10John Maynard Keynes, The General Theory of Employment, Interest and Money, Harcourt Brace Jovanovich, New York, 1936, p. 96.
early related to income, is an example of a mathematical model of the relationship between consumption and income that is called the consumption function in economics. A model is simply a set of mathematical equations. If the model has only one equation, as in the preceding example, it is called a single-equation model, whereas if it has more than one equation, it is known as a multiple-equation model (the latter will be considered later in the book).
In Eq. (I.3.1) the variable appearing on the left side of the equality sign is called the dependent variable and the variable(s) on the right side are called the independent, or explanatory, variable(s). Thus, in the Keynesian consumption function, Eq. (I.3.1), consumption (expenditure) is the dependent variable and income is the explanatory variable.
The purely mathematical model of the consumption function given in Eq. (I.3.1) is of limited interest to the econometrician, for it assumes that there is an exact or deterministic relationship between consumption and income. But relationships between economic variables are generally inexact. Thus, if we were to obtain data on consumption expenditure and disposable (i.e., aftertax) income of a sample of, say, 500 American families and plot these data on a graph paper with consumption expenditure on the vertical axis and disposable income on the horizontal axis, we would not expect all 500 observations to lie exactly on the straight line of Eq. (I.3.1) because, in addition to income, other variables affect consumption expenditure. For example, size of family, ages of the members in the family, family religion, etc., are likely to exert some influence on consumption.
To allow for the inexact relationships between economic variables, the econometrician would modify the deterministic consumption function (I.3.1) as follows:
where u, known as the disturbance, or error, term, is a random (stochastic) variable that has well-defined probabilistic properties. The disturbance term u may well represent all those factors that affect consumption but are not taken into account explicitly.
Equation (I.3.2) is an example of an econometric model. More technically, it is an example of a linear regression model, which is the major concern of this book. The econometric consumption function hypothesizes that the dependent variable Y (consumption) is linearly related to the explanatory variable X (income) but that the relationship between the two is not exact; it is subject to individual variation.
The econometric model of the consumption function can be depicted as shown in Figure I.2.
3. Specification of the Econometric Model of Consumption
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