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


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: question re: calculation of Shea partial R2 in ivreg2
Date   Thu, 20 Mar 2008 23:20:24 -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 23:07
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: RE: question re: calculation of Shea partial 
> R2 in ivreg2
> 
> 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.

The reason they aren't the same is that -regress- uses a small-sample
dof correction for the cov matrix, and -ivreg2-, by default, does not.
This is the only difference in the -regress- and -ivreg2- results with
no endogenous regressors.  And if you called -ivreg2- with the -small-
option, you would get identical SEs as well.

Put another way, if your calculations had use the IV var matrix with the
same dof correction that -regress- uses, you would have gotten the same
Shea partial R2.  Here is the example again, but this time the IV
results use the -small- option and the OLS results are estimated using
-regress-:

. sysuse auto
(1978 Automobile Data)

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

. 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 regress price mpg foreign

. mat vols=e(V)

. scalar vols1=vols[1,1]

. scalar r2ols=e(r2)

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

Voila!

Cheers,
Mark

> 
> 
> 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
> >>>> *   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/
> >>
> > 
> *
> *   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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