计量经济分析（第六版）答案 Notes-25.doc

Econometrics I Professor William Greene Notes 25. Discrete Choice, Duration and Censoring I. Discrete Choice Among Multiple Alternatives A. Random Utility Model U(i,j) = ??x(i,j) + ?(i,j) B. The Independent Utilities Extreme Value - Multinomial Logit Model ?(i,j) ~ exp(-exp(?(i,j))), all independent Leads to Prob[ individual i makes choice j] = Prob[ U(i,j) u(i,k) for all k not j] P(i,j) = IV = inclusive value = LogSum --- Used as a measure of consumer surplus C. Estimated by maximum likelihood: LogL = ?i log Prob[actual outcomes] D. Application: Survey of 210 people traveling between Sydney and Melbourne Mode = 0/1 for four alternatives: 1=Air, 2=Train, 3=Bus, 4=Car, Ttme = Terminal waiting time, 0 for Car Invc = Invehicle cost for all stages, Invt = Invehicle time for all stages, Gc = Generalized cost measure = Invc + Invt * value of time, Chair = Dummy variable for chosen mode is Air, Hinc = Household income in thousands, Psize = Traveling party size. +---------------------------------------------+ | Discrete choice (multinomial logit) model | | Maximum Likelihood Estimates | | Dependent variable Choice | | Weighting variable ONE | | Number of observations 210 | | Iterations completed 6 | | Log likelihood function -182.3383 | | Log-L for Choice model = -182.3383 | | R2=1-LogL/LogL* Log-L fncn R-sqrd RsqAdj | | No coefficients -291.1218 .37367 .36561 | | Constants only -283.7588 .35742 .34915 | | Chi-squared[ 5] = 202.84091 | | Significance for chi-squared = 1.00000 | | Response data are given as ind. choice. | | Number of obs.= 210, skipped 0 bad obs. | +---------------------------------------------+ +---------+--------------+----------------+--------+---------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|z] | +---------+