Specification Analysis for Quantal Choice Models

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 of the choice model, but exclusion of independent variables can lead to changes in the coefficients and the structure of the choice model. The sources of change 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 alternative least squares and maximum likelihood estimators arise because of different implicit error structures. The differences among the alternative estimators and the general effects of underspecification are examined empirically with simulated data.