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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

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section: Chapter Questions
Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...
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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
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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