On Omitted Variables, Proxies and Unobserved Effects in Analysis of Administrative Labour Market Data

In virtually any empirical regression analysis, there is limited availability of observed variables and limited prior knowledge on which variables belong to the model. This paper provides a unified framework that nests various approaches aiming at reducing omitted variable bias in linear regression analysis. We work out the mechanisms driving the size of the bias and how various models with different regressor sets or unobserved effects relate. Without imposing restrictions on the relationship and role of the variables, it is, however, not possible to derive model rankings that are valid in every application.
In our applications, we apply the various models to German linked administrative labour market data. We find evidence for sizeable omitted variable bias in a wage regression, while a labour market transition model appears to be less affected. Additional survey variables contribute only to the wage model, while the use of work history variables and panel models lead to changes in coefficients in the two models. Overall, panel data models with a restricted regressor set are found to control for more unobserved information than cross-sectional analysis with an extended variable set.