Overdetermined Estimating Equations with Applications to Panel Data

Panel data has important advantages over purely cross-sectional or time-series data in studying many economic problems, because it contains information about both the intertemporal dynamics and the individuality of the entities being investigated. A commonly used class of models for panel studies identifies the parameters of interest through an overdetermined system of estimating equations. Two important problems that arise in such models are the following: (1) It may not be clear {\it{a priori}} whether certain estimating equations are valid. (2) Some of the estimating equations may only "weakly" identify the parameters of interest, providing little information about these parameters and making inference based on conventional asymptotic theory misleading. A procedure based on empirical likelihood for choosing among possible estimators and selecting variables in this setting is developed. The advantages of the procedure over other approaches in the econometric literature are demonstrated through theoretical analysis and simulation studies. Related results on empirical likelihood, the generalized method of moments and generalized estimating equations are also presented.