Modeling Rational Expectations with System Dynamics
Posted: Sat Apr 05, 1997 9:17 pm
Dear Colleagues:
With respect to the question of how to represent rational expectations in SD
models -- a real nice presentation of the difference between adaptive
expectations formulations (i.e., simple smooths in SD models) and rational
expectations formulations is contained in Bill Bransons book: Macroeconomic
Theory and Policy, (Harper and Row), Third Edition, pp. 216-222.
Without getting into all of the details in this message, the difference
between the two formulations is that adpative expectations structures
generate serially correlated forecasting errors, which are considered
irrational and imply a violation of the "law of iterated expectations." Of
course, rational expectations formulations do not generate serially
correlated forecasting errors and hence do not violate the law of iterated
expectations (whether preserving the law of iterated expectations is
important or not when building an SD model is another matter).
The way to represent rational expectations in an SD model is to use a
"pipeline" information delay. Branson gives a neat example in which he shows
the overlaid time paths of the "expected price level," generated by BOTH a
rational expectations formulation and an adaptive expectations formulation,
in response to the same step (i.e., an SD step function) in the actual price
level. The adaptive expectations formulation generates the classic
goal-seeking response of an SD smooth, and the rational expectations
formulation generates the classic response of an SD pipeline delay (i.e.,
the expectations of the price level adjust perfectly (jump up) to the new
stepped-up price level after one period).
Branson provides all of the mathematical detail to support what Ive
descrived above. Be sure youve brushed up on your basic stats and
probability theory before trying to work through his presentation, however.
Hope this helps.
Peace.
Mike Radzicki
Michael J. Radzicki, Ph.D.
Associate Professor of Economics
Department of Social Science & Policy Studies
Worcester Polytechnic Institute
Worcester, Massachusetts 01609-2280
United States of America
(508) 831-5767 (Voice)
(508) 831-5896 (Fax)
mjradz@wpi.edu (Email)
and
President
Sustainable Solutions, Inc.
210 Park Avenue
Box 225
Worcester, Massachusetts 01609
United States of America
sustsol@sunspot.tiac.net (Email)
http://www.tiac.net/users/sustsol (Web)
With respect to the question of how to represent rational expectations in SD
models -- a real nice presentation of the difference between adaptive
expectations formulations (i.e., simple smooths in SD models) and rational
expectations formulations is contained in Bill Bransons book: Macroeconomic
Theory and Policy, (Harper and Row), Third Edition, pp. 216-222.
Without getting into all of the details in this message, the difference
between the two formulations is that adpative expectations structures
generate serially correlated forecasting errors, which are considered
irrational and imply a violation of the "law of iterated expectations." Of
course, rational expectations formulations do not generate serially
correlated forecasting errors and hence do not violate the law of iterated
expectations (whether preserving the law of iterated expectations is
important or not when building an SD model is another matter).
The way to represent rational expectations in an SD model is to use a
"pipeline" information delay. Branson gives a neat example in which he shows
the overlaid time paths of the "expected price level," generated by BOTH a
rational expectations formulation and an adaptive expectations formulation,
in response to the same step (i.e., an SD step function) in the actual price
level. The adaptive expectations formulation generates the classic
goal-seeking response of an SD smooth, and the rational expectations
formulation generates the classic response of an SD pipeline delay (i.e.,
the expectations of the price level adjust perfectly (jump up) to the new
stepped-up price level after one period).
Branson provides all of the mathematical detail to support what Ive
descrived above. Be sure youve brushed up on your basic stats and
probability theory before trying to work through his presentation, however.
Hope this helps.
Peace.
Mike Radzicki
Michael J. Radzicki, Ph.D.
Associate Professor of Economics
Department of Social Science & Policy Studies
Worcester Polytechnic Institute
Worcester, Massachusetts 01609-2280
United States of America
(508) 831-5767 (Voice)
(508) 831-5896 (Fax)
mjradz@wpi.edu (Email)
and
President
Sustainable Solutions, Inc.
210 Park Avenue
Box 225
Worcester, Massachusetts 01609
United States of America
sustsol@sunspot.tiac.net (Email)
http://www.tiac.net/users/sustsol (Web)