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

From   Jesper Kjr Hansen <>
To   <>
Subject   st: Est. of variance for non-linear comb. of parameters (Krinsky-Robb)
Date   Tue, 18 Jul 2006 12:14:47 +0200

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:


or do:


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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