appears to deteriorate, as suggested by negative time trends in empirical matching functions. We investigate whether these trends simply arise from omitted variable bias. Concretely, we consider the omission of job seekers beyond the unemployed, the omission of inflows as opposed to stocks, and the failure to account for vacancy dynamics. We first build a model of all labour market flows and use it to construct series for these flows from aggregate data on the U.S. labour market. Using these series, we obtain a measure for employed and non-participating job seekers. When we thus include all job seekers, the estimated time trend remains unchanged. We similarly obtain measures for inflows into unemployment and vacancies. When these are included, the magnitude of the time trend is halved but remains significant. When we account for basic vacancy dynamics, the estimated time trend can be fully explained by omitted variable bias. As suggested by this result, we present evidence that empirical matching functions can be interpreted as versions of the law of motion for vacancies: the coefficients in matching functions coincide with the coefficients in the law of motion after correcting for omitted variable bias.