Notice: On April 23, 2014, Statalist moved from an email list to a forum, based at statalist.org.
[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
RE: st: Spurious inference from endogeneity tests
From
[email protected]
To
[email protected]
Subject
RE: st: Spurious inference from endogeneity tests
Date
Fri, 27 Jan 2012 23:52:02 +0100
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
[email protected] schrieb: -----
An: <[email protected]>
Von: "Schaffer, Mark E"
Gesendet von: [email protected]
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: [email protected]
> [mailto:[email protected]] On Behalf Of
> Suryadipta Roy
> Sent: 26 January 2012 00:06
> To: [email protected]
> 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
> <[email protected]> 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: [email protected]
> >> An: [email protected]
> >> 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
> >>
> >>
> >> [email protected] schrieb: -----
> >> An: [email protected]
> >> Von: Suryadipta Roy
> >> Gesendet von: [email protected]
> >> 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
> <[email protected]>
> >> 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: [email protected]
> >> >> An: [email protected]
> >> >> 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
> >> >>
> >> >> [email protected] schrieb: -----
> >> >> An: [email protected]
> >> >> Von: "Justina Fischer"
> >> >> Gesendet von: [email protected]
> >> >> 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: [email protected]
> >> >> > An: [email protected]
> >> >> > 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
> >> >> >
> >> >> > [email protected] schrieb: -----
> >> >> > An: [email protected]
> >> >> > Von: "Justina Fischer"
> >> >> > Gesendet von: [email protected]
> >> >> > 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: [email protected]
> >> >> > > An: [email protected]
> >> >> > > 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?
> >> >> > >
> >> >> > > [email protected] schrieb: -----
> >> >> > > An: [email protected]
> >> >> > > Von: Austin Nichols
> >> >> > > Gesendet von: [email protected]
> >> >> > > 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
> >> <[email protected]>
> >> >> > > 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 <[email protected]>
> >> >> > > >> An: STATA LIST <[email protected]>
> >> >> > > >> 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: [email protected]
> >> >> > > >> > Subject: Re: st: Spurious inference from endogeneity
> >> >> > > >> > tests
> >> >> > > >> > To: [email protected]
> >> >> > > >> >
> >> >> > > >> > 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: [email protected]
> >> >> > > >> > > An: [email protected]
> >> >> > > >> > > 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: [email protected]. [email protected]
> >> >> > 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: [email protected]. [email protected]
> >> >> 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: [email protected]. [email protected]
> >> > 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: [email protected]. [email protected]
> > 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/