Endogeneity, time-varying coefficients, and incorrect vs. correct ways of specifying the error terms of econometric models - P. A. V. B. Swamy; Jatinder S. Mehta; I-Lok Chang (Econometrics, 2017)
Using the net effect of all relevant regressors omitted from a model to form its error term is incorrect because the coefficients and error term of such a model are non-unique. Non-unique coefficients cannot possess consistent estimators. Uniqueness can be achieved if; instead; one uses certain 'sufficient sets' of (relevant) regressors omitted from each model to represent the error term. In this case; the unique coefficient on any non-constant regressor takes the form of the sum of a bias-free component and omitted-regressor biases. Measurement-error bias can also be incorporated into this sum. We show that if our procedures are followed; accurate estimation of bias-free components is possible.
Keywords: C13; C51; 330; endogenous variable; exogenous variable; time-varying coefficient; unique coefficient and error term; accurate estimation of bias-free component