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st: RE: AW: RE: AW: RE: F-test Stata reg..., robust
From
DE SOUZA Eric <[email protected]>
To
"'[email protected]'" <[email protected]>
Subject
st: RE: AW: RE: AW: RE: F-test Stata reg..., robust
Date
Fri, 20 Aug 2010 14:03:53 +0200
For the reason I gave in my first reply.
Below is the output from OxMetrics (PcGive)
The correct calculation of the F-test - which tests the joint nullity of the coefficients on the explanatory variables takes into account the covariances between the coefficient estimators. As you can see below the covariances are very different from the OLS case
The formulat you are using and that EViews uses is only valid when there is no heteroscedasticity.
At the bottom of the output is the F-test supposing homoscedasticity and the F-test allowing for heteroscedasticity (robust).
EQ( 3) Modelling mpg by OLS (using auto.xls)
The estimation sample is: 1 - 74
Coefficient Std.Error JHCSE t-JHCSE t-prob Part.R^2
Constant 41.9595 2.378 1.856 22.6 0.000 0.8795
weight -0.00677585 0.0009048 0.0007394 -9.16 0.000 0.5454
foreign -1.85589 1.289 1.502 -1.24 0.221 0.0213
price 5.66021e-005 0.0001922 0.0002348 0.241 0.810 0.0008
sigma 3.42919 RSS 823.152295
R^2 0.66312 F(3,70) = 45.93 [0.000]**
log-likelihood -194.137 DW 2.43
no. of observations 74 no. of parameters 4
mean(mpg) 21.2973 var(mpg) 33.0197
Covariance matrix of estimated parameters:
Constant weight foreign price
Constant 5.6536 -0.0019706 -2.2561 0.00018266
weight -0.0019706 8.1872e-007 0.00085802 -1.2272e-007
foreign -2.2561 0.00085802 1.6617 -0.00013441
price 0.00018266 -1.2272e-007 -0.00013441 3.6955e-008
JHCSE Covariance matrix of estimated parameters:
Constant weight foreign price
Constant 3.4463 -0.0011716 -1.1807 0.00010498
weight -0.0011716 5.4667e-007 0.00068552 -1.2110e-007
foreign -1.1807 0.00068552 2.2567 -0.00021688
price 0.00010498 -1.2110e-007 -0.00021688 5.5144e-008
Heteroscedasticity consistent standard errors
Coefficients SE HACSE HCSE JHCSE
Constant 41.959 2.3777 1.8196 1.7330 1.8564
weight -0.0067758 0.00090483 0.00061354 0.00067767 0.00073937
foreign -1.8559 1.2891 1.0862 1.4197 1.5022
price 5.6602e-005 0.00019224 0.00016812 0.00020610 0.00023483
Coefficients t-SE t-HACSE t-HCSE t-JHCSE
Constant 41.959 17.647 23.060 24.211 22.602
weight -0.0067758 -7.4885 -11.044 -9.9987 -9.1643
foreign -1.8559 -1.4397 -1.7086 -1.3072 -1.2354
price 5.6602e-005 0.29444 0.33667 0.27463 0.24104
Test for excluding:
[0] = weight
[1] = foreign
[2] = price
Subset F(3,70) = 45.930 [0.0000]**
Subset F(3,70) = 166.53 [0.0000]** (using JHCSE)
Eric de Souza
College of Europe
Brugge (Bruges)
Belgium
-----Original Message-----
From: [email protected] [mailto:[email protected]] On Behalf Of Julian Dragendorf
Sent: 20 August 2010 12:10
To: [email protected]
Subject: st: AW: RE: AW: RE: F-test Stata reg..., robust
Thanks for the quick response!
Below (1) I show the outputs with "reg,..., robust" STATA and (2) EVIEWs with white hetero-const- st errors. As u see everything is equal except the f-test! Why?
(1) STATA
F( 3, 182) = 2.42
Prob > F = 0.0676
R-squared = 0.0596 adjusted R2= 0.04412889
Root MSE = 12.535
Robust
Y Coef. Std. Err. t P>t [95% Conf. Interval]
X1 3.487523 2.421257 1.44 0.151 -1.289821
8.264866
X2 -1.118751 2.103527 -0.53 0.595 -5.269187
3.031685
X3 0.305943 0.1843521 1.66 0.099 -0.0577991
0.6696852
cons -0.137852 1.45166 -0.09 0.924 -3.0021 2.726396
(2) EVIEWs:
White Heteroskedasticity-Consistent Standard Errors & Covariance
Coefficient Std. Error t-Statistic Prob.
