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st: RE: RE: RE: RE: RE: Interpreting Kleibergen Paap weak instrument statistic


From   "Fitzgerald, James" <J.Fitzgerald2@ucc.ie>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: RE: RE: RE: RE: RE: Interpreting Kleibergen Paap weak instrument statistic
Date   Mon, 25 Jun 2012 18:52:04 +0000

Mark,

________________________________________
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 18:17
To: statalist@hsphsun2.harvard.edu
Subject: st: RE: RE: RE: 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: 25 June 2012 16:50
> To: statalist@hsphsun2.harvard.edu
> Subject: st: RE: RE: RE: Interpreting Kleibergen Paap weak
> instrument statistic
>
> Mark,
>
> ________________________________________
> 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 15:54
> To: statalist@hsphsun2.harvard.edu
> Subject: st: RE: 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: 25 June 2012 14:53
> > To: statalist@hsphsun2.harvard.edu
> > Subject: st: RE: RE: Interpreting Kleibergen Paap weak instrument
> > statistic
> >
> > 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.
>
> I'm not sure I understand.  Do you estimate separately for
> the different subsamples, or do you interact your
> coefficients with indicator variables and estimate one big regression?
>
> I estimate separately for the different sub-samples.

I'm still confused.  How then do you test that the coefficients are
different in the different estimations?  This is possible with ivreg2
and xtivreg2 but it requires some gymnastics.  See e.g. Austin Nichols'
post here:

The capital structure theories I am testing make opposing prediction as to the signs of the effects of certain variables on the debt to value ratio. Thus my test of whether or not the coefficients are different is an "eyeball" test where I conclude a difference exists if the coefficients differ by three or more significance levels (I define the following significance levels; <0.1, <0.5, <0.01, <0.001, and thus a significant difference might constitute a negative coefficient with a <0.05 significance level in one  sub-sample changing to a positive coefficient with a <0.05 significance level in another sub-sample). 

http://www.stata.com/statalist/archive/2009-11/msg01485.html

> I
> decided to take this approach as I am interested in how the
> effects of a number of the independent variables vary across
> the sub-samples, and was advised that indicator variables can
> only be employed for one variable at a time in a model.
> Furthermore, it was pointed out to me that a binary indicator
> variable is no longer binary after a fixed effects
> transformation i.e. indicator variables coded as 1 or 0 can
> take the values -1, 0, 1 after a first differences
> transformation, and can take T values after an about-the-mean
> transformation.

I don't get this at all.  The fixed effects transformation is equivalent
to including a full set of dummies and then partialling them out.  There
is nothing special about partialling out dummies - the
Frisch-Waugh-Lovell theorem says that you can partial out anything in a
regression and get the same results.  If your argument about indicator
variables and fixed effects were correct, it would apply equally to any
regressors used alongside an indicator variable - partial out the
regressor and the indicator variable is no longer 0/1.  So what?

I initially came across this argument in an article published in the American Finance Association by Datta et al (2005). The following is an extract from that paper, along with a footnote:

In support of our hypothesis, we find that the coefficient of the interaction
term, MgtOwner * M/B dummy, is significantly negative in the regression model
Pooled 2 in Table IV. Our results indicate that for low-growth option firms, an
increase in MgtOwner from the median to the 95th percentile results in a 5.90%
reduction in DEBT3, in addition to the stand-alone effect of MgtOwner on debt
maturity.6

6We do not include the interaction terms in the cross-sectional and fixed effects regressions
because the classification of the dummy variable as 0 or 1 for a given firm can change over time.
As a result, the average of the dummy variable may no longer be binary. This precludes us from
strictly classifying firms as belonging to one category or the other in a cross-sectional and fixed
effects framework. Therefore, the interpretation of the interaction term consisting of a binary
dummy variable is unclear in these specifications.

