Re: st: Consistent estimation of the Double Hurdle model

[Nick Cox <njcoxstata@gmail.com>]

I have only partial comments on this as I never use these models and
am not familar with the literature.

1. I don't have access to the original paper by Moffatt, but the
program you give won't work. The same character ' is used for both
single quote characters in local macro references, so e.g. 'd' is
given when it should be `d'. There appear to be several other typos in
what you quote, including possibly confusion between 1 and I and 0 and
O. p11 is defined but never used, while p1 is used but never defined.
Some quote characters are unmatched. If some or all of these errors
are present in the original, it is basically not to be trusted.
However, the problem does not look very difficult so if you teach
yourself basic Stata programming you can write a better program.

2. Whether asinh() is better than Box-Cox to transforming to
non-normality depends on the variable in question. asinh() has one
advantage over Box-Cox in that its argument may be negative. How far
normality is assumed for the marginal distribution of the response in
your kind of model I can't say but over-emphasis on such normality is
very common in some literatures.

Nick

On Wed, Feb 8, 2012 at 10:19 AM, verdes <verdes@tcd.ie> wrote:
> Dear Statalisters,
>
> I've been trying to estimate a Double Hurdle model on alcohol expenditure
> data.
>
> -craggit- by William Burke allows for hetereschedasticity but not for
> non-normality. So, I guess estimates would still be subject to bias.
>
> I then came across -dh- written by Moffatt (2005) in the Journal of the
> Operational Research Society, Vol.56, No.9 (*see below the command). -dh-
> allows for non-normality by applying a Box-Cox transformation to the
> dependant variable.
>
> I'd like to ask you the following question:
>
> I was told that, to deal with non-normality, the Inverse Hyperbolic Sine
> transformation is a better solution than the Box-Cox transformation. Is that
> true? If so, why?
>
> Also, Moffatt's Stata code implies homoscedasticity (sigma is an invariant
> parameter). Will the estimates be consistent still?
>
> I'd greatly appreciate your help.
>
> Stefano Verde
>
> *
> program define dh
> version 6
> args Inf thetal theta2 theta3 theta4
> tempvar d p z p0 pll yt
> quietly gen double 'd'= $ML_yl >0
> quietly gen double 'p'= normprob('theta3')
> quietly gen double '1'= 'theta4'
> quietly gen double 'yt'= ($MLyl^'I'-1)/'l'
> quietly gen double 'z'= ('yt'-'thetal' )/('theta2')
> quietly gen double 'pO'= 1-('p'*normprob(-'z'))
> quietly gen double 'pl' = (($ML_yl + (1-'d'))^
> ('T'-1))*'p'*normd('z')/'theta2'
> quietly replace 'lnf = ln((1-'d')*'p0+' 'd'*'pl')
> end
> ml model If dh (y = 'listy') () (d - 'listd') ()
> ml init b, copy
> ml maximize
>
> Notes: 'listy' is a previously defined list of variables
> appearing in the second hurdle; 'listd' contains the variables
> of the first hurdle. 'thetal' corresponds to xi'f# in (14),
> 'theta2' to a, 'theta3' to zi'a, and 'theta4' to .. b is a vector of
> suitable starting values.
>
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/