Part 24: Stated Choice [1/117] Econometric Analysis of Panel Data William Greene Department of Economics Stern School of Business

Part 24: Stated Choice [2/68] Econometric Analysis of Panel Data 24. Multinomial Choice and Stated Choice Experiments

Part 24: Stated Choice [3/117] A Microeconomics Platform  Consumers Maximize Utility (!!!)  Fundamental Choice Problem: Maximize U(x 1,x 2,…) subject to prices and budget constraints  A Crucial Result for the Classical Problem: Indirect Utility Function: V = V(p,I) Demand System of Continuous Choices Observed data usually consist of choices, prices, income  The Integrability Problem: Utility is not revealed by demands

Part 24: Stated Choice [4/117] Implications for Discrete Choice Models  Theory is silent about discrete choices  Translation of utilities to discrete choice requires: Well defined utility indexes: Completeness of rankings Rationality: Utility maximization Axioms of revealed preferences  Consumers often act to simplify choice situations  This allows us to build “models.” What common elements can be assumed? How can we account for heterogeneity?  However, revealed choices do not reveal utility, only rankings which are scale invariant.

Part 24: Stated Choice [5/117] Multinomial Choice Among J Alternatives Random Utility Basis U itj =  ij +  i ’x itj +  ij z it +  ijt i = 1,…,N; j = 1,…,J(i,t); t = 1,…,T(i) N individuals studied, J(i,t) alternatives in the choice set, T(i) [usually 1] choice situations examined. Maximum Utility Assumption Individual i will Choose alternative j in choice setting t if and only if U itj > U itk for all k  j. Underlying assumptions Smoothness of utilities Axioms of utility maximization: Transitive, Complete, Monotonic

Part 24: Stated Choice [6/117] Features of Utility Functions  The linearity assumption U itj =  ij +  i x itj +  j z it +  ijt To be relaxed later: U itj = V(x itj,z it,  i ) +  ijt  The choice set: Individual (i) and situation (t) specific Unordered alternatives j = 1,…,J(i,t)  Deterministic (x,z,  j ) and random components (  ij,  i,  ijt )  Attributes of choices, x itj and characteristics of the chooser, z it. Alternative specific constants  ij may vary by individual Preference weights,  i may vary by individual Individual components,  j typically vary by choice, not by person Scaling parameters, σ ij = Var[ε ijt ], subject to much modeling

Part 24: Stated Choice [7/117] Unordered Choices of 210 Travelers

Part 24: Stated Choice [8/117] Data on Multinomial Discrete Choices

Part 24: Stated Choice [9/117] The Multinomial Logit (MNL) Model  Independent extreme value (Gumbel): F(  itj ) = Exp(-Exp(-  itj )) (random part of each utility) Independence across utility functions Identical variances (means absorbed in constants) Same parameters for all individuals (temporary)  Implied probabilities for observed outcomes

Part 24: Stated Choice [10/117] Multinomial Choice Models

Part 24: Stated Choice [11/117] Specifying the Probabilities Choice specific attributes (X) vary by choices, multiply by generic coefficients. E.g., TTME=terminal time, GC=generalized cost of travel mode Generic characteristics (Income, constants) must be interacted with choice specific constants. Estimation by maximum likelihood; d ij = 1 if person i chooses j

Part 24: Stated Choice [12/117] Willingness to Pay

Part 24: Stated Choice [13/117] An Estimated MNL Model Discrete choice (multinomial logit) model Dependent variable Choice Log likelihood function Estimation based on N = 210, K = 5 Information Criteria: Normalization=1/N Normalized Unnormalized AIC Fin.Smpl.AIC Bayes IC Hannan Quinn R2=1-LogL/LogL* Log-L fncn R-sqrd R2Adj Constants only Chi-squared[ 2] = Prob [ chi squared > value ] = Response data are given as ind. choices Number of obs.= 210, skipped 0 obs Variable| Coefficient Standard Error b/St.Er. P[|Z|>z] GC| *** TTME| *** A_AIR| *** A_TRAIN| *** A_BUS| ***

