[Part 15] 1/24 Discrete Choice Modeling Aggregate Share Data - BLP Discrete Choice Modeling William Greene Stern School of Business New York University 0Introduction 1Summary 2Binary Choice 3Panel Data 4Bivariate Probit 5Ordered Choice 6Count Data 7Multinomial Choice 8Nested Logit 9Heterogeneity 10Latent Class 11Mixed Logit 12Stated Preference 13Hybrid Choice 14. Spatial Data 15. Aggregate Market Data

[Part 15] 2/24 Discrete Choice Modeling Aggregate Share Data - BLP Aggregate Data and Multinomial Choice: The Model of Berry, Levinsohn and Pakes

[Part 15] 3/24 Discrete Choice Modeling Aggregate Share Data - BLP Resources  Automobile Prices in Market Equilibrium, S. Berry, J. Levinsohn, A. Pakes, Econometrica, 63, 4, 1995, (BLP)  A Practitioner’s Guide to Estimation of Random-Coefficients Logit Models of Demand, A. Nevo, Journal of Economics and Management Strategy, 9, 4, 2000, BLP.pdf  A New Computational Algorithm for Random Coefficients Model with Aggregate-level Data, Jinyoung Lee, UCLA Economics, Dissertation, BLP.pdf

[Part 15] 4/24 Discrete Choice Modeling Aggregate Share Data - BLP Theoretical Foundation  Consumer market for J differentiated brands of a good j =1,…, J t brands or types i = 1,…, N consumers t = i,…,T “markets” (like panel data)  Consumer i’s utility for brand j (in market t) depends on p = price x = observable attributes f = unobserved attributes w = unobserved heterogeneity across consumers ε = idiosyncratic aspects of consumer preferences  Observed data consist of aggregate choices, prices and features of the brands.

[Part 15] 5/24 Discrete Choice Modeling Aggregate Share Data - BLP BLP Automobile Market t JtJt

[Part 15] 6/24 Discrete Choice Modeling Aggregate Share Data - BLP Random Utility Model  Utility: U ijt =U(w i,p jt,x jt,f jt |), i = 1,…,(large)N, j=1,…,J w i = individual heterogeneity; time (market) invariant. w has a continuous distribution across the population. p jt, x jt, f jt, = price, observed attributes, unobserved features of brand j; all may vary through time (across markets)  Revealed Preference: Choice j provides maximum utility  Across the population, given market t, set of prices p t and features (X t,f t ), there is a set of values of w i that induces choice j, for each j=1,…,J t ; then, s j (p t,X t,f t |) is the market share of brand j in market t.  There is an outside good that attracts a nonnegligible market share, j=0. Therefore,

[Part 15] 7/24 Discrete Choice Modeling Aggregate Share Data - BLP Functional Form  (Assume one market for now so drop “’t.”) U ij =U(w i,p j,x j,f j |)= x j 'β – αp j + f j + ε ij = δ j + ε ij  E consumers i [ε ij ] = 0, δ j is E[Utility].  Will assume logit form to make integration unnecessary. The expectation has a closed form.

[Part 15] 8/24 Discrete Choice Modeling Aggregate Share Data - BLP Heterogeneity  Assumptions so far imply IIA. Cross price elasticities depend only on market shares.  Individual heterogeneity: Random parameters  U ij =U(w i,p j,x j,f j | i )= x j 'β i – αp j + f j + ε ij β ik = β k + σ k v ik.  The mixed model only imposes IIA for a particular consumer, but not for the market as a whole.

[Part 15] 9/24 Discrete Choice Modeling Aggregate Share Data - BLP Endogenous Prices: Demand side  U ij =U(w i,p j,x j,f j |)= x j 'β i – αp j + f j + ε ij  f j is unobserved  Utility responds to the unobserved f j  Price p j is partly determined by features f j.  In a choice model based on observables, price is correlated with the unobservables that determine the observed choices.

[Part 15] 10/24 Discrete Choice Modeling Aggregate Share Data - BLP Endogenous Price: Supply Side  There are a small number of competitors in this market  Price is determined by firms that maximize profits given the features of its products and its competitors.  mc j = g(observed cost characteristics c, unobserved cost characteristics h)  At equilibrium, for a profit maximizing firm that produces one product, s j + (p j -mc j )s j /p j = 0  Market share depends on unobserved cost characteristics as well as unobserved demand characteristics, and price is correlated with both.

[Part 15] 11/24 Discrete Choice Modeling Aggregate Share Data - BLP Instrumental Variables (ξ and ω are our h and f.)

[Part 15] 12/24 Discrete Choice Modeling Aggregate Share Data - BLP Econometrics: Essential Components

[Part 15] 13/24 Discrete Choice Modeling Aggregate Share Data - BLP Econometrics

[Part 15] 14/24 Discrete Choice Modeling Aggregate Share Data - BLP GMM Estimation Strategy - 1

[Part 15] 15/24 Discrete Choice Modeling Aggregate Share Data - BLP GMM Estimation Strategy - 2

[Part 15] 16/24 Discrete Choice Modeling Aggregate Share Data - BLP BLP Iteration

[Part 15] 17/24 Discrete Choice Modeling Aggregate Share Data - BLP ABLP Iteration ξ t is our f t.  is our (β,  ) No superscript is our (M); superscript 0 is our (M-1).

[Part 15] 18/24 Discrete Choice Modeling Aggregate Share Data - BLP Side Results

[Part 15] 19/24 Discrete Choice Modeling Aggregate Share Data - BLP ABLP Iterative Estimator

[Part 15] 20/24 Discrete Choice Modeling Aggregate Share Data - BLP BLP Design Data

[Part 15] 21/24 Discrete Choice Modeling Aggregate Share Data - BLP Exogenous price and nonrandom parameters

[Part 15] 22/24 Discrete Choice Modeling Aggregate Share Data - BLP IV Estimation

[Part 15] 23/24 Discrete Choice Modeling Aggregate Share Data - BLP Full Model

[Part 15] 24/24 Discrete Choice Modeling Aggregate Share Data - BLP Some Elasticities