Handbook of Econometrics Vols1-5 _ Chapter 24 pps

Chuppter 24 ECONOMETRIC ANALYSIS RESPONSE MODELS OF QUALITATIVE DANIEL L MCFADDEN Massachusetts Institute of Technology Contents The problem Binomial response models 2.1 2.2 2.3 2.4 Estimation Contingency table analysis 2.5 Minimum &i-square method 2.6 Latent variable specification Functional forms Discriminant analysis Multinomial response models 3.1 3.2 Foundations Statistical analysis 3.3 Functional form 3.4 The multinomial logit model 3.5 Independence from irrelevant alternatives 3.6 Limiting the number of alternatives 3.7 Specification tests for the MNL model 3.8 Multinomial probit 3.9 Elimination models 3.10 Hierarchical response models 3.11 An empirical example Further topics 4.1 Extensions 4.2 Dynamic models 4.3 Discrete-continuous 4.4 Self-selection and biased samples 4.5 Statistical methods systems Conclusion Appendix: Proof outlines for Theorems l-3 References Handbook of Econometrics, Volume II, Edited by Z Griliches and M.D Intriligator Elseoier Science Publishers BV, 1984 1396 1396 1396 1397 1398 1400 1400 1401 1403 1403 1406 1410 1411 1413 1415 1417 1418 1420 1422 1428 1433 1433 1433 1434 1436 1439 1442 1442 1446 D L McFadden 1396 The problem An example is potential bias in analysis of housing expenditure population of renters 2 I in a self-selected Binomial response models Latent variable specification The starting point for econometric analysis of a continuous response variable y is often a linear regression model: Y, = XrP- Et, (2.1) where x is a vector of exogenous variables, E is an unobserved disturbance, and t=l , , T indexes sample observations The disturbances are usually assumed to have a convenient cumulative distribution function F(E~x) such as multivariate normal The model is then characterized by the conditional distribution 1397 Ch 24: Qualitative Response Models up to the unknown parameters /3 and parameters of the distribution xp may have a structure derived exactly or approximately from theory For example, competitive firms may have x/3 determined by Shephard’s identity from a profit function The linear regression model is extended to binomial response by introducing an intermediate unobserved (latent) variable y* with: F(y - xplx), F In economic applications, Y: = X,P- and an 0, ify: > > m of the alternatives is the product of conditional probabilities of choice from successively