Testing Endogeneity, Convexity and Congestion in a Matching Function: Evidence from Finland

摘要

This study contributes to the literature on the efficiency of regional labor markets using matching function to model labor markets and nonparametric methods DEA and FDH to measure efficiency of those markets. DEA has been the most popular method in empirical studies measuring efficiency for an industry and there is also a literature applying DEA to study the efficiency of labor markets. However, this literature neglects two problems important for consistent estimation of a matching function: the possible endogeneity of inputs and non-convexity of the production set. Endogeneity manifests as correlation between inputs and efficiencies. In this paper, we first analyze whether the inputs of the matching function or unemployed jobseekers and open vacancies are exogenous. As our results do not reject exogeneity, we continue treating these inputs exogenous. Next, we evaluate convexity of production set. Testing convexity is an important prerequisite for the use of DEA, because DEA assumes convexity and supplies consistent efficiencies only when the production set is convex. However, convexity is rarely assessed when DEA is applied. In this paper, we evaluate convexity of the production set of the matching function. We use several tests including ones that are based on recently proposed central limit theorems for moments of DEA and FDH estimators. Out of ten tests performed, six ones reject convexity while four ones do not. The tests leave us with a strong belief in non-convexity, and this directs us to apply FDH instead of DEA in the sequel, when we study congestion of inputs. We find strong congestion of open vacancies concerning Helsinki travel-to-work area for several years. In 2017 the loss of matches due to congestion was more than 20 000, amounting to 2.5% of the labor force in Helsinki region, 0.8% in the whole country. Our research with data on 113 travel-to-work areas and 15 public employment (TE-) offices in 2007-19 in Finland, shows huge differences in labor market situation between regions, especially Helsinki and the rest of the country, calling attention from the decision-makers both in firms and government. Also, our study emphasizes the need to pretest data for exogeneity and convexity before applying DEA.