  # st: Re: double-bounded model

 From "Scott Merryman" To Subject st: Re: double-bounded model Date Thu, 15 Apr 2004 20:36:53 -0500

```Alejandro,

How about if rho is constrained to be close to 1?

For example:

. clear

. use http://www.stata-press.com/data/r8/school.dta

. local athrho=1/2*ln((1+.965)/(1-.965))

. constraint define 1 [athrho]_cons=`athrho'

. constraint define 2 [private]logptax=[vote]logptax

. biprobit priv vote logptax  , const(1 2) nolog

Bivariate probit regression                       Number of obs   =
95
Wald chi2(1)    =
0.30
Log likelihood = -182.59333                       Prob > chi2     =
0.5858

( 1)  [athrho]_cons = 2.01395
( 2)  [private]logptax - [vote]logptax = 0
----------------------------------------------------------------------------
--
|      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
private      |
logptax |  -.2258291   .4144413    -0.54   0.586    -1.038119
.586461
_cons |  -.0285155   2.877341    -0.01   0.992       -5.668
5.610969
-------------+--------------------------------------------------------------
--
vote         |
logptax |  -.2258291   .4144413    -0.54   0.586    -1.038119
.586461
_cons |   1.967759   2.880274     0.68   0.494    -3.677474
7.612991
-------------+--------------------------------------------------------------
--
/athrho |    2.01395          .        .       .            .
.
-------------+--------------------------------------------------------------
--
rho |       .965          .                            -1
1
----------------------------------------------------------------------------
--
Likelihood-ratio test of rho=0:     chi2(1) =  176.059    Prob > chi2 =
0.0000

----- Original Message -----
From: <feldman@primal.ucdavis.edu>
To: <statalist@hsphsun2.harvard.edu>
Sent: Thursday, April 15, 2004 3:06 PM
Subject: st: double-bounded model

> Have any of you estimated a double-bounded dichotomous
> choice model using Stata? For those not familiar with the
> concept it is a method used in contingent valuation to
> estimate willingness to pay. The log likelihood of the
> problem is similar to that of a regular probit model except
> that here you have 4 possible values for the indicator
>
> It is actually quite similar to the bivariate probit model
> but constrained to the case where b1=b2 , std1=std=2 and
> rho=1. Because of the later constraint I can't use the
> biprobit command to estimate since the likelihood function
> is not valid at rho=1.
>
> Any help will be greatly appreciated
>
> Thanks,
> Alejandro
>
>
> Alejandro Lopez-Feldman
> Ph.D. Candidate
> UC DAVIS
> Agricultural and Resource Economics

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```