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Unformatted text preview: ECON 103, Lecture 16: Instrumental Variables I Maria Casanova May 24 (version 0) Maria Casanova Lecture 16 1. Introduction 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: wage i = + 1 education i + u i One possible omitted variable in this regression is an individuals innate ability. Maria Casanova Lecture 16 1. Introduction Presumably, an individuals innate ability positively affects their expected wages ( > 0). Moreover, it seems likely that an individuals innate ability would be positively correlated with their education level. Thus the OLS estimator 1 may have omitted variable bias (which direction?) The problem here is that innate ability is pretty much an impossible variable to measure, so we cannot include it as an additional regressor. Instrumental variables will give us an alternative solution to the problem. Maria Casanova Lecture 16 1. Introduction Another example: Demand for cigarettes across US states. sales i =  1 price i + u i Is price i correlated with the omitted variables in u i ? Prices in each state are determined by the cigarette firms. If cigarette firms are smart, they can maximize profits by setting higher prices in states with higher 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 . Recall that this type of OVB results from simultaneous causality or reverse causality . This happens when Y i depends on X i and X i depends on Y i Maria Casanova Lecture 16 1. Introduction In the example above, sales depend on prices, but prices may also depend on sales. Another example of simultaneous causality: crime i = + 1 policing + u i , where i is a metropolitan area, policing is the number of policemen per resident, and crime can be the violent crime rate....
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 Spring '07
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