Entry for Daniel Mcfadden in the New Palgrave Dictionary of Economics 1

Entry for Daniel McFadden in the New Palgrave Dictionary of Economics 1. Introduction Daniel L. McFadden, the E. Morris Cox Professor of Economics at the University of Cali- fornia at Berkeley, was the 2000 co-recipient of the Nobel Prize in Economics, awarded “for his development of theory and methods of analyzing discrete choice.” 1 McFadden was born in North Carolina, USA in 1937 and received a B.S. in Physics from the University of Minnesota (with highest honors) in 1956, and a Ph.D. degree in Economics from Minnesota in 1962. His academic career began as a postdoctoral fellow at the University of Pittsburgh. In 1963 he was appointed as assistant professor of economics at the University of California at Berkeley, and tenured in 1966. He has also held tenured appointments at Yale (as Irving Fisher Research Professor in 1977), and at the Massachusetts Institute of Technology (from 1978 to 1991). In 1990 he was awarded the E. Morris Cox chair at the University of California at Berkeley, where he has also served as Department Chair and as Director of the Econometrics Laboratory. 2. Research Contributions McFadden is best known for his fundamental contributions to the theory and econometric methods for analyzing discrete choice. Building on a highly abstract, axiomatic literature on probabilistic choice theory due to Thurstone (1927), Block and Marschak (1960), and Luce (1959) and others in a literature that originated in mathematical psychology, McFadden developed the econometric methodology for estimating the utility functions underlying probabilistic choice theory. McFadden’s primary contribution was to provide the econometric tools that permitted widespread practical empirical application of discrete choice models, in economics and other disciplines. According to his autobiography2 , “In 1964, I was working with a graduate student, Phoebe Cottingham, who had data on freeway routing decisions of the California Department of Trans- portation, and was looking for a way to analyze these data to study institutional decision-making behavior. I worked out for her an econometric model based on an axiomatic theory of choice behavior developed by the psychologist Duncan Luce. Drawing upon the work of Thurstone and Marshak, I was able to show how this model linked to the economic theory of choice behavior. 1 The prize was split with James J. Heckman, awarded “for his development of theory and methods for analyzing selective samples.” Summary quotes were from Nobel prize summary at nobelprize.org. 2 From the Nobel prize web site, nobelprize.org. 1 2 These developments, now called the multinomial logit model and the random utility model for choice behavior, have turned out to be widely useful in economics and other social sciences. They are used, for example, to study travel modes, choice of occupation, brand of automobile purchase, and decisions on marriage and number of children.” This understates the huge impact that the discrete choice literature has had on the social sciences, and is characteristic of McFadden’s modesty. Thousands of papers applying his technique have been published since his path breaking papers, “Conditional Logit Analysis of Qualitative Choice Behavior” (1973) and “The Revealed Preferences of a Government Bureaucracy: Empirical Evidence” (1976). In December 2005, a search of the term “discrete choice” using the Google search engine yielded 10,200,000 entries, and a search on the Google Scholar search engine (which limits search to academic articles), returned 759,000 items. Besides the discrete choice literature itself, McFadden’s work has spawned a number of related literatures in econometrics, theory, and industrial organization that are among the most active and productive parts of the economic literature in the present day. This includes work in game theory and industrial organization (e.g. the work on discrete choice and product differentiation of Anderson, De Palma and Thisse (1992), estimation of discrete games of incomplete information, Bajari, Hong, Krainer and Nekipelov (2005), and discrete choice modeling in the empirical industrial organization literature, Berry, S. Levinsohn, J. and A. Pakes (1995) and Goldberg (1995)), the econometric literature on semiparametric estimation of discrete choice models (Manski, (1985), McFadden and Train (2000)), the literature on discrete/continuous choice models and its connection to durable goods and energy demand modeling (Dagsvik (1994), Dubin and McFadden (1984), Hannemann (1984)), the econometric literature on choice based and stratified sampling (Cosslett (1981), Manski and McFadden, (1981)), the econometric literature on “simulation estimation” (Lerman and Manski (1981), McFadden (1994), Hajivassiliou and Ruud (1994), Pakes and Pollard (1989)), and the work on structural estimation of dynamic discrete choice models and extensions thereof (Dagsvik (1983), Eckstein and Wolpin (1989), Heckman (1981), Rust, (1994)). These are only some of fields