This is a paragraph I subsequently wrote (about 2 years ago). It was the understanding I got from reading their paper at the time, but I fully accept it may be wrong:

Datta et al (2005) identify a potential problem when using interactive dummy variables in a fixed effects model. In order to benefit from the time series element of panel data when comparing coefficients across sub-samples, studies generally allow firm-year observations to move into and out of the relevant sub-samples over time. Thus the dummy variable value (DV) for a given firm may be 0 in t=3, 1 in t=2, and 0 in t=1. Now, if the firms are categorised into sub-samples based on variable levels i.e. not first differences, once the first differencing transformation takes place the dummy variable no longer results in a binary interaction variable. Consider DVt=3 and DVt=2. The first differenced DV value for the observation is DVt=3 - DVt=2 = 0 - 1 = -1. Thus, there are now three values for DV that an observation can have; 0, 1, or -1. Hence, one can no longer use the dummy variable to distinguish between the effects of a variable on two sub-samples of observations, as there ar!
 e now three classifications of observations under the dummy variable. This problem does not arise if one performs the first differencing transformation prior to the categorisation procedure, as observations can be categorised based on their first differenced values and a binary dummy variable can be produced. However, observations will be classed differently when classed on first differences rather than levels. Consider the scenario where observations are being classified based on a tangibility variable, say, the ratio of fixed to total assets (FA). Firm A has the following tangibility values; FAt=3 = 0.6, FAt=2 = 0.65, FAt=1 = 0.55. Assume that the categorisation rule is that observations with FA above 0.5, the median FA observation, are classified as high tangibility observations and those below 0.5 as low tangibility observations. In each time period, firm A observations are classified as high tangibility. This classification procedure has been based on levels. Now, cons!
 ider the scenario where observations are classified based on first dif

ferences. The first differences of observations t=3 and t=2 are -0.05 and 0.10 respectively. However, due to the fact that level classifications do not equate to first difference classifications, observations may be classed differently even though the value of the firm characteristic has not changed. For example, if the median first differeced FA is 0, observation t=2 is now classified as low tangibility. Thus, the two classification procedures are not interchangeable. One must decide to classify by levels and then first difference, or first difference and then classify by first differences, and this decision will determine whether or not an interacted variable can be appropriately interpreted. Which procedure is chosen will depend on the theoretical definition of a high or low tangible observation. 

Does this make sense? I also put forward the following argument:

Another problem with the interactive dummy variable approach occurs when one wishes to compare the coefficients of multiple variables across sub-samples simultaneously. In a model incorporating an interacted dummy variable, the only variable coefficient which can be compared across sub-samples is that which has been interacted with the dummy variable. Although the coefficients of other variables included in the model may differ when the interactive dummy variable is excluded and then included (over the sample as a whole and when divided into sub-samples) it is only the change in the coefficient of the interacted variable which can be inferred to occur due to group classification. Furthermore, in order to assign the cause of the change in the coefficient of the variable of interest to group classification, the only change to the model that can be made is the inclusion of a single interacted dummy variable. Thus, one cannot include multiple interacted dummy variables in a sing!
 le model, as the cause of the changes in the coefficients of interest cannot be inferred to occur due to the relevant group classifications. In order to compare the effects of multiple variables across sub-samples, separate regressions must be run where only the variable of interest is dummy interacted. The simultaneous effects of classification on multiple coefficients cannot be inferred. The sub-sampling approach does not suffer from these shortcomings. The effects of classification on the coefficients of multiple variables can be simultaneously analysed and attributed to classification by simply comparing the coefficients from regressions run on the different groups. This procedure can then be repeated to test hypotheses when firms are classified by a variety of characteristics. 



> > 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?
>
> This amounts to testing for heteroskedasticity or autocorrelation.
> -ivhettest- and -ivactest- will report such tests for IV
> models.  But you are using a fixed effects model, which
> complicates things a bit.
> How long is your T dimension?  I see from the estimation
> below that you are using a kernel-robust VCE, which implies T
> is biggish.  If so, you could apply the fixed effects
> transformation to your data by hand (e.g., using Ben Jann's
> -center- command) and then use these programs.  But this is a
> bit tricky.
>
> The simplest way to test the i.i.d. assumption is to do an
> eyeball version of a White-type test.  Estimate the model
> using kernel-robust VCEs, and then again without this option,
> i.e., using the classical VCE.
> Do the SEs look very different?  If so, it's likely that the i.i.d.
> assumption would fail if you tested formally using a
> White-type test, since the same principle is involved - the
> test stat is based on a vector of contrasts between the
> robust and classical VCEs.
>
> I am using an unbalanced panel dataset, so my T dimension
> varies from 1 to 20. My understanding of the kernel-robust
> option is very limited, and I specify it so that my output is
> robust to autocorrelation.

I think you have a problem, but one that is perhaps easily addressed.
The kernel-robust covariance estimator requires T to go to infinity for
the asymptotics to work.  20 isn't very far on the way to infinity, and
1 is obviously not even getting started.  Since you have a large
cross-section, you can instead use the cluster-robust covariance
estimator, i.e., cluster on the panel identifier.

