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From | "Fitzgerald, James" <J.Fitzgerald2@ucc.ie> |
To | "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu> |
Subject | st: RE: RE: Interpreting Kleibergen Paap weak instrument statistic |
Date | Mon, 25 Jun 2012 13:53:18 +0000 |
Mark, Thank you very much for your reply. I have a few follow-up questions that you might be able to help me with. First though I thought it might be helpful if I gave a quick synopsis of my research question. I am investigating the determinants of capital structure in UK Plcs, and my main hypothesis is that the theories espoused in the extant literature are only applicable to certain types of firms. As such, I divide my sample into sub-samples based on certain firm characteristics i.e. size, tangibility of assets etc., and compare regressor coefficients across the sub-samples. However, I was initially worried that such a categorisation procedure might introduce endogeneity issues that might vary across sub-samples, and thus I would not be able to reliably compare coefficients across sub-samples. Hence I decided to employ instrumental variables (lagged independent variables) to over come such issues. Within each sub-sample I test the orthogonality assumption of my included regressors (on an individual basis) using the orthog option in xtivreg2. Any variables I find to be potentially endogenous (C-stat p-value <0.100) are then instrumented where instruments are available. I am currently unaware of any method to correctly test the i.i.d. assumption using xtivreg2, and so I have decided to drop the assumption, and hence my question with regards the KP stat. With regards to your earlier reply, the following are some follow up questions I still have. 1. Is there an option in ivreg2 to test the i.i.d. assumption, and if not, how would i go about testing same? 2. With regards to the Anderson-Rubin statistic and the Stock-Wright LM S statistic, both of which are reported by xtivreg2, am I correct in my interpretation that given that they both test the joint hypotheses of weak instruments and orthogonality, the statistics are only interpretable from a weak instruments perspective as long as the Hansen J test of all excluded instruments indicates orthogonality conditions are valid? 3.Included below is the first stage regression results from one of the tests I run. As you can see the Cragg Donald and Kleibergen Paap stats both suggest that the instruments are not weak. However, the AR and SW stats suggest that the instruments, given that the Hansen J-test does not reject the null, are potentially weak. From the output these stats appear to me to be testing the explanatory power of the instrument rather than whether or not it is weak i.e. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid The coefficient significance level of the instrumented variable (liq) is relatively low (p-value = 0.084), but the instrument does not appear to be weak (based on CD and KP stats). However, I would conclude that it potentially is weak based on the AR and SW stats. Is my interpretation incorrect, and if so could you indicate how these stats ought to be interpreted? I greatly appreciate any help you can offer Best regards James Summary results for first-stage regressions (Underid) (Weak id) Variable F( 4, 2541) P-val AP Chi-sq( 4) P-val AP F( 4, 2541) liq 20.20 0.0000 81.78 0.0000 20.20 NB: first-stage test statistics heteroskedasticity and autocorrelation-robust Stock-Yogo weak ID test critical values for single endogenous regressor: 5% maximal IV relative bias 16.85 10% maximal IV relative bias 10.27 20% maximal IV relative bias 6.71 30% maximal IV relative bias 5.34 10% maximal IV size 24.58 15% maximal IV size 13.96 20% maximal IV size 10.26 25% maximal IV size 8.31 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(4)=58.30 