Bayesian Versus Frequentist Inference in Structural Equation Modeling: Finite-Sample Properties and Economic Applications

Structural Equation Modeling (SEM) is a key framework for analyzing complex economic relationships involving latent variables, mediation effects, and endogeneity, yet the choice between frequentist and Bayesian estimation remains theoretically and practically contested, especially in settings with non-stationary data and small samples. This study provides a formal comparison of the two approaches by formulating SEM as a probabilistic graphical model and deriving the corresponding estimation procedures, identifiability conditions, and uncertainty measures. We examine asymptotic properties of frequentist estimators and posterior consistency in Bayesian SEM, with particular attention to integrated time-series SEM applications such as shadow economy estimation. The analysis shows that while both approaches converge under large-sample conditions, important differences arise in finite samples. Bayesian methods exhibit more stable point estimates through coherent uncertainty quantification, particularly when prior information regularizes an otherwise ill-conditioned likelihood. Under model misspecification, Bayesian posteriors concentrate around the pseudo-true parameter defined by the Kullback-Leibler projection, providing a probabilistic representation of misspecification uncertainty through posterior spread—an advantage over frequentist inference, which typically conditions on the maintained model as exact. These findings carry direct implications for empirical economic modeling under realistic data constraints. In settings where sample sizes are small, identification is weak, and model uncertainty is substantial, conditions that routinely characterize macroeconomic research, the choice of inferential framework is not a matter of philosophical preference but a determinant of whether policy-relevant conclusions can be credibly defended. Bayesian SEM offers a principled and transparent path forward in precisely these conditions.