High wage workers and low wage firms: Negative assortative matching or limited mobility bias?

In the empirical literature on assortative matching using linked employer-employee data, unobserved worker quality appears to be negatively correlated with unobserved firm quality. We show that this can be caused by standard estimation error. We 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. We show that this bias is bigger the fewer movers there are in the data, which is 'limited mobility bias'. This result applies to any two-way (or higher) error components model that is estimated by fixed effects methods. We apply these bias corrections to a large German linked employer-employee data set. We find that, although the biases can be considerable, they are not sufficiently large to remove the negative correlation entirely.