Microeconometrics Methods and Applications

Introduction

The preceding chapter considered models for discrete outcome variables that can take one of two possible values. Here we consider several possible outcomes, usually mutually exclusive. Examples include different ways to commute to work (by bus, car, or walking), various types of health insurance (fee-for-service, managed care, or none), different employment status (full-time, part-time, or none), choice of recreational site, occupational choice, and product choice.

Statistical inference is relatively straight forward in principle, as the data must be multinomial distributed, just as binary data must be Bernoulli or binomial distributed. Estimation is most often by maximum likelihood because the data are clearly multinomial distributed. For some complications, however, moment-based estimation is used instead.

Different multinomial models arise owing to different functional forms for the probabilities of the multinomial distribution, similar to the differences between probit and logit in the binary case. A distinction is also made between models where regressors vary across alternatives for a given individual and models where regressors are constant across alternatives. For example, in transportation mode choice some regressors, such as travel time or cost, will vary with choices whereas others, such as age, are choice invariant.

The simplest multinomial model, the conditional or multinomial logit model, is quite straightforward to use but is viewed as too restrictive in practice, especially if the multinomial outcome data arise from individual choice. For unordered outcomes less restrictive models can be obtained using the random utility model.