Linear structural equation models (SEMs) are widely used to model dependencies among observed variables using mixed graphs with directed and bidirected edges. A central challenge is the identifiability and estimation of structural coefficients from observational data. The half-trek criterion (HTC) provides a sufficient graphical condition for generic identifiability and yields explicit rational formulas for parameters. In this work, we study the statistical properties of HTC-based plug-in estimators, interpreting them as M-estimators and generalized method of moments (GMM) estimators. We analyze their asymptotic variance using the sandwich formula and extend the framework to two-step GMM when sequential identification is required. Crucially, we investigate the existence of multiple valid HTC-identifying sets and study their impact on estimator efficiency. We develop theoretical and simulation-based methods to identify asymptotically optimal plug-in estimators, providing guidance for practical model estimation. Our results bridge graphical identifiability theory with statistical efficiency considerations, offering both methodological insights and applied tools.     «

Linear structural equation models (SEMs) are widely used to model dependencies among observed variables using mixed graphs with directed and bidirected edges. A central challenge is the identifiability and estimation of structural coefficients from observational data. The half-trek criterion (HTC) provides a sufficient graphical condition for generic identifiability and yields explicit rational formulas for parameters. In this work, we study the statistical properties of HTC-based plug-in estima...     »