[Limdep Nlogit List] Plotting Confidence Intervals

[William Greene]

Dear Mikołaj: The following little routine does the sort of thing
you are looking for. You have to modify it in several ways (sample 
size, function, etc.), but as a template, it will produce the kind
of figure you are looking for.  (Note, my function is just a 
meaningless function, not an elasticity of any sort.)  This uses 
the delta method to get the standard error. If you prefer K&R, just
add ;K&R to the WALD command.
Regards,
Bill Greene

samp;1-100$
crea;x=rnu(0,1);y=rnd(2)-1$
probit;lhs=y;rhs=one,x$
matrix ; mx=x ; me=init(n,1,0);ms=me$
calc;i=0$
proc$
calc;i=i+1$
sample;i$
wald;quietly; fn1=b_one*b_x*x^2$
matrix;me(i)=waldfns(1)$
matrix;ms(i)=varwald(1)$
endproc
exec;n=100$
samp;1-100$
crea;e=me$
crea;ve=ms$
crea;eu=e+1.96*sqr(ve);el=e-1.96*sqr(ve)$
plot;lhs=x;rhs=e,eu,el;fill;Grid
;Title=Confidence Interval for Elasticity of WTP$

----- Original Message -----
From: "Mikołaj Czajkowski" <miq at wne.uw.edu.pl>
To: "Limdep and Nlogit Mailing List" <limdep at limdep.itls.usyd.edu.au>
Sent: Tuesday, September 16, 2008 8:02:01 AM GMT -05:00 US/Canada Eastern
Subject: [Limdep Nlogit List] Plotting Confidence Intervals


Dear All,

I am running a Box-Cox model to estimate elasticities of WTP which would 
vary with income. I can plot the elasticities, but I would also get the 
confidence intervals (e.g. using K&R method) plotted.


The model looks like this:

(WTP)@THETA = b2*1 + b1*(HINCOME)@LAMBDA

where:
@ is a Box-Cox transformation
LAMBDA and THETA are ML estimates for transformation parameters
WTP and HINCOME is self explanatory

After estimating the model I am able to plot the changes in elasticity 
as a function of HINCOME by either:

create; elast=b(1)*hincome^(lambda)*((b(2)+b(1)*hincome)@lambda)^(-lambda)$
plot; lhs=hincome; rhs=elast; fill$

(which uses sample-based HINCOME)

or by:

calc	; bet1=b(1)
	; bet2=b(2)$
sample; 1$
fplot; FCN=bet1*hi^(lambda)/(theta*(bet2+bet1*hi at lambda)+1); labels=hi; 
start=500; plot (hi); pts=1000; limits=100,5000$

(which simulates any hincome between the given limits).

This works ok.

However, is there a nice way to plot confidence intervals of the 
elasticities? The only thing that comes to my mind is writing a 
procedure that would use K&R technique to find 0.05 and 0.95 percentile 
of the elasticity distribution for each of the points from the income 
range. This is possible, but it is probably the long way...

I would be grateful for any ideas on how to possibly make it easier.

Thank you in advance,


-- 
     Mikołaj Czajkowski

     Warsaw Ecological Economics Center
     Warsaw University
     http://www.woee.pl/
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