Econometric Theory/Methodology of Econometrics
How does the econometrician go ahead in analysing an economic theory? What is needed is a methodology, i.e. a step-by-step procedure. This is similar to other social sciences.
A theory should have a prediction. In statistics and econometrics, we also speak of hypothesis. One example is the marginal propensity to consume (MPC) proposed by Keynes. Other examples could be that lower taxes would increase growth, or maybe that it would increase economic inequality, and that introducing a common currency has a positive effect on trade.
Specification of the Mathematical Model
This is where the algebra enters. We need to use mathematical skills to produce an equation. Assume a theory predicting that more schooling increases the wage. In economic terms, we say that the return to schooling is positive. The equation is:
where Y is the variable for wage and is a constant and is the coefficient of schooling, and X is a measurement of schooling, i.e. the number of years in school. We also call intercept and a slope coefficient.
Normally, we would expect both and to be positive.
Specification of the Econometric Model
Here, we assume that the mathematical model is correct but we need to account for the fact that it may not be so. We add an error term, u to the equation above. It is also called a random (stochastic) variable. It represents other non-quantifiable or unknown factors that affect Y. It also represents mismeasurements that may have entered the data. The econometric equation is:
The error term is assumed to follow some sort of statistical distribution. This will be important later on.
We need data for the variables above. This can be obtained from government statistics agencies and other sources. A lot of data can also be collected on the Internet in these days. But we need to learn the art of finding appropriate data from the ever increasing huge loads of data To estimate the econometric model given in (I.3.2), that is, to obtain the numerical values of β 1 and β 2 , we need data. Although we will have more to say about the crucial importance of data for economic analysis in the next chapter, for now let us look at the data given in Table I.1, which relate to TABLE I.1 DATA ON Y (PERSONAL CONSUMPTION EXPENDITURE) AND X (GROSS DOMESTIC PRODUCT, 1982–1996), BOTH IN 1992 BILLIONS OF DOLLARS Year YX 1982 3081.5 4620.3 1983 3240.6 4803.7 1984 3407.6 5140.1 1985 3566.5 5323.5 1986 3708.7 5487.7 1987 3822.3 5649.5 1988 3972.7 5865.2 1989 4064.6 6062.0 1990 4132.2 6136.3 1991 4105.8 6079.4 1992 4219.8 6244.4 1993 4343.6 6389.6 1994 4486.0 6610.7 1995 4595.3 6742.1 1996 4714.1 6928.4 Source: Economic Report of the President, 1998, Table B–2, p. 282.
7 7000 6000 5000 GDP ( X ) 4000 3000 3500 4000 4500 PCE ( Y ) 5000 FIGURE I.3 Personal consumption expenditure ( Y ) in relation to GDP ( X ), 1982–1996, both in billions of 1992 dollars. the U.S. economy for the period 1981–1996. The Y variable in this table is the aggregate (for the economy as a whole) personal consumption expen- diture (PCE) and the X variable is gross domestic product (GDP), a measure of aggregate income, both measured in billions of 1992 dollars. Therefore, the data are in “real” terms; that is, they are measured in constant (1992) prices. The data are plotted in Figure I.3 (cf. Figure I.2). For the time being neglect the line drawn in the figure.
Estimation of the model
Here, we quantify and , i.e. we obtain numerical estimates. This is done by statistical technique called regression analysis
Now we go back to the part where we had economic theory. The prediction was that schooling is good for the wage. Does the econometric model support this hypothesis. What we do here is called statistical inference (hypothesis testing). Technically speaking, the coefficient should be greater than 0.
If the hypothesis testing was positive, i.e. the theory was concluded to be correct, we forecast the values of the wage by predicting the values of education. For example, how much would someone earn for an additional year of schooling? If the X variable is the years of schooling, the coefficient gives the answer to the question.
Use for Policy Recommendation
Lastly, if the theory seems to make sense and the econometric model was not refuted on the basis of the hypothesis test, we can go on to use the theory for policy recommendation. If your theory was really good, then maybe you will earn the Nobel Prize of Economics.