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Ch. 12 Instrumental Variables Regression

# Ch. 12 Instrumental Variables Regression - INSTRUMENTAL...

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1 | Instrumental Variables INSTRUMENTAL VARIABLES REGRESSION (Ch. 12) The recommended exercise questions from the textbook: Chapter 12: All except (12.3), (12.4), (12.6). [1] Motivation • Consider the following simple regression model: Y = β 0 + β 1 X 1 + u . • Least Square Assumption 1 requires E( u | X 1 ) = 0. This condition is violated if X 1 and u are correlated. • What happens if X and u are correlated? 1 1 1 1 cov( , ) ˆ var( ) p X u X .

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2 | Instrumental Variables • When can X 1 and u be correlated? • Omitted regressors: • True model: Y = β 0 + β 1 X 1 + β 2 X 2 + u * . • The model you estimate: Y = β 0 + β 1 X 1 + ( β 2 X 2 + u * ). 1 ˆ from your model (with the omitted variable X 2 ) * 1 2 2 1 2 2 1 1 1 1 1 2 1 2 1 cov( , ) cov( , ) var( ) var( ) cov( , ) . var( ) p X X u X X X X X X X
3 | Instrumental Variables • Measurement errors in the data on X ( X i ’s). • True model: Y = β 0 + β 1 X + u . • Observe Z = X + v where v is measurement error. • Model you estimate when you use Z instead of X : Y = β 0 + β 1 ( Z - v ) + u = β 0 + β 1 Z + ( u - β 1 v ). This model violates the LS Assumption 1. For this case, 2 1 1 2 2 ˆ X p X v .

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