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Problem 1. Consider the regression model with a single regressor: Y₁ = Bo + B₁X₁ + ui. Suppose the Least Squares Assumptions #1-#3 are satisfied. (i) Show that X, is a valid instrument, i.e., show that instrument Z₁ = X₁ nous. (ii) Show that the TSLS estimator constructed using Z₁ = = B₁. relevant and exoge- X, is identical to the OLS estimator of

Problem 1. Consider the regression model with a single regressor: Y₁ = Bo + B₁X₁ + ui. Suppose the Least Squares Assumptions #1-#3 are satisfied. (i) Show that X, is a valid instrument, i.e., show that instrument Z₁ = X₁ nous. (ii) Show that the TSLS estimator constructed using Z₁ = = B₁. relevant and exoge- X, is identical to the OLS estimator of

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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I just need help with part 2. 

**Problem 1.** Consider the regression model with a single regressor: \( Y_i = \beta_0 + \beta_1 X_i + u_i \). Suppose the Least Squares Assumptions #1-#3 are satisfied. (i) Show that \( X_i \) is a valid instrument, i.e., show that instrument \( Z_i = X_i \) is relevant and exogenous. (ii) Show that the TSLS estimator constructed using \( Z_i = X_i \) is identical to the OLS estimator of \( \beta_1 \).
Transcribed Image Text:**Problem 1.** Consider the regression model with a single regressor: \( Y_i = \beta_0 + \beta_1 X_i + u_i \). Suppose the Least Squares Assumptions #1-#3 are satisfied. (i) Show that \( X_i \) is a valid instrument, i.e., show that instrument \( Z_i = X_i \) is relevant and exogenous. (ii) Show that the TSLS estimator constructed using \( Z_i = X_i \) is identical to the OLS estimator of \( \beta_1 \).
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