Simultaneous equations

• In short, economic endogeneity is closely related to econometric (statistical) endogeneity.

Simultaneous equation Model

Let’s return to original model which allows additional observed determinants of demand and supply. Suppose we have two equations of demand and supply for some good such as

(p) = + p + + (1)

(p) = + p + + (2)

These equations (1) abd (2) are called structural equations.

Equilibrium condition requires that ==

.....> + p + + = + p + +

-- +

+ + (3)

Note that the random part of the error term – is surely correlated with both structural errors

 

Simultaneous Equation Model

• Substituting this into =
• --
• --- = + + (4)

The reduced forms for is

• + +
• = + +

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Simultaneous Model

• (p) = + p + + (1)
• (p) = + p + + (2)
• +
• + + (3)
• = + + (4)

•  

Simultaneous Model

, =

Obtaining parameters in reduced form equations, we can recover structural parameters. ---- This method is called indirect least square(ILS) estimation. ILS estimates of structural parameters are consistent

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Simultaneous Equation Model

• Reduced form equations are regressions: their errors are uncorrelated with RHS variables. This is because regressers in the reduced form ( and ) are assumed to be uncorrelated with the structural errors.

• In general, reduced form equations–one for each endogenous variable–are found by solving for all endogenous variables as a function of the exogenous variables in the system.

- The above example shows that the structural coefficients can be obtained from the reduced form. Here the structural coefficients are , , , , Estimating reduced form equation we can recover these structural coefficients.

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