# Oslo Summer School in Comparative Social Science Studies 2013

**Discrete Choice Modelling for Applied Economics**

Lecturer: Professor Erik Ø. Sørensen,

Department of Economics, NHH,

Norwegian School of Economics,

Norway

Main discipline: Economics

Dates: 29 July - 2 August 2013

Course Credits: 10 pts (ECTS)

Limitation: 30 participants

**Objectives**

Whereas most economic models are continuous, it is a fact that most economic data concerns behavior that is inherently discrete: The sets of cars, houses, and jobs available to choose from are discrete and finite, and most of the time, only integer units of each type of good are are available sale. Maybe the continuity of introductory micro economics is a useful approximation, but this is not enough to fit actual data. Data collected on a decision-by-decision bases often hints at more idiosyncratic variatey than deterministic continous models can account for. Standard models of discrete choice are built to account for randomness in individual behavior, and as such allows fitting to data on individual decisions. This course reviews the basic theory of discrete choice from both an economic and an econometric perspective, and we examine the diverse applications in which these models have been found useful.

**Prerequisites**

An understanding of basic probability theory and introductory econometrics at the graduate (master) level.

**Lectures**

Lecture 1: **Probabilistic Choice models I: Early theory. **

Very seldom economic theory provide direct probabilistic models that are fit for econometric modelling (although there are exceptions, such as Knowles et al (2001)). Early theory of discrete choice was developed from axiomatic choice theory (Luce, 1959), this was later given more behavioral interpretations (Train 2009, chapter 2, pp 11-33). McFadden (2001) gives a historical overview of this development.

Lecture 2: **Probabilistic Choice models II: The Logit class of random utility models. **

McFadden's work in transportation economics provided the basic formulation of the conditional logit model, and unified the axiomatic and behavioral approach. Train (2009, chapter 3, pp 34-75) states the most popular model in terms of modern micro theory, and lecture notes (Sørensen 2011) summarize the main unifying proofs. McKelvey and Palfrey (1995) extend the model to strategic interactions.

Lecture 3: **Solving the red-bus, blue-bus conundrum I: Generalized Extreme Value distributions. **

Gerard Debreu, in a book review of Luce (1959) provided the red-bus, blue-bus criticism of the "independence of irrelevant alternatives" axiom in the new theory of probabilistic choice. To what extent this is a problem in choice theory or in empirical applications is something we need to discuss. Train (2009, chapter 4, pp 76-96) discuss the Generalized Extreme Value solution to this problem, which has the additional benefit of being convenient to do welfare analysis on.

Lecture 4: **Solving the red-bus, blue-bus conundrum II: Mixed Logit.**

An alternative to the GEV approaches to sidestep the IIA is to allow for idiosyncratic variation in preferences. This can be given a "noise" or a heterogeneity interpretation. We discuss both, with the sideways view to other ways of allowing heterogeneity to provide probabilistic choice. We read Train (2009, chapter 6, pp 134-150), McFadden, Daniel and Kenneth Train (2000), Cappelen et al (2007), and Loomes (1995).

Lecture 5: **Inference for discrete choices. **

Refreshing standard inference the discrete choice setting, maximum likelihood and method of moments augmented with the complexity that the objective functions might themselves be seen as random variables when they are evaluted using simulation (Train 2009, chapter 10).

Lecture 6: **Market demand and market equilibrium. **

The classical application from which everything follows is Berry, Levinsohn, and Pakes (1995). We discuss this method in detail, pointing out where more recent developments have simplified calculations and sometime cast doubt on the realism of the approach.

Lecture 7: **Numerical methods for estimation. **

Often discrete choice models adapted to specific situations involve programming tailor-made estimation routines. Some restrictions on the formulation of discrete choice models follow from the demand that that these estimation routines should reasonably be expected to converge without exceptional luck or computational resources. We discuss some of the numerical issues that are germane to the formulation of discrete choice models (Train 2009, chapter 8, pp 185-204).

