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help for ^xttest3^                    (Statalist distribution, 15 Nov 2000)
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Modified Wald statistic for groupwise heteroskedasticity in fixed effect model
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    ^xttest3^ 


^xttest3^ is for use with cross-section time-series data, following use of 
^xtreg, fe^ or ^xtgls^.


Description
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^xttest3^ calculates a modified Wald statistic for groupwise heteroskedasticity
in the residuals of a fixed effect regression model, following Greene 
(2000, p. 598). ^xtreg, fe^ estimates this model assuming homoskedasticity. 
The most likely deviation from homoskedastic errors in the context of pooled
cross-section time-series data (or panel data) is likely to be error variances
specific to the cross-sectional unit. ^xttest3^ tests the hypothesis that
sigma^^2(i)==sigma for i=1,N_g, where N_g is the number of cross-sectional
units. The resulting test statistic is distributed Chi-squared(N_g) under the
null hypothesis of homoskedasticity. 

Greene's discussion of Lagrange multiplier, likelihood ratio and standard Wald
test statistics points out that these statistics are sensitive to the 
assumption of normality of the errors. The modified Wald statistic computed 
here is workable when the assumption of normality is violated, at least in 
asymptotic terms. In terms of small sample properties, simulations of the test 
statistic have shown that its power is very low in the context of fixed effects
>  
with "large N, small T" panels. In that circumstance, the test should be used 
with caution.

One modification to Greene's formulae has been applied to allow for unbalanced
panels (in which T(i), the number of observations per cross-sectional unit, is
not constant across units). All sums are computed over the actual T(i) 
for the cross-sectional unit.

The test statistic, degrees of freedom and p-value are placed in the return 
array.
 

Example
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        . ^use http://fmwww.bc.edu/ec-p/data/greene2000/tbl15-1.dta,clear^

        . ^iis firm^
        
        . ^xtreg i f c if firm!=2,fe^
        
        . ^xttest3^
        
        . ^xtgls i f c if firm!=2, p(h)^
        
        . ^xttest3^


References
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Greene, W. Econometric Analysis. New York:Prentice-Hall. 2000.


Acknowledgements
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Thanks to Francesco Zanetti for assistance with this routine, to 
Sylvain Friederich for suggesting that it be written, and to Bill
Gould for exhaustively testing it, determining its power properties,
and pointing out a minor bug that inflated the test statistic. 
The routine was originally circulated as xttest1, but that name 
has been used by another author's routine in STB-61. 
 
Author
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Christopher F Baum, Boston College, USA
baum@@bc.edu

Also see
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On-line:  help for @bpagan@ (if installed), @whitetst@ (if installed), @xttest2
> @ (if installed)