Abstract
We develop a procedure for removing four major specification errors from the usual formulation of binary choice models. The model that results from this procedure is different from the conventional probit and logit models. This difference arises as a direct consequence of our relaxation of the usual assumption that omitted regressors constituting the error term of a latent linear regression model do not introduce omitted regressor biases into the coefficients of the included regressors.
Highlights
It is well-known that binary choice models are subject to certain specification errors
The results proved by Yatchew and Griliches (YG) are: (i) even if the omitted regressor is uncorrelated with the remaining included regressor, the coefficient on the latter regressor will be inconsistent; (ii) If the errors in the underlying regression are heteroscedastic, the maximum likelihood estimators that ignore the heteroscedasticity are inconsistent and the covariance matrix is inappropriate (see Greene (2012, p. 713) [3])
Econometric model arises omitted these specification errors changes their results. We find that their model has nonunique regressors influencing the dependent variable
Summary
It is well-known that binary choice models are subject to certain specification errors. It can be shown that the usual approach of adding an error term to a mathematical function leads to a model with nonunique coefficients and error term In this model, the conditional expectation of the dependent variable given the included regressors does not always exist. Our model features varying coefficients (VCs) in which we interpret the VC on a continuous regressor as a function of three quantities: (i) bias-free partial derivative of the dependent variable with respect to the continuous regressor; (ii) omitted-regressor biases; and (iii) measurement-error biases This interpretation of the VCs is unique to our work and allows us to focus on the bias-free (i.e., partial derivatives) parts of the VCs. The remainder of this paper is comprised of three sections. The second section derives the information matrix for a binary choice model with unique coefficients and error term
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