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Alternative Approaches to the Econometrics of Panel Data

Abstract In this chapter we show that all the known estimators of the coefficients of econometric models are inconsistent if their coefficients and error terms are not unique. In their stead, we present models having unique coefficients and error terms, with specific applicability to the analyses of panel data sets. We show that the coefficient on an included nonconstant regressor of a model with unique coefficients and error term is the sum of bias-free and omitted-regressor bias components. This sum, when multiplied by the negative ratio of the measurement error to the observed regressor, provides a measurement-error bias component of the coefficient. This result is important because to measure the direct causal effect of an included nonconstant regressor of a model on its dependent variable, one needs the bias-free component of the coefficient on the regressor. A proof of the uniqueness of the coefficients and error term of a stochastic law is given in Appendix A, and conditions for the consistency of certain estimators of the coefficients of a stochastic law are given in Appendix B.