Part 24: Stated Choice [14/117] Discrete choice (multinomial logit) model Dependent variable Choice Log likelihood function Estimation based on N = 210, K = 5 Information Criteria: Normalization=1/N Normalized Unnormalized AIC Fin.Smpl.AIC Bayes IC Hannan Quinn R2=1-LogL/LogL* Log-L fncn R-sqrd R2Adj Constants only Chi-squared[ 2] = Prob [ chi squared > value ] = Response data are given as ind. choices Number of obs.= 210, skipped 0 obs Variable| Coefficient Standard Error b/St.Er. P[|Z|>z] GC| *** TTME| *** A_AIR| *** A_TRAIN| *** A_BUS| *** Estimated MNL Model

Part 24: Stated Choice [15/117] Estimated MNL Model Discrete choice (multinomial logit) model Dependent variable Choice Log likelihood function Estimation based on N = 210, K = 5 Information Criteria: Normalization=1/N Normalized Unnormalized AIC Fin.Smpl.AIC Bayes IC Hannan Quinn R2=1-LogL/LogL* Log-L fncn R-sqrd R2Adj Constants only Chi-squared[ 2] = Prob [ chi squared > value ] = Response data are given as ind. choices Number of obs.= 210, skipped 0 obs Variable| Coefficient Standard Error b/St.Er. P[|Z|>z] GC| *** TTME| *** A_AIR| *** A_TRAIN| *** A_BUS| ***

Part 24: Stated Choice [16/117] m = Car j = Train k = Price

Part 24: Stated Choice [17/117] m = Carj = Train k = Price j = Train

Part 24: Stated Choice [18/117]

Part 24: Stated Choice [19/117] Own effect Cross effects | Elasticity averaged over observations.| | Attribute is INVT in choice AIR | | Mean St.Dev | | * Choice=AIR | | Choice=TRAIN | | Choice=BUS | | Choice=CAR | | Attribute is INVT in choice TRAIN | | Choice=AIR | | * Choice=TRAIN | | Choice=BUS | | Choice=CAR | | Attribute is INVT in choice BUS | | Choice=AIR | | Choice=TRAIN | | * Choice=BUS | | Choice=CAR | | Attribute is INVT in choice CAR | | Choice=AIR | | Choice=TRAIN | | Choice=BUS | | * Choice=CAR | | Effects on probabilities of all choices in model: | | * = Direct Elasticity effect of the attribute. | Note the effect of IIA on the cross effects. Elasticities are computed for each observation; the mean and standard deviation are then computed across the sample observations.

Part 24: Stated Choice [20/117] A Multinomial Logit Common Effects Model  How to handle unobserved effects in other nonlinear models? Single index models such as probit, Poisson, tobit, etc. that are functions of an x it 'β can be modified to be functions of x it 'β + c i. Other models – not at all obvious. Rarely found in the literature.  Dealing with fixed and random effects?  Dynamics makes things much worse.

Part 24: Stated Choice [21/117] A Multinomial Logit Model

Part 24: Stated Choice [22/117] A Heterogeneous Multinomial Logit Model

Part 24: Stated Choice [23/117] Common Effects Multinomial Logit

Part 24: Stated Choice [24/117] Simulation Based Estimation

Part 24: Stated Choice [25/117] Application Shoe Brand Choice  S imulated Data: Stated Choice, N=400 respondents, T=8 choice situations, 3,200 observations  3 choice/attributes + NONE  J=4 Fashion = High / Low Quality = High / Low Price = 25/50/75,100 coded 1,2,3,4; and Price 2  H eterogeneity: Sex, Age (<25, 25-39, 40+)  U nderlying data generated by a 3 class latent class process (100, 200, 100 in classes)  T hanks to (Latent Gold)

Part 24: Stated Choice [26/117] Application

Part 24: Stated Choice [27/117] No Common Effects | Start values obtained using MNL model | | Log likelihood function | |Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| FASH | QUAL | PRICE | PRICESQ | ASC4 | B1_MAL1 | B1_YNG1 | B1_OLD1 | B2_MAL2 | B2_YNG2 | B2_OLD2 | B3_MAL3 | B3_YNG3 | B3_OLD3 |

