Abstract
This paper examines problems involved in the specification of the correct set of independent variables in choice models. The analytical approach is similar to Theil’s use of auxiliary regressions in the case of standard linear models. The key conclusions are that the inclusion of superfluous independent variables does not affect the consistency of the correct coefficients, but exclusion of independent variables can lead to inconsistent estimates. The sources of bias are the possible correlations between included and excluded independent variables and the change in the structure of the random error terms in the utility functions. Because of the flexibility of its error structure, particular attention is given to the multinomial probit model.
When independent variables are excluded, asymptotic differences among are alternative estimators arise because of different implicit error structures. The differences among the alternative estimators and the general effects of under specification are examined empirically with simulated data.