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/
>
--
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
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* http://www.ats.ucla.edu/stat/stata/