that have been been hugely influenced by McFadden’s contributions to discrete choice and econometrics: given space constraints I have not attempted to survey other fields that have benefited from McFadden’s contributions (e.g. production economics, McFadden (1978)). In order to give the reader an appreciation for the elegance and generality of McFadden’s contributions, I will provide a brief synopsis of the theory and econometrics of discrete choice, following the treatment in McFadden’s (1981) paper “Econometric Models of Probabilistic Choice.” The underlying theory is superficially rather simple: an agent chooses a single alternative d from 3 a finite set D(x) of mutually exclusive alternatives to maximize a well defined utility function. Agents’ choices as well as the choice set D(x) may vary across agents depending on values of a vector x that can reflect state-dependent or agent-dependent factors or choice constraints, similar to the way a consumer budget set depends on quantities such as income and prices in standard (continuous) consumer theory. The vector x can include characteristics (or “attributes”) of the alternatives in the choice set D(x). The vector x can also include agent characteristics such as income, age, sex, education and so forth. There is great flexibility in specifying how alternative- specific and agent-specific characteristics affect decisions, and McFadden was one of the first to appreciate the huge potential probabilistic choice theory offered for empirical work. In order to appreciate McFadden’s contribution, it is useful to briefly summarize the elements of the theory on which he built, most of which originated in the literature on mathematical psychology. Fundamental to this literature is the concept of a choice probability P (djx; D(x)) which represents the probability that an agent chooses a particular element d 2 D(x). Psychologists emphasized the seemingly random nature of subjects’ decisions in experiments. The earliest cited work on probabilistic choice is Thurstone (1927), who described subject choices as a “discriminal process” and used the normal distribution to model the impact of random factors affecting individual decisions. Thurstone’s formula for the choice probability when there only two possible alternatives is now known in economics as the binomial probit model. The mathematical psychology literature also gave considerable attention to how the choice probability depends on the choice set D(x), since a major focus of the theory was to explain behavior of subjects in laboratory experiments where choice sets can be controlled. The initial work was relatively abstract and axiomatic, and attention focused on determining what restrictions, if any, were placed on choice probability functions (over and above satisfying the ordinary laws of probability) implied by the random utility maximization model (RUM). More precisely, what are the necessary and sufficient conditions for a choice probability P (djx; D(x)) to be consistent with random utility maximization, where P is given by 0 P (djx; D(x)) = P r u~d ≥ u~d0; d 2 D(x) ; (2:1) n o and fu~djd 2 D(x)g are a collection of random variables representing random utility values of the alternatives in D(x)? This is the discrete choice analog of the integrability problem in consumer theory, i.e. what are the necessary and sufficient conditions for a system of demand equations to be derivable from some underlying utility function? 4 The (1959) book Individual Choice Behavior by Duncan Luce introduced the axiom of independence from irrelevant alternatives (IIA). He showed that if this axiom holds, choice prob- abilities must have a multinomial logit representation (MNL). That is, there exists functions fu(x; d)jd 2 D(x)g such that expfu(x; d)g P (djx; D(x)) = 0 : (2:2) d02D(x) expfu(x; d )g P The IIA axiom states that the odds of choosing alternative d over alternative d0 are not changed if the choice set is enlarged. That is, if d; d0 2 D(x) ⊂ E(x), then P (djx; D(x)) P (djx; E(x)) = : (2:3) P (d0jx; D(x)) P (d0jx; E(x)) The IIA axiom is a strong restriction that may not always be empirically plausible for reasons noted in Debreu’s (1960) review of Luce’s book. McFadden introduced an alternative example he called the “red bus/blue bus problem” that illustrates potential problems with using the MNL to forecast how agents will respond to changes in their choice sets. 3 Block and Marschak (1960) did not impose the IIA axiom, and derived a general necessary condition on the choice probability to be consistent with random utility maximization, i.e. conditions on fP (djx; D(x))jd 2 D(x)g to have the representation in equation (2.1) for some collection of random variables fu~djd 2 D(x)g. Falmagne (1978) showed the Block-Marschak condition was also a sufficient condition for the random utility representation to hold. 4 3 Consider a commuter who initially has only two alternatives to commute to work: walking (d = w) and taking the bus (d = b), D(x) = fw; bg.

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