RE: Interpretation RESET-Test: Problems with different test options

["Wooldridge, Jeffrey" <wooldri1@msu.edu>]

Properly using RESET can be tricky. I have argued in a paper, 

"Score Diagnostics for Linear Models Estimated by Two Stage Least
Squares," in Advances in Econometrics and Quantitative Economics.  G.S.
Maddala, P.C.B. Phillips, and T.N. Srinivasan (eds.), 66-87.  Oxford:
Blackwell, 1995,

that RESET is purely a functional form test. It should not be expected
to have systematic power for omitted variables or for detecting
heteroskedasticity. (A test for heteroskedasticity only makes sense
using squared residuals, not the residuals themselves, which is what
RESET uses.)

The argument is simple. Suppose E(y|x,z) = b0 + b1x + b2z and also
E(z|x) is linear in x. Then E(y|x) is linear in x -- and, of course, the
estimator is generally inconsistent for b1. That E(y|x) is linear in x
means no other functions of x will matter. So RESET will fail to reject
(more precisely, have power equal to size, asymptotically).


That using polynomials in fitted values leads to a rejection whereas
polynomials in the xj themselves is not surprising. They are different
functions of the explanatory variables, and often the first choice
conserves on degrees of freedom. Note that the squared fitted value, (b0
+ xi*b1)^2 includes interactions as well as squares of all variables.

The fact that adding another variable causes RESET to reject is also
easily explained. For example, suppose

E(y|x,z) = b0 + b1*x + b2*z + b3*z^2

If b3 != 0 and you regress y on x, z then RESET should reject because
the linear functional form is incorrect. But suppose z and x are
independent. Then E(y|x) is linear and RESET will not reject.

I hope this helps.

JMW

Jeffrey M. Wooldridge
University Distinguished Professor
Department of Economics
Michigan State University
110 Marshall-Adams Hall
East Lansing, MI 48824-1038
Phone: 517-353-5972
Fax: 517-432-1068
http://www.msu.edu/~ec/faculty/wooldridge/wooldridge.html
 
-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
matthias.stoetzer@bw.fh-jena.de
Sent: Friday, March 04, 2011 8:18 AM
To: statalist@hsphsun2.harvard.edu
Subject: Interpretation RESET-Test: Problems with different test options

Dear STATA community,

in order to test for specification errors I use the RESET-test. I 
understand that RESET is not a test for omitted variables but more a
test 
looking for non-linearities.
I have two problems as to the interpretation of my results:

1. There is a striking difference of the RESET test using powers of the 
fitted values of the dependent variable (default-option) and using
powers 
of the independent variables (rhs-option). In the first case with my
data 
set the Ho has to be rejected (5%-level). In the second case the Ho can 
not be rejected even at the 40%-level. For sure this has to do with a 
difference of the dependent and independet variables but is there any 
precise explanation as to this difference? 

2. I run a multiple regression. The RESET-test (default-option) does not

reject the Ho of correct specification (10% level). I run a regression 
with the same dependent variable and the same independent variables but
in 
addition I include one other independent variable: Now the RESET-test 
(default-option) rejects the Ho of correct specification. To my opinion 
including additional variables should reduce the probability of omitting

variables and neglecting non-linearities. 

In advance many thanks for any suggestions!

Matthias S. 

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