Applied Econometrics：Discrete Choice Modeling

Ui,suv > Ui,sed Ui,suv - Ui,sed > 0 (SUV-SED) + (PSUV-PSED) + (SUV-sed)Income + i,suv - i,sed > 0 i > -[ + (PSUV-PSED) + Income]
Chooses SUV:

First application: Fly or Other
Binary Choice Data
Choose Air 1.0000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 1.0000 1.0000 1.0000 .00000 1.0000 .00000 .00000 Gen.Cost 86.000 67.000 77.000 69.000 77.000 71.000 58.000 71.000 100.00 158.00 136.00 103.00 77.000 197.00 129.00 123.00 Term Time 25.000 69.000 64.000 69.000 64.000 64.000 64.000 69.000 64.000 30.000 45.000 30.000 69.000 45.000 64.000 64.000 Income 70.000 60.000 20.000 15.000 30.000 26.000 35.000 12.000 70.000 50.000 40.000 70.000 10.000 26.000 50.000 70.000
Applied Econometrics
Discrete Choice Mod Platform



Consumers Maximize Utility (!!!) Fundamental Choice Problem: Maximize U(x1,x2,…) subject to prices and budget constraints A Crucial Result for the Classical Problem:
Choosing Between Two Alternatives

Modeling the Binary Choice Ui,suv = suv + Psuv + suvIncome + i,suv Ui,sed = sed + Psed + sedIncome + i,sed

What Can Be Learned from the Data? (A Sample of Consumers, i = 1,…,N)
• Are the attributes “relevant?”
• Predicting behavior
- Individual
- Aggregate
• Analyze changes in behavior when
Income)]

Note the relationship between the unobserved and the outcome

Choice sets and consideration sets – consumers simplify choice situations Implication for choice among a set of discrete alternatives Commonalities and uniqueness
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


Indirect Utility Function: V = V(p,I) Demand System of Continuous Choices
x
* j
V (p, I) / p j V (p, I) / I

The Integrability Problem: Utility is not revealed by demands

Does this allow us to build “models?” What common elements can be assumed? How can we account for heterogeneity?

Revealed choices do not reveal utility, only rankings which are scale invariant
Theory for Discrete Choice

Theory is silent about discrete choices Translation to discrete choice

Existence of well defined utility indexes: Completeness of rankings Rationality: Utility maximization Axioms of revealed preferences
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 +