Labour Markets
Matching bias?

Most search models of unemployment involve `matching functions', which are really aggregate production functions describing the rate at which successful job matches form between stocks of unemployment and vacancies. This stylized assumption can be used to generate a theory of equilibrium unemployment whose extent and nature depend critically upon the returns to scale in the matching function. Many authors have presuppose constant returns, although increasing returns allow multiple equilibria. Estimates from US aggregate time-series data have typically found constant returns, but the underlying assumption that the US is a single labour market raises two problems: aggregation across separate markets may bias the estimate downward, and matching is certainly more effective for a labour market that is concentrated within a region.

In Discussion Paper No. 966, Melvyn Coles and Eric Smith test whether estimates of constant returns for the UK arise from a regional aggregation bias by estimating a matching function on a cross-section of city-level data on unemployment, vacancies and job placings for England and Wales. Their estimates are virtually identical to previous ones and also remarkably robust to different specifications. They also document the contributions of demographic and city-specific variables to show that matching rates are higher in towns with younger populations and lower in those with better-qualified populations. More significantly, wages and city size exhibit a positive relationship, which may reflect unobserved heterogeneity of workers if search in a thicker market yields better-quality matches rather than a faster matching rate. While the data imply constant returns on the observed matching relationship, it is well known that sorting effects can cause this to differ from the underlying contact technology. Increasing returns in the latter may therefore account for the higher wages observed in larger cities.

Cross-Section Estimation of the Matching Function: Evidence from England and Wales
Melvyn G Coles and Eric Smith

Discussion Paper No. 966, May 1994 (HR)