# st: RE: recursively defined variables

 From "Nick Cox" To Subject st: RE: recursively defined variables Date Thu, 15 Sep 2005 21:50:13 +0100

```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
n.j.cox@durham.ac.uk

> 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).
>

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```