|The Scientific Method and Mathematical Modelling in Economics.|
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, and
b) 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
problem we face
as economists is that it is very difficult to implement
in economics, since they are not likely to be repeatable
nor to have
a controllable environment. Consider that it is not
directly experiment with government spending policy. We
to 1981 and rescind all the tax cuts enacted during the
administration to see if the deficits of the 1980's do not
develop. Nor can we return to 2008 and rescind the Bush
financial bailout and spending programs to see if the
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
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:
"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).
Copyright 2003 Philip R. Martinez and Lane
Community College. All rights
Updated Jan. 6, 2013.