Part 24: Stated Choice [28/117] Random Effects MNL Model | Error Components (Random Effects) model | Restricted logL = | Log likelihood function | Chi squared(3) = (Crit.Val.=7.81) |Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Nonrandom parameters in utility functions FASH | QUAL | PRICE | PRICESQ | ASC4 | B1_MAL1 | B1_YNG1 | B1_OLD1 | B2_MAL2 | B2_YNG2 | B2_OLD2 | B3_MAL3 | B3_YNG3 | B3_OLD3 | Standard deviations of latent random effects SigmaE01| SigmaE02| SigmaE03|

Part 24: Stated Choice [29/117] Revealed and Stated Preference Data  Pure RP Data Market (ex-post, e.g., supermarket scanner data) Individual observations  Pure SP Data Contingent valuation (?) Validity  Combined (Enriched) RP/SP Mixed data Expanded choice sets

Part 24: Stated Choice [30/117] Revealed Preference Data  Advantage: Actual observations on actual behavior  Disadvantage: Limited range of choice sets and attributes – does not allow analysis of switching behavior.

Part 24: Stated Choice [31/117] Stated Preference Data  Pure hypothetical – does the subject take it seriously?  No necessary anchor to real market situations  Vast heterogeneity across individuals

Part 24: Stated Choice [32/117] Pooling RP and SP Data Sets - 1  Enrich the attribute set by replicating choices  E.g.: RP: Bus,Car,Train (actual) SP: Bus(1),Car(1),Train(1) Bus(2),Car(2),Train(2),…  How to combine?

Part 24: Stated Choice [33/117] Each person makes four choices from a choice set that includes either 2 or 4 alternatives. The first choice is the RP between two of the 4 RP alternatives The second-fourth are the SP among four of the 6 SP alternatives. There are 10 alternatives in total. A Stated Choice Experiment with Variable Choice Sets

Part 24: Stated Choice [34/117] Enriched Data Set – Vehicle Choice Choosing between Conventional, Electric and LPG/CNG Vehicles in Single-Vehicle Households David A. Hensher William H. Greene Institute of Transport Studies Department of Economics School of Business Stern School of Business The University of Sydney New York University NSW 2006 Australia New York USA September 2000

Part 24: Stated Choice [35/117] Fuel Types Study  Conventional, Electric, Alternative  1,400 Sydney Households  Automobile choice survey  RP + 3 SP fuel classes  Nested logit – 2 level approach – to handle the scaling issue

Part 24: Stated Choice [36/117] Attribute Space: Conventional

Part 24: Stated Choice [37/117] Attribute Space: Electric

Part 24: Stated Choice [38/117] Attribute Space: Alternative

Part 24: Stated Choice [39/117]

Part 24: Stated Choice [40/117] Mixed Logit Approaches  Pivot SP choices around an RP outcome.  Scaling is handled directly in the model  Continuity across choice situations is handled by random elements of the choice structure that are constant through time Preference weights – coefficients Scaling parameters  Variances of random parameters  Overall scaling of utility functions

Part 24: Stated Choice [41/117] Application Survey sample of 2,688 trips, 2 or 4 choices per situation Sample consists of 672 individuals Choice based sample Revealed/Stated choice experiment: Revealed: Drive,ShortRail,Bus,Train Hypothetical: Drive,ShortRail,Bus,Train,LightRail,ExpressBus Attributes: Cost –Fuel or fare Transit time Parking cost Access and Egress time

Part 24: Stated Choice [42/117] Nested Logit Approach Car Train Bus SPCar SPTrain SPBus RP Mode Use a two level nested model, and constrain three SP IV parameters to be equal.

Part 24: Stated Choice [43/117] Each person makes four choices from a choice set that includes either 2 or 4 alternatives. The first choice is the RP between two of the 4 RP alternatives The second-fourth are the SP among four of the 6 SP alternatives. There are 10 alternatives in total. A Stated Choice Experiment with Variable Choice Sets

Part 24: Stated Choice [44/117] Customers’ Choice of Energy Supplier  California, Stated Preference Survey  361 customers presented with 8-12 choice situations each  Supplier attributes: Fixed price: cents per kWh Length of contract Local utility Well-known company Time-of-day rates (11¢ in day, 5¢ at night) Seasonal rates (10¢ in summer, 8¢ in winter, 6¢ in spring/fall) (TrainCalUtilitySurvey.lpj)

Part 24: Stated Choice [45/117] Population Distributions  Normal for: Contract length Local utility Well-known company  Log-normal for: Time-of-day rates Seasonal rates  Price coefficient held fixed

Part 24: Stated Choice [46/117] Estimated Model Estimate Std error Price Contract mean std dev Local mean std dev Known mean std dev TOD mean* std dev* Seasonal mean* std dev* *Parameters of underlying normal.

