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From |
andreas.zweifel@uzh.ch |

To |
statalist@hsphsun2.harvard.edu |

Subject |
RE: st: Spurious inference from endogeneity tests |

Date |
Mon, 30 Jan 2012 16:19:49 +0100 |

Dear Mark, Thank you for pointing me out the difference between testing the exogeneity and strength of instruments. Indeed, my standard IV/GMM results suggests that I have somewhat weakish instruments and it may be worthwhile to try your A-R approach at last. Even though the manuals claim that the standard approach is good enough (at least for the special case of just one endogenous regressor), I understand now that your A-R approach may produce relatively more reliable results the higher the number of endogenous regressors and the lower the strength of the instruments suggested by the standard IV/GMM results. Andreas -----owner-statalist@hsphsun2.harvard.edu schrieb: ----- An: <statalist@hsphsun2.harvard.edu> Von: "Schaffer, Mark E" Gesendet von: owner-statalist@hsphsun2.harvard.edu Datum: 29.01.2012 14:55 Betreff: RE: st: Spurious inference from endogeneity tests Andreas, > -----Original Message----- > From: owner-statalist@hsphsun2.harvard.edu > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of > andreas.zweifel@uzh.ch > Sent: 29 January 2012 13:00 > To: statalist@hsphsun2.harvard.edu > Subject: RE: st: Spurious inference from endogeneity tests > > Dear Mark, > > The point is that if my model is exactly identified with 2 > problematic regressors and 2 instruments, the Sargan test > drops out of the -ivreg2- inference. However, I get the > results from the first-stage test of the joint significance > of the IV, the Anderson-Rubin test statistic (p-value < 0.01) > and the Stock-Yogo Wright F-statistic exceeding 10 for the > two instruments. I don't see what the "point" is, to be honest. These are two conceptually separate issues that relate to the two separate requirements for valid instruments in standard IV/GMM estimation: (1) exogeneity of instruments, which can be tested using an overid stat if the eqn is overidentified; (2) strength of instruments (weak or under-identification), which can be be tested using a Cragg-Donald or Anderson-type stat. The A-R test stat reported by -ivreg2- to which you refer relates to the A-R approach, which I described in my previous post. It using the A-R method to test whether 0 lies in the confidence interval for the endogenous regressor. There is no "Stock-Yogo-Wright" statistic. You are confusing the Stock-Wright S statistic (which is a close relative of the A-R test stat) with the Stock-Yogo critical values for the Cragg-Donald test stat (used to test instrument strength in standard IV estimation). > To what degree do I need to doubt these test statistics > because of lacking robustness to weak instruments and use an > alternative approach instead? If your standard IV/GMM results suggest that you have weak or weak-ish instruments, you can consider using the AR approach or its relatives (-rivtest-, -condivreg-, the extension to K>1 regressors I sketched out, etc.) --Mark > > Best, > Andreas > > -----owner-statalist@hsphsun2.harvard.edu schrieb: ----- > An: <statalist@hsphsun2.harvard.edu> > Von: "Schaffer, Mark E" > Gesendet von: owner-statalist@hsphsun2.harvard.edu > Datum: 29.01.2012 12:02 > Betreff: RE: st: Spurious inference from endogeneity tests > > Andreas, > > I don't know where you got the idea about trying to > artificially introduce overidentification, but it wasn't from > my suggestion about using the AR approach for >1 endogenous > regressors. I referred to the AR "approach" to constructing > confidence intervals and sets. The AR approach is what > -rivtest- and -condivreg- implement; ivreg2 does not > implement this. All discussed in the Dufour article I > pointed towards. > > The AR approach for one endogenous regressor is to find a > weak-instruments-robust confidence interval for the > coefficient beta1 on the endogenous regressors X1. > > To test whether a specfic value for beta1 - say b1 - is in > the confidence interval, the AR approach is to do the following: > > 1. Create a new dependent variable y from the original dep > var Y and the endogenous regressor X1. Specifically, > > y = Y-b1*X1 > > 2. Run an OLS regression with y as the dependent variable > and all the exogenous regressors and instruments as > independent variables. > > 3. Do a test of the joint significance of the IVs. If b1 is > inside the confidence interval, they will be insignificant. > If b1 is outside the confidence interval, they will be significant. > > The intuition is straightforward. If b1 is close to the true > value of B1, then y has most of the impact of X1 purged from > it. Since in that case y doesn't have X1 in it, the > instruments should be unrelated to y (after accounting for > the other regressors etc. etc.). > > To construct a confidence interval, just do a grid search > over various values of b1. (There's a shortcut for the > special case of iid, but a mechanical grid search always works.) > > The AR approach has the drawback of wasting degrees of > freedom in the overidentified case, and -rivtest- and > -condivreg- implement more modern approaches that address > this. In the exactly-identified case, the AR approach is the > same as these more modern approaches. > > The AR approach for 2 endogenous regressors proceeds in the > same way, except that now you are purging Y of the effects of > both regressors: > > y = Y - b1*X1 - b2*X2 > > And instead of a confidence interval you get a confidence > set. That is, you find out whether (b1,b2) is in the > confidence set (the IVs in step 3 are not signif) or outside > the confidence set (the IVs in step 3 ARE signif). And you > have to do a grid search over combinations of values for b1 > and b2. A hassle, but not too bad. > > The above is useful if you want to use -rivtest- or > -condivreg- but can't because they handle only the > one-endog-regressor case. The confidence set approach is the > K>1 generalization of these estimators. But if you don't > want to use this approach to inference anyway, this won't be > of much interest. > > --Mark > > > -----Original Message----- > > From: owner-statalist@hsphsun2.harvard.edu > > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of > > andreas.zweifel@uzh.ch > > Sent: 27 January 2012 22:52 > > To: statalist@hsphsun2.harvard.edu > > Subject: RE: st: Spurious inference from endogeneity tests > > > > I am not sure if conducting the AR test in the K-regressor is the > > optimal solution to my problem. As I said, X1hat is a combined > > instrument for the endogenous variable X1, which has been > estimated in > > a preliminary regression on all available instruments Z. > Analogously, > > the interaction X1hat*X2 (X2 > > exogenous) will be the instrument for the endogenous > interaction term > > X1*X2. Using this approach to properly instrument the endogenous > > interaction term, I will obtain no more instruments than endogenous > > regressors by construction. > > In other words, the model is exactly identified and testing for > > overidentifying restrictions will be redundant. I don't see why I > > should be worried as long as the weak instrument robust > Anderson Rubin > > test rejects its null ("H0: B1=0 and overidentifying > restrictions are > > valid") that the model is misspecified. Better still, weak > instrument > > robust inference might be of less concern if the F-statistic of the > > Stock Yogo > > (2002) test to detect weak instruments yields a value of > >10 with two > > instruments, right? Of course I can run a specification test by > > computing additional instruments from forming the powers of > X1hat and > > X1hat*X2 to invoke the Sargan test statistic in -ivreg2-. However, > > what is the lesson to be learned from artificially introducing > > overidentification? In case the Sargan test statistic is > > insignificant, nothing will indicate that the model is > overidentified > > or misspecified. > > Based on these results, I could eventually test whether the 2SLS > > coefficients substantially and systematically deviate from the OLS > > coefficients using a Hausman test and decide what to prefer for > > conducting statistical inference. > > > > I hope the methodology described above satisfies the current > > state-of-the-art requirements for statistical inference. > This does not > > just mean that I am tired of using sophisticated > econometrics, but the > > goal of my research is to gain empirical evidence from data > analysis > > rather than evaluating the most complex tools available to solve > > presumably simple endogeneity problems. > > > > Best, > > Andreas > > > > -----owner-statalist@hsphsun2.harvard.edu schrieb: ----- > > An: <statalist@hsphsun2.harvard.edu> > > Von: "Schaffer, Mark E" > > Gesendet von: owner-statalist@hsphsun2.harvard.edu > > Datum: 26.01.2012 23:05 > > Betreff: RE: st: Spurious inference from endogeneity tests > > > > Andreas, > > > > If you are feeling adventurous, you could try implementing the > > Anderson-Rubin (weak-instrument-robust) approach to the K-regressor > > case. I think it's discussed in Dufour (2003), > "Identification, Weak > > Instruments and Statistical Inference in Econometrics" > (full reference > > in the -ivreg2- help file references). > > > > In the 1-endogenous-regressor case, the AR approach (which > rivtest and > > condivreg extend) is to construct a confidence interval for the > > regressor beta_1. In the 2-endogenous-regressor case, the > AR approach > > is to construct a confidence *set* for the regressors (beta_1, > > beta_2). > > > > You could implement this by a simple grid search - a bit of > a hassle, > > but not that bad. > > > > HTH, > > Mark > > > > > -----Original Message----- > > > From: owner-statalist@hsphsun2.harvard.edu > > > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of > > Suryadipta > > > Roy > > > Sent: 26 January 2012 00:06 > > > To: statalist@hsphsun2.harvard.edu > > > Subject: Re: Antwort: Re: Antwort: Re: Antwort: Re: Antwort: > > > Re: RE: st: Spurious inference from endogeneity tests > > > > > > Andreas, > > > I see the problem. You are right; - condivreg- is not valid > > for more > > > than one endogenous variable. My first reaction will be > > similar what > > > has been probably suggested by another subscriber, i.e. to > > try using > > > powers of x1hat and that of the product of x1hat and x2 > to generate > > > additional instruments for testing overidentification in -ivreg2- > > > accompanied by > > > -first- (/-ffirst-) option. If x1 is a limited dependent > variable, > > > then you might probably get even more creative by using a > > non-linear > > > specification (or -rivtest- etc.) along with the usual > > linear model to > > > generate different values of x1hat, and then interact them > > with x2 and > > > see whether they retain sufficient independent information > > to be used > > > as instruments. Or, trying out a log-log model (and/or log linear > > > model) for x1 along with the linear model. Of course, one > can check > > > all the specifications checking the adjusted-r square, or > > the AIC/BIC > > > following the -estat ic- command. > > > > > > Best wishes, > > > Suryadipta. > > > > > > On Wed, Jan 25, 2012 at 5:49 AM, Justina Fischer > > <JAVFischer@gmx.de> > > > wrote: > > > > Dear Andreas, > > > > > > > > finding suitable instruments (in terms of > > > economic-theoretical coherence with the endogenous) is > > something this > > > list does not aim at. > > > > > > > > best > > > > > > > > Justina > > > > > > > > > > > > -------- Original-Nachricht -------- > > > >> Datum: Wed, 25 Jan 2012 08:40:54 +0100 > > > >> Von: andreas.zweifel@uzh.ch > > > >> An: statalist@hsphsun2.harvard.edu > > > >> Betreff: Antwort: Re: Antwort: Re: Antwort: Re: Antwort: > > > Re: RE: st: > > > >> Spurious inference from endogeneity tests > > > > > > > >> Hi Suyadipta, > > > >> > > > >> thank you for the suggestion to use -condivreg-. > > > Unfortunately, the > > > >> command works with one endogenous regressor only. However, > > > I have two > > > >> endogenous regressors due to an interaction of the original > > > >> endogenous variable X1 and an exogenous control X2, i.e. > > my model > > > >> looks like > > > >> > > > >> Y = X1 + X1*X2 + controls + e > > > >> > > > >> I have been recommended to estimate first X1 by instruments Zi > > > >> (i=1,...n) to obtain X1hat, than form interactions X1hat*X2 as > > > >> instruments to be used in the -ivreg2- command which > > then would be > > > >> > > > >> ivreg2 Y controls (X1 X1*X2 = X1hat X1hat*X2) > > > >> > > > >> (see > > http://www.stata.com/statalist/archive/2011-08/msg01496.html) > > > >> > > > >> This actually solves the endogeneity problem since the > > > F-statistic of > > > >> the weak instruments test substantially increases > > compared to the > > > >> canned 2SLS procedure > > > >> > > > >> ivreg2 Y controls (X1 X1*X2 = Zi Zi*X2) > > > >> > > > >> where each basic instrument Zi is interacted with X2 > yielding n > > > >> combined instruments. So in total, I have 2*n > instruments for 2 > > > >> endogenous regressors. > > > >> > > > >> In the special case of only one basic instrument Z1 (n=1), > > > the first > > > >> 2SLS approach and canned SLS just coincide because the > model is > > > >> exactly identified in both cases. However, to test whether the > > > >> instruments are really valid you should have n>1 > > > instruments for one > > > >> endogenous regressor. This yields another problem > because in the > > > >> first 2SLS approach there are always two endogenous > > regressors and > > > >> two instruments by construction. Thus I can see no way > > how to test > > > >> for overidentifying restrictions with this approach. > > > >> > > > >> I would appreciate any help with respect to a possible > > solution to > > > >> that problem. > > > >> > > > >> Andreas Zweifel > > > >> > > > >> > > > >> -----owner-statalist@hsphsun2.harvard.edu schrieb: ----- > > > >> An: statalist@hsphsun2.harvard.edu > > > >> Von: Suryadipta Roy > > > >> Gesendet von: owner-statalist@hsphsun2.harvard.edu > > > >> Datum: 24.01.2012 13:20 > > > >> Betreff: Re: Antwort: Re: Antwort: Re: Antwort: Re: RE: > > > st: Spurious > > > >> inference from endogeneity tests > > > >> > > > >> Andreas, > > > >> Along these lines, I would also suggest that you take a > > > look at the > > > >> condivreg command ( - findit condivreg - , the help > file and the > > > >> related papers) for detecting weak instruments. The > > Murray (2006) > > > >> paper cited below is suggesting in those lines. The > > Stata journal > > > >> references are Mikusheva and Poi (2003), Stata Journal 3: > > > 57-70, and > > > >> Mikusheva and Poi (2006), Stata Journal 6: 335-347. > > > >> > > > >> Best wishes, > > > >> Suryadipta. > > > >> > > > >> On Mon, Jan 23, 2012 at 10:18 AM, Justina Fischer > > > <JAVFischer@gmx.de> > > > >> wrote: > > > >> > Hi Andreas > > > >> > > > > >> > 1) true. This is why you should always consult several > > > test stats (incl. > > > >> t-stats, F-stats, Shea R2, robust-to-weak instr. stats, > > > etc.) to get > > > >> an overall picture. Selecting instruments is a hard and > > > complex business... > > > >> > > > > >> > 2) reduncancy tests make only sense when you have > > > managed to select > > > >> > good > > > >> instruments (it is based on the Sargan/Hansen-J test, if > > I recall > > > >> well -> consult ivreg2 help file). > > > >> > > > > >> > 3) practice shows it is in most cases to have no of > > instruments > > > > >> endogenous regressors, but not too many in absolute > > > number. For one > > > >> endogenous regressor, I usually try to find three > > instruments. You > > > >> can increase the number of instruments artificially by > > doing some > > > >> non-linear stuff, e.g. using a quadratic term. > > > >> > > > > >> > Best, > > > >> > justina > > > >> > > > > >> > > > > >> > -------- Original-Nachricht -------- > > > >> >> Datum: Mon, 23 Jan 2012 15:59:27 +0100 > > > >> >> Von: andreas.zweifel@uzh.ch > > > >> >> An: statalist@hsphsun2.harvard.edu > > > >> >> Betreff: Antwort: Re: Antwort: Re: Antwort: Re: RE: > > st: Spurious > > > >> inference from endogeneity tests > > > >> > > > > >> >> Hi Justina, > > > >> >> > > > >> >> thank you for the intuitive ideas with respect to the > > > quality of > > > >> >> the instruments. > > > >> >> > > > >> >> So I was wrong with my notion that one should have as many > > > >> >> instruments > > > >> as > > > >> >> endogenous variables in the regression. But I can tell > > > you that I > > > >> >> have already tested my model with one endogenous > > regressor under > > > >> overidentification, > > > >> >> that is with a whole set of instruments. The Sargan > > > test statistic > > > >> using > > > >> >> -ivreg2- (or -ivreg28- in Stata8) is clearly not > > > significant then, > > > >> >> so > > > >> the > > > >> >> null that the instruments are exogenous cannot be rejected. > > > >> >> However, I > > > >> fear > > > >> >> that this is weak evidence especially for my > setting, because > > > >> >> > > > >> >> 1) To my knowlegde, Sargan only allows to test whether the > > > >> >> instruments > > > >> are > > > >> >> *jointly* exogenous. It does yield no information about the > > > >> >> strength of one single instrument. > > > >> >> > > > >> >> 2) Using the -redundant- option in -ivreg2-, I get > > contradictory > > > >> results. > > > >> >> I tried a sensitivity test with a varying number of > > > possibly good > > > >> >> instruments and control variables to find the > > > following: Virtually > > > >> every instrument > > > >> >> candidate yields a more or less significant p-value for the > > > >> >> redundancy > > > >> test > > > >> >> if combined with many > > > >> >> other excluded instruments but few control variables. > > > But reducing > > > >> >> the number of instruments or increasing the number of > > > controls in > > > >> >> the regression model, the remaining > > > >> instruments > > > >> >> seem to become more redundant as well. > > > >> >> I don't know what is to be held of an instruments > > > relevance test > > > >> >> which reacts thus sensitively to minor changes in the > > > model specification. > > > >> >> > > > >> >> > > > >> >> Best, > > > >> >> Andreas > > > >> >> > > > >> >> -----owner-statalist@hsphsun2.harvard.edu schrieb: ----- > > > >> >> An: statalist@hsphsun2.harvard.edu > > > >> >> Von: "Justina Fischer" > > > >> >> Gesendet von: owner-statalist@hsphsun2.harvard.edu > > > >> >> Datum: 21.01.2012 01:35 > > > >> >> Betreff: Re: Antwort: Re: Antwort: Re: RE: st: Spurious > > > inference > > > >> >> from endogeneity tests > > > >> >> > > > >> >> HI Andreas, > > > >> >> > > > >> >> there are no 'right' instrumentsas such: there are only > > > good ones > > > >> (valid, > > > >> >> strong) and bad ones. Imagine ´good´ and ´bad´ being on a > > > >> continuous > > > >> >> scale: most instruments are somwhere on this scale, but > > > rarely at > > > >> >> the extreme. > > > >> >> > > > >> >> now to the Sargan: > > > >> >> "The Sargan test statistic [...] [is] under the > null that the > > > >> >> error > > > >> term > > > >> >> is