Applied Econometrics

1. How to simulate the AR(1) model in stata 

The AR(1) model is used to check the stationary property of the series.

Consider the following AR(1) 

Yt=bY(t-1)+et 

Where, et is an iid white noise process with mean 0 and standard deviation 1.

We will simulate this regression for various values of b : 0.1, 0.5, 0.8, 0.90, 1 

The stata codes for b=1are : 

 

clear
set obs 10000
gen obs = _n
gen et=rnormal(0,1)
quietly gen yt = et in 1
quietly replace yt = 1*yt[_n-1] + et in 2/L
egen i=seq()
tset i
tsline yt

 

Paste these codes in stata and you will see a plot like this: 

 

 

 Pls keep in mind that every time you run and rerun the code, you will find a different graph. However, as we can see , the variable yt is clearly non-stationary i.e. its mean value and variance is changing over time.

 

Now let us check b=0.1

 

clear
set obs 10000
gen obs = _n
gen et=rnormal(0,1)
quietly gen yt = et in 1
quietly replace yt = 0.1*yt[_n-1] + et in 2/L
egen i=seq()
tset i
tsline yt

If you check b=0.5,0.8 and 0.9, yt would behave as a stationary series just as in the case of b=0.1.

You can check it one by one.

A series of random walks can be generated by running the following codes in stata.

clear all
set seed 123
set obs 1000
egen i = seq(), block(100)
bysort i : gen t = _n
xtset i t
gen e = .
tokenize "1.0 0.5"
forval j = 1/2 {
       qui replace e = rnormal()
       gen y`j'= 0 if t == 1
       replace y`j' = ``j'' * L.y`j' + e if t > 1
}

line y1 t if _n < 1000, c(L) scheme(s1color)

 

 This will produce a group of series like below:

 

 

  You can also download the do file here

Download STATA 12 from here
Download data and do files from here.