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I had a project from before I graduated from college that was effectively me acting as a research aid to a politician. The project served as my senior thesis, as well. The portion of the report that I was working on focused on determining the effect of new fuel economy legislation for heavy-duty vehicles, such as 18-wheelers or large lorries and their drivers.

I managed to get the data cleaned up and put together, but when I ran a regression (with dummy variables for year, region, etc) I realized that I was seeing the police-and-crime problem in action: wages affected employment which affected wages etc. Indeed, I checked the regression by running it once with wages and employment against one another and had a very significant p-value spit back out at me, with a 99% R-value -- making me realize that I had a problem.

I know that I need to find some variable that only affects one (wages or employment) but not the other. (In the Levitt paper, he uses elections, which affect police presence and not crime.) What type of variable would this be in my wage/employment model? Are there other ways of working around the endogeneity problem?

I can post data if it is requested, though my question is more conceptual than data-focused.

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Are you looking into learning about instrumental variables? Also -- are you planning to do this analysis for the politician or is it a senior or masters thesis or something? –  dchandler Oct 22 '11 at 23:09
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Ahh -- if you were curious about instrumental variables in general, I'd recommend the following article by Josh Angrist, "Instrumental Variables and the search for identification": hec.unil.ch/hec/doctorats/phdmanagement/ResearchHandbook/…. Unfortunately, I can't think of an instrument off the top of my head for your circumstance, sorry! PS. Finding good instruments is hard. –  dchandler Oct 22 '11 at 23:20
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It would be helpful if you would post the equation you were trying to estimate, a short description of each variable and how you were trying to estimate it. Posting the data likely isn't necessary, but it is hard to answer without the specification. Thanks! –  Jason B Oct 24 '11 at 19:23
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I don't think the whole equation is necessary, just the parts that are generating the problem (for example, what was the dependent variable? wages? Did you have (un)employment as an explanatory variable?) –  Jason B Oct 25 '11 at 14:42
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How do you solve the endogeneity problem using econometrics? Most often you don't. Seems like a good time to break out the old John Tukey quote: "The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data." –  Michael Bishop Sep 22 '12 at 21:25
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2 Answers

As many have already answered, one of the easiest way to correct for endogeneity is a instrumental variable (IV) using a 2-stage least square regression (2SLS). Another method, is using a Heckman correction. For details, on the Heckman correction see his paper "Sample Selection Dias as a Specification Error" Econometrica Vol. 47, No. 1 (1979). However, instead of reading the whole paper, whatever software package you are using will probably have it already builded in. The paper is posted at the following url:

http://vanpelt.sonoma.edu/users/c/cuellar/econ411/Heckman.pdf

However, not sure how long the link will stay open.

Hope this helps! Good Luck!

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Since this is a question with a clear break, ie. when the legislation came into place, it may be helpful to look at matching estimators and regression discontinuity designs. These are often very good alternatives (or compliments) to the classic IV estimator. I would even argue they are often better than the classic IV since, as has already been mentioned, a good IV is very difficult to find.

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