Parameters Heterogeneity in a Model of Labour Supply: Exploring the Performance of Mixed Logit
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In this note we investigate the empirical differences between the Random Utility model with fixed coefficients (Conditional Logit), and the Random Utility model with random coefficients (Mixed Logit). We consider a model of household labour supply developed for a project aimed at the evaluation of alternative Basic Income mechanisms. Data are drawn from the 1998 Bank of Italy survey of household income and wealth (SHIW 1998) and choice alternatives are generated using EUROMOD. We compare the estimates of the Conditional Logit and Mixed Logit. We also compare the respective results from simulating the effects of a Flat Tax reform. Although on average the estimates of Conditional Logit and of Mixed Logit are very close, the Mixed Logit estimates reveal that there is a significant unobserved heterogeneity of preferences. We also compare the simulations of a hypothetical Flat Tax reform. Although the differences are small, yet the results would imply different policy conclusions depending on whether Conditional Logit or Mixed Logit is adopted.Keywords:
Mixed logit
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Labour supply
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In this article, we examine the aggregation properties of (nested) logit models to understand their exceptional macro-level performance. The problem of aggregating micro logit models involves integrating nonlinear functions of model parameters over a distribution of consumer heterogeneity. The aggregation problem is analyzed using a mixture of analytic and simulation techniques, with the simulation experiments using actual panel data to calibrate the distribution of heterogeneity. We conclude that the practice of fitting aggregate logit models is theoretically justified under the following three conditions: (1) All consumers are exposed to the same marketing-mix variables, (2) the brands are close substitutes, and (3) the distribution of prices is not concentrated at an extreme value. These conditions are frequently met in store-level scanner data.
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The article uses some results obtained in a preceding study regarding the estimation of the life insurance demand for a Romanian company. By employing a novel device - the ROC curve for Discrete Choice Models - we compare three models from a predictive power point of view: the Multinomial Logit, the Conditional Logit and the General Multinomial Logit.
Discrete choice
Multinomial probit
Multinomial distribution
Mixed logit
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Mixed logit
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Discrete choice
Market Segmentation
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We start from an aggregate random coefficients nested logit (RCNL) model to provide a systematic comparison between the tractable logit and nested logit (NL) models with the computationally more complex random coefficients logit (RC) model. We first use simulated data to assess possible parameter biases when the true model is a RCNL model. We then use data on the automobile market to estimate the different models, and as an illustration assess what they imply for competition policy analysis. As expected, the simple logit model is rejected against the NL and RC model, but both of these models are in turn rejected against the more general RCNL model. While the NL and RC models result in quite different substitution patterns, they give robust policy conclusions on the predicted price effects from mergers. In contrast, the conclusions for market definition are not robust across different demand models. In general, our findings suggest that it is important to account for sources of market segmentation that are not captured by continuous characteristics in the RC model.
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The empirical valuation of travel time savings is a derivative of the ratio of parameter estimates in a discrete choice model. The most common formulation (multinomial logit) imposes strong restrictions on the profile of the unobserved influences on choice as represented by the random component of a preference function. As we progress our ability to relax the restrictions we open up opportunities to benchmark the values derived from simple (albeit relatively restrictive) models. In this paper we contrast the values of travel time savings derived from five discrete choice models - multinomial logit, heteroskedastic extreme value, covariance heterogeneity logit, mixed (or random parameter) logit and multinomial probit. The empirical setting is urban car commuting and noncommuting in six locations in New Zealand. The evidence supports the growing position that less restrictive choice model specifications tend to produce higher estimates of values of time savings compared to the multinomial logit model; however the degree of under-estimation of multinomial logit remains quite variable, depending on the context. (a)
Multinomial probit
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Value of time
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We start from an aggregate random coefficients nested logit (RCNL) model to provide a systematic comparison between the tractable logit and nested logit (NL) models with the computationally more complex random coefficients logit (RC) model. We first use simulated data to assess possible parameter biases when the true model is a RCNL model. We then use data on the automobile market to estimate the different models, and as an illustration assess what they imply for competition policy analysis. As expected, the simple logit model is rejected against the NL and RC model, but both of these models are in turn rejected against the more general RCNL model. While the NL and RC models result in quite different substitution patterns, they give robust policy conclusions on the predicted price effects from mergers. In contrast, the conclusions for market definition are not robust across different demand models. In general, our findings suggest that it is important to account for sources of market segmentation that are not captured by continuous characteristics in the RC model.
Mixed logit
Product Differentiation
Discrete choice
Nested logit
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We calibrate and contrast the recent generalized multinomial logit model and the widely used latent class logit model approaches for studying heterogeneity in consumer purchases. We estimate the parameters of the models on panel data of household ketchup purchases, and find that the generalized multinomial logit model outperforms the best‐fitting latent class logit model in terms of the Bayesian information criterion. We compare the posterior estimates of coefficients for individual customers based on the two different models and discuss how the differences could affect marketing strategies (such as pricing), which could be affected by applying each of the models. We also describe extensions to the scale heterogeneity model that includes the effects of state dependence and purchase history. Copyright © 2011 John Wiley & Sons, Ltd.
Mixed logit
Multinomial probit
Multinomial distribution
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Mixed logit
Ordered logit
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Introduction the role of the logit model plan of the book notation the bivariate model the logit model for a single attribute justification of the model two common densities estimation from individual data - maximum likelihood estimation from individual data - implementation estimation from grouped data private car ownership and household income further analysis of private car ownership the history of the logit model the multinomial logit model the multinomial logit model properties of the model discrete choice theory the multinomial probit model estimation of multinomial probability models estimation of the standard model multinomial analysis of private car ownership further developments of the model the conditional logit model estimation choice of mode of payment general linear form of the argument the nested logit model prediction and fit introduction prediction of aggregate incidence prediction of individual outcomes measures of fit based on individual observations measures of fit for grouped observations.
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