One of the goals of this column is to try and inform the reader about how the economy works and what economists think about when studying the economy. Today this column is going to relate how economists reach conclusions. I should warn you that economics is the interweaving of thinking about the way the world works with mathematics. Lots and lots of mathematics. This article is going to refer to math used by economists but try and present it in a way that is easy (in a relative sort of way) to understand.

This interweaving of ideas and math culminates in economists creating mathematical models that predict how the economy or individuals will act given certain circumstances. Back in the 1930’s, with the great depression raging, most people did not have a high opinion of economists. In particular, they were critical of the models created by economists, saying that the models were too simplistic. No model could take into account all the variables present in a mature economic system. Milton Friedman wrote a wonderful article defending the economic models. He said that models should be judged on their predictive abilities not on how complicated they are.

A current example will help illustrate this point. Most of the apocalyptic prophecies you hear about global warming are based on computer models created by researchers. Critics of the anthropologic global warming hypothesis say that the models are too simplistic. Friedman would say it does not matter how simplistic the models are as long as they have good predictive abilities. Unfortunately, the global warming models have been horrible at predicting future weather patterns, so for now they should be ignored. Not because they are too simple, but because they do not predict accurately.

Economists are trying to understand what is happening on the margins. For example, what change is needed for that next car/orange/ipod etc. to be purchased or the next business to build a production plant. Economists do not deal in averages.

For example, if the price of an ipod dropped $20, then there are a certain number of additional people who would purchase ipods. These people are on the margin.

How do economists do margin analysis? Math. Calculus to be exact. All math points to calculus and calculus is very elegant (yes, I am a nerd) and helps people think about how things work. Calculus allows economists to determine what people on the margin are going to do when something changes. Like when the price of a product falls then the demand for that product increases.

OK, here is where it gets a bit technical. Calculus may allow you to determine the change in the slope of the model (function) you are working with. This is important because if the change is positive it means you are getting more of something when something else is changing and is negative then you are getting less. Remember price and demand. When price goes up then demand goes down. However, when price goes up supply also goes up. The first relationship is negative the second is positive. Trying to determine this positive or negative change in slope is called signing. It is possible not to be able to determine the sign and so the sign is indeterminate for the model.

Further use of calculus can help determine if the slope is changing at a faster or slower rate. Let’s call this the second sign. Examples are obviously needed.

Back to the global warming example. Scientists have been able to sign the effects of carbon dioxide on the atmosphere. The first sign is positive. This means that the next carbon dioxide molecule released in the atmosphere will make the planet warmer. The second sign is negative. This means that while the next carbon dioxide molecule will make the atmosphere warmer it will have less effect on the atmosphere than the last previous molecule released. The carbon dioxide effect is increasing at a decreasing rate.

So when you hear that an increase in the capital gains tax decreases the number of capital transactions you will know that the sign for this relationship is negative. Whether the increase will be implemented is a matter of politics.

Once you know how the research is done, you can use that knowledge to understand research in various other disciplines. They all use the same basic methodology.

Recently I heard that scientists were not able to sign the effects of water vapor on our climate. Water vapor is the most abundant greenhouse gas and whether the sign is positive or negative is very important. But hopefully you now know what to think when people talk about absolutes when it comes to global warming. When the most abundant greenhouse gas has not been signed, how can anyone be sure of anything.