Hausman Specification test to identify best estimator

[Faisal Abdullah]

Hello everyone,

I am Using Stata in my research. I applied 2 regressions ( regression 1 is OLS with time dummies, regression 2 is OLS with time + industry dummies). I would like to apply the Hausman specification to identify the best estimator.


actually, I am confused about the Hausman specification test. is it the Drubin -Wu-Hausman (DWH) test?? for what purpose this test is applied? and how I can apply it in Stata?

thank you so much for your kind support.

Faisal

[Joro Kolev]

In this case you should just test whether the industries are jointly equal to zero with -test- after you estimate your regression with the industry dummies.

Hausman test is not used usually in your situation.

[Faisal Abdullah]

Hello Joro, Thank you for your comment.
I am confused. since I am not using the xtreg (fe or re) estimators and thefore this may not mean the Hausman test which is used for comparing between fixed and random effects estimators.
I did some reading and I thought this can be the Hausman specification test which tests endogenaity.

[Carlo Lazzaro]

Faisal:
if regression 1 is nested within regression 2, you can also consider -lrtest-, like in the following toy-example:

. use "C:\Program Files (x86)\Stata15\ado\base\a\auto.dta"
(1978 Automobile Data)

. reg price mpg i.foreign

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(2, 71)        =     14.07
       Model |   180261702         2  90130850.8   Prob > F        =    0.0000
    Residual |   454803695        71  6405685.84   R-squared       =    0.2838
-------------+----------------------------------   Adj R-squared   =    0.2637
       Total |   635065396        73  8699525.97   Root MSE        =    2530.9

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -294.1955   55.69172    -5.28   0.000    -405.2417   -183.1494
             |
     foreign |
    Foreign  |   1767.292    700.158     2.52   0.014     371.2169    3163.368
       _cons |   11905.42   1158.634    10.28   0.000     9595.164    14215.67
------------------------------------------------------------------------------

. estimates store full

. reg price i.foreign

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(1, 72)        =      0.17
       Model |  1507382.66         1  1507382.66   Prob > F        =    0.6802
    Residual |   633558013        72  8799416.85   R-squared       =    0.0024
-------------+----------------------------------   Adj R-squared   =   -0.0115
       Total |   635065396        73  8699525.97   Root MSE        =    2966.4

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     foreign |
    Foreign  |   312.2587   754.4488     0.41   0.680    -1191.708    1816.225
       _cons |   6072.423    411.363    14.76   0.000     5252.386     6892.46
------------------------------------------------------------------------------

. estimates store part

. lrtest part full

Likelihood-ratio test                                 LR chi2(1)  =     24.53
(Assumption: part nested in full)                     Prob > chi2 =    0.0000

.