Palgrave Handbook of Econometrics: Applied Econometrics

492 Discrete Choice Modeling 11.3.3.1 Gibbs sampler for the binomial probit model ComputeW′Wonce at the outset and obtainLsuch ...

William Greene 493 whereGis an unknown continuous distribution function whose range is [0,1]. The functionGis not specifieda pri ...

494 Discrete Choice Modeling is an ambiguous virtue in this context. As we have seen, the raw coefficients are of questionable v ...

William Greene 495 This form of the moment equation, based on observables, can form the basis of a straightforward two-step gene ...

496 Discrete Choice Modeling Therefore: Prob[di= 1 |xi,zi]=# [ x′iβ+γzi+(ρ/σ )ui √ 1 −ρ^2 ] . Inserting the expression forui=(zi ...

William Greene 497 correlated with the included variables,xit. Since the model is nonlinear, the least squares estimator is unus ...

498 Discrete Choice Modeling population values of both coefficients are 1.0. The results, which are consistent with other studie ...

William Greene 499 For convenience, denote the “known”x′itβasbit. The first-order condition for maximizing lnLwith respect toαi, ...

500 Discrete Choice Modeling whereE[ui|xit]=0 and Var[ui|xit] = 1 and: dit=1ifd∗it>0, anddit=0 otherwise. (Since the random e ...

William Greene 501 Efficiency is a moot point for this estimator, since the probit MLE estimatesβ with a bias toward zero: plimβ ...

502 Discrete Choice Modeling wherewhandzhare the weights and nodes of the quadrature (see Abramovitz and Stegun, 1971) andHis th ...

William Greene 503 random effects model that can be estimated, as in the static case, by Hermite quadrature of maximum simulated ...

504 Discrete Choice Modeling The specification is completed by the assumptions about the process that generates the individual s ...

William Greene 505 Table 11.2 Variables in German health care data file Variable deviation Mean Standard Year Calendar year of t ...

506 Table 11.3 Estimated parameters for panel data binary choice models Variable Model Estimate lnL Constant Age Income Kids Edu ...

507 Probit:RE d (^2) ρ =0.44799 β (ME) − 16279.97 0.033290 0.020078(0.00715) − 0.002973 (− 0.00106) − 0.153579 (− 0.0547) − 0.03 ...

508 Discrete Choice Modeling the two models. The first two rows of partial effects in Table 11.3 compare the partial effects com ...

William Greene 509 of thousands of samples of potentially thousands of observations. We used only 500 replications to produce th ...

510 Discrete Choice Modeling The 5% critical value from the chi-squared distribution with 6 degrees of freedom is 12.592, so thi ...

William Greene 511 is the joint probability, Prob(di,1=1,di,2= 1 )=# 2 [ wi′,1θ 1 ,w′i,2θ 2 ,ρ ] , that is analyzed by Christofi ...