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

[Shawn Bauldry <sbauldry@email.unc.edu>]

Mark,

Thanks for your helpful responses. In working through my problem using 
your code, I realized that my error was in using the stata command 
regress to obtain the OLS s.e. as opposed to ivreg2 with no endogenous 
variables specified. I didn't realize that these two approaches would 
not produce equivalent s.e.'s.


Best,
Shawn

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 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
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> > > > *   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/
*
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