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Re: st: Collinearity in 2SLS


From   "Mark Schaffer" <M.E.Schaffer@hw.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Collinearity in 2SLS
Date   Fri, 16 Sep 2005 00:03:11 +0100 (BST)

It doesn't look like you have a scaling problem, as far as I can tell. 
When you change the scale, the results stay the same.  And the original
coefficient wasn't all that much bigger than some of the other
(significant) coefficients.  If the results are implausible, well, maybe
it's the model or some other type of problem such as outliers or dirty
data.

BTW, you might want to switch to ivreg2.  You get an automatic Sargan or
Hansen overid statistic, first-stage and identification diagnostics, etc.
etc.  Just -findit ivreg2- from within Stata and follow the links to
install.

Cheers,
Mark

> I tried to rescale the endogenous variable... actually used your pick
> of numbers (1000).  It sure did shrink the endogenous variables
> coefficient. However, it shrunk according to the scaling, so the
> interpretations stays the same. And the number is way to large to make
> sense in that context.
>
> The results are below. The first coefficient is the one of interest,
> and it did change as I mentioned before. However it only changed in
> number, but not in terms of the real effect DP1 has on the dependent
> variable. I tried rescaling the instrument also, but it didn't do
> anything either.
>
> Sorry if I am being slow here.  My code is below.
>
> Tinna
>
> . generate  dailysmoke1000= dailysmoke*1000
>
> . ivreg   hrstotal  centage centagesq (DP1= dailysmoke1000 )  edu2
> edu3 edu4 edu5 edu6 marr2 marr3 marr4 ch
>> ildren health   if male==1 &  empl3!=1 &  empl5!=1 & empl7!=1
>
> Instrumental variables (2SLS) regression
>
>       Source |       SS       df       MS              Number of obs =
> 404
> -------------+------------------------------           F( 13,   390) =
> 1.95
>        Model | -17608.5123    13 -1354.50095           Prob > F      =
> 0.0235
>     Residual |  116855.128   390  299.628533           R-squared     =
>   .
> -------------+------------------------------           Adj R-squared =
>   .
>        Total |  99246.6155   403  246.269517           Root MSE      =
> 17.31
>
> ------------------------------------------------------------------------------
>     hrstotal |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
> Interval]
> -------------+----------------------------------------------------------------
>          DP1 |   23.35439    9.64544     2.42   0.016     4.390822
> 42.31795
>      centage |   .0961063   .1157894     0.83   0.407    -.1315433
> .3237558
>    centagesq |  -.0162521   .0053245    -3.05   0.002    -.0267204
> -.0057839
>         edu2 |  -3.520445   3.875886    -0.91   0.364    -11.14069
> 4.099799
>         edu3 |   1.202756   2.779328     0.43   0.665    -4.261585
> 6.667097
>         edu4 |  -4.174515   2.603464    -1.60   0.110    -9.293094
> .9440648
>         edu5 |  -6.479983   3.118394    -2.08   0.038    -12.61095
> -.3490167
>         edu6 |   -5.05074   3.751378    -1.35   0.179     -12.4262
> 2.324715
>        marr2 |    1.79778   4.550819     0.40   0.693    -7.149427
> 10.74499
>        marr3 |   4.296739   4.445934     0.97   0.334    -4.444259
> 13.03774
>        marr4 |  -8.389899   11.09344    -0.76   0.450    -30.20032
> 13.42052
>     children |   .0359085   .7727457     0.05   0.963     -1.48336
> 1.555177
>       health |  -3.022827   1.383256    -2.19   0.029    -5.742398
> -.303256
>        _cons |   52.97049   5.593036     9.47   0.000     41.97421
> 63.96676
> ------------------------------------------------------------------------------
> Instrumented:  DP1
> Instruments:   centage centagesq edu2 edu3 edu4 edu5 edu6 marr2 marr3
> marr4
>                children health dailysmoke1000
> ------------------------------------------------------------------------------
>
> . ivreg   hrstotal  centage centagesq (DP1000= dailysmoke )  edu2 edu3
> edu4 edu5 edu6 marr2 marr3 marr4 chi
>> ldren health   if male==1 &  empl3!=1 &  empl5!=1 & empl7!=1
>
> Instrumental variables (2SLS) regression
>
>       Source |       SS       df       MS              Number of obs =
> 404
> -------------+------------------------------           F( 13,   390) =
> 1.95
>        Model | -17608.5123    13 -1354.50095           Prob > F      =
> 0.0235
>     Residual |  116855.128   390  299.628533           R-squared     =
>   .
> -------------+------------------------------           Adj R-squared =
>   .
>        Total |  99246.6155   403  246.269517           Root MSE      =
> 17.31
>
> ------------------------------------------------------------------------------
>     hrstotal |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
> Interval]
> -------------+----------------------------------------------------------------
>       DP1000 |   .0233544   .0096454     2.42   0.016     .0043908
