The Structure Beneath 2SLS: A Mean and Covariance Approach to Instrumental Variables Regression

Instrumental variables (IV) methods are central to econometrics, yet their connection to psychometric structural equation modeling (SEM) has remained largely unexplored. This article extends Browne’s weighted least squares (WLS) theory to multi-stage estimation of models that partition parameters into interdependent blocks, each estimated sequentially while conditioning on results from earlier stages. Within this unified framework, we show that the standard econometric estimator—two-stage least squares (2SLS)—is a special case of a multi-stage mean and covariance structure estimator. Under multivariate normality, SEM-based standard errors (SEs) are algebraically identical to econometric SEs under homoscedasticity, and Browne’s residual-based test coincides with Sargan’s overidentification test. Likewise, asymptotically distribution-free (ADF) SEs correspond exactly to heteroscedasticity-robust SEs, and Browne’s ADF residual test is asymptotically equivalent to Hansen’s J test. By revealing the mean–covariance structure underlying 2SLS, we clarify the conceptual and statistical unity between econometric IV estimation and psychometric SEM. The results demonstrate that both traditions rely on the same moment conditions, differ only in scope and inference, and can be viewed as complementary approaches within a single multi-stage estimation framework.