[Gretl-users] heteroscedastistic tobit model

Riccardo (Jack) Lucchetti r.lucchetti at univpm.it
Mon Jul 8 05:49:08 EDT 2013

On Sat, 6 Jul 2013, ROGER MCNEILL wrote:

> According to the gretl test for normality of residuals in my estimated 
> Tobit model, heteroscedasticity is a problem, meaning the Tobit 
> estimator is inconsistent.  Does gretl have an alternative estimator for 
> censored regressions such as a least absolute deviations estimator or an 
> maximum likelihood estimator that is consistent in the face of non 
> normal errors?

Not pre-cooked. However, if you have a specific alternative in mind, it 
shouldn't be difficult to code it in hansl. The following example uses 
data from Marno Verbeek's textbook to estimate a simple heteroskedastic 
Tobit model via mle:

function series het_tobit_ll(series y, list X, list Z, matrix param)
     scalar kx = nelem(X)
     list Z -= const # remove constant if present for identification
     scalar kz = nelem(Z)
     series ndx_m = lincomb(X, param[1:kx])
     series l_h = param[kx+1]

     if kz > 0
         matrix gamma = param[kx+2:kx+kz+1]
         series l_h += lincomb(Z, gamma)

     series u = (y - ndx_m)/exp(l_h)
     series ll = (y > 0) ? -0.5*(ln(2*$pi) + 2*l_h + u^2) : \

     return ll
end function

# -----------------------------------------------------------

open tobacco.gdt
series alcohol = misszero(w1)
list X = const age nadults nkids nkids2 lnx agelnx nadlnx
tobit alcohol X
matrix theta = $coeff | ln($sigma)

list Z = nkids lnx
theta |= zeros(nelem(Z), 1)
set warnings off
mle ll = het_tobit_ll(alcohol, X, Z, theta)
     params theta
end mle -h

   Riccardo (Jack) Lucchetti
   Dipartimento di Scienze Economiche e Sociali (DiSES)

   Università Politecnica delle Marche
   (formerly known as Università di Ancona)

   r.lucchetti at univpm.it

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