Indirect Least Squares (Basics - Applied Econometrics)

 ■ ILS

ILS is used to identify the parameters of the Just Identified model ( will discuss about rules of identification in upcoming blogs.

In the just identified, there is one correspondence between the reduced form coefficients and structural parameters.

So from the reduced form coefficients, we shall obtained the unique estimates of the structural parameters.

ILS has 3 steps:

a) First, obtain the reduced form equations (each reduced form equations express endogenous variables as a function of the pre determined variables and the stochastic error term).

b) Second, apply the OLS to the reeuced forl equations, (such estimators will be consistent).

As we will derive later that pi1, pi2, pi3, etc are the reduced form coefficients and the estimated reduced form coefficients are pihat1, pihat2, pihat3, etc.

In general they are consistent, but in the some condition these pi's will be 'best unbiased', if the explanatory variables are purely non stochastic, but explanatory variables will not contain the lagged values of the endogenous variables.

c) Third, we obtain the values of the structural parameters from the reduced form coefficients utilising the relationship between structural parameters and reduced form coefficients.

We are applying OLS not on structural equation so they are Indirect Least Squares.

To be contd ... 

Thank you

Aditya Pokhrel

MBA, MA Economics, MPA