This notation I understand to mean 
xt    -> x at time t 
xt-1  -> x at time t - 1
x1    -> x at time 1
If so, you initialise 
gen x = z in 1 
and then you replace 
replace x = b * x[_n-1] + z in 2/l 
where I guess b is a place-holder 
for a number you know and note that 
"l" stands for "l"ast. 
The principle is given by the title
of a useful Stata Tip by Roger Newson: 
generate and replace use the current sort order. 
Stata Journal 4(4):484--485 (2004)
Nick 
[email protected] 
[email protected]
 
> I was wondering if anybody could help me to define a variable
> recursively in stata? That is, I would like define each observation x
> as the sum of a flow variable, z, and the lagged x variable,
> discounted by a factor b:
> 
> xt = zt + b*xt-1
> 
> The three first x variables would then be:
> 
> x1 = z1
> 
> x2 = z2 + b*z1
> 
> x3 = z3 + b*z2 + b^2*z1
> 
> and so on).
> 
*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/