[R-SIG-Finance] R: [Fwd: R-SIG-Finance Digest, Vol 60, Issue 18]
Robert Iquiapaza
rbali at ufmg.br
Thu May 21 03:10:02 CEST 2009
See "The Hausman test statistic can be negative even asymptotically"
Schreiber, S. 2008 Jahrbucher fur Nationalokonomie und Statistik 228 (4), pp. 394-405
http://econ.schreiberlin.de/papers/schreiber_hausmantest_aug2008.pdf
From: Steven Archambault
Sent: Wednesday, May 20, 2009 5:18 PM
To: Robert Iquiapaza ; r-sig-finance at stat.math.ethz.ch
Subject: Re: [R-SIG-Finance] R: [Fwd: R-SIG-Finance Digest, Vol 60, Issue 18]
Thanks Robert. I have been playing around with sigmamore sigmaless. I cannot seem to duplicate the canned results when I do it by hand. Any ideas?
###STATA 9.2####
quietly xtreg lfdi_2000 lagdlfdi laglnstock2000 lagtradegdp lagdlgdp, fe;
. estimates store FIX, title(The FE);
. matrix bfe=e(b);
. matrix vfe=e(rmse);
. quietly xtreg lfdi_2000 lagdlfdi laglnstock2000 lagtradegdp lagdlgdp, re sa;
. estimates store RAND, title(The RE);
. matrix bre=e(b);
. matrix vre=e(rmse);
. matrix bdif=bfe-bre;
. matrix bdifp=bdif';
. matrix dv=vre-vfe;
. matrix dvi=inv(dv);
. matrix chi1=bdif*dvi;
. matrix chisq=chi1*bdifp;
. matrix list chisq;
symmetric chisq[1,1]
y1
y1 11.105892
. hausman FIX RAND, sigmamore;
---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| FIX RAND Difference S.E.
-------------+----------------------------------------------------------------
lagdlfdi | .1564758 .1632387 -.0067629 .0014297
laglnst~2000 | .762135 .8314432 -.0693082 .0151471
lagtradegdp | .0178568 .0119453 .0059115 .0015669
lagdlgdp | .2601478 .255801 .0043468 .0067502
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg
Test: Ho: difference in coefficients not systematic
chi2(4) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 31.32
Prob>chi2 = 0.0000
On Wed, May 20, 2009 at 11:22 AM, Robert Iquiapaza <rbali at ufmg.br> wrote:
Stev,
You will get the same Chi-sq for Hausman test if you use Swamy-Arora's transformation for RE in stata. To avoid the variance not positive definite maybe you should use options sigmamore or sigmaless in Stata (see http://www.stata.com/help.cgi?hausman), the results don't change.
I wonder why plm doesn't alert the variance not being positive definite.
Robert
# Stata 10.1
xtreg lfdi_2000 lagdlfdi laglnstock2000 lagtradegdp lagdlgdp, re sa
estimates store RANDsa, title(The REsa)
hausman FIX RANDsa
---- Coefficients ----
(b) (B) (b-B) sqrt(diag(V_b-V_B))
FIX RANDsa Difference S.E.
lagdlfdi .1564759 .1632388 -.0067629 .
laglnst~2000 .762135 .8314432 -.0693082 .0149396
lagtradegdp .0178568 .0119453 .0059115 .0015449
lagdlgdp .2601477 .2558009 .0043468 .0051777
b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg
Test: Ho: difference in coefficients not systematic
chi2(4) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 23.70
Prob>chi2 = 0.0001
(V_b-V_B is not positive definite)
From: Steven Archambault
Sent: Tuesday, May 19, 2009 4:16 PM
To: Robert Iquiapaza
Cc: r-sig-finance at stat.math.ethz.ch
Subject: Re: [R-SIG-Finance] R: [Fwd: R-SIG-Finance Digest, Vol 60, Issue 18]
Oh, you are right. Here is the correct file. I sure have botched this query, thanks for catching it Robert! Sorry for so many posts to the list.
Regards,
Steve
On Tue, May 19, 2009 at 12:19 PM, Robert Iquiapaza <rbali at ufmg.br> wrote:
Stev,
The data you provided is not complete, lagdlfdi and laglnstock2000 are not in the csv file
Robert
From: Steven Archambault
Sent: Monday, May 18, 2009 5:06 PM
To: Millo Giovanni
Cc: r-sig-finance at stat.math.ethz.ch ; Yves Croissant ; Christian Kleiber
Subject: Re: [R-SIG-Finance] R: [Fwd: R-SIG-Finance Digest, Vol 60, Issue 18]
I just realized I used Robust in my Stata 9.2 analysis. When I remove this, the Chi-sq values are much closer to the values I get in R (but negative, as the consistent model must be listed first in a chi-sq calculation). However, with my own data I do get this positive definite error in Stata. Is this a result of unbalanced data? R doesn't give an error, so I am inclined to ignore it in Stata. I am posting my own results from R and Stata, and attaching the data as a csv.
Thanks, hope I am not wasting too much of your time here.
-Steve
###R-Output###
> library("plm")
>
> fdi <- read.csv("C:/data/mydata.csv", na.strings=".")
> fdiplm<-plm.data(fdi, index = c("id_code_id", "year"))
series are constants and have been removed
>
> fdi_test<-(lfdi_2000~ lagdlfdi+ laglnstock2000+ lagtradegdp +lagdlgdp)
>
> fdi_test_fe <- plm(fdi_test, data=fdiplm, model="within")
> fdi_test_re <- plm(fdi_test, data=fdiplm, model="random")
>
> summary (fdi_test_fe)
Oneway (individual) effect Within Model
Call:
plm(formula = fdi_test, data = fdiplm, model = "within")
Unbalanced Panel: n=149, T=3-27, N=2697
Residuals :
Min. 1st Qu. Median 3rd Qu. Max.
