Simultaneous Equation Model
A Simultaneous Equation Model is an econometric framework used to analyze systems with multiple interdependent relationships. Unlike simple regression models, SEMs capture situations where one variable can act as both an independent and dependent variable across different equations.
Key Characteristics
- Interdependence:
- Variables are determined simultaneously, making it impossible to treat them as purely independent or dependent.
- Example: In supply and demand, price (PPP) and quantity (QQQ) are mutually dependent.
- Structural Form:
- SEMs are written as a system of equations that specify the relationships between endogenous and exogenous variables.
- Example:
- Demand Equation: Qd=a−bP+cI
- Supply Equation: Qs=d+eP
(P is endogenous; I is exogenous).
- Reduced Form:
- The endogenous variables are expressed solely in terms of exogenous variables and error terms.
- Example: P=f(I), Q=g(I)
- Endogeneity Problem:
- Ordinary Least Squares (OLS) cannot be used directly because endogenous variables are correlated with the error term, causing simultaneity bias.