say, there is a labor strike affecting output in one quarter, there is no reason to believe that this disruption will be carried over to the next quarter. That is, if output is lower this quarter, there is no reason to expect it to be lower next quarter. Similarly, if we are dealing with cross-sectional data involving the regression of family consumption expenditure on family income, the effect of an increase of one family's income on its consumption expenditure is not expected to affect the consumption expenditure of another family.
However, if there is such a dependence, we have autocorrelation. Symbolically,
In this situation, the disruption caused by a strike this quarter may very well affect output next quarter, or the increases in the consumption expenditure of one family may very well prompt another family to increase its consumption expenditure if it wants to keep up with the Joneses.
Before we find out why autocorrelation exists, it is essential to clear up some terminological questions. Although it is now a common practice to treat the terms autocorrelation and serial correlation synonymously, some authors prefer to distinguish the two terms. For example, Tintner defines autocorrelation as "lag correlation of a given series with itself, lagged by a number of time units,'' whereas he reserves the term serial correlation to "lag correlation between two different series.''3 Thus, correlation between two time series such as u1, u2,..., u10 and u2, u3,..., un, where the former is the latter series lagged by one time period, is autocorrelation, whereas correlation between time series such as u1, u2,..., u10 and v2, v3,..., v11, where u and v are two different time series, is called serial correlation. Although the distinction between the two terms may be useful, in this book we shall treat them synonymously.
Let us visualize some of the plausible patterns of auto- and nonautocor-relation, which are given in Figure 12.1. Figure 12.1a to d shows that there is a discernible pattern among the us. Figure 12.1a shows a cyclical pattern; Figure 12.1& and c suggests an upward or downward linear trend in the disturbances; whereas Figure 12.1d indicates that both linear and quadratic trend terms are present in the disturbances. Only Figure 12.1e indicates no systematic pattern, supporting the nonautocorrelation assumption of the classical linear regression model.
The natural question is: Why does serial correlation occur? There are several reasons, some of which are as follows:
Inertia. A salient feature of most economic time series is inertia, or sluggishness. As is well known, time series such as GNP, price indexes, production, employment, and unemployment exhibit (business) cycles.
3Gerhard Tintner, Econometrics, John Wiley & Sons, New York, 1965.
444 PART TWO: RELAXING THE ASSUMPTIONS OF THE CLASSICAL MODEL
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