st: WTP using simulation

[Lulu Zeng <luluzengnz@gmail.com>]

Dear Statalist,

This is a subsequent question from my earlier question. I posted this
question last night but got an error message from gmail and suspect it
may have failed to reach you. But please ignore if you have already
seen it.

I was trying to work out Willingness to Pay (wtp) from the
coefficients of a random utility model. I tried to use the simulation
method, which takes draws from 2 coefficients' distribution and divide
one by another.

As one of the coefficients is associated with a log normally
distributed price variable, I had to draw firstly from a normal
distribution and -exp it to obtain the log mean and sd. However, my
model outputs are in lognormal, so I had to convert the log normally
distributed mean and sd to normal before using Stata codes to take the
draws.

I got help from Alfonso and Roger and managed to obtain the correct
draws of the log normal (confirm the mean and sd from my draws equals
my original coefficients from the model after all these log to normal
conversions).

However, my wtp calculated is in the wrong range so I suspect I may
have made some mistakes. All I did was drawing from the 2
distributions (1 log the other one normal), put the in 2 columns, and
work out the ratio (attribute divide price). I am not sure if I need
to take random numbers from each distribution and do the division? If
so, it would be really appreciated if you could advise on the Stata
code to achieve this?

Also, regarding converting log normal to normal, I used the wiki
linked from Alfonso and it worked (above cross check). But I read
about other way of doing it but gives totally different results. For
example, equation 6 on page 3 of (this looks to me more like the
formula for converting normal to log normal, which is the other way
round....): http://www.econstor.eu/bitstream/10419/76151/1/613583167.pdf

In addition, a paper by Kennth Train below shows converting log normal
to normal (table 1.1 & table 1.2 on page 8 and 9 respectively) using
this method I was questioning about above too. I replicate the figures
in table 1.2 using the method based on data from table 1.1.
http://elsa.berkeley.edu/~train/trainweeks.pdf


It would be really appreciated if I could have your help on this.


Best Regards,
Lulu
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