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14.4 Time Series Regression with Additional Predictors and the Autoregressive Distributed Lag Model 585

This conjecture is readily checked by augmenting the AR(2) model in Equation
(14.12) to include the first lag of the term spread:

GDPGRt = 0 .95 + 0 .27 GDPGRt - 1 + 0 .19 GDPGRt - 2 + 0 .44 TSpreadt - 1.
(0.49) (0.08) (0 .08) (0.18) (14.15)

The t-statistic on TSpreadt -1 is −2.43, so this term is significant at the 1% level.
The R2 of this regression is 0.16, an improvement over the AR(2) R 2 of 0.14.

The forecast of the rate of change of GDP in 2013:Q1 is obtained by substitut-
ing the 2012:Q3 and 2012:Q4 values of the GDP growth into Equation (14.15),
along with the value of the term spread in 2012:Q4 (which is 1.62); the resulting
forecast is GDPGR2013:Q1͉2012:Q4 = 2.2%, and the forecast error is −1.1%.

If one lag of the term spread is helpful for forecasting GDP growth, more lags
might be even more helpful; adding an additional lag of the term spread yields

GDPGRt = 0 .97 + 0 .24 GDPGRt - 1 + 0 .18 GDPGRt - 2
(0.47) (0.08) (0.08)

- 0 .14 TSpreadt - 1 + 0 .66 TSpreadt - 2. (14.16)
(0.43) (0.43)

The t-statistic testing the significance of the second lag of the term spread is
1.53 (p-value = 0.13), so it falls just short of statistical significance at the 10% level.
The R2 of the regression in Equation (14.16) is 0.17, a slight improvement over
0.16 for Equation (14.15). The F-statistic on all the term spread coefficients is 4.43
(p-value = 0.01), indicating that this model represents a statistically significant
improvement over the AR(2) model of Section 14.3 [Equation (14.12)]. The stan-
dard error of the regression in Equation (14.16) is 3.06, a modest improvement
over the SER of 3.11 for the AR(2).

The forecasted rate of growth for GDP in 2013:Q1 using Equation (14.16) is
computed by substituting the values of the variables into the equation. The term
spread was 1.54 in 2012:Q3 and 1.62 in 2012:Q4. The forecast value of the rate of
growth in GDP in 2013:Q1, based on Equation (14.16), is

GDPGR2013:Q1͉2012:Q4 = 0.99 + 0.24 * 0.15 + 0.18 * 2.75
- 0.14 * 1.62 + 0.66 * 1.54 = 2.3. (14.17)

The forecast error is −1.2%.

The autoregressive distributed lag model. Each model in Equations (14.15)
and (14.16) is an autoregressive distributed lag (ADL) model: autoregressive