st: generating dynamic panel data

[billy mairs <mairs8@hotmail.com>]

Dear reader, I am having trouble trying to create dynamic panel data in stata.

I want to generate panel data with say n=20, t=5. I want the panel data to be ar(1) and follow the form y(t) = 0.8*y(t-1) + 2*x(t) + u(t), i.e dynamic panel data. x(t) is a standard normally distributed random variable and u(t) is an error term that I can change the distribution of to assess non-normality robustness.It is important that the panels are independent.
 
This is my attempt so far: 
 
clear all
set obs 20
gen i = _n
gen y = rnormal()
expand 5
sort i
by i: gen t=_n
gen x = rnormal()
gen u = rchi2(2) 
 
and then using something like 
 
by i: replace y = 0.8*y[_n-1] + 2*x + u
 
in the hope that I have 20 independent cross sections that follow an ar(1) process. However the above method will generate missing values. Any help will be greatly appreciated. 		 	   		  
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