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st: Consistent estimation of the Double Hurdle model


From   verdes <verdes@tcd.ie>
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?

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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