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# RE: st: RE: question re: calculation of Shea partial R2 in ivreg2

 From "Schaffer, Mark E" To Subject RE: st: RE: question re: calculation of Shea partial R2 in ivreg2 Date Thu, 20 Mar 2008 22:15:39 -0000

```Shawn,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
> Shawn Bauldry
> Sent: 20 March 2008 20:23
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: RE: question re: calculation of Shea partial
> R2 in ivreg2
>
> Mark,
>
> I appreciate your willingness to look at this.
>
> Below is a portion of a log file that has the following: (1)
> the 2SLS results with the Shea partial R2; (2) OLS results to
> obtain the inputs for the direct calculation; (3) the
> calculation of the Shea partial R2 following Godfrey's formula.

I think it's probably a mistake in the R2 for IV that you're calculating
by hand.  When I use the R2s saved by -ivreg2- and Godfrey's formula, I
reproduce the reported Shea R2:

. sysuse auto
(1978 Automobile Data)

. qui ivreg2 price (mpg foreign = weight trunk turn length), ffirst

. mat list e(first)

e(first)[6,2]
mpg    foreign
sheapr2  .10855718  .06782192
pr2  .66219852  .41371357
F  33.815496  12.172479
df          4          4
df_r         69         69
pvalue  1.307e-15  1.527e-07

. mat viv=e(V)

. scalar viv1=viv[1,1]

. scalar r2iv=e(r2)

. qui ivreg2 price mpg foreign

. mat vols=e(V)

. scalar vols1=vols[1,1]

. scalar r2ols=e(r2)

. di vols1/viv1*(1-r2iv)/(1-r2ols)
.10855718

--Mark

Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3296
email: m.e.schaffer@hw.ac.uk
web: http://www.sml.hw.ac.uk/ecomes

>
> Best,
> Shawn
>
>
> . *** 2sls model
> . ivreg2 y5 (y1 x1 = y2 y3 y4 x2 x3), first
>
> First-stage regressions
> -----------------------
>
> First-stage regression of y1:
>
> Ordinary Least Squares (OLS) regression
> ---------------------------------------
>
>                                                        Number
> of obs =
>       75
>                                                        F(  5,
>    69) =
>    21.28
>                                                        Prob >
> F      =
>   0.0000
> Total (centered) SS     =  509.0138607                Centered R2   =
> 0.6066
> Total (uncentered) SS   =  2748.707483                Uncentered R2 =
> 0.9272
> Residual SS             =  200.2393343                Root MSE      =
>   1.704
>
> --------------------------------------------------------------
> ----------------
>            y1 |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
> Interval]
> -------------+------------------------------------------------
> ----------
> -------------+------
>            y2 |   .1383487   .0727181     1.90   0.061    -.0067199
> .2834172
>            y3 |   .3186926   .0767732     4.15   0.000     .1655342
> .471851
>            y4 |    .231242   .1018089     2.27   0.026     .0281388
> .4343452
>            x2 |   .0954845   .2584685     0.37   0.713    -.4201462
> .6111151
>            x3 |  -.0905941   .2699537    -0.34   0.738    -.6291371
> .4479489
>         _cons |   1.619292   .7153105     2.26   0.027     .1922861
> 3.046297
> --------------------------------------------------------------
> ----------------
> Partial R-squared of excluded instruments:   0.6066
> Test of excluded instruments:
>    F(  5,    69) =    21.28
>    Prob > F      =   0.0000
>
> First-stage regression of x1:
>
> Ordinary Least Squares (OLS) regression
> ---------------------------------------
>
>                                                        Number
> of obs =
>       75
>                                                        F(  5,
>    69) =
>    62.97
>                                                        Prob >
> F      =
>   0.0000
> Total (centered) SS     =  39.74900527                Centered R2   =
> 0.8202
> Total (uncentered) SS   =  1955.758701                Uncentered R2 =
> 0.9963
> Residual SS             =  7.145301922                Root MSE      =
>   .3218
