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lecture7_140b_2011

# lecture7_140b_2011 - Lecture 7 Instrumental Variables...

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Olivier Deschenes, UCSB, Econ 140B, Winter 2011 Lecture 7: Instrumental Variables Regression Chapter 12 in S&W Overall Plan: IV regression in model with 1 regressor IV regression in multiple regression model Discussion of problem and implications of weak IV Test of over-identifying restrictions (i.e., test of instrument validity)

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Olivier Deschenes, UCSB, Econ 140B, Winter 2011 Overview and Motivation: Several problems in econometrics boil down to a correlation between the regression error term and the one regressor: Measurement error in X Omitted variable bias Simulataneous causality Instrumental variables regression provides a general approach to obtain a consistent estimator of the regression coefficients in that case But… you need to have a valid instrument in your data set to implement this approach!
Olivier Deschenes, UCSB, Econ 140B, Winter 2011 Terminology (more to come)… An endogenous variable is one that is correlated with u An exogenous variable is one that is uncorrelated with u Historical note: “Endogenous” literally means “determined within the system,” that is, a variable that is jointly determined with Y, and so a variable subject to simultaneous causality However, this definition is narrow and IV regression can be used to address omitted variables bias and errors-in- variable bias, not just to simultaneous causality bias

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Olivier Deschenes, UCSB, Econ 140B, Winter 2011 Basic Idea of IV Regression: Consider the basic linear model: Y i = 0 + 1 X i + u i Suppose X i is correlated with u i (X is endogenous) Consider decomposing X i into two components, P 1i and P 2i : X i = P 1i + P 2i Where P 1i is uncorrelated with u i and P 2i is correlated with u i The method of instrumental variables uses the “extra” information we have (the instrument) to isolate the variation in X i that is uncorrelated with u i (i.e., the variation in P 1i ) to estimate 1
Olivier Deschenes, UCSB, Econ 140B, Winter 2011 IV Regression in One Regressor Model Consider the basic linear model: Y i = 0 + 1 X i + u i If E[X i u i ] 0, the OLS estimator of 1 is not consistent Two conditions for a valid instrument in this model: 1. “Instrument relevance”: corr(Z i ,X i ) 0 2. “Instrument exogeneity”: corr(Z i ,u i )=0 In practice, another requirement is that you need to have access to the instrumental variable in your sample

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Olivier Deschenes, UCSB, Econ 140B, Winter 2011 Two Approaches to Estimate 1 by IV Regression 1. Two Stage Least Squares (TSLS) 2. Instrumental Variables Estimator Numerically equivalent in the 1 variable model
Olivier Deschenes, UCSB, Econ 140B, Winter 2011 Two Stage Least Squares First-stage: decompose X i into the “good” and “bad” variation (i.e. isolate variation in X uncorrelated with u) X i = 0 + 1 Z i + v i Two components: Exogenous component : 0 + 1 Z i . This is uncorrelated with u i by definition (“good”) Endogenous component : v i . This is correlated with u i (“bad”) The IV estimator use 0 + 1 Z i to estimate 1

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lecture7_140b_2011 - Lecture 7 Instrumental Variables...

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