Consider the structural equation Y1 Z0 11 Y 0 22 e with E Ze 0 where Y2 is k2 1 and treated as endogenous The variables Z (Z1,Z2) are treated as exogenous where Z2 is 2 1 and 2 k2 You are interested in testing the hypothesis H0 2 0 Consider the reduced formequation for Y1 Y1 Z0 11 Z0 22 u1 (12 95) Show how to test H0 using only the OLS estimates of (12 95) Hint This will require an analysis of the reduced form equations and their relation to the structural equation

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Question: Consider the structural equation Y1 Z0 11 Y 0 22 e with E[Ze] 0 where Y2 is k2 1 and treated as endogenous.

Consider the structural equation Y1 Æ Z0 1¯1 ÅY 0 2¯2 Åe with E[Ze] Æ 0 where Y2 is k2 £1 and treated as endogenous. The variables Z Æ (Z1,Z2) are treated as exogenous where Z2 is `2 £1 and

`2 ¸ k2. You are interested in testing the hypothesis H0 : ¯2 Æ 0.

Consider the reduced formequation for Y1 Y1 Æ Z0 1¸1 ÅZ0 2¸2 Åu1. (12.95)

Show how to test H0 using only the OLS estimates of (12.95).

Hint: This will require an analysis of the reduced form equations and their relation to the structural equation.

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