Shawn,
> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]] On Behalf Of
> Shawn Bauldry
> Sent: 20 March 2008 23:07
> To: [email protected]
> 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: [email protected]
> >> [mailto:[email protected]] On Behalf Of Shawn
> >> Bauldry
> >> Sent: 20 March 2008 20:23
> >> To: [email protected]
> >> 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: [email protected]
> > 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: [email protected]
> >>>> [mailto:[email protected]] On Behalf Of Shawn
> >>>> Bauldry
> >>>> Sent: 20 March 2008 18:34
> >>>> To: [email protected]
> >>>> 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/
>
--
Heriot-Watt University is a Scottish charity
registered under charity number SC000278
*
* 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/
