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. This analysis says that the way to understand the world is to follow a specific process of:
1. observing the world (identifying facts);2. perceiving patterns in the world (patterns connecting the facts, such as cause-and-effect, correlation, simultaneity, etc.)
3. developing testable theories which seek to explain why the facts appear to be related in the perceived pattern;
4. devising an experiment to test the accuracy, or usefulness of the theory.
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 document the connection between the variables.
5. Interpretting the results of the experiment, we draw logical conclusions about how the facts and patterns perceived interconnect and interact in the world.
6. We can then used the newly verified understanding of the world 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.
So, instead of direct experimentation in (neo-classical) 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 simplifications of the theories we develop. Thus, the economic modelling in step 4 above, is not the method we use to test our economic theories.
So what is it we, as economic modellers, 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 represenations of facts taken from the world). The results we get are the sets of numerical solutions that are outputted by the system of equations. We then interpret these numerical solutions to see if they exhibit similar or contradictory patterns to what we believe we perceive in the real world.
If the models generate useful results we can then use these results to attempt to forecast economic events, or impacts; and to develop economic policy.
Contemporary neo-classical economic models are based principly 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:
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