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# st: Consistent estimation of the Double Hurdle model

 From verdes To statalist@hsphsun2.harvard.edu Subject st: Consistent estimation of the Double Hurdle model Date Wed, 8 Feb 2012 02:19:34 -0800 (PST)

```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?

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.

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```