High wage workers and low wage firms : negative assortative matching or statistical artefact?

In the empirical literature on the estimation of firm and worker heterogeneity using linked employer-employee data, unobserved worker quality appears to be negatively correlated with unobserved firm quality. We investigate the possibility that this is simply caused by standard estimation error and develop formulae that show that the estimated correlation is biased downwards if there is true positive assortative matching and when any conditioning covariates are uncorrelated with the firm and worker fixed effects. This result applies to any two-way (or higher) error-components model estimated by fixed-effects methods. We apply these bias corrections to a large German linked employer-employee dataset. We find that although the biases can be considerable, they are not sufficiently large to remove the negative correlation entirely.