-8.2100 -0.4760 0.0452 0.5670 4.8700
Coefficients :
Estimate Std. Error t-value Pr(>|t|)
lagdlfdi 0.1564759 0.0180645 8.6621 < 2.2e-16 ***
laglnstock2000 0.7621350 0.0246798 30.8809 < 2.2e-16 ***
lagtradegdp 0.0178568 0.0025859 6.9055 5.003e-12 ***
lagdlgdp 0.2601477 0.0427744 6.0818 1.188e-09 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Total Sum of Squares: 4606.7
Residual Sum of Squares: 2938
F-statistic: 361.237 on 4 and 2544 DF, p-value: < 2.22e-16
> summary (fdi_test_re)
Oneway (individual) effect Random Effect Model
(Swamy-Arora's transformation)
Call:
plm(formula = fdi_test, data = fdiplm, model = "random")
Unbalanced Panel: n=149, T=3-27, N=2697
Effects:
var std.dev share
idiosyncratic 1.15487 1.07465 0.6617
individual 0.59044 0.76840 0.3383
theta :
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.3718 0.6700 0.7081 0.6955 0.7355 0.7401
Residuals :
Min. 1st Qu. Median Mean 3rd Qu. Max.
-9.15000 -0.47900 0.07270 -0.00713 0.59800 3.95000
Coefficients :
Estimate Std. Error t-value Pr(>|t|)
(Intercept) 16.7744214 0.1552868 108.0222 < 2.2e-16 ***
lagdlfdi 0.1632388 0.0181005 9.0185 < 2.2e-16 ***
laglnstock2000 0.8314432 0.0196444 42.3247 < 2.2e-16 ***
lagtradegdp 0.0119453 0.0020737 5.7605 8.386e-09 ***
lagdlgdp 0.2558009 0.0424599 6.0245 1.696e-09 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Total Sum of Squares: 9522.3
Residual Sum of Squares: 3140.8
F-statistic: 1367.42 on 4 and 2692 DF, p-value: < 2.22e-16
>
> phtest(fdi_test_re, fdi_test_fe)
Hausman Test
data: fdi_test
chisq = 23.7021, df = 4, p-value = 9.164e-05
alternative hypothesis: one model is inconsistent
###end R output###
###Stata 9.2 Output--canned###
xtreg lfdi_2000 lagdlfdi laglnstock2000 lagtradegdp lagdlgdp, fe;
Fixed-effects (within) regression Number of obs = 2697
Group variable (i): id_code_id Number of groups = 149
R-sq: within = 0.3622 Obs per group: min = 3
between = 0.8234 avg = 18.1
overall = 0.6998 max = 27
F(4,2544) = 361.24
corr(u_i, Xb) = 0.3536 Prob > F = 0.0000
------------------------------------------------------------------------------
lfdi_2000 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lagdlfdi | .1564758 .0180645 8.66 0.000 .1210532 .1918985
laglnst~2000 | .762135 .0246798 30.88 0.000 .7137404 .8105295
lagtradegdp | .0178568 .0025859 6.91 0.000 .0127861 .0229274
lagdlgdp | .2601478 .0427744 6.08 0.000 .1762716 .3440241
_cons | 17.01131 .1701713 99.97 0.000 16.67762 17.345
-------------+----------------------------------------------------------------
sigma_u | .93048942
sigma_e | 1.0746505
rho | .42847396 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(148, 2544) = 10.73 Prob > F = 0.0000
. estimates store FIX, title(The FE) ;
. xtreg lfdi_2000 lagdlfdi laglnstock2000 lagtradegdp lagdlgdp, re;
Random-effects GLS regression Number of obs = 2697
Group variable (i): id_code_id Number of groups = 149
R-sq: within = 0.3606 Obs per group: min = 3
between = 0.8402 avg = 18.1
overall = 0.7128 max = 27
Random effects u_i ~ Gaussian Wald chi2(4) = 2225.46
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
lfdi_2000 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lagdlfdi | .1631662 .0180937 9.02 0.000 .1277032 .1986291
laglnst~2000 | .830845 .0196843 42.21 0.000 .7922645 .8694255
lagtradegdp | .011992 .0020779 5.77 0.000 .0079195 .0160645
lagdlgdp | .2558113 .0424486 6.03 0.000 .1726136 .3390091
_cons | 16.77702 .1556693 107.77 0.000 16.47191 17.08212
-------------+----------------------------------------------------------------
sigma_u | .77431228
sigma_e | 1.0746505
rho | .34173973 (fraction of variance due to u_i)
------------------------------------------------------------------------------
. estimates store RAND, title(The RE) ;
. hausman FIX RAND;
---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| FIX RAND Difference S.E.
-------------+----------------------------------------------------------------
lagdlfdi | .1564758 .1631662 -.0066903 .
laglnst~2000 | .762135 .830845 -.06871 .014887
lagtradegdp | .0178568 .011992 .0058648 .0015393
lagdlgdp | .2601478 .2558113 .0043365 .0052695
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg
Test: Ho: difference in coefficients not systematic
chi2(4) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 22.94
Prob>chi2 = 0.0001
(V_b-V_B is not positive definite)
###End Stata 9.2####
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