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st: How to calculate fitted values from dynamic models


From   "Rio, Martin" <[email protected]>
To   [email protected]
Subject   st: How to calculate fitted values from dynamic models
Date   Tue, 3 Aug 2004 14:12:47 -0400

Dear Stata users,

I am trying to calculate fitted values from a very simple dynamic model, in
this case one with a lagged dependent variable. The model is:

x[t] = a*x[t-1] +b*y[t] + u[t], for t >= 1

I first create the variable 'x1' which is the lagged value of x, and then
run:

reg x x1 y

Now I want to create the fitted values from this regression. The command
'predict xhat', would simply calculate:

xhat[t]  = a*x1[t] + b*y[t]   for t >= 1, which is not dynamic. 

The equation I should be using is:

xhat[t]  = a*x1[t] + b*y[t]),   for t = 2 and
xhat[t]  = a*xhat[t-1] + b*y[t],  for t > 2

Does anyone know of a simple way of doing this in Stata? I realize I could
write a loop that calculates xhat observation by observation using the
parameters from the estimation, but that is a hassle when I have to run many
different specifications. I'm hoping Stata has a command similar to
'predict' that calculates the fitted values in simple dynamic models like
the one in this example. Any help will be appreciated.

Martin
____________________
Mart´┐Żn Rio
Charles River Associates
Washington, DC 
202.662.3957 (phone)
202.662.3910 (fax)
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