The Scientific
Method and Mathematical Modelling in
Economics. |

** Alfred
Marshall**

developed the graphical models of Supply and Demand

__The
Scientific Method__

The basic structure of analysis in Western academics is the scientific method. The scientific method is the only logical system we can use to prove the truth of our explanations about the world. This analysis says that the way to understand the world is to follow a specific process of:

1. observing the world (identifying facts);2. identifying patterns in the world (patterns connecting the facts, such as cause-and-effect, correlation, simultaneity, etc.);

3. developing testable hypotheses which seek to explain why the facts appear to be related in the identified pattern;

4. devising an experiment to test the accuracy, or usefulness of the hypothesis.

To be able to draw logical conclusions from the experiment it must meet 2 criteria:

a) It must be repeatable, andb) it must have a controlled environment in order to verify the connection between the variables.

5. Interpreting the results of the experiment, we determine of the experiments supported or disproved the hypothesis. We draw logical conclusions about how the facts and patterns interconnect and interact in the world. If the hypothesis is dis-proven, we seek to develop and test new hypotheses to explain the perceived patterns. If the hypothesis is verified and accepted as the best performing hypothesis it is called a

theory.

6. We can then use the newly verified understanding of the world (the theory) to try to forecast possible logical developments and to develop policies or methods to use to achieve some goal.

__Experimentation
in
Economics__

The
problem we face
as economists is that it is very difficult to implement
experiments
in economics, since they are not likely to be repeatable
nor to have
a controllable environment. Consider that it is not
possible to
directly experiment with government spending policy. We
cannot return
to 1981 and rescind all the tax cuts enacted during the
Reagan
administration to see if the deficits of the 1980's do not
develop. Nor can we return to 2008 and rescind the Bush
& Obama
financial bailout and spending programs to see if the
Great Recession
would have been worse without these programs.

So, instead of direct experimentation in (Neoclassical) economics we use mathematical models (systems of equations which represent different aspects of the patterns which we believe we perceive in the world). The models are both simplifications of the actual conditions in the world, and often simplifications of the hypotheses we develop. Thus, the economic modeling in step 4 above, is an alternative method we use to test our economic theories, when we cannot do direct experimentation.

So what is it we,
as economic modelers, actually do?

We devise systems of equations which represent relationships, or potential relationships, between events or facts in the world. We test these models by inputting data (sets of numbers that are measures of facts or representations of facts taken from the world). The results we get are the sets of numerical solutions that are generated by the system of equations. We then interpret these numerical solutions to see if they exhibit similar or contradictory patterns to those that we identified in the real world.

If the models
generate consistent, useful results then we can conclude
that the models are providing evidence that our hypothesis
is verified. We can then use these results ( and the
verified hypothesis) to attempt to
forecast economic events, or impacts; and to develop
economic policy.

__The Construction
of Economic Models__

When we analyze the
usefulness of economic models, we are primarily concerned
with how well they explain economic processes and
relationships. In order for an economic model to be useful
it should represent the actual relationships between
economic behaviors and events as accurately as possible.
In other words, the model should be plausible. We can
refer to such a model as "*valid*".

For example, here a
plausible or valid model of consumer behavior:

When the price of a good rises consumers respond by buying fewer units of that good.

This is a valid model because it conforms closely to
actual patterns that we see in economic transactions. A
bad or implausible or less valid model would be:

When the price of a good rises consumers respond by buying more units of the good.

This would not be a
plausible or valid model, because in actual transactions
we never, or at best rarely, see this pattern.

Well constructed models
will also be evaluated based upon the *assumptions*
that the model makes about the context or environment that
the model operates in. A model that makes assumptions that
closely reflect the actual economic environment or
economic context that occurs is a better or a more *sound*
model than one that assumes an unusual context.

For example, if we are
evaluating a model for a tax cut policy that claims that a
tax cut will reduce the national debt because it assumes
the the growth rate will be above 6% for 10 years, we
would conclude that this is an unsound model, because we
know that the long run average growth rate for the US is
3% per year, and we have never generated anything close to
10 years of growth above 3% per year.

In other words, we
evaluate the usefulness of models based upon:

the accuracy of their predictions,

the validity of their arguments,

and the soundness of their assumptions.

Contemporary Neoclassical economic models are based principally on Algebra, Calculus, and Statistics. At the undergraduate level, these are all easily represented in two-dimensional graphs.

Some of the economic models we will study this year are:

- The Production Possibility Curve - in Econ 200
- Supply and Demand Curves - in Econ 200
- The Utility Curve - in Econ 201
- Indifference Curves - in Econ 201
- The Production Curve - in Econ 201
- Cost Curves - in Econ 201
- The Circular Flow of Expenditures - in Econ 200 & 202
- The Keynesian Income-Expenditure Model - in Econ 202
- Aggregate Demand and Aggregate Supply - in Econ 202

Limitations
of Mathematical Modeling in Economics

While mathematical modelling is both useful and in many cases necessary to evaluate economic theories and their policy implications, they also have shortcomings. The problems of modeling arise because they are simplifications (or translations) of real world events and phenomena into perfectly precise and perfectly logical mathematical relationships. In most circumstances real world human behavior is far more complex than the mathematical models that we use to represent those behaviors.

