When and How Much Do Fixed Effects Matter?

The number of possible specifications of the fixed effects, including interacting ones, grows exponentially when the number of panel dimensions increases. The relevance of the exact fixed effects specification is unclear even when one is only concern with the parameter estimates of the covariates. With growing dimensions it is less and less likely that the fixed effects of a model reflect the true data generating process. In this chapter we investigate to what extent the misspecification of the fixed effects affects the unbiasedness and consistency of the least square dummy variable and Within estimators. We find the surprising result that in many cases this does not really matter and even with a misspecified model we can get an unbiased and consistent estimator for the parameters of explanatory variables, as long as some not too restrictive conditions hold. In addition, we also explore the possibility of using partially penalized regression, when shrinkage is only applied to the fixed effects, while the parameters of the other covariates are not part of the regularization, to select the right fixed effects specification.