Hausman Specification test - chi2-calculation

[Alex Alexeev]

Hausman specification test, "hausman", for panel data regression models FE vs RE produces a value of Chi-sq. statistic that is essentially different from that calculated directly using coefficient vectors e(b) and variance-covariance matrices e(V). (The values of chi-2 calculated directly here are the same to those calculated in R both directly and using "phtest" from "plm" ). The data are from https://research.stlouisfed.org/publ...t-cold-war-era . Stata 17 MP
The code is:

xtset countryid year
xtreg raid gdpcap gdpcap2 infmort infmort2 rights goveff popmil pop2 y2 y3, fe
est store fem
matrix b=e(b)
matrix Vb=e(V)
xtreg raid gdpcap gdpcap2 infmort infmort2 rights goveff popmil pop2 y2 y3, re
est store rem
matrix B=e(b)
matrix VB=e(V)
*** Hausman test
hausman fem rem
hausman fem rem, sigmaless 
*** Manual calculations of Housman test Chi-sq
matrix b_B= (b-B)'
matrix Vdiff=Vb-VB
***constant term remove
matrix b_B=b_B[1..10, 1]
matrix Vdiff=Vdiff[1..10, 1..10]
***Chi-sq-calc
matrix chi=b_B'*syminv(Vdiff)*b_B
matrix list chi

Results:

Test of H0: Difference in coefficients not systematic

   chi2(10) = (b-B)'[(V_b-V_B)^(-1)](b-B)
            =  10.73
Prob > chi2 = 0.3790

. *** Manual calculations of Housman test Chi-sq
. matrix b_B= (b-B)'
. matrix Vdiff=Vb-VB

. ***constant term remove
. matrix b_B=b_B[1..10, 1]
. matrix Vdiff=Vdiff[1..10, 1..10]

. ***Chi-sq-calc
. matrix chi=b_B'*syminv(Vdiff)*b_B
. matrix list chi

symmetric chi[1,1]
           y1
y1  23.531672

What might be a matter of such difference? Thanks.

[Carlo Lazzaro]

Alex:
welcome to this forum.
Does the same issue creep up if you do not invoke the -sigmaless- option available from -hausman-?

[Alex Alexeev]

Carlo, thank you. I have been a reader for a long time.
Yes, the issue holds. The chi2 is slightly different (smaller) without -sigmaless- . The reason for -sigmaless- was the receiving of -not positive definite- warning. As i mentioned above - R produces same result to the matrix calculations . I attached the data in Stata format for the case one may want to look at.