## Info

470,377

354,961

1,329,722

1,921,457

4,434,093

Note: Y and Xare in millions of dollars, seasonally adjusted.

Source: Economic Report of the President, 2001, Table B-57, p. 340. The Z's are as shown in (17.13.13).

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

694 PART THREE: TOPICS IN ECONOMETRICS

EXAMPLE 17.11 (Continued)

A brief comment on the preceding results. Of the three Z variables, only Z0 is individually statistical significant at the 5 percent level, but the others are not, yet the F value is so high that we can reject the null hypothesis that collectively the Z's have no effect on Y As you can suspect, this might very well be due to multicollinearity. Also, note that the computed d value is very low. This does not necessarily mean that the residuals suffer from autocorrelation. More likely, the low dvalue suggests that the model we have used is probably mis-specified. We will comment on this shortly.

From the estimated a's given in (17.13.3), we can easily estimate the original fa's easily, as shown in (17.13.8). In the present example, the results are as follows:

fa3 = (a 0 + 3a1 + 9a2) = —0.5394 Thus, the estimated distributed-lag model corresponding to (17.13.11) is:

?t = 25,845.0 + 1.1150X0 + 0.6836Xt—1 + 0.1321 Xf—2 — se = (6596.99) (0.5381) (0.4672) (0.4656) t = (3.9177) (2.0718) (1.4630) (0.2837) Geometrically, the estimated fa, is as shown in Figure 17.8.

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