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st: RE: AW: RE: AW: RE: F-test Stata reg..., robust

 From DE SOUZA Eric To "'statalist@hsphsun2.harvard.edu'" 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

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: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Julian Dragendorf
Sent: 20 August 2010 12:10
To: statalist@hsphsun2.harvard.edu
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: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von DE SOUZA Eric
Gesendet: Freitag, 20. August 2010 11:58
An: 'statalist@hsphsun2.harvard.edu'
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
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: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Julian Dragendorf
Sent: 20 August 2010 11:52
To: statalist@hsphsun2.harvard.edu
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: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von DE SOUZA Eric
Gesendet: Freitag, 20. August 2010 11:24
An: 'statalist@hsphsun2.harvard.edu'
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: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Julian Dragendorf
Sent: 20 August 2010 11:13
To: statalist@hsphsun2.harvard.edu
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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