Re: Gretl-users Digest, Vol 111, Issue 13 Hausman Test in IV estimation

Gretl uses a regression-based method to calculate the Hausman Statistic.

If we want to use the matrix-expression for the test statistic, two vcv matrices are involved. For each a different error variance estimate is used. So one has to decide whether he will use the difference error variance estimate or a common one.
I executed the test using the matrix form and the OLS error variance estimate for both vcv matrices: I obtain  Statistic =  4.9480036    which is pretty close to what Gretl gives (as it should)

Then I executed the test using the matrix form , but for the vcv from the IV estimation I used the error variance estimate obtained from the IV regression : et voila! I got Statistic =  2.7559288

So it is not a bug, but a choice that has to be made.

    
Alecos Papadopoulos
PhD Candidate
Athens University of Economics and Business, Greece
School of Economic Sciences
Department of Economics
https://alecospapadopoulos.wordpress.com/
On 13/4/2016 03:37, gretl-users-request@lists.wfu.edu wrote:
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Today's Topics:

   1. Instrumental variables and Hausman test (Javier Garc?a)


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Message: 1
Date: Wed, 13 Apr 2016 02:28:36 +0200
From: Javier Garc?a <javier.garcia@ehu.eus>
To: <gretl-users@lists.wfu.edu>
Subject: [Gretl-users] Instrumental variables and Hausman test
Message-ID:
	<570d92ba.e567c20a.767b.fffffbe5SMTPIN_ADDED_BROKEN@mx.google.com>
Content-Type: text/plain; charset="utf-8"

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

 

 

	


JAVIER GARC?A 

 

Departamento de Econom?a Aplicada III (Econometr?a y Estad?stica)

Facultad de Econom?a y Empresa (Secci?n Sarriko)
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T.: +34 601 7126 F.: +34 601 3754
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