Regression: An Introduction to Econometrics
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 relationships. For example, in microeconomics one of the central concepts was demand. It is one half of the supply-demand model that economists use to explain prices, whether it is the price of stock, the exchange rate, wages, or the price of bananas. One of the fundamental rule of economics is the downward sloping demand curve - an increase in price will result in lower demand.
Knowing this, would you be in a position to decide on a pricing strategy for your product? For example, armed with the knowledge that demand is negatively related to price, do you have enough information to decide whether a price increase or decrease will raise sales revenue? You may recall from a discussion in an intro econ course that the answer depends upon the elasticity of demand, a measure of how responsive demand is to price changes.
But how do we get the elasticity of demand? In your earlier work you were just given the number and asked how this would influence your choices, while here you will be asked to figure out what the elasticity figure is. 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 that 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 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. These are problems that must be dealt with because they can produce biases in the results which reduces the reliability of the regression and increases the chance that we will not end up an understanding of the true relationship. 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 we will begin with a discussion of Specification. What equation will we estimate. Does demand depend upon price alone, or does income also matter? Is demand linearly or nonlinearly related to price? These are the types of questions that will be discussed in this section. We will then shift to Interpretation, a discussion of how to interpret the results of our regression. What if we find out that demand is negatively relate to price? Should we believe the result? And what about the times where demand turns out to be positively related to price. How could we explain this result and do we actually have proof that demand curves should be positively sloped. 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 complete 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 diagnostics to evaluate the model, and correct 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.
For an on-line overview of regression analysis you might want to check out the Mathematics 220DX Statistics at the New Hampshire College, DAU, and Stockburger sites.
You should also check out Regression, the output from an excel regression. The data on sheet simple is for years, inflation rate, unemployment rate, and interest rate appear in cells A2 - D50. Once the data set is complete, you then select Data Analysis in the Tools menu. You will then select Regression which will bring up a dialogue box. At this time you highlight the data set for the input box. The Y variable is the variable that you want to explain, in this case and it is the the interest rate. The X variable is the explainer, in this case the inflation rate. We are going to use regression to see the extent to which the inflation rate explains interest rates. You then specify the top left cell of the space where you want the output to appear. The for an interpretation of the results, you should check out the Interpretation page. In these results you find the coefficient of inflation to be .68 - every time the inflation rate rises by one percentage point, interest rates rise by nearly .7 percent. The t-statistic is 7.22 which indicates that you should believe in this relationship, and the R2 tells you that the model helps explain about one half the variation in interest rates.