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FIGURE 22.9 First differences of the logs of CPI.

(Continued)

29I am thankful to Gregory M. Ogborn and Marc C. Ogborn (West Point, Class of 2001) for collecting and analyzing the data.

864 PART FOUR: SIMULTANEOUS-EQUATION MODELS

ARCH MODEL OF THE U.S. INFLATION RATE: . . . {Continued)

Following the procedure outlined in regressions (22.10.12) and (22.10.13), we first regressed the logged first differences of CPI on a constant and obtained residuals from this equation. Squaring these residuals, we obtained the following ARCH(3) model:

U2 = 0.000052 + 0.3399U2-1 + 0.1338U2-2 + 0.0920Uf-3 t = (5.1893) (8.7270) (3.5620) (2.5387) (22.11.4)

As you can see, there is quite a bit of persistence in the volatility, as volatility in the current month depends on volatility in the preceding 3 months. The reader is advised to obtain CPI data from government sources and try to see if another model does a better job, preferably a GARCH model.

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