X1 3.487523 2.421257 1.440377 0.1515
X2 -1.118751 2.103527 -0.531845 0.5955
X3 0.305943 0.184352 1.659559 0.0987
C -0.137852 1.45166 -0.094962 0.9244
R-squared 0.05963
Adjusted R-squared 0.044129 S.D. dependent var
12.82129
S.E. of regression 12.5352 Akaike info criterion 7.91623
Sum squared resid 28597.9 Schwarz criterion
7.985601
Log likelihood -732.2094 Hannan-Quinn criter.
7.944341
F-statistic 3.846913 Durbin-Watson stat
1.868423
Prob(F-statistic) 0.010593
-----Ursprüngliche Nachricht-----
Von: [email protected]
[mailto:[email protected]] Im Auftrag von DE SOUZA Eric
Gesendet: Freitag, 20. August 2010 11:58
An: '[email protected]'
Betreff: st: RE: AW: RE: F-test Stata reg..., robust
Which standard errors don't change?
In the example below, without robust you get the OLS standard errors for the coefficients, whereas with the robust option you get the robustified standard errors:
. webuse auto
. reg mpg weight foreign price
Source | SS df MS Number of obs =
74
-------------+------------------------------ F( 3, 70) =
45.93
Model | 1620.30716 3 540.102388 Prob > F =
0.0000
Residual | 823.152295 70 11.7593185 R-squared =
0.6631
-------------+------------------------------ Adj R-squared =
0.6487
Total | 2443.45946 73 33.4720474 Root MSE =
3.4292
----------------------------------------------------------------------------
--
mpg | Coef. Std. Err. t P>|t| [95% Conf.
Interval]
-------------+----------------------------------------------------------
-------------+----
--
weight | -.0067758 .0009048 -7.49 0.000 -.0085805
-.0049712
foreign | -1.855891 1.289063 -1.44 0.154 -4.426846
.7150641
price | .0000566 .0001922 0.29 0.769 -.0003268
.00044
_cons | 41.95948 2.377726 17.65 0.000 37.21725
46.7017
----------------------------------------------------------------------------
--
. reg mpg weight foreign price, robust
Linear regression Number of obs =
74
F( 3, 70) =
62.39
Prob > F =
0.0000
R-squared =
0.6631
Root MSE =
3.4292
----------------------------------------------------------------------------
--
| Robust
mpg | Coef. Std. Err. t P>|t| [95% Conf.
Interval]
-------------+----------------------------------------------------------
-------------+----
--
weight | -.0067758 .0006777 -10.00 0.000 -.0081274
-.0054243
foreign | -1.855891 1.419701 -1.31 0.195 -4.687396
.9756145
price | .0000566 .0002061 0.27 0.784 -.0003545
.0004677
_cons | 41.95948 1.733047 24.21 0.000 38.50302
45.41593
----------------------------------------------------------------------------
--
Eric de Souza
College of Europe
Brugge (Bruges)
Belgium
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Julian Dragendorf
Sent: 20 August 2010 11:52
To: [email protected]
Subject: st: AW: RE: F-test Stata reg..., robust
Thx! But then the St. Errors should change also! or? But st. errors stay the same! And MSS and RSS are not displayed automatically but used a command to get the information "display e(mss)"!
-----Ursprüngliche Nachricht-----
Von: [email protected]
[mailto:[email protected]] Im Auftrag von DE SOUZA Eric
Gesendet: Freitag, 20. August 2010 11:24
An: '[email protected]'
Betreff: st: RE: F-test Stata reg..., robust
Robustification only affects the variances and the covariances.
Coefficients stay the same, which means that Model SS, Residual SS and d.f.
remains the same.
But the F-test should take into account the new variances and covariances calculated under robustification.
Why don't you post some output using a commonly accessible file such as auto.dta webuse auto will get you the file
By the way, Stata v10.1 does not produce the model ss, residual ss, under robustification.
Eric de Souza
College of Europe
Brugge (Bruges)
Belgium
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Julian Dragendorf
Sent: 20 August 2010 11:13
To: [email protected]
Subject: st: F-test Stata reg..., robust
Hello!
I have a short question regarding the F-test for STATA 10.0 and EVIEWs 6.0 when using a simple OLS multiple regression model: If I use the Stata command "reg..., robust" to estimate a multiple regression model I get the same coef., std. err, t-stat and r2 as if I use Eviews OLS regression with white heteroskedasticity-const std error & covariance. However, the only thing which differs is the F-test which is higher for Eviews than for Stata.
When I use the Model SS, Residual SS and the respective d.f. of model estimated with STATA I can calculate the F-test manually whereby I get out the same F-test as in Eviews. Does somebody know why there is a difference in the F-test but everything else is equal when using STATA (reg...,robust) and Eviews (reg with white hetero. consist. st errors)?
Many thanks!
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