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

Exercise 2

Write a two-equation system in "supply and demand form," that is, with the same variable y1 (typically, "quantity") appearing on the left-hand side:

y1= ?1y2+ ?1z1+u1

y1 = ?2y2+ ?2z2+u2

(i) If ?1 = 0 or ?2 = 0, explain why a reduced form exists for y1. (Remember, a reduced form expresses y1 as a linear function of the exogenous variables and the structural errors.) If ?1 ? 0 and ?2 = 0, find the reduced form for y2.

(ii) If ?1? 0, ? 2? 0, and ? 1 ? ? 2, find the reduced form for y1. Does y2 have a reduced form in this case?

(iii) Is the condition ?1?? 2 likely to be met in supply and demand examples? Explain.

Step 1 of 3

(i)

Given the two-equation system in “supply and demand form”, where is the “quantity”:

The reduced form for is said to exist if is shown to depend only on exogenous variable and expressed as a linear function of exogenous variables and the structural errors

Thus, when ,the reduced form for is expressed as:

Similarly, when,the reduced form foris expressed as:

When , the reduced form foris: