From the Deseret News today, April 30, 2013

In my last article, I talked about economics as a science and focused on the role of statistical analysis in evaluating natural experiments. This time I want to talk about economic theory.

The scientific method requires hypothesis testing. Experiments test hypotheses and ultimately prove them right or wrong. Based on this acceptance or rejection of a hypothesis, scientists go back to their original theories and revise them as needed. This is the gist of the scientific method.

But how are hypotheses created in the first place? They are derived from some underlying theory. And theory needs to be carefully constructed to generate meaningful hypotheses.

The word "theory" can mean a variety of things. Sometimes theory is quite informal and is driven mostly by intuition. "Heavy cannon balls will fall faster than light ones" is an intuitive theory, for example. It is also a testable hypothesis. Galileo is said to have performed an experiment at the Tower of Pisa that disproved this hypothesis.

Testable hypotheses do not always emerge so easily from theory, however. The commonly accepted way of constructing a theory and hypothesis is as follows. First, state a set of axioms or assumptions. These assumptions need to be realistic for the theory to have any use in describing the real world. Reasonable people can and will disagree about the validity of the assumptions, and this is OK.

Second, use tools of logic to derive a testable hypothesis. Tools of logic include the use of mathematics. So when formulating a hypothesis one could translate the assumptions into mathematics and then use the tools of mathematics to derive a hypothesis. Unlike the statement of assumptions, there should be no disagreement about this step.

Here is a quick and simple example. Assumption 1: a hot dog consists of a sausage and a bun. Assumption 2: sausages cost 50 cents each and buns cost 25 cents each. Now let's translate this into math. Let S be the price of a sausage, S = 50. Let B be the price of a bun, B = 25. These come from assumption 2. Let C be the cost of ingredients for a hot dog. By assumption 1 we get C = S + B. Using the tools of math we have, C = 50 + 25 or C = 75. Our testable hypothesis is that the ingredients used to produce one hot dog will cost 75 cents.

Notice that we could disagree about the assumptions. Maybe a proper hot dog is more than just a sausage and a bun. Maybe sausages cost more than 50 cents each. However, once we accept the assumptions, it follows incontrovertibly that the cost of ingredients is 75 cents.

This is a trivially simple example, but it's exactly what economic theory (and theory in most scientific disciplines, for that matter) actually does. It is one of the reasons that math is so important in economics. We write our assumptions in mathematical form. In many cases the hypotheses are not obvious and must be formally proved. Often we need to rely on results from various fields of mathematics in order to show that a hypothesis follows naturally from the assumptions.

Among the widely used assumptions in economics are the following: 1) Firms act to maximize their profits. This is the basis for standard economic theory of the firm. 2) Households act to maximize utility or well-being. This is the basis for consumer theory.

In both these cases, the theorist needs to define very carefully what he means by "profit" and "utility." Does profit include revenue earned in the future as well as that earned today, for example?

By carefully building up a set of assumptions and then testing the implied hypotheses against real world data, economics as a science has managed over time to build up a widely accepted set of core theories that describe the general functioning of the real economy reasonably well.

Much economic theory can be done using a pencil and paper. However, it is not uncommon for theory to generate results that depend critically on the values assumed for key components of the model. In addition, in some cases models can become very complex and deriving general results that can be tested against data may be very difficult.

In these cases, numerically simulating a model can be informative. This is the realm of computational economics, a relatively new field that has been expanding rapidly along with the rapid rise in computational capability. I will talk about computational economics in my next installment.