Abstract
Three methods can be used to estimate simultaneous equation models with latent dependent variables: two-stage, minimum distance (MD) and full-information maximum likelihood. Theoretically all the three methods provide asymptotically consistent estimates, but the performance of these estimators in finite samples cannot be determined in theory. This letter evaluates the performance of these estimators in finite samples using Monte Carlo simulation. The results show that the MD estimator performs very poorly; overall the full information maximum likelihood estimator performs better than the other two estimators.
Notes
1For example, such models have been used to examine the relationship between health and labour force status (Stern, Citation1989; Cai and Kalb, Citation2006) and job satisfaction and life satisfaction (Rain et al., Citation1991).
2The estimation methods discussed here apply to models with more than two latent dependent variables, but here we focus on models with two endogenous variables for ease of exposition.
3For illustration purposes we let the observed counterparts of the latent variables take a dichotomous form, but the methods can be generalized to polychotomous forms (Cai and Kalb, Citation2006).
4The construction of V 1 may require some initial consistent estimates of α1 which can be derived by applying the ordinary lease square procedure to Equation 12.
5Due to the latent nature of the dependent variables, the variance of ϵ1 and ϵ2 has to be normalized to one.
6Gauss codes for implementing the FIML method as discussed in the letter can be provided by the author on request.