[Limdep Nlogit List] Testing heterosc. sample selection model

JK dwakotki at wp.pl
Thu Oct 9 19:26:08 EST 2008


Thank you for your answer about logl0.
I've rewritten the procedure with more varibles in XH ;-) - thanks

Regards,
Jadwiga Kostrzewska
Katedra Statystyki
Uniwersytet Ekonomiczny w Krakowie


Dnia 8-10-2008 o godz. 14:57 William Greene napisał(a):
> JK. Interesting question.  The reason for the discrepancy is as follows:
> The maximum likelihood estimator for the homoscedasticity model as you
> have specified it is reestimating the probit equation. You will notice
> that the output for this model includes results for the probit equation.
> The MLE for the heteroscedasticity model is a two step estimator that does
> not reestimate the probit equation. It uses the previously computed
> probit model as is.  Thus, the output for it does not
> include a set of results for the probit equation. Unfortunately, that
> means
> that your strategy for testing for heteroscedasticity won't produce
> the right results.  What you can do, as you suggested below, is constrain
> the parameters in the variance equation to equal zero in the
> heteroscedasticity model, using Rst=kxw_b,0,b19,b20.  I think, however,
> that if you have more than one variable in the XH namelist, you need
> to change the list in this restriction. In any event, this will get you
> an appropriate test statistic.
> Regards,
> Bill Greene
> 
> 
> 
> ----- Original Message -----
> From: "JK" <dwakotki at wp.pl>
> To: "limdep" <limdep at limdep.itls.usyd.edu.au>
> Sent: Wednesday, October 8, 2008 3:58:10 AM GMT -05:00 US/Canada Eastern
> Subject: [Limdep Nlogit List] Testing heterosc. sample selection model
> 
> Dear LimDep Users,
> I'm testing a heteroscedasticity in the sample selection model, so my
> procedure is:
> 
> ? model homosk. (restr.)
>  PROBIT; Lhs=SELEKCJA; Rhs=W; Hold$
>  SELECT; Lhs=ZAL; Rhs=XW; MLE$
>   CALC; LOGhom=LOGL$
> ? model heterosk. (unrestr.)
>  PROBIT; Lhs=SELEKCJA; Rhs=W; Hold$
>  SELECT; Lhs=ZAL; Rhs=XW; Hfn=XH; MLE$
>   CALC; khe=Col(XH)$
>   CALC; LOGhet=LOGL; StatLR=2*(LOGhet-LOGhom)
>    ;pvLR=1-Chi(StatLR,khe)$
> (...)
> 
> The problem is that StatLR<0. I was looking for a mistake in my
> procedure and I find that there are two possible restricted logL:
> 1)
> --> PROBIT; Lhs=SELEKCJA; Rhs=W; Hold$
> --> SELECT; Lhs=ZAL; Rhs=XW; MLE$
> +---------------------------------------------+
> | ML Estimates of Selection Model
> | Maximum Likelihood Estimates
> | Dependent variable ZAL
> | Weighting variable None
> | Number of observations 6988
> | Iterations completed 30
> | Log likelihood function -24312.41    <=====
> | Number of parameters 28
> | Info. Criterion: AIC = 6.96635
> | Finite Sample: AIC = 6.96638
> | Info. Criterion: BIC = 6.99380
> | Info. Criterion:HQIC = 6.97581
> | Model estimated: Oct 01, 2008, 01:49:07PM
> | FIRST 9 estimates are probit equation.
> +-------------------------------------------+
> 
> 2)
> --> PROBIT; Lhs=SELEKCJA; Rhs=W; Hold$
> --> SELECT; Lhs=ZAL; Rhs=XW; Hfn=XH; MLE; Matrix; Rst=kxw_b,0,b19,b20$
> +---------------------------------------------+
> | Selection with heteroscedasticity
> | Maximum Likelihood Estimates
> | Dependent variable ZAL
> | Weighting variable None
> | Number of observations 6988
> | Iterations completed 2
> | Log likelihood function -24997.32   <====
> | Number of parameters 19
> | Info. Criterion: AIC = 7.15979
> | Finite Sample: AIC = 7.15981
> | Info. Criterion: BIC = 7.17842
> | Info. Criterion:HQIC = 7.16621
> | Restricted log likelihood -24997.32
> | McFadden Pseudo R-squared .0000000
> | Chi squared .1236913E-09
> | Degrees of freedom 1
> | Prob[ChiSqd > value] = .9999911
> | Model estimated: Oct 01, 2008, 01:25:51PM
> +---------------------------------------------+
> 
> In the sample selection model with hetroskedasticity, the restricted
> logL is the same as in the model with Rst=kxw_b,0,b19,b20 above:
> --> PROBIT; Lhs=SELEKCJA; Rhs=W; Hold$
> --> SELECT; Lhs=ZAL; Rhs=XW; Hfn=XH; MLE; Matrix$
> +---------------------------------------------+
> | Selection with heteroscedasticity
> | Maximum Likelihood Estimates
> | Dependent variable ZAL
> | Weighting variable None
> | Number of observations 6988
> | Iterations completed 27
> | Log likelihood function -24991.37    <====
> | Number of parameters 20
> | Info. Criterion: AIC = 7.15838
> | Finite Sample: AIC = 7.15839
> | Info. Criterion: BIC = 7.17799
> | Info. Criterion:HQIC = 7.16514
> | Restricted log likelihood -24997.32  <====
> | McFadden Pseudo R-squared .0002379
> | Chi squared 11.89333
> | Degrees of freedom 1
> | Prob[ChiSqd > value] = .5633534E-03
> | Model estimated: Oct 01, 2008, 01:30:10PM
> +---------------------------------------------+
> 
> I would like to know which version is correct and why the restricted
> logL, which is computed in the homoscedastic model, is different from
> the restricted logL which is computed in model with restrictions
> Rst=kxw_b,0,b19,b20. I thought it should be the same because the
> likelihood function of the homoscedastic sample selection model is a
> special case of the likelihood function of the heteroscedastic sample
> selection model (E30-12; E30-19).
> Have you got any suggestions for me?
> Thanks,
> 
> Jadwiga Kostrzewska
> Zakład Teorii Prognoz
> Katedra Statystyki
> Uniwersytet Ekonomiczny w Krakowie
> Polska
> 
> 
> 
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