What Is Econometrics?

1.1 What Is Econometrics?

1.2 Economic and Econometric Models

1.3 The Aims and Methodology of Econometrics

1.4 What Constitutes a Test of an Economic Theory? Summary and an Outline of the Book

1.1 What Is Econometrics?

Literally speaking, the word "econometrics" means "measurement in economics." This is too broad a definition to be of any use because most of economics is concerned with measurement. We measure our gross national product, employment, money supply, exports, imports, price indexes, and so on. What we mean by econometrics is:

The application of statistical and mathematical methods to the analysis of economic data, with a purpose of givmg empirical content to economic theories and verifying them or refuting them.

In this respect econometrics is distinguished from mathematical economics, which consists of the application of mathematics only, and the theories derived need not necessarily have an empirical content.

The application of statistical tools to economic data has a very long history. Stigler notes that the first "empirical" demand schedule was published in 1699 by Charles Davenant and that the first modern statistical demand studies were made by Rodulfo Enini, an Italian statistician, in 1907. The main impetus to the development of econometrics, however, came with the establishment of the Econometric Society in 1930 and the publication of the journal Econometrica in January 1933.

Before any statistical analysis with economic data can be done, one needs a clear mathematical formulation of the relevant economic theory. To take a very simple example, saying that the demand curve is downward sloping is not enough. We have to write the statement in mathematical form. This can be done in several ways. For instance, defining q as the quantity demanded and p as price, we can write

(7 = a + 3/7 <0

q = Ap < 0

As we will see later in the book, one of the major problems we face is the fact that economic theory is rarely informative about functional forms. We have to use statistical methods to choose the functional form, as well.

1.2 Economic and Econometric Models

The first task an econometrician faces is that of formulating an econometric model. What is a model?

A model is a simplified representation of a real-world process. For instance, saying that the quantity demanded of oranges depends on the price of oranges is a simplified representation because there are a host of other variables that one can think of that determine the demand for oranges. For instance, income of consumers, an increase in diet consciousness ("drinking coffee causes cancer, so you better switch to orange juice," etc.), an increase or decrease in the price of apples, and so on. However, there is no end to this stream of other variables. In a remote sense even the price of gasoline can affect the demand for oranges.

Many scientists have argued in favor of simplicity because simple models are easier to understand, communicate, and test empirically with data. This is the position of Karl Popper and Milton Friedman. The choice of a simple model to explain complex real-world phenomena leads to two criticisms:

G. J. Stigler, "The Early History of Empirical Studies of Consumer Behavior," The Journal of Political Economy, 1954 [reprinted in G. J. Stigler, Essays in the History of Economics (Chicago: University of Chicago Press, 1965)].

K. F. Popper, The Logic of Scientific Discovery (London: Hutchinson, 1959), p. 142.

M. Friedman, "The Methodology of Positive Economics," in Essays in Positive Economics

(Chicago: University of Chicago Press, 1953), p. 14.

1.2 ECONOMIC AND ECONOMETRIC MODELS 3

1. The model is oversimplified.

2. The assumptions are unrealistic.

For instance, in our example of the demand for oranges, to say that it depends on only the price of oranges is an oversimplification and also an unrealistic assumption. To the criticism of oversimplification, one can argue that it is better to start with a simplified model and progrsesively construct more complicated models. This is the idea expressed by Koopmans." On the other hand, there are some who argue in favor of starting with a very general model and simplifying it progressively based on the data available. The famous statistician L. J. (Jimmy) Savage used to say that "a model should be as big as an elephant." Whatever the relative merits of this alternative approach area, we will start with simple models and progressively build more complicated models.

The other criticism we have mentioned is that of "unrealistic assumptions." To this criticism Friedman argued that the assumptions of a theory are never descriptively realistic. He says:

The relevant question to ask about the "assumptions" of a theory is not whether they are descriptively "realistic" for they never are, but whether they are sufficiently good approximations for the purpose at hand. And this question can be answered by only seeing whether the theory works, which means whether it yields sufficiently accurate predictions.

Returning to our example of demand for oranges, to say that it depends only on the price of oranges is a descriptively unrealistic assumption. However, the inclusion of other variables, such as income and price of apples in the model, does not render the model more descriptively realistic. Even this model can be considered to be based on unrealistic assumptions because it leaves out many other variables (like health consciousness, etc.). But the issue is which model is more useful for predicting the demand for oranges. This issue can be decided only from the data we have and the data we can get.

In practice, we include in our model all the variables that we think are relevant for our purpose and dump the rest of the variables in a basket called "disturbance." This brings us to the distinction between an economic model and an econometric model.

An economic model is a set of assumptions that approximately describes the behavior of an economy (or a sector of an economy). An econometric model consists of the following:

1. A set of behavioral equations derived from the economic model. These equations involve some observed variables and some "disturbances" (which are a catchall for all the variables considered as irrelevant for the purpose of this model as well as all unforeseen events).

"T. C. Koopmans, Essays on the State of Economics Science (New York: McGraw-Hill, 1957), pp. 142-143.

This is the approach suggested by J. D. Sargan and notably David F. Hendry. Friedman, "Methodology," pp. 14-15.