# Re: st: Est. of variance for non-linear comb. of parameters (Krinsky-Robb)

 From "Arne Risa Hole" To statalist@hsphsun2.harvard.edu Subject Re: st: Est. of variance for non-linear comb. of parameters (Krinsky-Robb) Date Tue, 18 Jul 2006 11:54:09 +0100

```Hi Jesper

You can calculate the bootstrap variances (and CIs) of your WTP
measures by runnning the following command:

bootstrap (-_b[H1]/_b[H5]) (-_b[H2]/_b[H5]) (-_b[H3_varm]/_b[H5]) ///
(-_b[H3_kold]/_b[H5]) (-_b[H4]/_b[H5]) (-_b[_cons]/_b[H5]), ///
reps(1000): xtlogit  choice H1 H2 H3_varm H3_kold H4 H5, re

I have written a Stata module that calculates Krinsky Robb CIs for WTP
measures which should be straightforward to tweak into calculating the
variance as well. I will send this to you off-list.

Best wishes
Arne

On 18/07/06, Jesper Kjær Hansen <kjaer.hansen@oncable.dk> wrote:
```
```Would anyone on the list be kind enough to give me advice on how
to implement the procedure for estimation of variance for non-
linear combinations of parameter estimates (e.g. elasticities),
as described by Krinsky & Robb (1986), in Stata?

I use data from a Discrete Choice Expmeriment to estimate a
choice model with xtlogit, i.e.

-xtlogit choice H1 H2 H3_varm H3_kold H4 H5, re-

where H* are the attributes describing the choice situation.
Afterwards, I calculate Willingness-to-Pay measures, e.g.

(WTP_H4: - _b[H4]/_b[H5])
where H5 is the price attribute.

I would like to estimate the variance of WTP using the
(simulation) method proposed by Krinsky-Robb or alternatively
another simulation method (for example, I know how to bootstrap
the original parameter estimates, but is it possible to obtain
bootstrap estimates of var(WTP)?).

I know that I can obtain a very neat output with WTP's and
variance estimates, using -nlcom-, which uses the delta method
for estimating variance estimates. I have already done that. I
would like to compare the various variance estimates obtained,
which is why I'm trying to implement alternative methods.

-- J. K. Hansen

For an example, see:

view http://www.nat.sdu.dk/users/nat-sdu/jkha01/data/jorgen.txt

or do:

do http://www.nat.sdu.dk/users/nat-sdu/jkha01/data/jorgen.do

Reference:
Krinsky, Itzhak & A. Leslie Robb (1986), "On Approximating the
Statistical Properties of Elasticities", The Review of Economics
and Statistics, MIT Press, vol. 68(4), pages 715-19, November.

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```
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```