A Computationally Practical Simulation Estimator for Panel Data

In this paper I develop a practical extension of McFadden's method of simulated
moments estimator for limited dependent variable models to the panel data case. The
method is based on a factorization of the MSM first order condition into transition
probabilities, along with the development of a new highly accurate method for similating
these transition probabilities. A series of Monte-Carlo tests show that this MSM estimator
performs quite well relative to quadrature-based ML estimators, even when large
numbers of quadrature points are employed. The estimator also performs well relative to
simulated ML, even when a highly accurate method is used to simulate the choice
probabilities. In terms of computational speed, complex panel data models involving
random effects and ARMA errors may be estimated via MSM in times similar to those
necessary for estimation of simple random effects models via ML-quadrature.
KEYWORDSM: ethod of simulated moments, panel data, limited dependent variables,
equicorrelation, importance sampling, multinomial probit.
1. INTRODUCTION
AN IMPORTANT PROBLEM in the panel data literature is the estimation of limited
dependent variable (LDV) models in the presence of serially correlated errors.
Maximum likelihood estimation (ML) of these models generally requires the
evaluation of choice probabilities which are multivariate integrals-with the
order of integration proportional to the number of time periods in the panel. In
order to make estimation practical, it is typically assumed that the covariance
matrix of the errors has some simple form which allows the order of integration
to be reduced. In particular, it is generally assumed that the errors are i.i.d. or
that they are equicorrelated. The latter assumption leads to the popular random
effects model (see Heckman (1981)) which is practical to estimate using the
Gaussian quadrature procedure described by Butler and Moffitt (1982).
The assumption that errors are either equicorrelated or i.i.d. can be undesirable
in many situations. Economic theory often suggests of serially correlated
error components. Furthermore, if we wish to use an LDV model for prediction
purposes, it is important to determine the error structure which gives the best fit
to the data, rather than imposing a particular structure a priori.