# st: How to estimat the parameters of a Tobit model with friction using stata

 From mariam ouchen To statalist@hsphsun2.harvard.edu Subject st: How to estimat the parameters of a Tobit model with friction using stata Date Wed, 19 Aug 2009 15:16:06 +0200

```Good day  Stata-listers

I'm confronted to a problem to which i' haven't found yet a solution,
i'have to use stata to estimate  the parameters  of  a tobit model
with friction (this model is based on the limited dependant variable
(LDV) model of Tobin (1958) and Rosett (1959).

here is the model

y*t = xtβ + εt

·         yt = y*t - α1  if    y*t> α1

·          yt=0        if          α1< y*t< α2

·          yt = y*t- α2   if    y*t< α2

y*t   is the latent variable

with α1< 0 et  α2>0  and ε i.i.d, residuals of the estimation with
variance  σj². The parameters β, α1 α2 and σ are solved by maximising
a  log-likelihood function (a function i've written in the ado file)

Ln L =   ∑ ln (1/2πσj²)1/2 -∑(yjt+α1j-βjxt)²/2 σj² +

t€ψ1

∑ ln (1/2πσj²)1/2 -∑(yjt+α2j-βjxt)²/2 σj²+

t€ψ2

∑ln[Ф((α2j-βjxt)/ σj)- Ф((α2j-βjxt)/ σj)]

t€ψ3

program my tobit_lf
version 10.0
args lnf sigma alpha1 alph2 beta
quietly replace `Lnf'=
ln(1/sqrt((2*_pi*`sigma'^2))-(\$ML_y1+`alpha1'-`beta'*\$ML_y1)^2/(2*`sigma'^2)if
\$ML_y1>0
quitely replace `Lnf'=
ln(1/sqrt((2*_pi*`sigma'^2))-(\$ML_y1+`alpha2'-`beta'*\$ML_y1)^2/(2*`sigma'^2)if
\$ML_y1<0
quitely replace `Lnf'=
ln(cdf((`alpha2'-\$ML_y1*`beta')/`sigma)-cdf((`alpha'-\$ML_y1*`beta')/`sigma'))if
\$ML_y1==0
end

to obtain the result i've put

ml model lf my tobit_lf  (  yt=xt) () [ i'konw that's not accurate]

maximize

Questions

What should I put as a  dependant variable?
what should i put in the equation to estimate alpha1 and alpha2?
is there any special command in my case?

I' could get the Code in Gauss, but i'need it in stata because of the
command Ml search which helps to get the starting points automatically

If someone can give me hand to   make the right code , please don't
hesitate , this is a real emergency