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Unformatted text preview: Imbens/Wooldridge, Lecture Notes 5, Summer 07 1 Whats New in Econometrics NBER, Summer 2007 Lecture 5, Monday, July 30th, 4.30-5.30pm Instrumental Variables with Treatment Effect Heterogeneity: Local Average Treatment Effects 1. Introduction Here we investigate the interpretation of instrumental variables estimators allowing for general heterogeneity in the effect of the endogenous regressor. We shall see that instrumental variables estimators generally estimate average treatment effects, with the specific average depending on the choice of instruments. Initially we focus on the case where the endogenous regressor is binary. The example we will use is based on work by Joshua Angrist on estimating the effect of veteran status on earnings (Angrist, 1990). We also discuss the case where the endogenous variable takes on multiple values. The general theme of this lecture is that with heterogenous treatment effects, endogeneity creates severe problems for identification of population averages. Population average causal effects are only estimable under very strong assumptions on the effect of the instrument on the endogenous regressor (identification at infinity, or under the constant treatment effect assumptions). Without such assumptions we can only identify average effects for subpopulations that are induced by the instrument to change the value of the endogenous regressors. We refer to such subpopulations as compliers , and to the average treatment effect that is point identifed as the local average treatment effect . This terminology stems from the canonical example of a randomized experiment with noncompliance. In this example a random subpopulation is assigned to the treatment, but some of the individuals do not comply with their assigned treatment. These complier subpopulations are not necessarily the subpopulations that are ex ante the most interesting subpopulations, but the data is in general not informative about av- erage effects for other subpopulations without extrapolation, similar to the way in which a randomized experiment conducted on men is not informative about average effects for Imbens/Wooldridge, Lecture Notes 5, Summer 07 2 women without extrapolation. The set up here allows the researcher to sharply separate the extrapolation to the (sub-)population of interest from exploration of the information in the data. The latter relies primarily on relatively interpretable, and substantively meaningful assumptions and avoids functional form or distributional assumptions. Given estimates for the compliers, one can then use the data to assess the plausibility of extrapolating the local average treatment effect to other subpopulations, using the information on outcomes given one of the two treatment levels and covariates....
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