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Q: Solving econometric models

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  • Subject: [mg30859] Q: Solving econometric models
  • From: "Mark S. Coleman" <mcoleman at>
  • Date: Thu, 20 Sep 2001 03:52:11 -0400 (EDT)
  • Sender: owner-wri-mathgroup at


I apologize in advance for the rather vague nature of this question, 
but I am hoping that MathGroup members might be able to point me in 
the right direction. 

I am working with a number of small econometric models that I have 
estimated (using Regress) in Mathematica v4.0. The models support a number of 
out-of-sample economic forecasting applications. As part of the 
research I am conducting, I need to 'solve' these equations -- that 
is, generate projections of future economic activity. This type of  
functionality is generally a standard part of "conventional" 
statistical/econometric packages, and I am seeking to replicate this 
functionality in Mathematica.

To illustrate the problem, consider the following very simple 
two-equation model (note that I am not using Mathematica notation here):

y(t) = a + b*y(t-1) + c*x(t)
z(t) = d + e*z(t-1) + f*y(t-1)

where t denotes time, y,z, and x are variables, and {a...f} are=
numbers (say estimated using Regress). Assume that 

Assume that the models were estimated using the sample of data from 
1,...,n. The objective is to solve or forecast this model over the 
future periods n+1, n+2,...,T. Also assume that x(t) is known over 
the future periods.

In my attempts to solve this problem in Mathematica, I've created a list of 
rules (taken from the BestFit option in Regress) and then 'looped' 
over the list of future periods, one period at a time, and used the 
ReplaceAll function.

This raises a couple of questions. First, to use prior solved values, 
I've had to create a new equation to define each of the lagged 
values, y(t-1) and z(t-1). Is there a better way to handle this?

Second, can the model be written in Mathematica notation to solve over the 
entire set of future time periods without the use of an explicit

Any help would be greatly appreciated.


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