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lect16_103_2010_Compatibility_Mode_ - Instrumental...

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5/31/2010 1 Instrumental Variables Intro - I Recall that one solution to OVB problems was to measure the omitted variables that were causing the problem and include them as additional X ’s in a multiple regression. But sometimes there are important omitted variables that are hard if not impossible to measure. For example, recall trying to measure the effect of years of education completed on wages: 0 1 = i i i wage education u β β + Instrumental Variables Intro - II One possible omitted variable in this regression is an individual’s “innate ability”. Presumably, an individual’s innate ability positively affects their expected wages ( δ >0). Moreover, it seems likely that an individual’s innate ability would be positively correlated with their education level. Thus the OLS estimator β 1 may have omitted variable bias (which direction?) 0 1 = i i i wage education u β β +
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5/31/2010 2 Instrumental Variables Intro - III The problem here is that “innate ability” is pretty much an impossible variable to measure. IQ tests might measure some part of it, but it’s hard to get IQ test data for large samples of individuals. And IQ tests are definitely not a perfect measure of innate ability. So we can’t solve this problem by measuring the omitted variable and including it as an additional X . Instrumental variables will give us an alternative solution to the problem. But first another example… Instrumental Variables Intro - IV Demand for cigarettes across US states Is price i correlated with the omitted variables in u i ? There is a convincing argument that it will be. Prices in each state are determined by the cigarette firms. If cigarette firms are smart, they may want to adjust price based on demand conditions, e.g.. it can maximize profits to set higher prices in states with higher demand for cigarettes. What does it mean when a state has a high u i ? It means that this state has an unusually high demand for cigarettes. Thus, price i may tend to be set higher in states with higher u i ’s, i.e. price i may be positively correlated with u i .
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