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I've been looking for a good explanation of the difference between running a regression with year dummies as fixed effects vs. year dummies as instrumental variables.

A prominent example of this comes from Josh Angrist's 1991 paper, "Grouped-data estimation and testing in simple labor-supply models"

http://www.sciencedirect.com/science/article/pii/030440769190101I

d_a_c321
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  • As I do not have the access to the article at the moment, I would say that the difference is in the assumptions. If you run regression with instrumental variables you assume that some of your variables are endogenous, i.e. they correlate with the regression disturbances. If they truly are, running the fixed effects regression will not solve this, hence your estimates will be inconsistent and biased. Are you looking for such type of explanation? – mpiktas Oct 16 '11 at 10:17
  • I suppose I'd want a good example of how they differ when you use years. In general, I know fixed effects are good for only using variation within a group. IV is good for overcoming endogeneity. I don't quite have a grasp on a good example though of what it means to use both with year dummies and under what circumstances it'd make sense to use them. Apologies for the gated paper. – d_a_c321 Oct 16 '11 at 14:51

2 Answers2

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I think the question you are looking to answer is, if you should use a fixed effect model with or without time dummies. The classical text on Panel Econometrics is Econometric Analysis of Cross Section and Panel Data by Jeffrey M Wooldridge. I would suggest this book to answer your question(s). Most university libraries will probably have a copy of this text. If not the economics department probably will. Also, there is an old version of a paper by I. Murtazashvili and J. Wooldridge on that should be enough to answer your question from their department. The title is “FIXED EFFECTS INSTRUMENTAL VARIABLES ESTIMATION IN CORRELATED RANDOM COEFFICIENT PANEL DATA MODELS” and the link can be found below. Hope this helps, good luck!

https://www.msu.edu/~ec/faculty/wooldridge/current%20research/rancoefiv1je.pdf

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Years as fixed effects allow the outcome to have a different average in each year; the fixed effects allow the intercept of the regression to vary by year.

Years as instruments overcome endogeneity in the treatment variable. Remember what needs to be true about instruments:

  • They need to impact (be correlated with) the treatment variable and
  • They can only impact the outcome via the treatment variable (they don't belong in the equation of interest by themselves).

To use years as instruments, they can't be in the main specification. This implies that the average outcome must be the same in every year. Put another way, the outcome can't be directly impacted by time (though you might be able to include a linear time trend in lieu of year fixed effects in the main specification to incorporate time).

Charlie
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