4 1 WHAT IS -»

2. A statement of whether there are errors of observation in the observed variables.

3. A specification of the probability distribution of the "disturbances" (and errors of measurement).

With these specifications we can proceed to test the empirical validity of the economic model and use it to make forecasts or use it in policy analysis.

Taking the simplest example of a demand model, the econometric model usually consists of:

1. The behavioral equation

q = a + +

where q is the quantity demanded and p the price. Here p and q are the observed variables and is a disturbance term.

2. A specification of the probability distribution of which says that E{u\p) = 0 and that the values of for the different observations are independently and normally distributed with mean zero and variance .

With these specifications one proceeds to test empirically the law of demand or the hypothesis that p < 0. One can also use the estimated demand function for prediction and policy purposes.

1.3 The Aims and Methodology of Econometrics

The aims of econometrics are:

1. Formulation of econometric models, that is, formulation of economic models in an empirically testable form. Usually, there are several ways of formulating the econometric model from an economic model because we have to choose the functional form, the specification of the stochastic structure of the variables, and so on. This part constitutes the specification aspect of the econometric work.

2. Estimation and testing of these models with observed data. This part constitutes the inference aspect of the econometric work.

3. Use of these models for prediction and policy purposes.

During the 1950s and 1960s the inference aspect received a lot of attention and the specification aspect very little. The major preoccupation of econome-tricians had been the statistical estimation of correctly specified econometric models. During the late 1940s the Cowles Foundation provided a major breakthrough in this respect, but the statistical analysis presented formidable computational problems. Thus the 1950s and 1960s were spent mostly in devising alternative estimation methods and alternative computer algorithms. Not much

1.3 THE AIMS AND METHODOLOGY OF ECONOMETRICS

Economic theory or economic model

Some prior infomiation

Econometric model or a statement of the economic theory in an empirically testable form

Data

Estimation of the model

Tests of any hypotheses suggested by the economic model

Using the model for prediction and policy

Figure 1.1. Schematic description of the steps involved in an econometric analysis of economic models.

dttention was paid to errors in the specification or to errors in observations. With the advent of high-speed computers, aJ] this has, however, changed. The estimation problems are no longer formidable and econometricians have turned attention to other aspects of econometric analysis.

We can schematically depict the various steps involved in an econometric analysis, as was done before the emphasis on specification analysis. This is hown in Figure 1.1. Since the entries in the boxes are self-explanatory, we will not elaborate on them. The only box that needs an explanation is box 4, "prior information." This refers to any information that we might have on the unknown parameters in the model. This information can come from economic theory or from previous empirical studies.

There has, however, been considerable dissatisfaction with the scheme shown in Figure 1.1. Although one can find instances of dissatisfaction earlier.

There was some work on specification errors in the early 1960s by Theil and Griliches, but this cferred to omitted-variable bias (see Chapter 4). Griliches lecture notes (unpublished) at the Lniversity of Chicago were titled "Specification Errors in Econometrics."

it was primarily during the 1970s that arguments were levied against the oneway traffic shown in Figure 1.1. We will discuss three of these arguments.

1. In Figure 1.1 there is no feedback from the econometric testing of economic theories to the formulation of economic theories (i.e., from box 6 to box 1). It has been argued that econometricians are not just handmaidens of economic theorists. It is not true that they just take the theories they are given and test them, learning nothing from the tests. So we need an arrow from box 6 to box 1.

2. The same is true regarding the data collection agencies. It is not true that they just gather whatever data they can and the econometricians use whatever data are given them. (The word data comes from the Latin word datum, which means given.) There ought to be feedback from boxes 2 and 5 to box 3.

3. Regarding box 6 itself, it has been argued that the hypothesis testing refers only to the hypotheses suggested by the original economic model. This depends on the assumption that the specification adopted in box 2 is correct. However, what we should be doing is testing the adequacy of the original specification as well. Thus we need an extra box of specification testing and diagnostic checking. There will also be feedback from this box to box 2, that is, the specification tests will result in a new specification for the econometric models. These problems, which have been one of the most important major developments in econometrics in the 1970s, are treated in Chapter 12.

The new developments that have been suggested are shown figuratively in Figure 1.2. Some of the original boxes have been deleted or condensed. The schematic description in Figure 1.2 is illustrative only and should not be interpreted literally. The important things to note are the feedback

1. From econometric results to economic theory.

2. From specification testing and diagnostic checking to revised specification of the economic model.

3. From the econometric model to data.

In the foregoing scheme we have talked of only one theory, but often there are many competing theories, and one of the main purposes of econometrics is to help in the choice among competing theories. This is the problem of model selection, which is discussed in Chapter 12.

1.4 What Constitutes a Test of an Economic Theory?

Earlier, we stated that one of the aims of econometrics was that of testing economic theories. An important question that arises is: What constitutes a test? As evidence of a successful test of economic theory, it is customary to