This article develops a method for implementing a simulated multivariate random-effects probit model for unbalanced panels (with gaps) and illustrates the model by using artificial data. Halton draws generated by mdraws are used to simulate multivariate normal probabilities with the mvnp() egen function. The estimator can be easily adjusted, for example, to allow for autocorrelated errors. The advantages of this simulated estimation, when compared with existing commands such as redpace, are high accuracy and improved stability.
ArulampalamW.1999. A note on estimated coefficients in random effects probit models. Oxford Bulletin of Economics and Statistics61: 597–602.
2.
CappellariL., and JenkinsS. P.2003. Multivariate probit regression using simulated maximum likelihood. Stata Journal3: 278–294.
3.
CappellariL., and JenkinsS. P.2005. Software update: st0045_1: Multivariate probit regression using simulated maximum likelihood. Stata Journal5: 285.
4.
CappellariL., and JenkinsS. P.2006a. Calculation of multivariate normal probabilities by simulation, with applications to maximum simulated likelihood estimation. Stata Journal6: 156–189.
5.
CappellariL., and JenkinsS. P.2006b. Software update: st0045_2: Multivariate probit regression using simulated maximum likelihood. Stata Journal6: 284.
6.
ChamberlainG.1984. Panel data. In Handbook of Econometrics, ed. GrilichesZ., and IntriligatorM. D., vol. 2, 1247–1318. Amsterdam: Elsevier.
7.
DrukkerD. M., and GatesR.2006. Generating Halton sequences using Mata. Stata Journal6: 214–228.
8.
GouldW., PitbladoJ., and PoiB.2010. Maximum Likelihood Estimation with Stata. 4th ed. College Station, TX: Stata Press.
9.
HaanP., and UhlendorffA.2006. Estimation of multinomial logit models with unobserved heterogeneity using maximum simulated likelihood. Stata Journal6: 229–245.
10.
HeckmanJ. J.1981a. Heterogeneity and state dependence. InStudies in Labor Markets, ed. RosenS., 91–140. Chicago: University of Chicago Press.
11.
HeckmanJ. J.1981b. The incidental parameters problem and the problem of initial conditions in estimating a discrete time—Discrete data stochastic process. In Structural Analysis of Discrete Data with Econometric Applications, ed. ManskiC. F., and McFaddenD., 179–195. Cambridge: MIT Press.
12.
HoleA. R.2007. Fitting mixed logit models by using maximum simulated likelihood. Stata Journal7: 388–401.
13.
KeaneM. P.1994. A computationally practical simulation estimator for panel data. Econometrica62: 95–116.
14.
KolenikovS.2005. primes: Stata module to generate prime numbers. Statistical Software Components S456504, Department of Economics, Boston College.http://ideas.repec.org/c/boc/bocode/s456504.html.
15.
MundlakY.1978. On the pooling of time series and cross section data. Econometrica46: 69–85.
StewartM. B.2006b. Maximum simulated likelihood estimation of random-effects dynamic probit models with autocorrelated errors. Stata Journal6: 256–272.
18.
TrainK. E.2009. Discrete Choice Methods with Simulation. 2nd ed. Cambridge: Cambridge University Press.
19.
WooldridgeJ. M.2005. Simple solutions to the initial conditions problem in dynamic, nonlinear panel data models with unobserved heterogeneity. Journal of Applied Econometrics20: 39–54.
