Econometric Analysis of Panel Data,William Greene Department of Economics Stern School of Business,Econometric Analysis of Panel Data,15. Models for Binary Choice,Agenda and References,Binary choice modeling the leading example of formal nonlinear modeling Binary choice modeling with panel data Models for heterogeneity Estimation strategies Unconditional and conditional Fixed and random effects The incidental parameters problem JW chapter 15, Baltagi, ch. 11, Hsiao ch. 7, Greene ch. 23.,Two Fundamental Building Blocks,Underlying Behavioral Theory: Random utility modelThe link between underlying behavior and observed data Empirical Tool: Stochastic, parametric model for binary choiceA platform for models of discrete choice,Behavioral Assumptions,Preferences are transitive and complete wrt choice situations Utility is defined over alternatives: Uit Utility maximization assumptionIf Uit1 Uit2, consumer chooses alternative 1, not alternative 2. Revealed preference (duality)If the consumer chooses alternative 1 and not alternative 2, then Uit1 Uit2.,Random Utility Functions,Uit = + xit + zi + ui + it,xit = Attributes of choice presented to person = Taste or preference weights zi = Characteristics of the person = Weights on person specific characteristics it = Unobserved random component of utilityMean: Eit = 0, Varit = 1,Health Satisfaction Scale,0 = Not Healthy,1 = Healthy,A Model for Binary Choice,Yes or No decision (Buy/Not buy) Example, choose to fly or not to fly to a destination when there are alternatives. Model: Net utility of flyingUfly = +1Cost + 2Time + Income + Choose to fly if net utility is positive Data: X = 1,cost,terminal timeZ = incomey = 1 if choose fly, Ufly 0, 0 if not.,What Can Be Learned from the Data? (A Sample of Consumers, i = 1,n),Are the attributes relevant?Predicting behaviorIndividualAggregateAnalyze changes in behavior when attributes change,Application,210 Commuters Between Sydney and Melbourne Available modes = Air, Train, Bus, Car Observed: Choice Attributes: Cost, terminal time, other Characteristics: Household income First application: Fly or other,The Data,Listing of raw data (Current sample) Line Observ MODE GC TTME HINC1 1 0 70 69 352 5 0 68 64 303 9 0 129 69 404 13 0 59 64 705 17 0 82 64 456 21 0 70 69 207 25 1 160 45 458 29 0 137 69 129 33 0 70 69 4010 37 0 65 69 7011 41 0 68 64 1512 45 0 79 64 3513 49 0 63 64 5014 53 0 72 64 4015 57 0 109 64 2616 61 0 73 69 2617 65 0 69 69 2618 69 0 76 69 619 73 0 75 69 2020 77 0 72 64 7221 81 0 69 69 622 85 0 98 64 1023 89 1 153 90 5024 93 1 132 50 5025 97 1 92 15 1826 101 1 106 30 6027 105 1 87 80 4528 109 1 106 45 1829 113 0 101 64 830 117 0 70 69 6,An Econometric Model,Choose to fly iff UFLY 0 Ufly = +1Cost + 2Time + Income + Ufly 0 -(+1Cost + 2Time + Income) Probability model: For any person observed by the analyst, Prob(fly) = Prob -(+1Cost + 2Time + Income) Note the relationship between the unobserved and the outcome,+1Cost + 2TTime + Income,Econometrics,How to estimate , 1, 2, ? Its not regression It looks like regression: If there are many repeated observations for each xi so 0 -(+1Cost + 2Time + Income)Proby=0 = 1 - Proby=1 Requires a model for the probability,Completing the Model: F(),The distribution Normal: PROBIT, natural for behavior Logistic: LOGIT, allows “thicker tails” Gompertz: EXTREME VALUE, asymmetric, underlies the basic logit model for multiple choice Does it matter? Yes, large difference in estimates Not much, quantities of interest are more stable. We focus on parametric models; Specific distributions Semiparametric models exist. They estimate parameters “up to scale.” No probabilities, no partial effects.,