Hello everybody,
I am trying to perform the Hausman test within a instrumental variables context. Using the smoke.gdt data from the Wooldridge's book, I regress the variable called lincome on a constant, cigs, educ, age and agesq. In order to do this I apply "instrumental variables->2sls", providing one instrument (in particular the variable called restaurn) for cigs, a variable that we suspect that could be correlated with the perturbation. As it can be seen below, the asymptotic test statistic is 5.00976. However, if I do it manually (or using another program like Stata), that value is totally different, getting 2.76 aproximately (the square of the estimates differences, (0.00173057-(-0.0413845))^2, over the variances differences, 0.0260279^2-0.00171372^2). What am I doing wrong? It could be a Gretl bug?
Thanks a lot in advance.
Javi
Model 1: OLS, using observations 1-807
Dependent variable: lincome
coefficient std. error t-ratio p-value
-----------------------------------------------------------
const 7.79544 0.170427 45.74 1.05e-225 ***
cigs 0.00173057 0.00171372 1.010 0.3129
educ 0.0603605 0.00789834 7.642 6.10e-014 ***
age 0.0576907 0.00764359 7.548 1.21e-013 ***
agesq −0.000630589 8.33822e-05 −7.563 1.08e-013 ***
Mean dependent var 9.687315 S.D. dependent var 0.712695
Sum squared resid 341.8539 S.E. of regression 0.652880
R-squared 0.164978 Adjusted R-squared 0.160813
F(4, 802) 39.61341 P-value(F) 2.68e-30
Log-likelihood −798.5010 Akaike criterion 1607.002
Schwarz criterion 1630.469 Hannan-Quinn 1616.013
Model 2: TSLS, using observations 1-807
Dependent variable: lincome
Instrumented: cigs
Instruments: const restaurn educ age agesq
coefficient std. error z p-value
---------------------------------------------------------
const 7.78114 0.228129 34.11 5.52e-255 ***
cigs −0.0413845 0.0260279 −1.590 0.1118
educ 0.0400241 0.0161607 2.477 0.0133 **
age 0.0932076 0.0236787 3.936 8.27e-05 ***
agesq −0.00104373 0.000272324 −3.833 0.0001 ***
Mean dependent var 9.687315 S.D. dependent var 0.712695
Sum squared resid 611.6565 S.E. of regression 0.873306
R-squared 0.024886 Adjusted R-squared 0.020022
F(4, 802) 22.62942 P-value(F) 9.92e-18
Log-likelihood −7885.899 Akaike criterion 15781.80
Schwarz criterion 15805.26 Hannan-Quinn 15790.81
Log-likelihood for income = −8614.4
Hausman test -
Null hypothesis: OLS estimates are consistent
Asymptotic test statistic: Chi-square(1) = 5.00976
with p-value = 0.0252048
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