I understand. Instead of using bw(2) robust, I use cluster(firm) (firm being the panel identifier)

> I think I will try your "eyeball" test suggestion, as I have
> about reached the limit of my econometric abilities! Thus, if
> I "see" major differences in the SEs the i.i.d assumption is invalid?

Yes, that's right.

The following is a table comparing the SEs from the test I included in the previous e-mail, where the cluster vce is compared to the traditional vce. 
Do these results suggest non-i.i.d errors? My intuition is that the differences in SEs is minor.

Variable       SE Cluster VCE         SE Traditional VCE
Liq               .0049592                    .0038118
Lnsale          .005608                      .0037871
Tang            .071302                      .0484051
Itang            .0306583                    .017645
Itangdum      .0070073                   .0069813
Tax              .009587                     .0093917
Prof             .0021683                   .0016921
Mtb             .0019428                   .0011142
Capexsa      .0084232                   .0090759
Ndts            .0032625                   .0025671


> > 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?
>
> Sort of ... it's a litte more complicated than that.  I
> recommend reading the Finlay-Magnusson paper on this.
>
> > 3.Included below is the first stage regression results from
> one of the
>
> > tests I run.
>
> Maybe I am misreading the output, but it looks like only the
> summary stats for the first stage are reported.
>
> Yes, I only included the summary first stage regression
> results. Below is the complete output produced by STATA.
>
> > 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.
>
> No, that's a misintepretation of the AR and SW tests.  See below.
>
> > 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
>
> Neither.  These are not tests of the strength or explanatory
> power of the IV.  They are just what the output says: tests
> of the significance of the endogenous regressor.
>
> Your endogenous regressor is liq.  In the main output, the
> coeff on liq is -.0085538, with a z-stat of -1.73 and a
> p-value of 0.084.  That is, the Wald test stat for the null
> that the coeff on liq=0 has a p-value of 0.084.
>
> The A-R test stat (F version) for the same hypothesis, i.e.,
> B1=0, augmented by the additional hypothesis that the IVs are
> exogenous, has a p-value of 0.0607.  Very similar.
>
> The A-R-type approach can be extended to generate
> weak-instrument-robust confidence intervals.  That's what
> Finlay & Magnusson's -rivtest- will do for you.
>
> I think I now understand what the AR tests are reporting; the
> AR stat p-value (0.067) is interpreted in the same manner as
> the p-value for liq in the main output (0.084), but with the
> added orthogonality condition.

Right.

> And given that both p-values
> are very similar, I can infer with some degree of reliability
> that the instrument is not weak (that degree of reliability
> being dependent on the confidence intervals I can generate
> using Finlay and Magnusson's -rivtest-). Is that correct?

Not really.  "Weakness" or otherwise of the instruments is not being
tested in the A-R test of the null that the coeff=0.  What you can infer
is just what the test stat allows you to infer about the null.

Finlay and Magnusson have a discussion of the relationship between the
A-R stat and the J stat (which tests the orthgonality conditions) -
worth having a look.

That said, the A-R test does have the feature that the weaker the
instruments, the wider the confidence interval for the parameter of
interest; this is its main appeal (in my view, anyway).  But you can see
that you can reject the null of a zero coeff for two reasons: (a) the
coefficient is hugely different from zero; (b) the coefficient is very
close to zero, but your estimation determines its value so precisely
that you can reject it being zero.  In other words, even if your
instruments are weak (case a) you can still reject the null of a zero
coeff.  And anyway, if you want to know whether or not your instruments
are correlated with your endogenous regressor, you can just test this
directly - it's the same thing as a test of underidentification.

I am concerned though that unless the instruments are "not weak", I cannot reliably compare the coefficient of, say, liq in subsample A when liq is endogenous and hence instrumented, with the coefficient of liq in sample B when liq is exogenous (a scenario that I find happens regularly when comparing across the sub-samples, as my C-Stats indicate different variables are endogenous in different sub-samples).

Thanks again!

