Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 12

(i) In the model with one endogenous explanatory variable, one exogenous explanatory variable, and one extra exogenous variable, take the reduced form for y2, , and plug it into the structural equation . This gives the reduced form for y1:

y1 = ?0 + ?1Z1 + ?2Z2 + V

Find the ?j. in terms of the ?j and the ?j.

(ii) Find the reduced form error, v1, in terms of u1, v2, and the parameters.

(iii) How would you consistently estimate the aj?

Step 1 of 3

(i)

Consider the model with one endogenous explanatory variable and one exogenous explanatory variable

Now consider the reduced form of

On plugging in, the result is:

On comparing with