Econometric Analysis of Panel Data : [PDF Download]

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“Phillips & Hansen (1990) proposed a semi-parametric correction to the OLS estimator which eliminates the second-order bias induced by the endogeneity of the regressors. The same principle can also be applied to the panel OLS estimator that we have explored in the previous subsection.

The key difference in constructing our estimator for the panel data case will be to account for the heterogeneity that is present in the fixed effects as well as in the short-run dynamics. These features lead us to modify the form of the standard single equation fully modified OLS estimator.

We will also find that the presence of fixed effects has the potential to alter the asymptotic distributions in a nontrivial manner. The following proposition establishes an important preliminary result which facilitates intuition for the role of heterogeneity and the consequences of dealing with both temporal and cross-sectional dimensions for fully modified OLS estimators.”

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