uncorrelated with the instruments." > > > >> >> source: http://en.wikipedia.org/wiki/Instrumental_variable > > > >> >> > > > >> >> so you want a p-value > 0.10 > > > >> >> > > > >> >> no rejection is what you want: the null means you have good > > > >> instruments. > > > >> >> > > > >> >> I recommend to use ivreg2 whih allows you to test the > > > redundany of > > > >> >> instruments. > > > >> >> > > > >> >> Best > > > >> >> Justina > > > >> >> > > > >> >> > > > >> >> -------- Original-Nachricht -------- > > > >> >> > Datum: Fri, 20 Jan 2012 21:22:54 +0100 > > > >> >> > Von: andreas.zweifel@uzh.ch > > > >> >> > An: statalist@hsphsun2.harvard.edu > > > >> >> > Betreff: Antwort: Re: Antwort: Re: RE: st: Spurious > > inference > > > >> >> > from > > > >> >> endogeneity tests > > > >> >> > > > >> >> > Hi > > > >> >> > > > > >> >> > I think you are quite right, and my intuition > also tells me > > > >> >> > something else. Let's assume I have only one endogenous > > > >> >> > regressor, but more than one instrument candidates > > > since there > > > >> >> > is no theoretical foundation for choosing the 'right' > > > >> >> > instruments for the endogenous variable. If I > > include all of > > > >> >> > these instruments and the > > > >> >> > -overid- test statistic is still not significant, > there is > > > >> >> > likely something wrong with the instruments. This > > is because > > > >> >> > theory > > > >> >> claims > > > >> >> > that one instrument should suffice here, and each > > additional > > > >> >> > instrument included merely increases the standard > > > >> deviation > > > >> >> of > > > >> >> > the IV estimator. As a consequence, the model must be > > > >> >> > overidentified from a theoretical view. However, if > > the Sargan > > > >> test > > > >> >> > fails to detect overidentification, this can only be > > > due to the > > > >> >> > fact that the selected instruments are quite weak... > > > >> >> > > > > >> >> > Best, > > > >> >> > Andreas > > > >> >> > > > > >> >> > -----owner-statalist@hsphsun2.harvard.edu schrieb: ----- > > > >> >> > An: statalist@hsphsun2.harvard.edu > > > >> >> > Von: "Justina Fischer" > > > >> >> > Gesendet von: owner-statalist@hsphsun2.harvard.edu > > > >> >> > Datum: 19.01.2012 23:22 > > > >> >> > Betreff: Re: Antwort: Re: RE: st: Spurious inference from > > > >> >> > endogeneity tests > > > >> >> > > > > >> >> > nope.. the bias could turn the direction of observed > > > influence - > > > >> >> > how > > > >> do > > > >> >> > you know then which one is correct (OLS or IV)? > > > >> >> > > > > >> >> > Rule of thumb is: better no instrument (OLS) than > > weak ones !! > > > >> >> > > > > >> >> > it is sufficient to provide good convincing > > arguments why you > > > >> selected > > > >> >> the > > > >> >> > instruments; there is no need for theoretical models > > > suggesting > > > >> >> > the instrument explicitly. Let your phantasy work ! > > > >> >> > > > > >> >> > Cheers > > > >> >> > Justina > > > >> >> > > > > >> >> > -------- Original-Nachricht -------- > > > >> >> > > Datum: Thu, 19 Jan 2012 23:00:00 +0100 > > > >> >> > > Von: andreas.zweifel@uzh.ch > > > >> >> > > An: statalist@hsphsun2.harvard.edu > > > >> >> > > Betreff: Antwort: Re: RE: st: Spurious inference from > > > >> >> > > endogeneity > > > >> >> tests > > > >> >> > > > > >> >> > > Thanks for this clarifying remark. > > > >> >> > > > > > >> >> > > In addition, literature always stresses the > > > requirement that > > > >> >> > > IVs should be selected in line with theoretically > > motivated > > > >> >> > > arguments. But economic theory may sometimes be > > > limited in its > > > >> >> > > capability to yield valid instruments. However, when > > > >> >> > > instruments are therefore weak, I expect the bias > > of the IV > > > >> >> > > estimator to be similarly large as the OLS > > estimator. Maybe > > > >> >> > > then it would make sense to prefer one of the two > > > estimators > > > >> >> > > in terms of theory driven expectations as the > lesser evil? > > > >> >> > > > > > >> >> > > -----owner-statalist@hsphsun2.harvard.edu schrieb: ----- > > > >> >> > > An: statalist@hsphsun2.harvard.edu > > > >> >> > > Von: Austin Nichols > > > >> >> > > Gesendet von: owner-statalist@hsphsun2.harvard.edu > > > >> >> > > Datum: 18.01.2012 16:37 > > > >> >> > > Betreff: Re: RE: st: Spurious inference from > > > endogeneity tests > > > >> >> > > > > > >> >> > > In re > > > >> >> > > the poster's central question: > > > >> >> > > "I have to conclude from my specification tests that my > > > >> >> > > coefficient estimates from both OLS and 2SLS cannot be > > > >> >> > > interpreted because 2SLS does not succeed in > > > resolving the endogeneity problem?" > > > >> >> > > I would answer yes. Without better > instruments, you have > > > >> >> > > learned