Marco,
I know one can use -intreg- to obtain robust standard errors (Stata FAQ:
http://www.stata.com/support/faqs/stat/tobit.html which also contains the
following
"Note: In Stata 9, use the vce option with the tobit command to obtain
estimates of the standard errors using nonparametric bootstrap or
jackknife." ), however, I am not sure what this accomplishes.
Heteroskedasticity will result in inconsistent estimates in a tobit model.
What good is a robust variance if the parameter estimates are wrong?
Suppose we take the simple example:
clear
set obs 5000
set seed 1234567890
generate x =10+ 50*uniform()
generate y = -50 + 2*x+ x*invnorm(uniform())
generate ycen = cond(y<0,0,y)
qui tobit ycen x, ll(0) nolog
est store A
tobcm
gen y2 = ycen
replace y2 = . if ycen<=0
gen y3 = ycen
replace y3 =0 if ycen<=0
qui intreg y2 y3 x , robust nolog
est store B
qui clad ycen x, q(.5) ll(0)
est store C
esta *, mtitle("Tobit" "Robust Tobit" "CLAD") ///
drop(sigma:_cons lnsigma:_cons) c( b(fmt(2)) "ci(fmt(2)par)" )
This produces:
--------------------------------------------------
(1) (2) (3)
Tobit Robust Tobit CLAD
---------------------------------------------------
main
x 2.74 2.74 2.01
[2.63,2.84] [2.63,2.85] [1.88,2.14]
_cons -84.26 -84.26 -50.82
[-88.66,-79.86] [-88.51,-80.01] [-56.55,-45.09]
---------------------------------------------------
N 5000 5000 3539
---------------------------------------------------
Perhaps this is not a very good example, but I am not sure that a robust
tobit accounts for heteroskedasticity.
Scott
> -----Original Message-----
> From: [email protected] [mailto:owner-
> [email protected]] On Behalf Of marco stampini
> Sent: Tuesday, November 28, 2006 10:17 AM
> To: [email protected]
> Subject: Re: st: RE: tobit with autocorrelated and heteroscedastic
> disturbances
>
> Thank you Scott. I will try to answer myself, with what I found out, and
> try to stimulate more discussion.
>
> The command intreg can be used to address heteroscedasticity. I copy the
> code below.
>
> I think that the same could be exploited to address autocorrelation, but I
> doubt that the code below is correct. Intreg allows modelling the variance
> of the error term as function of some variables. Would modelling the
> variance as a function of the lagged dependent variable be equivalent to a
> Cochrane-Orcut correction of autocorrelation in OLS?
>
> Any help/comment would be much appreciated. Thank you.
> Marco Stampini
>
>
> *the tobit
> xi:tobit y $X, ll(0)
>
> *some necessary variables
> gen y2 = y
> replace y2 = . if y<=0
> gen y3 = y
> replace y3 =0 if y<=0
>
> *intreg which replicates the tobit
> xi:intreg y2 y3 $X
>
> *intreg which replicates the tobit and accounts for heteroscedasticity
> xi:intreg y2 y3 $X, r
>
> *intreg which replicates the tobit, accounts for heteroscedasticity
> *and MAYBE(??????) takes care of autocorrelation
> xi:intreg y2 y3 $X, r het(y_lag)
>
>
>
> ----- Original Message ----
> From: Scott Merryman <[email protected]>
> To: [email protected]
> Sent: Wednesday, November 22, 2006 9:00:01 PM
> Subject: st: RE: tobit with autocorrelated and heteroscedastic
> disturbances
>
>
> You might want to try -clad- which allows heteroskedastic errors.
>
> Scott
>
>
>
> > -----Original Message-----
> > From: [email protected] [mailto:owner-
> > [email protected]] On Behalf Of marco stampini
> > Sent: Wednesday, November 22, 2006 8:38 AM
> > To: [email protected]
> > Subject: st: tobit with autocorrelated and heteroscedastic disturbances
> >
> > Hello.
> >
> > I would need to estimate jointly two tobit equations, in which errors
> are
> > both autocorrelated and heteroscedastic.
> > Does anybody have any idea on how to solve at least part of the problem?
> >
> > For example, how to take care of autocorrelation and heteroscedasticity
> in
> > each of the two tobits?
> > As a second step, if possible, how to estimate jointly?
> >
> > Are you aware of any routine doing anything similar?
> >
> > Thank you very much in advance,
> > Marco Stampini
> >
>
>
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>
>
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