st: RE: IVREG2 contradicting results Kleibergen Paap and Angrist Pischke weak identification test.

["Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>]

V.L.,

My interpretation of your results is in terms of the different null
hypotheses involved.  You can reject the null that X1 is not identified;
you can reject the null that X1^2 is not identified; but you can't
reject the null that either X1 or X1^2 is not identified.

I think your explanation is probably right - X1 and X1^2 are so closely
correlated that you can identify one, or the other, but not both.

HTH,
Mark

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of v 
> van kervel
> Sent: 31 March 2011 13:57
> To: statalist@hsphsun2.harvard.edu
> Subject: st: IVREG2 contradicting results Kleibergen Paap and 
> Angrist Pischke weak identification test.
> 
> Dear Statalist,
> 
> I run an instrumental variables regression with a linear and 
> quadratic endogenous variable: X1 and X1square = X1^2. I have 
> 4 instruments: Z1, Z2, and Z1square = Z1^2, Z2square=Z2^2. I 
> have exogenous control variables C.
> 
> Model: 
> xtivreg2 Y (X1 X1square = Z1 Z2 Z1square Z2square) C , fe gmm2s robust
> 
> The Angrist Pischke weak ID test after the two first stage 
> regressions are highly rejected (values 266 and 207), meaning 
> each individual endogenous regressor is strongly identified 
> by the instruments, after partialling out the linear 
> projection of the other endogenous regressor (Baum, Schaffer 
> and Stillman, 2007 Stata journal).
> 
> However, the Kleibergen-Paap Wald F statistic (weak ID test) 
> is only 6.1; very low. Both Kleibergen-Paap and Angrist 
> Piscke test for weak identification, but have mixed 
> predictions. Is this a consequence of multi-collinearity 
> between the endogenous variables, or alternatively, 
> multi-collinearity between the excluded instruments?
> 
> Specifically, because X1 and X1square are multi-collinear, 
> the {4*2} matrix of first stage coefficients {Z1 Z2 Z1square 
> Z2square} * {X1 X1square } is not of full column rank, 
> causing the Kleibergen-Paap rank test to not reject. However, 
> as the instruments are individually strong, the 
> Angrist-Pischke weak ID test is rejected. Is this line of 
> reasoning correct? 
> 
> A multi-collinearity issue seems confirmed by the second 
> stage coefficients on X1 and X1square: X1 is highly positive, 
> while X1square highly negative, both having very large 
> standard errors compared to using only X1 as endogenous variable.
> 
> Thanks for your consideration,
> 
> --------------------------------
> V.L. van Kervel
> Ph.D. Candidate in Finance
> CentER Graduate School
> Tilburg University
> The Netherlands
> 
> 
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