P-val=0.0000 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 78.65 Kleibergen-Paap Wald rk F statistic 20.20 Stock-Yogo weak ID test critical values for K1=1 and L1=4: 5% maximal IV relative bias 16.85 10% maximal IV relative bias 10.27 20% maximal IV relative bias 6.71 30% maximal IV relative bias 5.34 10% maximal IV size 24.58 15% maximal IV size 13.96 20% maximal IV size 10.26 25% maximal IV size 8.31 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(4,2541)= 2.26 P-val=0.0607 Anderson-Rubin Wald test Chi-sq(4)= 9.14 P-val=0.0577 Stock-Wright LM S statistic Chi-sq(4)= 9.22 P-val=0.0557 NB: Underidentification, weak identification and weak-identification-robust test statistics heteroskedasticity and autocorrelation-robust Number of observations N = 3021 Number of regressors K = 28 Number of endogenous regressors K1 = 1 Number of instruments L = 31 Number of excluded instruments L1 = 4 2-Step GMM estimation Estimates efficient for arbitrary heteroskedasticity and autocorrelation Statistics robust to heteroskedasticity and autocorrelation kernel=Bartlett; bandwidth=2 time variable (t): year group variable (i): firm Number of obs = 3021 F( 28, 2544) = 3.02 Prob > F = 0.0000 Total (centered) SS = 21.06783592 Centered R2 = 0.0261 Total (uncentered) SS = 21.06783592 Uncentered R2 = 0.0261 Residual SS = 20.51803233 Root MSE = .08932 Robust ltdbv Coef. Std. Err. z P>z [95% Conf. Interval] liq -.0085538 .0049465 -1.73 0.084 -.0182487 .0011411 lnsale .0053743 .0052578 1.02 0.307 -.0049307 .0156794 tang .1170177 .0610377 1.92 0.055 -.0026139 .2366493 itang .0557467 .0239463 2.33 0.020 .0088127 .1026806 itangdum .0123551 .0065003 1.90 0.057 -.0003853 .0250955 tax -.0193497 .00924 -2.09 0.036 -.0374598 -.0012396 prof .0025405 .0027681 0.92 0.359 -.0028849 .0079659 mtb -.0019451 .0019992 -0.97 0.331 -.0058635 .0019733 capexsa .0108254 .0087886 1.23 0.218 -.0064 .0280507 ndts -.0022495 .0032416 -0.69 0.488 -.008603 .004104 yr90 -.0860865 .1693451 -0.51 0.611 -.4179968 .2458238 yr91 -.0057954 .0156291 -0.37 0.711 -.036428 .0248371 yr92 .0060493 .0148008 0.41 0.683 -.0229596 .0350583 yr93 -.0066494 .0154936 -0.43 0.668 -.0370163 .0237174 yr94 -.0038801 .0137634 -0.28 0.778 -.0308559 .0230956 yr95 -.0021814 .0139629 -0.16 0.876 -.0295482 .0251854 yr96 .007044 .0137418 0.51 0.608 -.0198895 .0339775 yr97 .0119441 .0134385 0.89 0.374 -.0143949 .0382831 yr98 .0069794 .013185 0.53 0.597 -.0188627 .0328216 yr99 .0132963 .0125952 1.06 0.291 -.0113898 .0379825 yr00 .0080221 .0119826 0.67 0.503 -.0154633 .0315074 yr01 -.0000815 .0107388 -0.01 0.994 -.0211291 .0209661 yr02 .0001449 .0106504 0.01 0.989 -.0207295 .0210193 yr03 .0106314 .0115621 0.92 0.358 -.0120299 .0332926 yr04 .0097052 .0102908 0.94 0.346 -.0104643 .0298748 yr05 .0156916 .0108831 1.44 0.149 -.0056388 .0370221 yr06 .0093837 .0108831 0.86 0.389 -.0119467 .0307142 yr07 .005672 .0086985 0.65 0.514 -.0113768 .0227207 Underidentification test (Kleibergen-Paap rk LM statistic): 58.301 Chi-sq(4) P-val = 0.0000 Weak identification test (Cragg-Donald Wald F statistic): 78.647 (Kleibergen-Paap rk Wald F statistic): 20.198 Stock-Yogo weak ID test critical values: 5% maximal IV relative bias 16.85 10% maximal IV relative bias 10.27 20% maximal IV relative bias 6.71 30% maximal IV relative bias 5.34 10% maximal IV size 24.58 15% maximal IV size 13.96 20% maximal IV size 10.26 25% maximal IV size 8.31 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Hansen J statistic (overidentification test of all instruments): 5.596 Chi-sq(3) P-val = 0.1330 Instrumented: liq Included instruments: lnsale tang itang itangdum tax prof mtb capexsa ndts yr90 yr91 yr92 yr93 yr94 yr95 yr96 yr97 yr98 yr99 yr00 yr01 yr02 yr03 yr04 yr05 yr06 yr07 Excluded instruments: tang1 itang1 mtb1 liq1 Dropped collinear: yr08 . ________________________________________ From: owner-statalist@hsphsun2.harvard.edu [owner-statalist@hsphsun2.harvard.edu] on behalf of Schaffer, Mark E [M.E.Schaffer@hw.ac.uk] Sent: 25 June 2012 12:33 To: statalist@hsphsun2.harvard.edu Subject: st: RE: Interpreting Kleibergen Paap weak instrument statistic James, > -----Original Message----- > From: owner-statalist@hsphsun2.harvard.edu > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of > Fitzgerald, James > Sent: 21 June 2012 14:02 > To: statalist@hsphsun2.harvard.edu > Subject: st: Interpreting Kleibergen Paap weak instrument statistic > > Hi Statalist users > > I am using xtivreg2 to estimate a GMM-IV model (I specify the > following options; fe robust bw(2) gmm2s). I am not assuming > i.i.d errors, and thus when testing for weak instruments I am > using the Kleibergen Paap rk wald F statistic rather than the > Cragg Donald wald F statistic. > > xtivreg2 produces Stock-Yogo critical values for the Cragg > Donald statistic assuming i.i.d errors, so I'm not sure how > to interpret the KP rk wald F stat. > > The help file for ivreg2 (Baum, Schaffer and Stillman, 2010) > does however mention the following: > > When the i.i.d. assumption is dropped and ivreg2 is invoked > with the robust, bw or cluster options, the > Cragg-Donald-based weak instruments test is no longer valid. > ivreg2 instead reports a correspondingly-robust > Kleibergen-Paap Wald rk F statistic. The degrees of freedom > adjustment for the rk statistic is (N-L)/L1, as with the > Cragg-Donald F statistic, except in the cluster-robust case, > when the adjustment is N/(N-1) * (N_clust-1)/N_clust, > following the standard Stata small-sample adjustment for > cluster-robust. In the case of two-way clustering, N_clust is > the minimum of N_clust1 and N_clust2. The critical values > reported by ivreg2 for the Kleibergen-Paap statistic are the > Stock-Yogo critical values for the Cragg-Donald i.i.d. case. > The critical values reported with 2-step GMM are the > Stock-Yogo IV critical values, and the critical values > reported with CUE are the LIML critical values. > > > My understanding of the end of the paragraph is that the KP > stat can still be compared to the Stock-Yogo values produced > by STATA in determining whether or not instruments are weak. > > If someone could confirm or reject this I would be eternally > grateful!! I wrote that paragraph, so the ambiguity is partly my fault. But the problem is that there are no concrete results in the literature for testing for weak IVs when the i.i.d. assumption fails. The only thing one can do (that I'm aware of, anyway) is to point to stats that have an asymptotic justification in a test of underidentification, which is what the output of -ivreg2- does. That is, the K-P stat can be used to test for underidentification without the i.i.d. assumption, and under i.i.d. it has the same distribution under the null as the Cragg-Donald stat. This justification is different from that underlying the Stock-Yogo critical values, so this is pretty hand-wavey. The alternative is weak-instrument-robust estimation, a la Anderson-Rubin, Moreira, Kleibergen, etc. The Finlay-Magnusson -rivtest- command, available via ssc ideas in the usual way, supports this. Also see their accompanying SJ paper (vol. 9 no. 3). The command doesn't directly support panel data estimation, which is what you have, but you could just demean your variables by hand. HTH, Mark > Best wishes > > James Fitzgerald > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > -- Heriot-Watt University is the Sunday Times Scottish University of the Year 2011-2012 Heriot-Watt University is a Scottish charity registered under charity number SC000278. * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/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/statalist/faq * http://www.ats.ucla.edu/stat/stata/