st: testing for significant changes in r squared within

[Jan Mammen <jan.mammen@googlemail.com>]

Dear Statalist,



I have a panel data model in which  the dependent variable is firm
risk and one independent variable the degree of multinationality of
the firm. I would like to test the hypothesis of a nonlinear
relationship by adding first a linear term, afterwards the squared and
finally the cubic term of multinationality. I am looking for a
possibility to show that the inclusion of the squared and cubic term
significantly improves the model. As I am using a fixed effects model
my first guess was to look for changes in R² within. In the article
Strategic Management Article (2008, Issue 2) “WITHIN-INDUSTRY
DIVERSIFICATION AND FIRM PERFORMANCE IN THE PRESENCE OF NETWORK
EXTERNALITIES: EVIDENCE FROM THE SOFTWARE INDUSTRY” written by
Tanrverdi and Lee the authors test the changes in R² within for
significance. Unfortunately the authors do not provide abundant
information how this test is performed.



As far as I have understood I would first have to simulate the
distribution of R² within to be able to test the change for
significance. I would be very grateful if anybody could tell me if
this guess is right or has any suggestion for literature in which such
a test or rather the procedure is described.



Best regards

Jan

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