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From | "Tobias Pfaff" <tobias.pfaff@uni-muenster.de> |
To | <statalist@hsphsun2.harvard.edu> |
Subject | RE: st: Problem with IV regression and two-way clustering |
Date | Fri, 28 Sep 2012 16:11:25 +0200 |
Thanks Mark. But what do you mean by "parametric approach"? Regards, Tobias > -----Original Message----- > From: owner-statalist@hsphsun2.harvard.edu > [mailto:owner-statalist@hsphsun2.harvard.edu] "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk> > Sent: Fri, 28 Sep 2012 12:23:38 +0100 > To: statalist@hsphsun2.harvard.edu > Subject: Re: st: Problem with IV regression and two-way clustering > Tobias, > My reaction is that 14 clusters is too small. Consistency of the > cluster-robust VCE requires the number of clusters to go to infinity, > and 14 is just not very far on the way to infinity. You note that with > a small number of clusters, the SEs are biased downwards, but the > problem isn't just bias - you are going to get noisy estimates of the > SEs, i.e., in repeated samples with 14 clusters they can be all over the > place. > You might instead want to investigate a parametric approach to the > problem...? > HTH, > Mark > -----Original Message----- > From: owner-statalist@hsphsun2.harvard.edu > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of > Tobias Pfaff > Sent: Thursday, September 27, 2012 9:30 PM > To: statalist@hsphsun2.harvard.edu > Subject: Re: st: Problem with IV regression and two-way clustering > > Dear Austin, > > Yes, some individuals move across regions. > If I do the IV regression with two-way clustering, I just > find it strange > that the tests point to an invalid instrument, given the rather high > correlation of the focus variable and the instrument. > > Regards, > Tobias > > ________________________________________ > From Austin Nichols <austinnichols@gmail.com> > To statalist@hsphsun2.harvard.edu > Subject Re: st: Problem with IV regression and two-way clustering > Date Thu, 27 Sep 2012 16:03:38 -0400 > ________________________________________ > > Are individuals moving across regions? If not, the pid clustering is > subsumed in region, and you need only cluster at the region level. > You might consider 2-d clustering by region and year as well. > Clustering by pid is not enough; you have strong correlation of errors > and predictors within region across people. > > On Thu, Sep 27, 2012 at 3:29 PM, Tobias Pfaff > <tobias.pfaff@uni-muenster.de> wrote: > > Dear Statalisters, > > > > I would kindly ask you for comments on an instrumental-variables > regression > > with (two-way) clustered standard errors, which is a > challenge for me. > > I'm afraid that the whole problem cannot be written in just > a few lines. > > Below is the whole story (which is hopefully interesting to > some of you). > > > > Any help is greatly appreciated! > > > > Now the setting: > > > > Unbalanced individual panel data set, single country > > Obs.: 170,000 > > Individuals: 28,000 > > Regions: 14 > > Years: 9 > > Dependent variable measured on the individual level > > Independent variable of interest (focusvar) measured on the > regional level > > Further control variables: 10, all at the individual level, > plus region > and > > year dummies (20 dummies) > > > > I use individual fixed effects and I cluster on the > individual level to > > control for correlation of the errors over time and get the > result that my > > focus variable is significant: > > -xtivreg2 depvar focusvar controlvars, fe cluster(pid)- > > > > My focus variable is aggregated at a higher level (region) than the > > dependent variable (individual), and I know from Moulton > (1990) that my > > standard errors can be biased downwards dramatically if I > do not cluster > at > > the regional level. Additionally, Donald and Lang (2007) > say that without > > clustering on the regional level, I dramatically overstate the > significance > > of the coefficients. Therefore, I use two-way clustering on > the individual > > and on the regional level: > > -xtivreg2 depvar focusvar controlvars, fe cluster(pid region)- > > > > Now my focus variable is insignificant. However, the number > of clusters is > > small (14), which again leads to biased results (Donald and > Lang 2007). > > Cameron et al. (2011) tell me that "With a small number of > clusters the > > cluster-robust standard errors are downwards biased" (p. > 414). Since my > > focus variable is already insignificant, I would expect the > coefficient to > > be even more insignificant, if I would correct for the bias > induced by the > > small number of clusters, and I conclude that I find no evidence for > > significance. > > > > Now comes the challenge (as if it has not yet been enough): > > I want to do an IV regression to make sure that my results are not > > influenced by endogeneity bias. I found a variable on the > regional level > > which is theoretically a fine instrument for my regional > focus variable. > The > > correlation between the focus variable and the instrument is .60. > > > > I now estimate the IV model with two-way clustered standard errors: > > -xtivreg2 depvar (focusvar = instrumentvar) controlvars, fe > cluster(pid > > region) first- > > > > The size of the coefficient of my focus variable has decreased. The > standard > > errors have increased drastically, and the coefficient is by far not > > significant. In the first-stage regression, the instrument is not > > significant. The tests say that the instrument is weak and > I cannot reject > > the null of underidentification. I interpret this as > evidence that I have > a > > bad instrument or that my focus variable is not endogenous. > > > > However, a different picture appears when I only cluster at > the individual > > level: > > -xtivreg2 depvar (focusvar = instrumentvar) controlvars, fe > cluster(pid) > > first- > > > > The standard errors of my focus variable are still much > larger than the > > non-IV estimates, but smaller compared to IV with two-way > clustering. The > > focus variable is again not significant. The instrument is highly > > significant in the first-stage regression. The tests > indicate that the > > hypotheses of a weak instrument and of underidentification can be > rejected. > > I would interpret this as evidence that my instrument is > valid and that my > > focus variable is endogenous. > > > > Conclusion: > > My interpretation is that the results generally suggest > that my focus > > variable is not significant. > > > > Open questions: > > Is my interpretation wrong? > > Is my instrument good or bad - should I trust the results > from the one-way > > or two-way clustering for the IV approach? > > In case I want to cluster on the regional level and correct > for the bias > due > > to a small number of clusters, I could use > wild-bootstrapping as proposed > by > > Cameron et al. (2011), but does that work for IV as well? > > > > Thanks very much for any clarification, > > Tobias > > > > Cited literature: > > Cameron, Gelbach, Miller (2008), Bootstrap-Based Improvements for > Inference > > with Clustered Errors. The Review of Economics and > Statistics, 90 (3), > > 414-427. > > Donald, Lang (2007), Inference with > Difference-in-Differences and Other > > Panel Data. The Review of Economics and Statistics, 89 (2), 221-233. > > Moulton (1990), An Illustration of a Pitfall in Estimating > the Effects of > > Aggregate Variables on Micro Units. The Review of Economics and > Statistics, > > 72 (2), 334-338. > > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/faqs/resources/statalist-faq/ > * http://www.ats.ucla.edu/stat/stata/ > * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/