## The Consumption Function

Suppose a person receives a salary increase of \$2000 in annual pay, and suppose that this is a "permanent" increase in the sense that the increase in salary is maintained. What will be the effect of this increase in income on the person's annual consumption expenditure?

Following such a gain in income, people usually do not rush to spend all the increase immediately. Thus, our recipient may decide to increase consumption expenditure by \$800 in the first year following the salary increase in income, by another \$600 in the next year, and by another \$400 in the following year, saving the remainder.

By the end of the third year, the person's annual consumption expenditure will be increased by \$1800. We can thus write the consumption function as

where Y is consumption expenditure and X is income.

Equation (17.1.1) shows that the effect of an increase in income of \$2000 is spread, or distributed, over a period of 3 years. Models such as (17.1.1) are therefore called distributed-lag models because the effect of a given cause (income) is spread over a number of time periods. Geometrically, the distributed-lag model (17.1.1) is shown in Figure 17.1, or alternatively, in Figure 17.2. 0 ti t2 t3 FIGURE 17.1 Example of distributed lags.

Time

Gujarati: Basic I III. Topics in Econometrics I 17. Dynamic Econometric I I © The McGraw-Hill

Econometrics, Fourth Models: Autoregressive Companies, 2004 Edition and Distributed-Lag

Models

658 PART THREE: TOPICS IN ECONOMETRICS

EXAMPLE 17.1 (Continued)

EXAMPLE 17.1 (Continued)  