Estimation of simultaneous equation models with latent dependent variables: a Monte Carlo evaluation

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, 1989; Cai and Kalb, 2006) and job satisfaction and life satisfaction (Rain et al., 1991).

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, 2006).

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.