>
> --------------------------------------------------------------
> ----------------
>            x1 |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
> Interval]
> -------------+------------------------------------------------
> ----------
> -------------+------
>            y2 |  -.0245964   .0137366    -1.79   0.078    -.0520001
> .0028072
>            y3 |   .0048132   .0145026     0.33   0.741    -.0241187
> .033745
>            y4 |   .0384214   .0192319     2.00   0.050     .0000549
> .076788
>            x2 |   .3542929   .0488251     7.26   0.000     .2568894
> .4516963
>            x3 |    .069175   .0509947     1.36   0.179    -.0325566
> .1709066
>         _cons |   3.012472   .1351233    22.29   0.000     2.742908
> 3.282035
> --------------------------------------------------------------
> ----------------
> Partial R-squared of excluded instruments:   0.8202
> Test of excluded instruments:
>    F(  5,    69) =    62.97
>    Prob > F      =   0.0000
>
>
>
> Summary results for first-stage regressions
> -------------------------------------------
>
>                  Shea
> Variable    | Partial R2    |    Partial R2    F(  5,    69)
>   P-value
> y1          |   0.5606      |      0.6066          21.28
>    0.0000
> x1          |   0.7580      |      0.8202          62.97
>    0.0000
>
> Underidentification tests:
>                                                   Chi-sq(4)
>    P-value
> Anderson canon. corr. likelihood ratio stat.       61.62
>    0.0000
> Cragg-Donald N*minEval stat.                       95.55
>    0.0000
> Ho: matrix of reduced form coefficients has rank=K-1 (underidentified)
> Ha: matrix has rank>=K (identified)
>
> Weak identification statistics:
> Cragg-Donald (N-L)*minEval/L2 F-stat      17.58
>
>
> Anderson-Rubin test of joint significance of endogenous
> regressors B1 in main equation, Ho:B1=0
>    F(5,69)=       17.18     P-val=0.0000
>    Chi-sq(5)=     93.35     P-val=0.0000
>
> Number of observations N           =         75
> Number of regressors   K           =          3
> Number of instruments  L           =          6
> Number of excluded instruments L2  =          5
>
>
> Instrumental variables (2SLS) regression
> ----------------------------------------
>
>                                                        Number
> of obs =
>       75
>                                                        F(  2,
>    72) =
>    53.22
>                                                        Prob >
> F      =
>   0.0000
> Total (centered) SS     =  505.1010621                Centered R2   =
> 0.6276
> Total (uncentered) SS   =  2483.682344                Uncentered R2 =
> 0.9243
> Residual SS             =  188.0785007                Root MSE      =
>   1.584
>
> --------------------------------------------------------------
> ----------------
>            y5 |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
> Interval]
> -------------+------------------------------------------------
> ----------
> -------------+------
>            y1 |   .7242857   .1014416     7.14   0.000     .5254638
> .9231076
>            x1 |   1.123234   .3121788     3.60   0.000     .5113746
> 1.735093
>         _cons |  -4.498983   1.423827    -3.16   0.002    -7.289633
> -1.708332
> --------------------------------------------------------------
> ----------------
> Anderson canon. corr. LR statistic (identification/IV
> relevance test):
> 61.616
>                                                     Chi-sq(4) P-val =
>   0.0000
> --------------------------------------------------------------
> ----------------
> Sargan statistic (overidentification test of all instruments):
>   0.801
>                                                     Chi-sq(3) P-val =
>   0.8492
> --------------------------------------------------------------
> ----------------
> Instrumented:         y1 x1
> Excluded instruments: y2 y3 y4 x2 x3
> --------------------------------------------------------------
> ----------------
>
> .
