LN+13+Instrumental+Variables

LN+13+Instrumental+Variables - Empirical Methods II...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Empirical Methods II (API-202) Kennedy School of Government Harvard University 1 Lecture Notes 13 Instrumental Variables I - INTRODUCTION Three important threats to internal validity (causal identification): 1) Omitted variable bias: a. Certain variable affects Y but is unobservable, so it cannot be included in the SR b. this variable is correlated with X 2) Reverse causality bias: X causes Y , Y causes X 3) Measurement error bias: X is measured with error These 3 problems each signify a violation of the zero conditional mean condition o i.e. E[u|X 1 ,X 2 ,…,X k ]=0 or simply E[u|X]=0 o roughly speaking: the error term cannot be correlated with any RHS variable o Cannot infer causality from SR if zero conditional mean condition doesn’t hold Instrumental variables (IV) is a method used to try to eliminate bias from all three sources in order to obtain unbiased estimates.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Empirical Methods II (API-202) Kennedy School of Government Harvard University 2 II – LOGIC OF INSTRUMENTAL VARIABLES (1) Basics Assume our model of interest is the following: SR: Y = 0 ˆ 1 ˆ X 1 + ˆ SEQ: Y =   X 1 + Regressor of interest is X 1 Assume X and u are correlated Ergo: E( |X) 0, 1 ˆ  and 1 ˆ is biased Key idea : the variation in X 1 can be separated into: "bad" variation: variation in X 1 that is correlated with "good" variation: remaining variation in X 1 (not correlated with ) Goal of instrumental variables (IV) : eliminate the part of X 1 that is correlated with and use the “good” variation to estimate an unbiased 1 ˆ How? In simple terms: o Find a variable that is correlated with X 1 and uncorrelated with . o We call this variable an instrumental variable (Z) o This instrumental variable allows us to identify the “good” variation o We estimate 1 ˆ in two stages. First, we run a regression to capture the “good” variation of X 1 , our regressor of interest. (i) SR: X 1 = 0 ˆ + 1 ˆ Z + (ii) Good variation : 1 ˆ X = 0 ˆ + 1 ˆ Z (fitted/predicted value) o Second, we run our model of interest with 1 ˆ X , the “good” variation of X 1 , to get an unbiased estimate of Y = 0 ˆ 1 ˆ 1 ˆ X + ˆ
Background image of page 2
Empirical Methods II (API-202) Kennedy School of Government Harvard University 3 (2) Validity of Instrumental Variable For an instrumental variable Z to be valid, it must satisfy two conditions: 1. Instrument relevance : corr( Z , X ) 0 The instrument is correlated with X, the regressor of interest. 2. Instrument exogeneity : corr( Z , u ) = 0 The instrument is not correlated with the error term in the equation of interest. Another way to put this: the instrument is correlated with Y, the outcome of interest, only
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/12/2009 for the course HKS API202A taught by Professor Levy during the Spring '09 term at Harvard.

Page1 / 12

LN+13+Instrumental+Variables - Empirical Methods II...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online