nothing from 2SLS, including whether OLS is > > > biased or > > > >> >> > > not. The > > > >> overID > > > >> >> > > test is no good if you don't have strong > > instruments, since > > > >> >> > > its failure to reject the overID restrictions > > could be due > > > >> >> > > merely to > > > >> the > > > >> >> > > weakness of your excluded instruments. > > > >> >> > > > > > >> >> > > On Tue, Jan 17, 2012 at 6:44 PM, Justina Fischer > > > >> <JAVFischer@gmx.de> > > > >> >> > > wrote: > > > >> >> > > > wow. I am deeply impressed :-) > > > >> >> > > > > > > >> >> > > > Let us hope the authors provide user-written > > > Stata commands > > > >> soon.... > > > >> >> > > > > > > >> >> > > > justina > > > >> >> > > > -------- Original-Nachricht -------- > > > >> >> > > >> Datum: Tue, 17 Jan 2012 18:41:27 -0500 > > > >> >> > > >> Von: Cameron McIntosh <cnm100@hotmail.com> > > > >> >> > > >> An: STATA LIST <statalist@hsphsun2.harvard.edu> > > > >> >> > > >> Betreff: RE: st: Spurious inference from > > > endogeneity tests > > > >> >> > > > > > > >> >> > > >> The following papers will also be helpful: > > > >> >> > > >> Murray, M.P. (2006). Avoiding Invalid > Instruments and > > > >> >> > > >> Coping > > > >> with > > > >> >> > Weak > > > >> >> > > >> Instruments. Journal of Economic Perspectives, 20(4), > > > >> >> > > >> > > > >> >> > > > > > >> >> > > > > >> >> > > > >> > > > > > > 111-132.http://www.eui.eu/Personal/Guiso/Courses/Econometrics/Murray_ > > > >> IV_jep_06.pdf > > > >> >> > > >> > > > >> >> > > >> Chao, J.C., & Swanson, N.R. (2005). Consistent > > > estimation > > > >> >> > > >> with a > > > >> >> > large > > > >> >> > > >> number of weak instruments. Econometrica, 73(5), > > > >> >> > > >> > > > >> >> > > > > > >> >> > > > > >> >> > > > >> > > > > > > 1673-1692.http://gemini.econ.umd.edu/jrust/econ623/files/chao_swanson > > > >> _econometrica.pdf > > > >> >> > > >> > > > >> >> > > >> Nevo, A., & Rosen, A.M. (2010). Identification with > > > >> >> > > >> Imperfect > > > >> >> > > Instruments. > > > >> >> > > >> The Review of Economics and Statistics, Accepted for > > > >> publication. > > > >> >> > > >> > > > >> >> > > >> Kolesár, M., Chetty, R., Friedman, J.N., > > Glaeser, E.L., & > > > >> Imbens, > > > >> >> > G.W. > > > >> >> > > >> (October 2011). Identification and Inference > > with Many > > > >> >> > > >> Invalid > > > >> >> > > Instruments. > > > >> >> > > >> NBER Working Paper No. 17519. > > > >> >> > > >> http://www.nber.org/papers/w17519 > > > >> >> > > >> > > > >> >> > > >> Cam > > > >> >> > > >> > Date: Wed, 18 Jan 2012 00:06:34 +0100 > > > >> >> > > >> > From: JAVFischer@gmx.de > > > >> >> > > >> > Subject: Re: st: Spurious inference from > endogeneity > > > >> >> > > >> > tests > > > >> >> > > >> > To: statalist@hsphsun2.harvard.edu > > > >> >> > > >> > > > > >> >> > > >> > Hi Andreas > > > >> >> > > >> > > > > >> >> > > >> > for judging whether instruments are weak or > > > not I would > > > >> >> > > >> > as > > > >> first > > > >> >> > step > > > >> >> > > >> look into the first stage regression results, > > > look at the > > > >> >> > > >> Shea > > > >> R2, > > > >> >> > the > > > >> >> > > F-test > > > >> >> > > >> on the instruments, the single estimates....that > > > tells you > > > >> already > > > >> >> a > > > >> >> > > lot. > > > >> >> > > >> Maybe use ivreg2. > > > >> >> > > >> > > > > >> >> > > >> > Maybe you have only one weak instrument in a set of > > > >> instruments > > > >> >> you > > > >> >> > > >> should exclude (so the set is then strong, even > > > though one > > > >> single > > > >> >> > weak > > > >> >> > > >> instrument may bias your results) > > > >> >> > > >> > > > > >> >> > > >> > Best > > > >> >> > > >> > > > > >> >> > > >> > Justina > > > >> >> > > >> > > > > >> >> > > >> > > > > >> >> > > >> > -------- Original-Nachricht -------- > > > >> >> > > >> > > Datum: Tue, 17 Jan 2012 22:12:36 +0100 > > > >> >> > > >> > > Von: andreas.zweifel@uzh.ch > > > >> >> > > >> > > An: statalist@hsphsun2.harvard.edu > > > >> >> > > >> > > Betreff: st: Spurious inference from > > > endogeneity tests > > > >> >> > > >> > > > > >> >> > > >> > > Dear Statausers, > > > >> >> > > >> > > > > > >> >> > > >> > > I am concerned with an endogeneity problem > > > in my sample > > > >> >> > > >> > > of > > > >> 126 > > > >> >> > > firms > > > >> >> > > >> when > > > >> >> > > >> > > investigating the relationship between > managerial > > > >> >> > > >> > > disclosure > > > >> >> and > > > >> >> > > cost > > > >> >> > > >> of > > > >> >> > > >> > > capital effects. After running the ivreg28 > > > command, the > > > >> >> > > Cragg-Donald > > > >> >> > > >> test > > > >> >> > > >> > > F-statistic is 2.27, which indicates that my > > > >> >> > > >> > > instruments are > > > >> >> > rather > > > >> >> > > >> weak. > > > >> >> > > >> > > However, my model appears to be correctly > > identified, > > > >> because > > > >> >> the > > > >> >> > > >> Anderson test > > > >> >> > > >> > > statistic for the first stage equation > > > yields a p-value > > > >> lower > > > >> >> > than > > > >> >> > > >> 0.01 > > > >> >> > > >> > > and the Sargan test statistic is > > > insignificant (p-value > > > >> >> > > >> > > = > > > >> >> 0.59). > > > >> >> > > Since > > > >> >> > > >> my > > > >> >> > > >> > > instruments have passed the > > > overidentification test, I > > > >> >> > > >> > > run > > > >> the > > > >> >> > > ivendog > > > >> >> > > >> command > > > >> >> > > >> > > which is equivalent to a Hausman test. > > > Again, the test > > > >> >> statistic > > > >> >> > is > > > >> >> > > >> > > insignificant (p-value = 0.48). > > > >> >> > > >> > > > > > >> >> > > >> > > If I compare OLS and 2SLS, I find that only > > > the former > > > >> yields a > > > >> >> > > >> > > significant coefficient of managerial > > > disclosure in the > > > >> model > > > >> >> > > >> regressing cost of > > > >> >> > > >> > > capital on managerial disclosure. Considering the > > > >> specification > > > >> >> > > tests > > > >> >> > > >> above, it > > > >> >> > > >> > > seems unlikely that 2SLS is an improvement > > over OLS. > > > >> >> > > >> > > Thus I > > > >> >> > assume > > > >> >> > > >> that I > > > >> >> > > >> > > can take the OLS estimates for causal > > inference. Is > > > >> >> > > >> > > this > > > >> >> correct? > > > >> >> > > If > > > >> >> > > >> yes, > > > >> >> > > >> > > the point why I should not use 2SLS is > > likely due to > > > >> >> > > >> > > the > > > >> >> weakness > > > >> >> > > of > > > >> >> > > >> the > > > >> >> > > >> > > instruments and the small-sample bias. So > > I have to > > > >> >> > > >> > > conclude > > > >> >> from > > > >> >> > > my > > > >> >> > > >> > > specification tests that my coefficient > > > estimates from > > > >> >> > > >> > > both > > > >> OLS > > > >> >> > and > > > >> >> > > >> 2SLS cannot be > > > >> >> > > >> > > interpreted because 2SLS does not succeed in > > > resolving > > > >> >> > > >> > > the > > > >> >> > > endogeneity > > > >> >> > > >> > > problem? > > > >> >> > > > > > >> >> > > * > > > >> >> > > * 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/ > > > >> >> > > > > >> >> > -- > > > >> >> > Justina AV Fischer, PhD > > > >> >> > COFIT Fellow > > > >> >> > World Trade Institute > > > >> >> > University of Bern > > > >> >> > > > > >> >> > homepage: http://www.justinaavfischer.de/ > > > >> >> > e-mail: javfischer@gmx.de. justina.fischer@wti.org > > > >> >> > papers: http://ideas.repec.org/e/pfi55.html > > > >> >> > > > > >> >> > > > > >> >> > * > > > >> >> > * 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/ > > > >> >> > > > >> >> -- > > > >> >> Justina AV Fischer, PhD > > > >> >> COFIT Fellow > > > >> >> World Trade Institute > > > >> >> University of Bern > > > >> >> > > > >> >> homepage: http://www.justinaavfischer.de/ > > > >> >> e-mail: javfischer@gmx.de. justina.fischer@wti.org > > > >> >> papers: http://ideas.repec.org/e/pfi55.html > > > >> >> > > > >> >> > > > >> >> * > > > >> >> * 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/ > > > >> > > > > >> > -- > > > >> > Justina AV Fischer, PhD > > > >> > COFIT Fellow > > > >> > World Trade Institute > > > >> > University of Bern > > > >> > > > > >> > homepage: http://www.justinaavfischer.de/ > > > >> > e-mail: javfischer@gmx.de. justina.fischer@wti.org > > > >> > papers: http://ideas.repec.org/e/pfi55.html > > > >> > > > > >> > > > > >> > * > > > >> > * 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/ > > > >> * > > > >> * 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/ > > > > > > > > -- > > > > Justina AV Fischer, PhD > > > > COFIT Fellow > > > > World Trade Institute > > > > University of Bern > > > > > > > > homepage: http://www.justinaavfischer.de/ > > > > e-mail: javfischer@gmx.de. justina.fischer@wti.org > > > > papers: http://ideas.repec.org/e/pfi55.html > > > > > > > > > > > > * > > > > * 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 a Scottish charity registered > under charity > > number SC000278. > > > > Heriot-Watt University is the Sunday Times Scottish > University of the > > Year 2011-2012 > > > > > > > > * > > * 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 a Scottish charity registered under > charity number SC000278. > > Heriot-Watt University is the Sunday Times Scottish > University of the Year 2011-2012 > > > > * > * 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 a Scottish charity registered under charity number SC000278. Heriot-Watt University is the Sunday Times Scottish University of the Year 2011-2012 * * 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/