Part 24: Stated Choice [47/117] Distribution of Brand Value Brand value of local utility Standard deviation 10% dislike local utility 02.5¢ =2.0¢

Part 24: Stated Choice [48/117] Random Parameter Distributions

Part 24: Stated Choice [49/117] Time of Day Rates (Customers do not like – lognormal coefficient. Multiply variable by -1.)

Part 24: Stated Choice [50/117] Estimating Individual Parameters  Model estimates = structural parameters, α, β, ρ, Δ, Σ, Γ  Objective, a model of individual specific parameters, β i  Can individual specific parameters be estimated? Not quite – β i is a single realization of a random process; one random draw. We estimate E[β i | all information about i] (This is also true of Bayesian treatments, despite claims to the contrary.)

Part 24: Stated Choice [51/117] Expected Preferences of Each Customer Customer likes long-term contract, local utility, and non-fixed rates. Local utility can retain and make profit from this customer by offering a long-term contract with time-of-day or seasonal rates.

Part 24: Stated Choice [52/117] Posterior Estimation of  i Estimate by simulation

Part 24: Stated Choice [53/117] Application: Shoe Brand Choice  S imulated Data: Stated Choice, 400 respondents, 8 choice situations, 3,200 observations  3 choice/attributes + NONE Fashion = High / Low Quality = High / Low Price = 25/50/75,100 coded 1,2,3,4  H eterogeneity: Sex (Male=1), Age (<25, , 40+)  U nderlying data generated by a 3 class latent class process (100, 200, 100 in classes)

Part 24: Stated Choice [54/117] Stated Choice Experiment: Unlabeled Alternatives, One Observation t=1 t=2 t=3 t=4 t=5 t=6 t=7 t=8

Part 24: Stated Choice [55/117] Random Parameters Logit Model Individual parameters

Part 24: Stated Choice [56/117] Individual parameters

Part 24: Stated Choice [57/117] Individual parameters

Part 24: Stated Choice [58/117] Panel Data  Repeated Choice Situations  Typically RP/SP constructions (experimental)  Accommodating “panel data” Multinomial Probit [marginal, impractical] Latent Class Mixed Logit

Part 24: Stated Choice [59/117] Customers’ Choice of Energy Supplier  California, Stated Preference Survey  361 customers presented with 8-12 choice situations each  Supplier attributes: Fixed price: cents per kWh Length of contract Local utility Well-known company Time-of-day rates (11¢ in day, 5¢ at night) Seasonal rates (10¢ in summer, 8¢ in winter, 6¢ in spring/fall)

Part 24: Stated Choice [60/117]

Part 24: Stated Choice [61/117] Application: Shoe Brand Choice  S imulated Data: Stated Choice, 400 respondents, 8 choice situations, 3,200 observations  3 choice/attributes + NONE Fashion = High / Low Quality = High / Low Price = 25/50/75,100 coded 1,2,3,4  H eterogeneity: Sex (Male=1), Age (<25, 25-39, 40+)  U nderlying data generated by a 3 class latent class process (100, 200, 100 in classes)

Part 24: Stated Choice [62/117] Stated Choice Experiment: Unlabeled Alternatives, One Observation t=1 t=2 t=3 t=4 t=5 t=6 t=7 t=8

Part 24: Stated Choice [63/117] This an unlabelled choice experiment: Compare Choice = (Air, Train, Bus, Car) To Choice = (Brand 1, Brand 2, Brand 3, None) Brand 1 is only Brand 1 because it is first in the list. What does it mean to substitute Brand 1 for Brand 2? What does the own elasticity for Brand 1 mean? Unlabeled Choice Experiments

Part 24: Stated Choice [64/117] Aggregate Data and Multinomial Choice: The Model of Berry, Levinsohn and Pakes

