Abstract
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.
Highlights
The quality of econometric practice is reflected in the assumptions made to build a model.We compare two kinds of practice: one labeled “conventional” and the other labeled “new”.In conventional practice, the structural form of each equation in a complete model of linear simultaneous equations has (i) one of the jointly dependent or endogenous variables as its dependent variable;(ii) some relevant endogenous and exogenous variables with relevant predetermined variables as its included regressors; and (iii) relevant but omitted regressors constituting the structural disturbance.as shown by Pratt and Schlaifer (1984, 1988) [1,2], problems in estimation arise because the error term of an equation made up of relevant regressors omitted from the equation is non-unique
As shown by Pratt and Schlaifer (1984, 1988) [1,2], problems in estimation arise because the error term of an equation made up of relevant regressors omitted from the equation is non-unique
If the error term of this regression represents the net effect on the earnings of relevant regressors omitted from the regression, both of its coefficients and error term are non-unique, as we show in this paper
Summary
The quality of econometric practice is reflected in the assumptions made to build a model. We begin by demonstrating exactly how conventional practice gives rise to (i) non-unique coefficients that cannot be consistently estimated and (ii) a conflict between non-uniqueness of the coefficients and error term of an equation and the exogeneity of some or all of its regressors. We follow this discussion by introducing our new practice, which, as promised, employs models with unique coefficients and error terms, as laid out in a series of papers by Swamy and his associates, a recent contribution to which is Swamy et al (2016) [3].
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