# st: Re: WTP from double bounded data

 From "P. Wilner Jeanty" To statalist@hsphsun2.harvard.edu Subject st: Re: WTP from double bounded data Date Fri, 1 Feb 2008 11:45:24 -0500

```On Jan 31, 2008 5:42 PM, Henrik Andersson <henrik.andersson@vti.se> wrote:
> Dear Wilner,
>
> my ultimate goal is to estimate mean and median WTP. However, for that my code below works fine. The reason why I want to redefine my log-likelihood is to have a more direct relationship between WTP and my covariates. By replacing (\$ML_y6*`bid'+`xb') with ((`bid'-`xb'/\$c)) in my log-likelihood function I have a direct interpretation of how my covariates (x) influences my WTP (bid).
>
> I don't feel to comfortable to distribute my data at this stage. We have just started to analyze it our self and I'm only one partner in the project which means that I cannot decide on my own whether to give other access to the data.
>
> If you just want to check your code, I can recommend you to simulate data. See previous message on Stata list, http://www.stata.com/statalist/archive/2007-12/msg00121.html.
>
> Henrik

Do not bother about the data. Although your question is a bit
confusing (<is it possible to specify my log-likelihood to get b and c
directly?> you probably meant to say c and d),  it seems to me that
you are trying to get non-standardized parameter estimates, c, and an
estimate of sigma, d. Remember that relying on the cumulative standard
normal or logistic distribution to estimate a model involves
normalization of the error term, which gives rise to probabilities in
terms of parameters divided by an unknown variance. Thus, parameters
can only be estimated up to a scalar multiple, because the dependent
variable, taking on zero or one, has no scale in it.
The answer to your question is a resounding no. However, in the linear
WTP model, since the coefficient on the bid variable is an estimate of
-1/sigma and what is estimated in the model is b/sigma (normalized or
standardized parameters), you have everything you need to calculate
WTP and obtain a direct relationship between WTP and the covariates.

One clarification, for this linear model, mean WTP and median WTP are equal.

Hope this helps

> -----Ursprungligt meddelande-----
> Från: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] För P. Wilner Jeanty
> Skickat: den 31 januari 2008 16:43
> Till: statalist@hsphsun2.harvard.edu
> Ämne: st: Re: WTP from double bounded data
>
>
> > Dear all,
> >
> > I have estimated a ml logistic model on double bounded WTP data. The
> > model I have estimated is an extension of the standard logit and it
> > looks as follows:
> >
> > * ml DB ***
> >
> > capture program drop double_cv
> > program double_cv
> >         version 9.2
> >         args lnf xb bid
> >         qui replace `lnf' = ln(invlogit(\$ML_y6*`bid'+`xb')) if \$ML_y1
> > ==
> > 1
> >         qui replace `lnf' = ln(invlogit(-(\$ML_y7*`bid'+`xb'))) if
> > \$ML_y2 == 1
> >         qui replace `lnf' = ln(invlogit(-(\$ML_y6*`bid'+`xb')) - ///
> >         invlogit(-(\$ML_y5*`bid'+`xb'))) if \$ML_y3 == 1
> >         qui replace `lnf' = ln(invlogit(-(\$ML_y5*`bid'+`xb')) - ///
> >         invlogit(-(\$ML_y7*`bid'+`xb'))) if \$ML_y4 == 1 end
> >
> > ** Estiamte model **
> >
> > ml model lf double_cv (xb: q28_YY q28_NN q28_YN q28_NY = q28_dp
> > q28_p_high) (bid: q28bidca1000 q28bidY1000 q28bidN1000 = ) ml search
> > ml maximize
> >
> > **********
> >
> > Based on the model above one can then estimate mean and median WTP. As
> > an alternative to the model above, one can estiamte WTP directly. Let
> > exp(-zb) define the standard definition of the elements of the
> > log-likelihood, where z=[bid,x] refers to variables from my program
> > above, and b to the vector of parameters. Hence, this is what is
> > estimate above. To estimate WTP directly, the elements should instead
> > be
> > exp((bid-xc)/d) where c are my new parameters of interest for my
> > covariates and d is a constant to be estimated.
> >
> > I have tried to estimate my model above by replacing
> > (\$ML_y6*`bid'+`xb') with ((`bid'+`xb'/\$c)) but I get the error message
> > "Unknown function (), r(133);". One way to obtain by c-vector is to
> > estimate my model above and to calculate c=b/\$ML_yi (\$ML_yi produces a
> > single parameter for `bid'). However, that means that I have to
> > recalcualte all coefficient estiamtes. My question is therefore, is it
> > possible to specify my log-likelihood to get b and c directly.
> >
> > Thanks
> >
> > Henrik
>
> Henrick, for the model outlined above, would your ultimate goal be to calculate mean and/or median WTP and eventually Krinsky and Robb confidence interval  If so, can you send me the data for those variables in the model? The data would be for me to double-check my code.
>
>

--
P. Wilner Jeanty, Post-doctoral researcher
Dept. of Agricultural, Environmental, and Development Economics
The Ohio State University