st: Generating a bounded AR(1) series for Monte-Carlo Simulation

[Paddy Carter <Paddy.Carter@bristol.ac.uk>]

Dear Statalisters

I have a puzzle, concerning a section of a program intended to generate an 
AR(1) series for `aid' that is bounded between 0 and 0.3

Prior to this section of the program, I have already generated countries, 
time (and xtset the data) and a variable `aid' consisting of random draws 
from a uniform distribution on [0,0.3]  - all but the first observation of 
which for each country, I wish to replace, using the following code:

if year>1 {
        if  L.aid<0  {
           replace aid=const+`rho'*L.aid+rnormal(0.1,0.01)
                   }
        else if L.aid>0.3 {
           replace aid=const+`rho'*L.aid+rnormal(-0.1,0.01)
                   }
        else {	
	    replace aid=const+`rho'*L.aid+(rnormal()/100)
                   }

           }

I expect this code to do the following: whenever aid wanders beyond the 
bounds 0 and 0.3, the shock in the next period is set to bounce it away 
from these bounds. Hence I would expect to see observations of aid that do 
stray beyond 0 and 0.3 but which bounce back in the subsequent period. My 
puzzle is that when I run this code with large T, the aid series never 
strays beyond bounds. By my understanding, that shouldn't be happening.

I would actually like to write a program such that aid never strays beyond 
bounds, but I didn't know how to; I appear to have done so inadvertently, 
but the fact I don't understand what it's doing makes me fear I've gone 
totally wrong.

I apologise if I'm missing something obvious; this is my first ever attempt 
at programming.

This is on Stata/IC 10.1 for Windows

----------------------
Paddy Carter
Department of Economics
University of Bristol
paddy.carter@bristol.ac.uk
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