> .042318
>      centage |   .0961063   .1157894     0.83   0.407    -.1315433
> .3237558
>    centagesq |  -.0162521   .0053245    -3.05   0.002    -.0267204
> -.0057839
>         edu2 |  -3.520445   3.875886    -0.91   0.364    -11.14069
> 4.099799
>         edu3 |   1.202756   2.779328     0.43   0.665    -4.261585
> 6.667097
>         edu4 |  -4.174515   2.603464    -1.60   0.110    -9.293094
> .9440648
>         edu5 |  -6.479983   3.118394    -2.08   0.038    -12.61095
> -.3490167
>         edu6 |   -5.05074   3.751378    -1.35   0.179     -12.4262
> 2.324715
>        marr2 |    1.79778   4.550819     0.40   0.693    -7.149427
> 10.74499
>        marr3 |   4.296739   4.445934     0.97   0.334    -4.444259
> 13.03774
>        marr4 |  -8.389899   11.09344    -0.76   0.450    -30.20032
> 13.42052
>     children |   .0359085   .7727457     0.05   0.963     -1.48336
> 1.555177
>       health |  -3.022827   1.383256    -2.19   0.029    -5.742398
> -.303256
>        _cons |   52.97049   5.593036     9.47   0.000     41.97421
> 63.96676
> ------------------------------------------------------------------------------
> Instrumented:  DP1000
> Instruments:   centage centagesq edu2 edu3 edu4 edu5 edu6 marr2 marr3
> marr4
>                children health dailysmoke
> ------------------------------------------------------------------------------
>
>
> On 9/15/05, Tinna <statalist@gmail.com> wrote:
>> Thanks Mark,
>> I think you understood my problem right and I am going to try your
>> suggestions.  It is very good to know what this problem is called.
>>
>> Tinna
>>
>>
>>
>>
>> On 9/15/05, Mark Schaffer <M.E.Schaffer@hw.ac.uk> wrote:
>> > Tinna,
>> >
>> > I don't think you have a collinearity problem, strictly speaking.
>> Rather,
>> > it sounds like you have a scaling problem that could be causing you
>> > numerical problems with your estimator.
>> >
>> > When you say the instrumented coefficient in the second stage is
>> "blowing
>> > up", do you mean that the estimated size of the coefficient is very
>> large
>> > (several+ orders of magnitude) compared to the other coefficients?
>> Then
>> > you could indeed have a scaling problem.
>> >
>> > The way to find out (and to deal with the problem, if it exists) is to
>> > rescale your endogenous variable.  Just create a new variable that is
>> 1000
>> > or whatever times your original variable, and use it in the regression
>> > instead.  Your excluded instruments and other variables might need
>> > rescaling too.  It's easy enough to work out what to do once you see
>> what
>> > is going on.
>> >
>> > Hope this helps.
>> >
>> > Cheers,
>> > Mark
>> >
>> >
>> > > Dear Statalisters,
>> > >
>> > > I am running 2SLS estimations. The instrument used in the first
>> stage
>> > > is quite good according to traditional standards and tests and its
>> > > coefficient in the first stage regression is highly significant.
>> > > HOWEVER, the coefficient although significant is very small. I think
>> > > this is causing collinearity (if it can be called that in this
>> context
>> > > - makes sense to me). The instrumented coefficient in the second
>> stage
>> > > is blowing up big time. However, it is significant and my
>> > > Durbin-Wu-Hausman test is indicating endogeneity, so that the 2SLS
>> > > would really be what is called for.
>> > >
>> > > 1. Someone told me that I could still trust the sign on the
>> > > instrumented coefficient, although it is blown up.  This "someone"
>> > > says they read it "somewhere" but are not sure where.  I have
>> reached
>> > > the end of the Internet without finding much. Can I trust the sign
>> of
>> > > the instrumented coefficient?
>> > >
>> > > 2. Can I trust my Durbin-Wu-Hausman test?
>> > >
>> > > 3. Any suggestion for what I should do?
>> > >
>> > > Tinna
>> > >
>> > > *
>> > > *   For searches and help try:
>> > > *   http://www.stata.com/support/faqs/res/findit.html
>> > > *   http://www.stata.com/support/statalist/faq
>> > > *   http://www.ats.ucla.edu/stat/stata/
>> > >
>> >
>> >
>> > Prof. Mark Schaffer
>> > Director, CERT
>> > Department of Economics
>> > School of Management & Languages
>> > Heriot-Watt University, Edinburgh EH14 4AS
>> > tel +44-131-451-3494 / fax +44-131-451-3294
>> > email: m.e.schaffer@hw.ac.uk
>> > web: http://www.sml.hw.ac.uk/ecomes
>> >
>> >
>> >
>> > __________________________________________________________________
>> >
>> > DISCLAIMER:
>> >
>> > This e-mail message is subject to http://www.hw.ac.uk/disclaim.htm
>> > __________________________________________________________________
>> >
>> > *
>> > *   For searches and help try:
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>> >
>>
>
> *
> *   For searches and help try:
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>


Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3294
email: m.e.schaffer@hw.ac.uk
web: http://www.sml.hw.ac.uk/ecomes



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