All Terrain Thinking

A Compendium of things I think are Important

Statistics: It's not just whats' in your wallet

Overview

The goal in the econometric work is to help us move from the qualitative analysis in the theoretical work favored in the textbooks to the quantitative world in which policy makers operate. The focus in this work is the quantification of the economic relationships at the center of our economic theory, a measure of the strength of the causal link between two or more variables.

For example, at the heart of all microeconomic analysis of the firm's output choice is a revenue function which specifies total revenue as a function of output. You will recall that the for all firms, regardless of market structure, profit maximization can be achieved only when the firm is operating at an output level where marginal revenue equals marginal cost (MR=MC). In the textbooks this is often simply an exercise in applied mathematics where we specify revenue and cost functions and simply solve for the maximum profit level of output.

For the practitioner, however, things are a bit messier. Where does one come up with the specific cost and revenue functions that are at the heart of the theoretical analysis? It may be nice to know that the optimal condition is MR=MC, but this is of little value if we do not have the information to know the relationship between MR, MC and output for the firm or industry being analyzed. It is here that things become interesting, where we must move from the deterministic world of algebra and calculus to the probabilistic world of statistics. To make this move, a working knowledge of econometrics, a fancy name for applied statistics, is extremely valuable.

As you will see, this is not a place for the meek at heart. There are a number of valuable techniques which you will be exposed to in econometrics. You will work hard on setting up the 'right experiment' for your study, collecting the data and specifying the equation. Fortunately, this is only the beginning. There will never be that magic button that produces 'truth' at the end of some regression, the favorite econometric technique for estimating economic relationships. You can also be assured that you will not get it quite right the first time. There is, however, something to be learned from your 'mistakes'. To the trained eye, the summary statistics produced by any regression package paint a vivid, if somewhat blurred picture, of the problems with the model as specified, problems which must be dealt with because they can produce biases in the parameter estimates and thereby reduce the reliability of the regression. With existing software packages, anyone can produce regression results so one needs to be aware of the limitations of the analysis when evaluating regression results.

In this overview of econometrics, applied statistics in economics, we will begin with a discussion Specification. What equation will we estimate. We will then shift to Interpretation, a discussion of how to interpret the results of our regression. This will be followed by a discussion of the assumptions of the Classical Linear Model, all of the things that must go right if we are to have confidence in our results. And for those instances where we have some reason to believe there is a problem, we have a discussion of the Limitations of the Classical Linear Model where the potential problems as well as solutions are discussed.

When you have completed this section, you should be well aware of the fact that the estimation of 'economic relationships' has both an art and a science component. Given the technology available to people today, anyone can run regressions with the use of some magic buttons. Computer programs exist that allow us to estimate the regressions, perform some diagnostics to evaluate the model, and the procedures for correcting any problems encountered. Do not, however, be misled into thinking that your empirical work will be easy. As you will find with your own work, there is a long road of painful, time consuming work ahead of anyone who embarks on an empirical project. Furthermore, there are many places where you can take a wrong turn. This paper was designed to offer you some guidance as you make the journey, to help you know in advance the obstacles you are likely to encounter and the best way of dealing with them.

There is a second reason for spending the time studying regression analysis and conducting your own empirical project. The scientific advances are not a guarantee that we are more likely to uncover the 'truth' which we are searching for. The world is in many respects the same as it was when was prompted to write his wonderful little book entitled, How to Lie With Statistics. In the hands of an unscrupulous researcher, the modern econometric software increases the chances that someone can find the results they want. The complexities of the statistical analysis simply make it harder to find the biases in the study. Your time spent here will simply increase the chances of recognizing the biases.

 

 

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