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From |
"Schaffer, Mark E" <[email protected]> |

To |
<[email protected]> |

Subject |
st: RE: RE: RE: xtivreg2: orthog option |

Date |
Thu, 5 Jul 2012 16:20:03 +0100 |

James, > -----Original Message----- > From: [email protected] > [mailto:[email protected]] On Behalf Of > Fitzgerald, James > Sent: 05 July 2012 14:57 > To: [email protected] > Subject: st: RE: RE: xtivreg2: orthog option > > Mark, > > ________________________________________ > From: [email protected] > [[email protected]] on behalf of Schaffer, > Mark E [[email protected]] > Sent: 05 July 2012 13:48 > To: [email protected] > Subject: st: RE: RE: RE: RE: RE: RE: RE: RE: RE: RE: > xtivreg2: orthog option > > James, > > > > -----Original Message----- > > From: [email protected] > > [mailto:[email protected]] On Behalf Of > > Fitzgerald, James > > Sent: 05 July 2012 11:15 > > To: [email protected] > > Subject: st: RE: RE: RE: RE: RE: RE: RE: RE: RE: xtivreg2: > > orthog option > > > > Mark, > > > > I followed your suggestion as far as I understood it. As > > such, I undertook the following steps: > > > > 1. I estimated the model with suspect instruments treated as > > endogenous. As I have no reason to suspect any one regressor > > is endogenous and others are not, I ran the model with all > > regressors assumed to be endogenous and used 3 lags as > > exluded instruments. > > > > xtivreg2 ltdbv yr* (lnsale tang itang itangdum tax prof mtb > > capexsa liq ndts=l.lnsale l2.lnsale l3.lnsale l.tang l2.tang > > l3.tang l.itang l2.itang l3.itang l.itangdum l2.itangdum > > l3.itangdum l.tax l2.tax l3.tax l.prof l2.prof l3.prof l.mtb > > l2.mtb l3.mtb l.capexsa l2.capexsa l3.capexsa l.liq l2.liq > > l3.liq l.ndts l2.ndts l3.ndts), fe cluster(firm) gmm2s > > > > The p-value on the Hansen J-Stat turned out to be 0.01. > > > > 2. I then tested the orthogonality of the different lags > > orthog(l.lnsale l.tang . . . l.ndts) gave a C stat > > p-value of 0.5196 > > orthog(l2.lnsale l2.tang . . . l2.ndts) gave a C stat > > p-value of 0.3318 > > orthog(l3.lnsale l3.tang . . . l3.ndts) gave a C stat > > p-value of 0.0022 > > > > 3. I dropped the l3 lags and the Hansen J Stat p-value was 0.5588. > > I then used the endog option on each of the endogenous > > variables i.e. > > > > xtivreg2 ltdbv yr* (lnsale tang itang itangdum tax prof mtb > > capexsa liq ndts=l.lnsale l2.lnsale l3.lnsale l.tang l2.tang > > l.itang l2.itang l.itangdum l2.itangdum l.tax l2.tax l.prof > > l2.prof l.mtb l2.mtb l.capexsa l2.capexsa l.liq l2.liq l.ndts > > l2.ndts), fe cluster(firm) gmm2s endog(lnsale) > > > > And replaced lnsale with tang, itang etc. > > > > 4. All the endog tests indicated the regressors are not > > endogenous, so I conclude there is no need to use xtivreg2, > > fe and instead I can use xtreg, fe > > > > How does this sound?? > > > > James > > ________________________________________ > > <snip> > > This looks reasonable. Just a few thoughts: > > In steps 1-2, it looks like you are getting a large C stat for L3 > because L1 and L2 are identifying one beta_hat, and L3 is > identifying a > different beta_hat. At least one of these two beta_hats must be > inconsistent. You're concluding that the 2nd one is inconsistent, and > so you're dropping the L3s as IVs. > > This could be defensible, but it looks a bit odd. The more usual case > is that older lags are more likely to be valid IVs than recent lags. > > An alternative interpretation of your results is that the 1st beta_hat > is inconsistent, and so you should drop the L1s and L2s and > use just the > L3s as IVs. You might want to try that and see what happens. > (There's > no point doing a C test for the L1s and L2s, by the way, because using > just the L3s gives you an exactly identified equation, and the C stat > will the same large J stat you got when you used all the IVs.) > > I just tried this and I found that all my estimates become > completely insignificant when I use L3s as IVs, but are > aprroximately what would be expected when i use L1s and L2s. > Also, the underidentification statistic is completely > insignificant with the L3s, but marginally significant when I > use the L1s and L2s This is a problem. The weak ID stat with L1s and L2s is probably very low, suggesting that even your L1-L2-based estimates aren't reliable, or more precisely, at least one of the coeffs in the beta_hat vector isn't well identified. See also below. > (I think it is only marginally > significant as for some of the regressors the lags may not be > good instruments). > Does this suggest that beta_hat based on L1 and L2 is consistent? Not quite. It suggests that the beta_hat based on L3 is inconsistent, or to be more precise, at least one of the coeffs in the beta_hat vector is inconsistent. > Also, in step 3, you can test for the endogeneity of all your regressors > lnsale-ndts all at once - the endog option takes varlists. > > When I test them one at a time (employing L1 and L2 as lags) > I get the following endogeneity test p-values: > lnsale = 0.6859 > tang = 0.2336 > itang = 0.7719 > itangdum = 0.001 > tax = 0.0068 > prof = 0.7691 > mtb = 0.7357 > capexsa = 0.2933 > liq = 0.2511 > ndts = 0.5358 > > I conclude that itangdum and tax need to be instrumented. > Please ignore my earlier comment that all regressors are exogenous! But be a bit careful here. There are 11 coeffs. You shouldn't be too surprised if p-values for the endogeneity tests are spread around - that's what you would expect to see under the null of exogeneity. Some big p-values, some small, some in-between. > When i test for the endogeneity of all my regressors at once > I get a p-value of 0.0002. > This tells me that one or more of my regressors are indeed endogenous Which is an effective rejoinder to my point just above. But see also below. > Given the p-values from the individual endog tests I now > specify itangdum and tax as endogenous, and the other > variables as exogenous. > To confirm the other variables are exogenous, I specify > orthog(varlist) and I get a C Stat p-value of 0.4742. > > Does this seem right? > > Now I am left with the issue of assessing the "strength" of > the instruments. Ah - you should have done this first. The tests for orthogonality, endogeneity, etc., all assume that the underlying IV/GMM estimations are well-specified, and that includes being strongly identified. See my note above. > > I get the following statistics (I have kept all of the > excluded instruments i.e. L1s and L2s of all 10 explanatory variables) > > Summary results for first-stage regressions > > (Underid) > (Weak id) > Variable F( 20, 1049) P-val AP Chi-sq( 19) P-val AP > F( 19, 1049) > itangdum 111.58 0.0000 2194.99 0.0000 114.94 > tax 3.66 0.0000 72.32 > 0.0000 3.79 > NB: first-stage test statistics cluster-robust > Stock-Yogo weak ID test critical values for single endogenous > regressor: > 5% maximal IV relative bias 21.38 > 10% maximal IV relative bias 11.46 > 20% maximal IV relative bias 6.31 > 30% maximal IV relative bias 4.51 > 10% maximal IV size 59.92 > 15% maximal IV size 31.58 > 20% maximal IV size 21.90 > 25% maximal IV size 16.99 > 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(19)=59.63 > P-val=0.0000 > Weak identification test > Ho: equation is weakly identified > Cragg-Donald Wald F statistic > 5.56 > Kleibergen-Paap Wald rk F statistic > 3.60 > Stock-Yogo weak ID test critical values for K1=2 and L1=20: > 5% maximal IV relative bias 20.48 > 10% maximal IV relative bias 11.03 > 20% maximal IV relative bias 6.11 > 30% maximal IV relative bias 4.39 > 10% maximal IV size 46.62 > 15% maximal IV size 24.96 > 20% maximal IV size 17.61 > 25% maximal IV size 13.84 > 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(20,1049)= 2.82 > P-val=0.0000 > Anderson-Rubin Wald test Chi-sq(20)= 56.61 > P-val=0.0000 > Stock-Wright LM S statistic Chi-sq(20)= 47.94 > P-val=0.0004 > NB: Underidentification, weak identification and > weak-identification-robust > test statistics cluster-robust > > > My intuition is that the stats relating to itangdum are > strong, but the stats relating to tax are weak. That looks right, though strictly speaking you shouldn't use the A-P stats like that. They're actually meant for the case where you are interested a priori in one coeff and not in another. > I specify the first option and STATA It's "Stata", by the way. > generates the first > stage regressions of tax and itangdum. The results suggest > that many of the instruments do not explain variation in > either variable. > Can I remove these instruments and, as long as my Hansen J > stat indicates the remaining excluded instruments are still > valid, still conclude that the variables specified as > exogenous can still be considered exogenous? The reason I > want to do this is that I find that the weak i.d stats often > improve dramatically when these instruments are removed. Too much specification tweaking makes me uneasy, but that's my personal view. Maybe someone else wants to comment. > Also, if I find an instrument to be weak, as I believe tax > is, tax is a regressor, not an instrument. I think I know what you mean, though. > should I; drop tax from the model, leave the instrument > in and just conclude that it is uninterpretable, or specify > tax as exogenous but that it is uninterpretable? Dropping tax is defensible. So is specifying it as exogenous - including it doesn't necessary mean the results are uninterpretable. I'm running out of steam on this thread and have to turn to other things. But I can see you're on top of the issues now. And perhaps someone else will want to comment. --Mark > > Thanks again > > James > > > > > > Cheers, > Mark > > > -- > 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/ > -- 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/

**Follow-Ups**:**st: RE: RE: RE: RE: xtivreg2: orthog option***From:*"Fitzgerald, James" <[email protected]>

**References**:**st: RE: RE: xtivreg2: orthog option***From:*"Fitzgerald, James" <[email protected]>

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