Dear Statalisters
I would like to perform a robust Hausman test on a regression model. Specifically, I would like to implement the auxiliary regression approach described in Wooldridge (2010, Section 10.7.3). Unfortunately, however, I don't know how to interpret the following result from a "robust" Hausman test:
*** snip Stata code ***
* Load the Grunfeld dataset
webuse grunfeld, clear
xtset company year, yearly
* Generate a market level factor variable and interaction terms with the market factor:
by year, sort: egen tvar = mean(invest - kstock + mvalue/10)
gen mvalue_tvar = mvalue*tvar
gen kstock_tvar = kstock*tvar
* Generate time averages
xtset
by company: egen mvalue_bar = mean(mvalue)
by company: egen kstock_bar = mean(kstock)
* To analyze whether the random effects assumption holds, I then test for joint significance of the coefficient estimates for mvalue_bar and kstock_bar as follows:
reg invest mvalue kstock mvalue_tvar kstock_tvar tvar mvalue_bar kstock_bar, cluster(year)
test mvalue_bar kstock_bar
* Here is an alternative version of the same test, but this time without
reg invest mvalue kstock mvalue_tvar kstock_tvar tvar mvalue_bar kstock_bar
test mvalue_bar kstock_bar
*** snip end of Stata code ***
When comparing the results from the above Wald tests, then I observe that the first Wald test (i.e. the one based on SE that are robust to cross-sectional dependencies) rejects the RE assumption on the 5% level whereas the second Wald test (i.e. the one based on model SE) does not reject the null on the 5% level. However, the t-stats of mvalue_bar and kstock_bar are higher in case of model SE (0.04 and -1.93) than with clustered SE (where the t-stats are -1.31 and 0.03, respectively). Intuitively, I would therefore rather expect the "non-robust" Hausman test to reject the RE assumption than the "robust" one. Obviously, differences in the VCV-matrix underlying the two Hausman tests should explain the result. However, I quite frequently observe this situation and therefore wonder which Wald test I should/can trust more in such a case, the "robust" one or the "non-robust" one?
Any guidance on this is highly appreciated.
Kind regards,
Daniel
I would like to perform a robust Hausman test on a regression model. Specifically, I would like to implement the auxiliary regression approach described in Wooldridge (2010, Section 10.7.3). Unfortunately, however, I don't know how to interpret the following result from a "robust" Hausman test:
*** snip Stata code ***
* Load the Grunfeld dataset
webuse grunfeld, clear
xtset company year, yearly
* Generate a market level factor variable and interaction terms with the market factor:
by year, sort: egen tvar = mean(invest - kstock + mvalue/10)
gen mvalue_tvar = mvalue*tvar
gen kstock_tvar = kstock*tvar
* Generate time averages
xtset
by company: egen mvalue_bar = mean(mvalue)
by company: egen kstock_bar = mean(kstock)
* To analyze whether the random effects assumption holds, I then test for joint significance of the coefficient estimates for mvalue_bar and kstock_bar as follows:
reg invest mvalue kstock mvalue_tvar kstock_tvar tvar mvalue_bar kstock_bar, cluster(year)
test mvalue_bar kstock_bar
* Here is an alternative version of the same test, but this time without
reg invest mvalue kstock mvalue_tvar kstock_tvar tvar mvalue_bar kstock_bar
test mvalue_bar kstock_bar
*** snip end of Stata code ***
When comparing the results from the above Wald tests, then I observe that the first Wald test (i.e. the one based on SE that are robust to cross-sectional dependencies) rejects the RE assumption on the 5% level whereas the second Wald test (i.e. the one based on model SE) does not reject the null on the 5% level. However, the t-stats of mvalue_bar and kstock_bar are higher in case of model SE (0.04 and -1.93) than with clustered SE (where the t-stats are -1.31 and 0.03, respectively). Intuitively, I would therefore rather expect the "non-robust" Hausman test to reject the RE assumption than the "robust" one. Obviously, differences in the VCV-matrix underlying the two Hausman tests should explain the result. However, I quite frequently observe this situation and therefore wonder which Wald test I should/can trust more in such a case, the "robust" one or the "non-robust" one?
Any guidance on this is highly appreciated.
Kind regards,
Daniel
