Zero root of one single equation

[Ulrich Glogowsky]

Hi.

I want to find the zero root of one single equation. I know how to find roots for a system of nonlinear equations. I also know the mm_root() function. But in my case, this function returns just a missing value. My code is as follows:

mata
mata clear
 function myfunc(n, k1, t1, t3, p) return(-k1+ (n/(1-p))*(((1-t1)*k1/n)^(1-p))-n*((1-t3)^(1/p-1))*(p/(1-p)))
 k1 = 52000
 t1 = 0.07
 t3 = 0.5
 p=1/(0.8+1)
 mm_root(n=., &myfunc(), 0, 1000000, 0, 1000, k1, t1, t3, p)
 n
end

So the problem seems to be that the functions evaluates to missing at some point in the algorithm. Solving the same equation in Matlab or Julia works fine, but I need to use stata here.

So I end up with two questions:
1) Did I do something wrong when applying the mm_root() function?
2) Are there any alternatives?

Thank you for your help!

[Steve Samuels]

There are two problems with your code:

1. Your lower limit for the search is n = 0 but your function contains a term in k1/n, which is undefined at n = 0. Up the lower-limit.
2. You have too few iterations. Up the value to, say, 10,000.

Note: Long-standing Statalist practice is to register with full, real names, first and last (FAQ Section 6). Please re-register; use the CONTACT US button at the bottom right of the screen. The FAQ also ask that we identify the source of contributed commands. mm_root() is a function in Ben Jann's moremata package, available via ssc.

[Steve Samuels]

Actually, it looks like 1,000 iterations was fine (I needed a higher number in some experiments with other values), Therefore th missing value was for n was due entirely to the the zero lower limit.