Simultaneous Equations Systems

Flashcards about Simultaneous Equations Systems.

Simultaneity

Occurs if at least two variables are jointly determined, often resulting from separate behavioral mechanisms coordinated in equilibrium.

Typical case of simultaneity

Observed outcomes are the result of separate behavioral mechanisms that are coordinated in an equilibrium.

Simultaneous Equations Model (SEM)

A system where observed wage and hours are determined by the intersection of supply and demand.

Endogenous Variables

Variables determined within the model.

Exogenous Variables

Variables determined outside the model.

Note about Exogenous Variables

Without separate exogenous variables in each equation, the two equations could never be distinguished/separately identified.

Structural error terms

Uncorrelated with the exogenous variables.

Simultaneity bias

Arises because an explanatory variable is correlated with the error term.

Why OLS is inconsistent in the presence of simultaneity

Variable is correlated with the error because the error is indirectly a part of the variable; OLS applied to this equation will therefore be inconsistent.

First stage of 2SLS

Each endogenous variable is regressed on the full list of exogenous variables.

Second stage of 2SLS

The system equations are estimated by OLS with the endogenous regressors being replaced by predictions from stage one.

Order condition

A necessary condition for the identification of an equation where there are more excluded exogenous variables than endogenous regressors.

Rank condition

The equation is identified if, and only if, the other equation contains at least one exogenous variable that is excluded from the first equation.

Hypothesis B22 = B23 = 0

Rejecting this implies that the labor supply function is identified.

Reduced form equation

Can be consistently estimated by OLS as it contains only exogenous variables.