ECO321: Economic Statistics II Chapter 12: Instrument Variable Regressiona Hiroshi Morita hmorita@hunter.cuny.edu Department of Economics Hunter College, The City University of New York ac 2010 by Hiroshi Morita. This document may be reproduced for educational purpose, so long as the copies contain this notice and are retained for personal use or distributed free. ECO321: Economic Statistics II – p. 1/11
Review: OLS Assumption [Reviews] OLS estimators are unbiased and consistent if: Assumption #1: “Exogeneity”: E(ui|X1,i,X1,i, · · · ,Xk,i) = 0 Assumption #2: (Yi,X1,i,X1,i, · · · ,Xk,i) are i.i.d. Assumption #3: Large outliers are unlikely Assumption #4: No perfect multicollinearity ECO321: Economic Statistics II – p. 2/11
Review: OLS Assumption [Reviews] OLS estimators are unbiased and consistent if: Assumption #1: “Exogeneity”: E(ui|X1,i,X1,i, · · · ,Xk,i) = 0 Assumption #2: (Yi,X1,i,X1,i, · · · ,Xk,i) are i.i.d. Assumption #3: Large outliers are unlikely Assumption #4: No perfect multicollinearity In practice, however, many cases violates Assumption #1. In Chapter 12, we’ll study Instrumental Variable Regression to deal with one of these issues: simultaneous causality bias. ECO321: Economic Statistics II – p. 2/11
Simultaneous Causality In the regression: Yi = 0 + 1Xi + ui assuming that X causes Y (or Y depends on X). But if the opposite causality is true, i.e., Y causes X as well, then the simultaneous causality occurs. ECO321: Economic Statistics II – p. 3/11
Simultaneous Causality In the regression: Yi = 0 + 1Xi + ui assuming that X causes Y (or Y depends on X). But if the opposite causality is true, i.e., Y causes X as well, then the simultaneous causality occurs. In the other words, X and u are correlated, which violates the OLS Assumption #1. As a result, the OLS estimators become biased. =) Go for instrumental variables (IV) regression instead of OLS. ECO321: Economic Statistics II – p. 3/11
Simultaneous Causality: Example Suppose that you want to…