lect20_06apr10

# lect20_06apr10 - Imbens, Lecture Notes 20, ARE213 Spring...

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Imbens, Lecture Notes 20, ARE213 Spring ’06 1 ARE213 Econometrics Spring 2006 UC Berkeley Department of Agricultural and Resource Economics Endogeneity IV: Heterogeneity and Local Average Treatment Effects Here we investigate the interpretation of instrumental variables estimators given hetero- geneity in the eﬀect of the endogenous regressor. We shall see that instrumental variables estimates estimate diﬀerent averages depending on the instruments. We focus on the case where the endogenous regressor is binary. The example we will use is based on work by Angrist on estimating the eﬀect of veteran status on earnings. 1. Potential Outcomes First we set up the problem in a slightly diﬀerent way, using potential outcomes. Let Y i (0) and Y i (1) be two potential outcomes for unit i , one for each value of the endogenous regressor or treatment. The ±rst potential outcome Y i (0) gives the outcome if person i were to serve in the military, irrespective of whether this person served or not. The second gives the potential outcome given military service, again irrespective of whether the person served or not. We are interested in the causal eﬀect of military service, Y i (1) - Y i (0). We cannot directly observe this since we can only observe either Y i (0) or Y i (1), but not both. Let D i be the actual value of the endogenous regressor, equal to zero or one. We observe D i and Y i = Y i ( D i )= ± Y i (1) if D i =1 Y i (0) if D i =0 . Now we introduce the instrumental variable set up by de±ning similar potential outcomes for the treatment. We focus on the case with a binary instrument Z i . De±ne two potential outcomes D i (0) and D i (1), representing the value of the endogenous regressor given the two values for the instrument. The actual value of the endogenous variable is

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## This note was uploaded on 08/01/2008 for the course ARE 213 taught by Professor Imbens during the Spring '06 term at University of California, Berkeley.

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lect20_06apr10 - Imbens, Lecture Notes 20, ARE213 Spring...

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