[Limdep Nlogit List] confidence intervals

[Mikołaj Czajkowski]

Caroline Johanna Biehl wrote:
> Dear all, 
> I try to estimate confidence intervalls for willingsness to pay estimates of a mnl model. Is there a command in nlogit for the krisky and robb (1986)-parametric bootstrapping or anything else similar?
> Thank you very much!
> Caroline

You can get confidence intervals for WTP using the delta method with the 
wald command, e.g. like this:

matrix; 	b1=b(1:4);
		varb1=varb(1:4,1:4)$ ? where parameter 4 is monetary

wald; start=b1; var=varb1; labels=la1,la2,la3,la4; pts=10000;
	fn1=la1/-la4;
	fn2=la2/-la4;
	fn3=la3/-la4$

CALC    ; List ;
         ; WTP01_hi    = WALDFNS(1,1) + ((Sqr(VARWALD(1,1))*1.96))
         ; WTP01_lo    = WALDFNS(1,1) - ((Sqr(VARWALD(1,1))*1.96))
         ; WTP02_hi    = WALDFNS(2,1) + ((Sqr(VARWALD(2,2))*1.96))
         ; WTP02_lo    = WALDFNS(2,1) - ((Sqr(VARWALD(2,2))*1.96))
         ; WTP03_hi    = WALDFNS(3,1) + ((Sqr(VARWALD(3,3))*1.96))
         ; WTP03_lo    = WALDFNS(3,1) - ((Sqr(VARWALD(3,3))*1.96))$

The same is possible with additional ; K&R switch in the wald command. 
This will simulate draws from the structural parameters, but the upper 
and lower bounds of the confidence intervals are again derived assuming 
normal distribution (i.e. using 1.96 critical value).

Alternatively I use the following procedure to get c.i. without the 
normality assumption (however, the draws are still from multivariate 
normal):

matrix; reset$
matrix;
	B1=B(1:4);		? manipulate these matrices to get K&R for only the 
variables you want
	VARB1=VARB(1:4,1:4);	? useful to cut b and varb for big n, if the 
matrix size would exceed 50000 cells
	T2=init(10000,4,0)$	? change n for no. of trials and 4 for no. of 
variables to keep (including cost)
calc; ran(179424673);
	cont=1$

Proc
matrix; 	coef=Rndm(B1,VARB1);
		T1=coef'*{-1/coef(4)};	? adjust 4 if necessary
		T2(cont,*)=T1;
		cont=cont+1$
endproc
execute; n=10000$

create; 	a1=0;a2=0;a3=0;a4=0$
namelist; 	CIV=a1,a2,a3,a4$
create; 	CIV=T2$
dstats;	rhs=CIV;all;quantiles;normality test;matrix$

calc; list; qnt(a1,.05);
		qnt(a1,.95);
		qnt(a2,.05);
		qnt(a2,.95);
		qnt(a3,.05);
		qnt(a3,.95)$

The results of all the methods should be quite similar for most 
applications.

Best regards,

-- 
     Mikołaj Czajkowski

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