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st: RE: xtivreg, fe or fd (time-invariant instrument issue)


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: RE: xtivreg, fe or fd (time-invariant instrument issue)
Date   Mon, 10 Jun 2013 15:49:06 +0000

Priya,

See below...

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
> statalist@hsphsun2.harvard.edu] On Behalf Of priya joshi
> Sent: 09 June 2013 05:40
> To: statalist@hsphsun2.harvard.edu
> Subject: st: xtivreg, fe or fd (time-invariant instrument issue)
> 
> I am trying to instrument for a competition measure, private market share
> (psvw) with the number of private schools in 1982 (20 years ago)
> (nvw1982) in a regression of mathematics score (mat) on control and
> explanatory variables. the instrumental variable validity checks worked out
> and the instrument seems to be a good predictor of the competition
> measure.
> 
> I ran the following regressions and got the following results:
> 
> . mi estimate, cmdok post: xtivreg mat selective fees dalit enr female
> pdropout snew permshare comproom yeardum2 yeardum3 yeardum4
> yeardum5 (psvw = nvw1982),fe
> 
> Multiple-imputation estimates                   Imputations        =        10
>                                                 Number of obs      =      1029
> Group variable: id_ss
>                                                 Number of groups   =       212
>                                                 Obs per group: min =         3
>                                                                avg =       4.9
>                                                                max =         5
>                                                 Average RVI        =    0.0911
>                                                 Largest FMI        =    0.3560
> DF adjustment:   Large sample                   DF:     min        =     78.01
>                                                         avg        =  20980.52
>                                                         max        = 176681.52
> Model F test:       Equal FMI                   F(  13,13901.3)    =     26.16
> Within VCE type: Conventional                   Prob > F           =    0.0000
> 
> ------------------------------------------------------------------------------
>          mat |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
> -------------+----------------------------------------------------------
> -------------+------
>         psvw |   .8624825    .131875     6.54   0.000     .6037581    1.121207
>    selective |  -.0278851   2.359545    -0.01   0.991    -4.652874    4.597103
>         fees |   .3143015   .1130965     2.78   0.007     .0891442    .5394588
>        dalit |  -1.938628   1.000959    -1.94   0.054    -3.912356    .0351003
>          enr |   1.230128   .4774831     2.58   0.010     .2920233    2.168233
>       female |  -.5203193   .9466472    -0.55   0.583    -2.376803    1.336164
>     pdropout |  -.2030307   .2400717    -0.85   0.398    -.6740312    .2679699
>         snew |   .0260768   .1462648     0.18   0.859    -.2606485    .3128021
>    permshare |   .1165564    .150686     0.77   0.439    -.1792443    .4123572
>     comproom |   .4153309   .9967468     0.42   0.677     -1.53827    2.368932
>     yeardum2 |  -10.66012   .6900084   -15.45   0.000    -12.01264   -9.307597
>     yeardum3 |  -8.298525   .6960532   -11.92   0.000    -9.662844   -6.934207
>     yeardum4 |   -5.97942   .7454801    -8.02   0.000    -7.440567   -4.518273
>     yeardum5 |          0  (omitted)
>        _cons |   7.328137   8.134599     0.90   0.368    -8.628109    23.28438
> ------------------------------------------------------------------------------
> 
> 
> 
> I then tried to run the xtivreg2 on the same to get errors corrected for
> heteroskedasticity and clustering. I got the following error
> message:
> 
> " . mi estimate, cmdok post: xtivreg2 mat selective fees dalit enr female
> pdropout snew permshar
> > e comproom yeardum2 yeardum3 yeardum4 yeardum5 (psvw =
> nvw1982),fe
> 
> equation not identified; must have at least as many instruments not in the
> regression as there are instrumented variables an error occurred when mi
> estimate executed xtivreg2 on m=1 r(481); "
> 
> 
> I noted another Stata discussion on this issue
> (http://www.stata.com/statalist/archive/2010-09/msg01344.html). The
> discussion seems to conclude that the fact that the instrument was time-
> invariant is the problem.

It's not clear from your question - are you saying that the excluded instrument in your case (nvw1982) is time-invariant?  If so, then you definitely have a problem.  Any regressors or instruments that are time-invariant will get wiped out by the within-transformation that is at the heart of the FE estimator.  That makes your proposed IV FE estimation un-estimate-able.

The last time I looked into this, Stata's official -xtivreg- was somewhat more forgiving than -xtivreg2- when it came to dropped variables, collinearities, and the like.  If official -xtivreg,fe- is reporting estimation results when the endogenous regressor is instrumented with a time-invariant variable, I'm not sure what they are but they are unlikely to be FE estimates.  Perhaps you want to have a look at the first-stage regressions to confirm

Also see below.

> I wanted to ask if:
> 
> 1. the xtivreg results for fe can be trusted - especially since this is an
> important specification for my analysis.

The answer is "no", I think.

> 2. if not, is there a way to do an fe iv regression for this time-invariant
> instrumental variable?

No.  Another way to put it is that the time-invariant instrument is collinear with the fixed effects.  Still another way to put it is that the FE estimator uses only within-panel variation, and if there is no within-panel variation, there's nothing there to use.

> a time-invariant measure made the most sense as an
> instrument since it is a lagged value of private entry. should i instead
> construct a 5-year instrumental variable with the number of private schools
> that existed in each year?

That's your call!  But you should be clear on what you are claiming for your instrument.  Your endogenous variable is private market share (psvw).  You are using the IV FE estimator, so you are using only the time-varying (=within-panel) changes in psvw.  You need an instrument that is also time-varying, and the changes in this IV need to be correlated with the changes in psvw.

HTH,
Mark

> thank you,
> Priya
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