Lecture 8: **Dynamic models. **

Rust (1987) provided an early example that consistent and practical models of dynamic decision making with discounted utility could be estimated on individual level data. This classical example is still used as a reference for more modern approaches. The identification of these dynamic models was contested from the start, and we also introduce Hotz and Miller (1993), an alternative empirical approach that is a useful reference for later discussion of identification.

Lecture 9: **Discrete models that are not choice models. **

In this lecture, we review often used models of discrete outcomes that are not revealed choice models in the sense of Luce and McFadden, such as ranked and ordered outcomes, in addition to count and multinomial (not conditional) logit models. This is covered in Train (2009, chapter 7.1-5, pp 151-166), with the exception of count data (covered in Winkelman and Zimmerman, 1995). Schaumans and Verboven (2008) provide an interesting contrast to the random utility class of models.

Lecture 10: **Non-parametric identification. **

Models without continuous variation face special problems with idenfication, often they will be set identified or identified only with some parametric assumptions. Matzkin (1993) provided an early discussion, and Hotz and Miller (1993) and Magnac and Thesmar (2002) discuss problems specific to dynamic contexts.

**Books to purchase**

- Luce, R. Duncan (1959).
*Individual Choice Behavior*. Reprinted by Dover Publications 2005 (153 pages). - Train, Kenneth (2009).
*Discrete Choice Methods with Simulation*. Cambridge University Press, Second Edition (388 pages).

**Papers (will be provided)**

- Berry, Steven, James Levinsohn, and Ariel Pakes (1995). "Automobile Prices in Market Equilibrium,"
*Econometrica*, 63(4), 841-890 (50 pages). - Cappelen, Alexander W., Astri Drange Hole, Erik Ø. Sørensen, and Bertil Tungodden (2007). "The Pluralism of Fairness Ideals: An Experimental Approach,"
*American Economic Review*, 97(3), 818-827 (10 pages). - Hotz, V. Joseph and Robert A. Miller (1993). "Conditional Choice Probabilities and the Estimation of Dynamic Models,"
*Review of Economic Studies*, 60(3), 497-523 (27 pages). - Knowles, John and Nicola Persico, and Petra Todd (2001). "Racial Bias in Motor Vehicle Searches: Theory and Evidence,"
*Journal of Political Economy*, 109(1), 203-229 (18 pages). - Loomes, Graham and Robert Sugden (1995). "Incorporating a stochastic element into decision theories,"
*European Economic Review*, 39 (3-4), 641-648 (8 pages). - Magnac, Thierry and David Thesmar (2002). "Identifying Dynamic Discrete Decision Processes,"
*Econometrica*, 70(2), 801-816 (8 pages). - Matzkin, Rosa L. (1993). "Nonparametric identification and estimation of polychotomous choice models,"
*Journal of Econometrics*, 58(1-2), 137-168 (32 pages). - McFadden, Daniel (2001). "Economic Choices,"
*American Economic Review*, 91(3), 351-378 (28 pages). - McFadden, Daniel and Kenneth Train (2000). "Mixed MNL Models for Discrete Response,"
*Journal of Applied Econometrics*, 15(5), 447-470 (24 pages). - McKelvey, Richard D. and Thomas R. Palfrey (1995). "Quantal Response Equilibria for Normal Form Games,"
*Games and Economic Behavior*, 10(1), 6-38 (35 pages). - Rust, John (1987). "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher,"
*Econometrica*, 55(5), 999-1033 (35 pages). - Schaumans, Catherine and Frank Verboven (2008). "Entry and regulation: evidence from health care professions,"
*Rand Journal of Economics*, 39(4), 949-972 (24 pages). - Sørensen, Erik Ø. (2011). "Lecture Notes: Two results on discrete choice". Mimeo, NHH Norwegian School of Economics (5 pages).
- Winkelmann, Rainer and Klaus F. Zimmermann (1995). "Recent Developments in Count Data Modelling: Theory and Application,"
*Journal of Economic Surveys*, 9(1), 1-24 (24 pages).

**The lecturer**

Erik Ø. Sørensen is Professor of Economics at the Norwegian School of Economics, Norway, and a network member (researcher) of the Equality, Social Organization, and Performance center at University of Oslo.