Problem 3. Consider the simple regression model: Y; = Bo + B1X; + U; where X; is an endogenous regressor and Z; is a valid instrumental variable for X;. Let B1 be the OLS estimator and B2 be the IV estimator. Consider the R and R of the two estimations, which one is larger (i.e., which estimator fits in-sample Y; better)? Recall that R² is defined as: Σ E,(Y; – Ý)² EL(Y: – Ý;)? E(Yi – Ý)² E(Yi – X;ß)² E, (Y; – Ý )² - R? = 1 – = 1 %3D | i=1
Problem 3. Consider the simple regression model: Y; = Bo + B1X; + U; where X; is an endogenous regressor and Z; is a valid instrumental variable for X;. Let B1 be the OLS estimator and B2 be the IV estimator. Consider the R and R of the two estimations, which one is larger (i.e., which estimator fits in-sample Y; better)? Recall that R² is defined as: Σ E,(Y; – Ý)² EL(Y: – Ý;)? E(Yi – Ý)² E(Yi – X;ß)² E, (Y; – Ý )² - R? = 1 – = 1 %3D | i=1
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
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Transcribed Image Text:Problem 3. Consider the simple regression model:
Y; = Bo + B1X; + U;
where X; is an endogenous regressor and Z; is a valid instrumental variable for
X;.
Let 3, be the OLS estimator and 3, be the IV estimator. Consider the R? and
R of the two estimations, which one is larger (i.e., which estimator fits in-sample
Y; better)?
Recall that R² is defined as:
Σ
E(Y: – Ý)²
E (Yi – Ý;)²
E(Y; – Y)?
EL(Y: – X;8)²
X;B)?
-
R = 1 –
i=1
1 -
E(Y; – Y)?
i=1
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