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

[v van kervel <v.l.vankervel@uvt.nl>]

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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