Refer to Section 8.8 and the data in the following table concerning disposable personal income and personal savings for the period 1970€“1995. In that section, the Chow test was introduced to see if a structural change occurred within the data between two time periods. Table 8.11 includes updated data containing the values from 1970€“2005.

According to the National Bureau of Economic Research, the most recent U.S. business contraction cycle ended in late 2001. Split the data into three sections:

(1) 1970€“1981, (2) 1982€“2001, and (3) 2002€“2005.

a. Estimate both the model for the full dataset (years 1970€“2005) and the third section (post-2002). Using the Chow test, determine if there is a significant break between the third period and the full dataset.

b. With this new data in Table 8.11, determine if there is still a significant difference between the first set of years (1970€“1981) and the full dataset, now that there are more observations available.

c. Perform the Chow test on the middle period (1982€“2001) versus the full dataset to see if the data in this period behave significantly differently than the rest of the data.

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Observation Observation Savings Income Savings Income 1970 61.0 727.1 1983 167.0 2522.4 1971 68.6 790.2 1984 235.7 2810.0 855.3 965.0 206.2 196.5 1972 63.6 1985 3002.0 1973 89.6 1986 3187.6 1987 1974 97.6 1054.2 168.4 3363.1 1975 1988 104.4 1159.2 189.1 3640.8 1273.0 1401.4 187.8 1976 96.4 1989 3894.5 1977 92.5 1990 208.7 4166.8 1978 112.6 1580.1 1991 246.4 4343.7 1979 130.1 1769.5 1992 272.6 4613.7 1980 161.8 1973.3 1993 214.4 4790.2 2200.2 2347.3 1981 199.1 1994 189.4 5021.7 1995 1982 205.5 249.3 5320.8