**References**:**RE: st: Spurious inference from endogeneity tests***From:*"Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>

**RE: st: Spurious inference from endogeneity tests***From:*"Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>

**RE: st: Spurious inference from endogeneity tests***From:*"Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>

**Re: Antwort: Re: Antwort: Re: Antwort: Re: RE: st: Spurious inference from endogeneity tests***From:*Suryadipta Roy <sroy2138@gmail.com>

**Re: Antwort: Re: Antwort: Re: RE: st: Spurious inference from endogeneity tests***From:*"Justina Fischer" <JAVFischer@gmx.de>

**Re: Antwort: Re: RE: st: Spurious inference from endogeneity tests***From:*"Justina Fischer" <JAVFischer@gmx.de>

**Re: RE: st: Spurious inference from endogeneity tests***From:*Austin Nichols <austinnichols@gmail.com>

**st: Spurious inference from endogeneity tests***From:*andreas.zweifel@uzh.ch

**Re: st: Spurious inference from endogeneity tests***From:*"Justina Fischer" <JAVFischer@gmx.de>

**RE: st: Spurious inference from endogeneity tests***From:*Cameron McIntosh <cnm100@hotmail.com>

**Re: RE: st: Spurious inference from endogeneity tests***From:*"Justina Fischer" <JAVFischer@gmx.de>

**Antwort: Re: RE: st: Spurious inference from endogeneity tests***From:*andreas.zweifel@uzh.ch

**Antwort: Re: Antwort: Re: RE: st: Spurious inference from endogeneity tests***From:*andreas.zweifel@uzh.ch

**Antwort: Re: Antwort: Re: Antwort: Re: RE: st: Spurious inference from endogeneity tests***From:*andreas.zweifel@uzh.ch

**Re: Antwort: Re: Antwort: Re: Antwort: Re: RE: st: Spurious inference from endogeneity tests***From:*"Justina Fischer" <JAVFischer@gmx.de>

**Antwort: Re: Antwort: Re: Antwort: Re: Antwort: Re: RE: st: Spurious inference from endogeneity tests***From:*andreas.zweifel@uzh.ch

**Re: Antwort: Re: Antwort: Re: Antwort: Re: Antwort: Re: RE: st: Spurious inference from endogeneity tests***From:*"Justina Fischer" <JAVFischer@gmx.de>

**RE: st: Spurious inference from endogeneity tests***From:*andreas.zweifel@uzh.ch

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