The easiest example of this kind of error in our models is the treatment of human motivation. In all of our neoclassical economic models we reduce all human motivation to the assumption that all human behavior is motivated by the pursuit of maximum pleasure in all situations. But this model of human decision-making is easily refuted by a multitude of studies in cognitive psychological, social psychology, and behavioral economics.

Consequently, many of our models do not adequately reflect real world conditions enough to have strong implications in the real world. Rather, they often better reflect the results of a an ideal or a utopian economy.

This problem is made worse when economists, policymakers, and the general public do not understand or acknowledge this limitation. When people insist that a theoretical result MUST also occur in the real world they are usually confusing the theoretical, perfect world with our actual real world. This can then be the source of extraordinarily poor policy decisions.

This problem has been well known for quite a long time. Consider some of the comments below.

While mathematical modelling is both useful and in many cases necessary to evaluate economic theories and their policy implications, they also have shortcomings. The problems of modeling arise because they are simplifications (or translations) of real world events and phenomena into perfectly precise and perfectly logical mathematical relationships. In most circumstances real world human behavior is far more complex than the mathematical models that we use to represent those behaviors.

The easiest example of this kind of error in our models is the treatment of human motivation. In all of our neoclassical economic models we reduce all human motivation to the assumption that all human behavior is motivated by the pursuit of maximum pleasure in all situations. But this model of human decision-making is easily refuted by a multitude of studies in cognitive psychological, social psychology, and behavioral economics.

Consequently, many of our models do not adequately reflect real world conditions enough to have strong implications in the real world. Rather, they often better reflect the results of a an ideal or a utopian economy.

This problem is made worse when economists, policymakers, and the general public do not understand or acknowledge this limitation. When people insist that a theoretical result MUST also occur in the real world they are usually confusing the theoretical, perfect world with our actual real world. This can then be the source of extraordinarily poor policy decisions.

This problem has been well known for quite a long time. Consider some of the comments below.

“To confuse the
model with the world is to embrace a future
disaster driven by the belief that humans obey
mathematical rules.”

Emmanuel Derman, Models, in Financial
Analysts Journal, Jan./Feb. 2009,

Emmanuel Derman is a physicist who became a managing director at Goldman Sachs, a quantitative analyst whose name is on a few financial models. He is the author of “My Life as a Quant — Reflections on Physics and Finance” (Wiley, 2004) and "Models. Behaving. Badly. Why Confusing Illusion with Reality Can Lead to Disaster on Wall Street and in Life" (Free Press, 2011).

Emmanuel Derman is a physicist who became a managing director at Goldman Sachs, a quantitative analyst whose name is on a few financial models. He is the author of “My Life as a Quant — Reflections on Physics and Finance” (Wiley, 2004) and "Models. Behaving. Badly. Why Confusing Illusion with Reality Can Lead to Disaster on Wall Street and in Life" (Free Press, 2011).

*"Too large a
proportion of recent "mathematical" economics are mere
concoctions, as
imprecise as the initial assumptions they rest on, which
allow the
author to lose sight of the complexities and
interdependencies of the
real world in a maze of pretentious and unhelpful
symbols."*

John
Maynard Keynes, __The
General Theory__, page 298, (1936).

"Given
what we know about cognitive psychology,
utility maximization is a ludicrous concept; equilibrium
pretty foolish
outside of financial markets; perfect competition a howler for
most
industries.
The reason for making these assumptions is not that they are
reasonable
but that they seem to help us produce models that are helpful
metaphors
for things that we think happen in the real world."

How I Work, 37
American Economist 25 (1993)

Paul
Krugman, PhD

Nobel Prize Economics,
2008

Prof.
of Economics & Int'l Affairs, Princeton
University

The Modelers' Hippocratic Oath

~ I will remember that I didn't make the
world, and it doesn't satisfy my equations.

~ Though I will use models boldly to estimate value, I will not be overly impressed by mathematics.

~ I will never sacrifice reality for elegance without explaining why I have done so.

~ Nor will I give the people who use my model false comfort about its accuracy.

Instead, I will make explicit its assumptions and oversights.

~ I understand that my work may have enormous effects on society and the economy,

many of them beyond my comprehension.

~ Though I will use models boldly to estimate value, I will not be overly impressed by mathematics.

~ I will never sacrifice reality for elegance without explaining why I have done so.

~ Nor will I give the people who use my model false comfort about its accuracy.

Instead, I will make explicit its assumptions and oversights.

~ I understand that my work may have enormous effects on society and the economy,

many of them beyond my comprehension.

Emanuel Derman and Paul
Wilmott

January 7, 2009

January 7, 2009

Copyright 2003 Philip R. Martinez and Lane
Community College. All rights
reserved.

Updated Jan. 6, 2013.