The IV Regression Assumptions KEY CONCEPT 12.4 The variables and errors in the IV regression model in Key Concept 12.1 satisfy the following: 1. E(u;|W1; ..., W„) = 0; 2. (X1, ..., Xi, W1;, ..., Wi, Zi, . .., ZmY;) are i.i.d. draws from their joint distribution; 3. Large outliers are unlikely: The X's, W's, Z's, and Y have nonzero finite fourth moments: and 4. The two conditions for a valid instrument in Key Concept 12.3 hold.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 32EQ
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Consider the instrumental variable regression model
                   Yi = β01Xi + β2Wi + ui,
where Xi is correlated with ui and Zi is an instrument. Suppose that the first
three assumptions in Key Concept 12.4 are satisfied. Which IV assumption
is not satisfied when:
a. Zi is independent of (Yi, Xi, Wi)?
b. Zi = Wi?
c. Wi = 1 for all i?
d. Zi = Xi?

The IV Regression Assumptions
KEY CONCEPT
12.4
The variables and errors in the IV regression model in Key Concept 12.1 satisfy
the following:
1. E(u;|W1; ..., W„) = 0;
2. (X1, ..., Xi, W1;, ..., Wi, Zi, . .., ZmY;) are i.i.d. draws from their joint
distribution;
3. Large outliers are unlikely: The X's, W's, Z's, and Y have nonzero finite
fourth moments: and
4. The two conditions for a valid instrument in Key Concept 12.3 hold.
Transcribed Image Text:The IV Regression Assumptions KEY CONCEPT 12.4 The variables and errors in the IV regression model in Key Concept 12.1 satisfy the following: 1. E(u;|W1; ..., W„) = 0; 2. (X1, ..., Xi, W1;, ..., Wi, Zi, . .., ZmY;) are i.i.d. draws from their joint distribution; 3. Large outliers are unlikely: The X's, W's, Z's, and Y have nonzero finite fourth moments: and 4. The two conditions for a valid instrument in Key Concept 12.3 hold.
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