ADDRESSING SIMULTANEITY CHALLENGES IN SIMULTANEOUS EQUATION MODELS: THEORETICAL COMPARISON BETWEEN SEQUENTIAL (ILS, 2SLS LIML) AND SYSTEM (3SLS & FIML) METHODS

Abstract

Simultaneous Equations Models (SEMs) represent an essential category of statistical models where dependent variables are determined not only by independent variables but also by other dependent variables within the system. This scenario introduces simultaneity in the system making estimation cumbersome. This implies that the explanatory variables may be interrelated with the dependent variables, reflecting equilibrium mechanisms commonly found in economic models. For example, in a standard supply and demand model, both the quantity supplied, and the quantity demanded are influenced by the market price. Although sequential estimation methods like 2SLS and LIML are widely used in practice, they have certain limitations when applied to systems of equations with strong interdependencies between the equations. In such cases, system methods like, Three-Stage Least Squares (3SLS) and Full Information Maximum Likelihood (FIML), estimate all equations in the system simultaneously, are often more appropriate. The choice of appropriate estimation method depends on the structure of the simultaneous equation model and the nature of the relationships between the endogenous and exogenous variables. While Sequential equation methods like 2SLS and IV provide practical solutions for addressing endogeneity, system equation methods like 3SLS and FIML offer more efficient estimates by considering the full interdependence of the system.