> . *** ols model
> . regress y5 y1 x1
>
>        Source |       SS       df       MS
> Number of obs =
>       75
> -------------+------------------------------           F(  2,
>    72) =
>   63.89
>         Model |  323.070276     2  161.535138           Prob
> > F      =
>   0.0000
>      Residual |  182.030786    72  2.52820536
> R-squared     =
>   0.6396
> -------------+------------------------------           Adj
> R-squared =
> 0.6296
>         Total |  505.101062    74  6.82569003           Root
> MSE      =
>     1.59
>
> --------------------------------------------------------------
> ----------------
>            y5 |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
> Interval]
> -------------+------------------------------------------------
> ----------------
>            y1 |   .6102657   .0762614     8.00   0.000     .4582413
>   .76229
>            x1 |   1.179284   .2729019     4.32   0.000     .6352644
> 1.723304
>         _cons |  -4.159203   1.292575    -3.22   0.002    -6.735903
> -1.582502
> --------------------------------------------------------------
> ----------------
>
> .
> . *** parameters
> . * ols: se(x1) = 0.2729019; R2 = 0.6396
> . * 2sls: se(x1) = 0.3121788; TSS = 505.1010621; RSS = 188.0785007;
> .
> . *** calculating Shea partial R2 for x1
> . dis (0.2729019^2)/(0.3121788^2)*(188.0785007/505.1010621)/(1-0.6396)
> .78955501
>
> .
> .
> . capture log close
>
> Schaffer, Mark E wrote:
> > Shawn,
> >
> >> -----Original Message-----
> >> From: owner-statalist@hsphsun2.harvard.edu
> >> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
> >> Shawn Bauldry
> >> Sent: 20 March 2008 18:34
> >> To: statalist@hsphsun2.harvard.edu
> >> Subject: st: question re: calculation of Shea partial R2 in ivreg2
> >>
> >> I have a question about how ivreg2 calculates the Shea
> >> partial R2. I have a data set with 75 cases, 2 endogenous
> >> regressors (y1,x1), and 5 instruments (y2,y3,y4,x2,x3). When
> >> I run ivreg2, it reports a Shea partial R2 for y1 of 0.5606
> >> and for x1 of 0.7580. However, when I calculate these using
> >> the formula provided by Godfrey (1999) and referenced in
> >> Baum, Schaffer, and Stillman's (2003) - R2_p =
> >> (v_b1[ols]/v_b1[2sls])[(1-R2[2sls])/(1-R2[ols])] - I get
> >> somewhat different results.
> >>
> >> Based on the formula and maintaining 7 digits after the
> >> decimal for the inputs, I obtain R2_p for y1 of 0.5840 and
> >> for x1 of 0.7896. These aren't that far off, but I expected
> >> them to be closer.
> >
> > -ivreg2- agrees with -ivregress-, e.g.:
> >
> > . sysuse auto
> > (1978 Automobile Data)
> >
> > . which ivreg2
> > c:\ado\personal\ivreg2.ado
> > *! ivreg2 2.2.08  15oct2007
> > *! authors cfb & mes
> > *! see end of file for version comments
> >
> > . ivreg2, version
> > 02.2.08
> >
> > . qui ivreg2 price (mpg foreign = weight trunk turn length), ffirst
> >
> > . mat list e(first)
> >
> > e(first)[6,2]
> >                mpg    foreign
> > sheapr2  .10855718  .06782192
> >     pr2  .66219852  .41371357
> >       F  33.815496  12.172479
> >      df          4          4
> >    df_r         69         69
> >  pvalue  1.307e-15  1.527e-07
> >
> > .
> > . qui ivregress 2sls price (mpg foreign = weight trunk turn length)
> >
> > . qui estat firststage
> >
> > . mat list r(multiresults)
> >
> > r(multiresults)[2,2]
> >            c1         c2
> > r1  .10855718  .07035248
> > r2  .06782192  .02787143
> >
> > The first row in the -ivreg2- saved matrix is identical to the first
> > column in the -ivregress- saved matrix.
> >
> > Maybe you could show us the steps you went through to
> calculate the Shea
> > partial R-sqs?
> >
> > --Mark
> >
> >> Has anyone else found a similar difference or does anyone
> >> know why I would see this difference?
> >>
> >>
> >> Best,
> >> Shawn
> >>
> >>
> >> *
> >> *   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/
> >>
> >
> *
> *   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/
>

--
Heriot-Watt University is a Scottish charity
registered under charity number SC000278

*
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```

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