Page 570 -

14.1 Using Regression Models for Forecasting 569

improved by adding additional predictor variables and their past values, or “lags,” as
regressors, and these so-called autoregressive distributed lag models are introduced
in Section 14.4. For example, we find that GDP forecasts made using lagged values
of the term spread, the difference between the interest rate on long-term and short-
term bonds, improve upon the autoregressive GDP forecasts. A practical issue is
deciding how many past values to include in autoregressions and autoregressive
distributed lag models, and Section 14.5 describes methods for making this decision.

The assumption that the future will be like the past is an important one in time
series regression, sufficiently so that it is given its own name: “stationarity.” Time
series variables can fail to be stationary in various ways, but two are especially rele-
vant for regression analysis of economic time series data: (1) The series can have
persistent, long-run movements—that is, the series can have trends; and (2) the
population regression can be unstable over time—that is, the population regres-
sion can have breaks. These departures from stationarity jeopardize forecasts and
inferences based on time series regression. Fortunately, there are statistical proce-
dures for detecting trends and breaks and, once detected, for adjusting the model
specification. These procedures are presented in Sections 14.6 and 14.7.

14.1 Using Regression Models for Forecasting

The empirical application of Chapters 4 through 9 focused on estimating the
causal effect on test scores of the student–teacher ratio. The simplest regression
model relates in Chapter 4 related test scores to the student–teacher ratio (STR):

TestScore = 989.9 - 2.28 * STR. (14.1)

As was discussed in Chapter 6, a school superintendent, contemplating hiring
more teachers to reduce class sizes, would not consider this equation to be very
helpful. The estimated slope coefficient in Equation (14.1) fails to provide a useful
estimate of the causal effect on test scores of the student–teacher ratio because of
probable omitted variable bias arising from the omission of school and student
characteristics that are determinants of test scores and that are correlated with the
student–teacher ratio.

In contrast, as discussed in Chapter 9, a parent who is considering moving to
a school district might find Equation (14.1) more helpful. Even though the coef-
ficient does not have a causal interpretation, the regression could help the parent
forecast test scores in a district for which they are not publicly available. More
generally, a regression model can be useful for forecasting even if none of its