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The mixed or heterogeneous multinomial logit (MIXL) model has become popular in a number of fields, especially marketing, health economics, and industrial organization. In most applications of the model, the vector of consumer utility weights on product attributes is assumed to have a multivariate normal (MVN) distribution in the population. Thus, some consumers care more about some attributes than others, and the IIA property of multinomial logit (MNL) is avoided (i.e., segments of consumers will tend to switch among the subset of brands that possess their most valued attributes). The MIXL model is also appealing because it is relatively easy to estimate. Recently, however, some researchers have argued that the MVN is a poor choice for modelling taste heterogeneity. They argue that much of the heterogeneity in attribute weights is accounted for by a pure scale effect (i.e., across consumers, all attribute weights are scaled up or down in tandem). This implies that choice behaviour is simply more random for some consumers than others (i.e., holding attribute coefficients fixed, the scale of their error term is greater). This leads to a “scale heterogeneity” MNL model (S-MNL). Here, we develop a generalized multinomial logit model (G-MNL) that nests S-MNL and MIXL. By estimating the S-MNL, MIXL, and G-MNL models on 10 data sets, we provide evidence on their relative performance. We find that models that account for scale heterogeneity (i.e., G-MNL or S-MNL) are preferred to MIXL by the Bayes and consistent Akaike information criteria in all 10 data sets. Accounting for scale heterogeneity enables one to account for “extreme” consumers who exhibit nearly lexicographic preferences, as well as consumers who exhibit very “random” behaviour (in a sense we formalize below).choice models, mixture models, consumer heterogeneity, choice experiments

We construct two models of the behavior of consumers in an environment where there is uncertainty about brand attributes. In our models, both usage experience and advertising exposure give consumers noisy signals about brand attributes. Consumers use these signals to update their expectations of brand attributes in a Bayesian manner. The two models are (1) a dynamic model with immediate utility maximization, and (2) a dynamic “forward-looking” model in which consumers maximize the expected present value of utility over a planning horizon. Given this theoretical framework, we derive from the Bayesian learning framework how brand choice probabilities depend on past usage experience and advertising exposures. We then form likelihood functions for the models and estimate them on Nielsen scanner data for detergent. We find that the functional forms for experience and advertising effects that we derive from the Bayesian learning framework fit the data very well relative to flexible ad hoc functional forms such as exponential smoothing, and also perform better at out-of-sample prediction. Another finding is that in the context of consumer learning of product attributes, although the forward-looking model fits the data statistically better at conventional significance levels, both models produce similar parameter estimates and policy implications. Our estimates indicate that consumers are risk-averse with respect to variation in brand attributes, which discourages them from buying unfamiliar brands. Using the estimated behavioral models, we perform various scenario evaluations to find how changes in marketing strategy affect brand choice both in the short and long run. A key finding obtained from the policy experiments is that advertising intensity has only weak short run effects, but a strong cumulative effect in the long run. The substantive content of the paper is potentially of interest to academics in marketing, economics and decision sciences, as well as product managers, marketing research managers and analysts interested in studying the effectiveness of marketing mix strategies. Our paper will be of particular interest to those interested in the long run effects of advertising. Note that our estimation strategy requires us to specify explicit behavioral models of consumer choice behavior, derive the implied relationships among choice probabilities, past purchases and marketing mix variables, and then estimate the behavioral parameters of each model. Such an estimation strategy is referred to as “structural” estimation, and econometric models that are based explicitly on the consumer's maximization problem and whose parameters are parameters of the consumers' utility functions or of their constraints are referred to as “structural” models. A key benefit of the structural approach is its potential usefulness for policy evaluation. The parameters of structural models are invariant to policy, that is, they do not change due to a change in the policy. In contrast, the parameters of reduced form brand choice models are...

The authors would like to thank Zvi Griliches, the participants at the Econometrica/SSRI conference "Empirical Applications of Structural Models," held in Madison, Wisconsin, in May 1990, and the participants at several other conferences and university workshops for comments. Support from the Federal Reserve Bank of Minneapolis is also appreciated.

I survey the male and female labor supply literatures, focusing on implications for effects of wages and taxes. For males, I describe and contrast results from three basic types of model: static models (especially those that account for nonlinear taxes), life-cycle models with savings, and life-cycle models with both savings and human capital. For women, more important distinctions are whether models include fixed costs of work, and whether they treat demographics like fertility and marriage (and human capital) as exogenous or endogenous. The literature is characterized by considerable controversy over the responsiveness of labor supply to changes in wages and taxes. At least for males, it is fair to say that most economists believe labor supply elasticities are small. But a sizable minority of studies that I examine obtain large values. Hence, there is no clear consensus on this point. In fact, a simple average of Hicks elasticities across all the studies I examine is 0.31. Several simulation studies have shown that such a value is large enough to generate large efficiency costs of income taxation. For males, I conclude that two factors drive many of the differences in results across studies. One factor is use of direct versus ratio wage measures, with studies that use the former tending to find larger elasticities. Another factor is the failure of most studies to account for human capital returns to work experience. I argue that this may lead to downward bias in elasticity estimates. In a model that includes human capital, I show how even modest elasticities—as conventionally measured—can be consistent with large efficiency costs of taxation. For women, in contrast, it is fair to say that most studies find large labor supply elasticities, especially on the participation margin. In particular, I find that estimates of "long-run" labor supply elasticities—by which I mean estimates that allow for dynamic effects of wages on fertility, marriage, education and work experience—are generally quite large. ( JEL D91, J13, J16, J22, J31, H24)