       Q: Solving econometric models

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

```Greetings:

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=
real
numbers (say estimated using Regress). Assume that
t=1,...,n,n+1,n+2,...,T.

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
loop?

Any help would be greatly appreciated.

-Mark

```

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