Kenneth Train

MIXED MNL MODELS FOR DISCRETE RESPONSE

This paper considers mixed, or random coefficients, multinomial logit (MMNL) models for discrete response, and establishes the following results. Under mild regularity conditions, any discrete choice model derived from random utility maximization has choice probabilities that can be approximated as closely as one pleases by a MMNL model. Practical estimation of a parametric mixing family can be carried out by Maximum Simulated Likelihood Estimation or Method of Simulated Moments, and easily computed instruments are provided that make the latter procedure fairly efficient. The adequacy of a mixing specification can be tested simply as an omitted variable test with appropriately defined artificial variables. An application to a problem of demand for alternative vehicles shows that MMNL provides a flexible and computationally practical approach to discrete response analysis. Copyright

A Control Function Approach to Endogeneity in Consumer Choice Models

Endogeneity arises for numerous reasons in models of consumer choice. It leads to inconsistency with standard estimation methods that maintain independence between the models error and the included variables. The authors describe a control function approach for handling endogeneity in choice models. Observed variables and economic theory are used to derive controls for the dependence between the endogenous variable and the demand error. The theory points to the relationships that contain information on the unobserved demand factor, such as the pricing equation and the advertising equation. The authors’ approach is an alternative to Berry, Levinsohn, and Pakess (1995) product-market controls for unobserved quality. The authors apply both methods to examine households’ choices among television options, including basic and premium cable packages, in which unobserved attributes, such as quality of programming, are expected to be correlated with price. Without correcting for endogeneity, aggregate demand is estimated to be upward-sloping, suggesting that omitted attributes are positively correlated with demand. Both the control function method and the product-market controls method produce downward-sloping demand estimates that are similar.

Discrete Choice Models in Preference Space and Willingness-to Pay Space

In models with unobserved taste heterogeneity, distributional assumptions can be placed in two ways: (1) by specifying the distribution of coefficients in the utility function and deriving the distribution of willingness to pay (wtp), or (2) by specifying the distribution of wtp and deriving the distribution of coefficients. In general the two approaches are equivalent, in that any mutually compatible distributions for coefficients and wtp can be represented in either way. However, in practice, convenient distributions, such as normal or lognormal, are usually specified, and these convenient distributions have different implications when placed on wtps than on coefficients. We compare models that use normal and lognormal distributions for coefficients (models in preference space) with models using these distributions for wtp (models in wtp space). We find that the models in preference space fit the data better but provide less reasonable distributions of wtp than the models in wtp space.

Mixed Logit with Bounded Distributions of Correlated Partworths

The use of a joint normal distribution for partworths is computationally attractive, particularly with Bayesian MCMC procedures, and yet is unrealistic for any attribute whose partworth is logically bounded (e.g., is necessarily positive or cannot be unboundedly large). A mixed logit is specified with partworths that are transformations of normally distributed terms, where the transformation induces bounds; examples include censored normals, log-normals, and S B distributions which are bounded on both sides. The model retains the computational advantages of joint normals while providing greater flexibility for the distributions of correlated partworths. The method is applied to data on customers’ choice among vehicles in stated choice experiments. The flexibility that the transformations allow is found to greatly improve the model, both in terms of fit and plausibility, without appreciably increasing the computational burden.

THE GOODS/LEISURE TRADEOFF AND DISAGGREGATE WORK TRIP MODE CHOICE MODELS

In disaggregate work trip mode choice models, the wage of the worker often enters as an explanatory variable. In some models, the cost of travel is divided by the workers wage, while in other models the travel times are multiplied by the wage. This paper analyzes the use of wage in mode choice models and shows how different assumptions about the workers indifference mapping between goods and leisure lead to different methods of entering wage.

A DISAGGREGATE MODEL OF AUTO-TYPE CHOICE

Previous models of auto-type choice have not been able to disentangle very much of the structure of the households auto-choice decision: the models assumed that very few auto characteristics affect choice, and often these few parameters were estimated with low precision. Hence the models had only limited use in forecasting the effects of government policies to influence transportation energy consumption. The present paper introduces a multinomial logit model for the type of car that households will choose to buy. The model includes a large variety of auto characteristics as explanatory variables, as well as a large number of characteristics of the household and the driving environment. The model fits the data quite well, and all of the variables enter with the correct signs and plausible magnitudes.

Consumers' Evaluation of New Products: Learning from Self and Others

When offered a new product whose attributes are unknown, customers can determine whether they like the product by trying it themselves or can wait to observe the experience of other customers who try the product. We specify a rational decision process and investigate the implications of learning from others on the sales of new products and the impact of advertising.

On the Similarity of Classical and Bayesian Estimates of Individual Mean Partworths

An exciting development in modeling has been the ability to estimate reliable individual-level parameters for choice models. Individual partworths derived from these parameters have been very useful in segmentation, identifying extreme individuals, and in creating appropriate choice simulators. In marketing, hierarchical Bayes models have taken the lead in combining information about the aggregate distribution of tastes with the individuals choices to arrive at a conditional estimate of the individuals parameters. In economics, the same behavioral model has been derived from a classical rather than a Bayesian perspective. That is, instead of Gibbs sampling, the method of maximum simulated likelihood provides estimates of both the aggregate and the individual parameters. This paper explores the similarities and differences between classical and Bayesian methods and shows that they result in virtually equivalent conditional estimates of partworths for customers. Thus, the choice between Bayesian and classical estimation becomes one of implementation convenience and philosophical orientation, rather than pragmatic usefulness.

QUASI-RANDOM SIMULATION OF DISCRETE CHOICE MODELS

We describe the properties of (t,m,s)-nets and Halton draws. Four types of (t,m,s)-nets, two types of Halton draws, and independent draws are compared in an application of maximum simulated likelihood estimation of a mixed logit model. All of the quasi-random procedures are found to perform far better than independent draws. The best performance is attained by one of the (t,m,s)-nets. The properties of the nets imply that two of them should outperform the other two, and our results confirm this expectation. The two more-accurate nets perform better than both types of Halton draws, while the two less-accurate nets perform worse than the Halton draws.

Consumption Patterns and Self-selecting Tariffs

The authors describe and apply methods for empirically investigating the relation between consumption and tariff choice. These methods allow (1) testing of alternative specifications for the relations of tariff choice and consumption patterns, (2) estimation of parameters that provide information on the response of customers to marginal prices and fixed fees, and (3) a determination of the extent to which the assumptions embodied in welfare results on self-selecting tariffs are valid in a particular setting. They apply the procedures to residential demand for local telephone service in an area where households are offered a choice among tariffs. Copyright 1989 by MIT Press.