The Mathematical Foundations of Bayesian Versus Frequentist Inference in Structural Equation Modeling: Resolving the Dilemma for 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 inference through coherent uncertainty quantification and greater robustness to model misspecification, especially when prior theoretical information is available. In contrast, frequentist estimators rely more heavily on asymptotic assumptions that may be violated in typical economic datasets. These findings suggest that Bayesian SEM offers practical advantages for empirical economic modeling under realistic data constraints, without rejecting the theoretical validity of frequentist methods in large-sample settings.