James

--Mark

> Thanks again for your help
>
> James
>
>
> > 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
> >
> . xtivreg2 ltdbv lnsale tang itang itangdum tax prof mtb
> capexsa ndts yr* (liq=tang1 itang1 mtb1 liq1) if lnsalesubs<1 & ta
> > ngsubs<1, fe robust bw(2) gmm2s first
> Warning - singleton groups detected.  91 observation(s) not used.
> Warning - collinearities detected
> Vars dropped:  yr08
> FIXED EFFECTS ESTIMATION
> Number of groups =       449                    Obs per
> group: min =         2
> avg =       6.7
> max =        19
> First-stage regressions
>
> First-stage regression of liq:
> FIXED EFFECTS ESTIMATION
> Number of groups =       449                    Obs per
> group: min =         2
> avg =       6.7
> max =        19
> OLS estimation
>
> Estimates efficient for homoskedasticity only Statistics
> robust to heteroskedasticity and autocorrelation
> kernel=Bartlett; bandwidth=2 time variable (t):  year group
> variable (i): firm
> Number of obs =     3021
> F( 31,  2541) =     8.82
> Prob > F      =   0.0000
> Total (centered) SS     =  6087.457806
> Centered R2   =   0.2732
> Total (uncentered) SS   =  6087.457806
> Uncentered R2 =   0.2732
> Residual SS             =  4424.113333                Root
> MSE      =     1.32
>
> Robust
> liq       Coef.   Std. Err.      t    P>t     [95% Conf. Interval]
> lnsale   -.3992946   .1006038    -3.97   0.000    -.5965684
> -.2020207
> tang   -6.503772   1.007147    -6.46   0.000    -8.478685   -4.528859
> itang   -2.818454   .3907103    -7.21   0.000    -3.584597   -2.052311
> itangdum     .003545   .1125097     0.03   0.975     -.217075
>    .2241649
> tax    .0972279   .1132478     0.86   0.391    -.1248395    .3192952
> prof    .0405595   .0546733     0.74   0.458    -.0666492    .1477683
> mtb   -.0525982   .0277353    -1.90   0.058    -.1069843    .0017878
> capexsa    .8377125   .3265792     2.57   0.010      .197324
>   1.478101
> ndts   -.0143917   .0282565    -0.51   0.611    -.0697998    .0410164
> yr90    1.155508   3.618686     0.32   0.750    -5.940366    8.251382
> yr91   -.2388175   .2513692    -0.95   0.342    -.7317268    .2540919
> yr92   -.3008198   .2453313    -1.23   0.220    -.7818894    .1802499
> yr93   -.1499197   .2490001    -0.60   0.547    -.6381835     .338344
> yr94   -.2144308   .2420701    -0.89   0.376    -.6891055    .2602439
> yr95   -.2142347   .2435146    -0.88   0.379     -.691742    .2632725
> yr96   -.0750504   .2473898    -0.30   0.762    -.5601566    .4100559
> yr97   -.0568015   .2405942    -0.24   0.813    -.5285822    .4149792
> yr98   -.2275228   .2263855    -1.01   0.315    -.6714416     .216396
> yr99     .065933   .2331514     0.28   0.777    -.3912531    .5231191
> yr00    .3334675   .2521301     1.32   0.186    -.1609339    .8278688
> yr01   -.0156419   .2300491    -0.07   0.946    -.4667446    .4354608
> yr02    .1622597   .2160337     0.75   0.453    -.2613603    .5858797
> yr03    .0200205   .2144716     0.09   0.926    -.4005365    .4405775
> yr04    .2405879    .219952     1.09   0.274    -.1907155    .6718912
> yr05    .1176199   .2308627     0.51   0.610    -.3350784    .5703182
> yr06   -.1331952   .2180932    -0.61   0.541    -.5608537    .2944633
> yr07    -.370854   .2144122    -1.73   0.084    -.7912944    .0495865
> tang1    2.766925   .7109139     3.89   0.000     1.372896    4.160955
> itang1    1.893136   .3687716     5.13   0.000     1.170012
>  2.616259
> mtb1    .1395775   .0310299     4.50   0.000      .078731     .200424
> liq1    .3000688   .0442671     6.78   0.000     .2132655    .3868721
> 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 tang1 itang1 mtb1 liq1 F test
> of excluded instruments:
> F(  4,  2541) =    20.20
> Prob > F      =   0.0000
> Angrist-Pischke multivariate F test of excluded instruments:
> F(  4,  2541) =    20.20
> Prob > F      =   0.0000
>
> 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:
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> *   http://www.stata.com/support/statalist/faq
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> *
> *   For searches and help try:
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> *   http://www.stata.com/support/statalist/faq
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>


--
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.


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