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lect17_06apr10 - Imbens Lecture Notes 17 ARE213 Spring'06...

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Imbens, Lecture Notes 17, ARE213 Spring ’06 1 ARE213 Econometrics Spring 2006 UC Berkeley Department of Agricultural and Resource Economics Endogeneity I: Linear Models and Indirect Least Squares 1. Introduction When we discussed the linear model we assumed that the regressors were exogenous, that is independent of or uncorrelated with the disturbances. Often if we are looking at economic data where the covariates are the result of choices made by the economic units, there is reason to believe that the regressors are correlated with the disturbances. In that case we view (some of) the regressors as endogenous. Instrumental variables is one approach to dealing with that. The general setting is as follows. We have a linear model relating an outcome of interest, Y i , to some covariates X i : Y i = X i β + ε i . We are concerned that at least some of the covariates may be correlated with the disturbances ε . To make this specific, consider a wage regression where we are interested in the relation between log wages and education. We may be concerned that the disturbances partly rep- resent (unobserved) ability differences between individuals. If so, ability could be correlated with levels of education as well, and thus lead to an upward bias in the ols coefficient as we have seen before. To deal with this we exploit the presence of instrumental variables, which are variables not correlated with the disturbances, and with no direct effect on the outcome, but correlated with the endogenous regressor. Thus we are looking for Z i such that Z i ε i ,
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Imbens, Lecture Notes 17, ARE213 Spring ’06 2 and Z i correlated with X i .
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