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

 From Shawn Bauldry To statalist@hsphsun2.harvard.edu Subject Re: st: RE: question re: calculation of Shea partial R2 in ivreg2 Date Thu, 20 Mar 2008 16:23:15 -0400

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.

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
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
*! 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

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