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Consistent estimation of the Double Hurdle model

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Consistent estimation of the Double Hurdle model

verdes
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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.



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Re: Consistent estimation of the Double Hurdle model

Tebza
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Dear statalister,

I'm using an inverse hyperbolic sine transformation to transform my net worth variable (dependent). I've tried the ml command but stata gives me an error "can't find a derivative because your data has a breaking point".
 
Could you please show me the step by step stata code.

Regards,
Paul
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