An Alternative Two Stage Least Squares (2SLS) Estimator for Latent Variable Equations

The Maximum-likelihood estimator dominates the estimation of general structural equation models. Noniterative, equation-by-equation estimators for factor analysis have received some attention, but little has been done on such estimators for latent variable equations. I propose an alternative 2SLS estimator of the parameters in LISREL type models and contrast it with the existing ones. The new 2SLS estimator allows observed and latent variables to originate from nonnormal distributions, is consistent, has a known asymptotic covariance matrix, and is estimable with standard statistical software. Diagnostics for evaluating instrumental variables are described. An empirical example illustrates the estimator.