Chapter 9 . Simultaneous equations estimation

1. General definitions

Simultaneous equations contain equilibrium equations.

Endogenous variables are determined inside the system. Exogenous variables are determined externally.

Equations of the original system are called structural because they describe the structure of (a part of) the economy. A reduced form equation is of type:

Endogenous variable = Function(Exogenous variables, error term)

Often structural equations contain lags of endogenous variables.

A system of structural equations is called complete if:

1) The number of endogenous variables equals the number of equations, and

2) The system can be solved for the endogenous variables expressing each of them in a reduced form.

It is the duty of the researcher to make the system complete.

Important: the dependence between the coefficients of the original system and the coefficients of the reduced form is usually nonlinear.

Comparison:

1) Structural equations allow one to check the explanatory power of economic theories.

2) Reduced form equations are easier to use for prediction purposes, and also to see how exogenous variables affect endogenous ones.

Structural equation types:

1) Behavioral (which are hypotheses and describe the behavior of a sector of an economy).

2) Definitional (identities of type that are deduced logically).

3) Institutional (of type Tax = Tax rate times Income, which are introduced by government institutions).

Example 1: determination of prices and wages. = price level, = wage level, = unemployment level

(1) price inflation equation: (from the producers point of view)

(2) wage inflation equation: (from the workers point of view)

Using this example, illustrate all relevant definitions given above.

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