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Discrete Choice Lecture

Discrete Choice Lecture - Imbens/Wooldridge Lecture Notes...

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Imbens/Wooldridge, Lecture Notes 11, NBER, Summer ’07 1 What’s New in Econometrics NBER, Summer 2007 Lecture 11, Wednesday, Aug 1st, 9.00-10.30am Discrete Choice Models 1. Introduction In this lecture we discuss multinomial discrete choice models. The modern literature on these models goes back to the work by Daniel McFadden in the seventies and eighties, (McFadden, 1973, 1981, 1982, 1984). In the nineties these models received much attention in the Industrial Organization literature, starting with Berry (1994), Berry, Levinsohn, Pakes (1995, BLP), and Goldberg (1995). In the IO literature the applications focused on demand for differentiated products, in settings with relatively large numbers of products, some of them close substitutes. In these settings a key feature of the conditional logit model, namely the Independence of Irrelevant Alternatives (IIA), was viewed as particularly unattractive. Three approaches have been used to deal with this. Goldberg (1995) used nested logit models to avoid the IIA property. McCulloch and Rossi (1994), and McCulloch, Polson and Rossi (2000) studied multinomial probit models with relatively unrestricted covariance matrices for the unobserved components. BLP, McFadden and Train (2000) and Berry, Levinsohn and Pakes (2004) uses random effects or mixed logit models, in BLP in combination with unobserved choice characteristics and using methods that allow for estimation using only ag- gregate choice data. The BLP approach has been very influential in the subsequent empirical IO literature. Here we discuss these models. We argue that the random effects approach to avoid IIA is indeed very attractive, both substantively and computationally, compared to the nested logit or unrestricted multinomial probit models. In addition to the use of random effects to avoid the IIA property, the inclusion in the BLP methodology of unobserved choice characteristics, and the ability to estimate the models with market share rather than individual level data makes their methods very flexible and widely applicable. We discuss extensions to the BLP set up allowing multiple unobserved choice characteristics, and the richness required for these
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Imbens/Wooldridge, Lecture Notes 11, NBER, Summer ’07 2 models to rationalize general choice data based on utility maximization. We also discuss the potential benefits of using Bayesian methods. 2. Multinomial and Conditional Logit Models First we briefly review the multinomial and conditional logit models. 2.1 Multinomial Logit Models We focus on models for discrete choice with more than two choices. We assume that the outcome of interest, the choice Y i takes on non-negative, un-ordered integer values between zero and J ; Y i ∈ { 0 , 1 , . . . , J } . Unlike the ordered case there is no particular meaning to the ordering. Examples are travel modes (bus/train/car), employment status (employed/unemployed/out-of-the-laborforce), car choices (suv, sedan, pickup truck, con- vertible, minivan), and many others.
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