Part 24: Stated Choice [65/117] 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, A New Computational Algorithm for Random Coefficients Model with Aggregate-level Data, Jinyoung Lee, UCLA Economics, Dissertation, Elasticities of Market Shares and Social Health Insurance Choice in Germany: A Dynamic Panel Data Approach, M. Tamm et al., Health Economics, 16, 2007,

Part 24: Stated Choice [66/117]

Part 24: Stated Choice [67/117]

Part 24: Stated Choice [68/117]

Part 24: Stated Choice [69/117]

Part 24: Stated Choice [70/117]

Part 24: Stated Choice [71/117]

Part 24: Stated Choice [72/117]

Part 24: Stated Choice [73/117]

Part 24: Stated Choice [74/117]

Part 24: Stated Choice [75/117] Aggregate Data and Multinomial Choice: The Model of Berry, Levinsohn and Pakes

Part 24: Stated Choice [76/117] 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 24: Stated Choice [77/117] BLP Automobile Market t JtJt

Part 24: Stated Choice [78/117] 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 24: Stated Choice [79/117] 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 24: Stated Choice [80/117] 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 24: Stated Choice [81/117] 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 24: Stated Choice [82/117] 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 24: Stated Choice [83/117] Instrumental Variables (ξ and ω are our h and f.)

Part 24: Stated Choice [84/117] Econometrics: Essential Components

Part 24: Stated Choice [85/117] Econometrics

Part 24: Stated Choice [86/117] GMM Estimation Strategy - 1

Part 24: Stated Choice [87/117] GMM Estimation Strategy - 2

Part 24: Stated Choice [88/117] BLP Iteration

Part 24: Stated Choice [89/117] ABLP Iteration ξ t is our f t.  is our (β,  ) No superscript is our (M); superscript 0 is our (M-1).

Part 24: Stated Choice [90/117] Side Results

Part 24: Stated Choice [91/117] ABLP Iterative Estimator

Part 24: Stated Choice [92/117] BLP Design Data

Part 24: Stated Choice [93/117] Exogenous price and nonrandom parameters

Part 24: Stated Choice [94/117] IV Estimation

Part 24: Stated Choice [95/117] Full Model

Part 24: Stated Choice [96/117] Some Elasticities

Part 24: Stated Choice [97/68] Fixed Effects Multinomial Logit: Application of Minimum Distance Estimation

Part 24: Stated Choice [98/117] Binary Logit Conditional Probabiities

Part 24: Stated Choice [99/117] Example: SevenPeriod Binary Logit

Part 24: Stated Choice [100/117]

Part 24: Stated Choice [101/117]

Part 24: Stated Choice [102/117] The sample is 200 individuals each observed 50 times.

Part 24: Stated Choice [103/117] The data are generated from a probit process with b1 = b2 =.5. But, it is fit as a logit model. The coefficients obey the familiar relationship, 1.6*probit.

Part 24: Stated Choice [104/117] Multinomial Logit Model: J+1 choices including a base choice.

Part 24: Stated Choice [105/117] Estimation Strategy  Conditional ML of the full MNL model. Impressively complicated.  A Minimum Distance (MDE) Strategy Each alternative treated as a binary choice vs. the base provides an estimator of   Select subsample that chose either option j or the base  Estimate  using this binary choice setting  This provides J different estimators of the same  Optimally combine the different estimators of 

Part 24: Stated Choice [106/117] Minimum Distance Estimation

Part 24: Stated Choice [107/117] MDE Estimation

Part 24: Stated Choice [108/117] MDE Estimation

Part 24: Stated Choice [109/117]

Part 24: Stated Choice [110/117]

Part 24: Stated Choice [111/117]

Part 24: Stated Choice [112/117]

Part 24: Stated Choice [113/117]

Part 24: Stated Choice [114/117]

Part 24: Stated Choice [115/117]

Part 24: Stated Choice [116/117]

Part 24: Stated Choice [117/117] Why a 500 fold increase in speed?  MDE is much faster  Not using Krailo and Pike, or not using efficiently  Numerical derivatives for an extremely messy function (increase the number of function evaluations by at least 5 times)