Endogeneity in Econometrics: Simultaneous Equations Models Ming LU

Simultaneity This arises when one or more of the explanatory variables is jointly determined with the dependent variable, typically through an equilibrium mechanism. The method of instrumental variables. Why do we need to estimate structural model rather than reduced-form model?

THE NATURE OF SIMULTANEOUS EQUATIONS MODELS

Concepts Endogenous variables Exogenous variables Structural errors Each equation should have a behavioral, ceteris paribus interpretation on its own.

SIMULTANEITY BIAS IN OLS

simultaneity bias

IDENTIFYING AND ESTIMATING A STRUCTURAL EQUATION Identification in a Two-Equation System The first is supply equation. The second is demand equation.

A general two-equation model

Exclusion restrictions In other words, we assume that certain exogenous variables do not appear in the first equation and others are absent from the second equation.

RANK CONDITION FOR IDENTIFICATION OF A STRUCTURAL EQUATION The first equation in a two-equation simultaneous equations model is identified if and only if the second equation contains at least one exogenous variable (with a nonzero coefficient) that is excluded from the first equation. The order condition is necessary for the rank condition. The rank condition requires more: at least one of the exogenous variables excluded from the first equation must have a nonzero population coefficient in the second equation.

Estimation by 2SLS This is similar in the previous chapter.

SYSTEMS WITH MORE THAN TWO EQUATIONS

ORDER CONDITION FOR IDENTIFICATION An equation in any SEM satisfies the order condition for identification if the number of excluded exogenous variables from the equation is at least as large as the number of right-hand side endogenous variables. Overidentified equation, just identified equation, and unidentified equation.

Estimation 2SLS 3SLS – More efficient using the residuals to do GLS estimation at the third stage. More sensitive to variable selection.

SIMULTANEOUS EQUATIONS MODELS WITH PANEL DATA (1) eliminate the unobserved effects from the equations of interest using the fixed effects transformation or first differencing; (2) find instrumental variables for the endogenous variables in the transformed equation. Challenging, because for a convincing analysis we need to find instruments that change over time.

How to do if you want to identify the fixed-effects? Put time dummies and fixed-effects dummies in the structural model.

The end.