# Re: st: RE: recursively defined variables

 From bpersson@bu.edu To statalist@hsphsun2.harvard.edu Subject Re: st: RE: recursively defined variables Date Thu, 15 Sep 2005 17:02:46 -0400

```Thanks very much!

Best
Bjorn

Quoting Nick Cox <n.j.cox@durham.ac.uk>:

```
```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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```
```

*
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```