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Using penalized likelihood to select parameters in a random coefficients multinomial logit model

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  • Joel L. Horowitz

    (Institute for Fiscal Studies and Northwestern University)

  • Lars Nesheim

    (Institute for Fiscal Studies and University College London)

Abstract

The multinomial logit model with random coefficients is widely used in applied research. This paper is concerned with estimating a random coefficients logit model in which the distribution of each coefficient is characterized by finitely many parameters. Some of these parameters may be zero or close to zero in a sense that is defined. We call these parameters small. The paper gives conditions under which with probability approaching 1 as the sample size approaches infinity, penalized maximum likelihood estimation (PMLE) with the adaptive LASSO (AL) penalty function distinguishes correctly between large and small parameters in a random-coefficients logit model. If one or more parameters are small, then PMLE with the AL penalty function reduces the asymptotic mean-square estimation error of any continuously differentiable function of the model’s parameters, such as a market share, the value of travel time, or an elasticity. The paper describes a method for computing the PMLE of a random-coefficients logit model. It also presents the results of Monte Carlo experiments that illustrate the numerical performance of the PMLE. Finally, it presents the results of PMLE estimation of a random-coefficients logit model of choice among brands of butter and margarine in the British groceries market.

Suggested Citation

  • Joel L. Horowitz & Lars Nesheim, 2018. "Using penalized likelihood to select parameters in a random coefficients multinomial logit model," CeMMAP working papers CWP29/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:29/18
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    References listed on IDEAS

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    1. Salanié, Bernard & Wolak, Frank, 2018. "Fast, “Robust†, and Approximately Correct: Estimating Mixed Demand Systems," CEPR Discussion Papers 13236, C.E.P.R. Discussion Papers.
    2. Bernard Salanie & Frank A. Wolak, 2018. "Fast, "robust", and approximately correct: estimating mixed demand systems," CeMMAP working papers CWP64/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Juan Carlos Escanciano, 2020. "Irregular Identification of Structural Models with Nonparametric Unobserved Heterogeneity," Papers 2005.08611, arXiv.org.

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