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st: Re: Re: Monte Carlo Simulation for Heteroskedastic Tobit Model

From   "Martin Weiss" <>
To   <>
Subject   st: Re: Re: Monte Carlo Simulation for Heteroskedastic Tobit Model
Date   Thu, 16 Apr 2009 23:46:37 +0200


On the second point:, lines 41 to 50 contains the modelling strategy for heteroscedastic errors...

----- Original Message ----- From: "Sachin Chintawar" <>
To: <>
Sent: Thursday, April 16, 2009 11:41 PM
Subject: st: Re: Monte Carlo Simulation for Heteroskedastic Tobit Model

Dear all
Thank you Martin & other statalist users

Well I did find the book very helpful. Find a program that I have been
able to now develop. But has a few problems
clear all

quietly set obs 30
global numobs 100             // sample size N
global numsims "1000"         // number of simulations
set seed 678643594

program tobit, rclass
version 10.1
drop _all
set obs $numobs
scalar a = 0
scalar b = 12
scalar mu = 5
scalar sigma = 4
generate u= runiform()
generate y=normal((a-mu)/sigma)+u*(normal((b-mu)/sigma)-normal((a-mu)/sigma))
generate ytrunc = mu + sigma*invnorm(y)
generate x = rnormal()

regress ytrunc x
return scalar b2 = _b[x]
return scalar se2 = _se[x]
return scalar t2 = (_b[x]-2)/_se[x]
return scalar r2 = abs(return(t2))> invttail($numobs-2,.025)
return scalar p2 = 2*ttail($numobs-2,abs(return(t2)))

simulate b2r=r(b2) se2r=r(se2) t2r=r(t2) reject2r=r(r2) p2r=r(p2), ///
reps($numsims): tobit
mean b2r se2r reject2r

My Questions now are:
1. Since I had generated 'ytrunc' as a truncated normal distribution,
then to know the bias I cannot tell stata to generate 'ytrunc' based
on a equation such as
        y = b1 + b2*x + u
    where b1 and b2 are specified. But if I do this then y goes to
having a normal distribution and not a truncated normal distribution.

2. Another problem is to develop a heteroskedastic error term. Can I
develop that using
          generate u= runiform() * c*z_factor

            Where c is a constant varying from 0.1 to 1.0 and the
z_factor changes for each 'i' - then how do I define the z_factor?

I would greatly appreciate any pointers that you could provide me in this regard

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