Forecasting with simultaneous equation models: a synthetic data generator for structural evaluation

Abstract Simultaneous equation models (SEM), an econometric technique traditionally employed in economics, have seen their application expand into disparate disciplines in recent decades. These models facilitate the representation of bidirectional, simultaneous relationships among variables within a complex system of equations. An SEM delineates the interdependent influences among a set of endogenous variables, which are concurrently influenced by a set of exogenous variables. The magnitude of this influence is quantified via model coefficients, which are estimable using established techniques including, inter alia, two-stage least squares (2SLS), three-stage least squares (3SLS), and indirect least squares (ILS). In numerous SEM-related research domains—such as analyzing the computational cost of SEM resolution, identifying optimal model fit for a given dataset, or determining the optimal estimator for SEM coefficients based on data variability—utilizing simulated data is essential. Simulated data permit researchers to rigorously evaluate a comprehensive spectrum of scenarios within the SEM parameter space. Consequently, robust libraries and algorithms capable of generating SEM-based synthetic data are indispensable for the investigation and refinement of subsequent econometric models. The primary objective of this study is to comparatively evaluate the forecast accuracy of endogenous variables within an SEM framework. This comparison contrasts forecasts incorporating future exogenous variable values against those that disregard the underlying structural information of said exogenous variables. This paper proposes and analyzes a novel synthetic data generator for simultaneous equation models, capable of constructing models adhering to an SEM structure based on predefined characteristics (e.g., model dimensionality, stochastic variability). This generator integrates contemporaneous relationships among dependent (endogenous) variables, incorporates their lagged values as determinants, and considers exogenous variables that affect the system without being reciprocally influenced. The proposed generator offers a flexible and robust tool, poised to advance research and experimentation within the SEM domain.