# Consistent estimation of the Double Hurdle model

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## Consistent estimation of the Double Hurdle model

 This post has NOT been accepted by the mailing list yet. 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.