Table 5.10 gives annual data on the Consumer Price Index (CPI) and the Wholesale Price Index (WPI), also called Producer Price Index (PPI), for the U.S. economy for the period 1960-1999.
a. Plot the CPI on the vertical axis and the WPI on the horizontal axis. A priori, what kind of relationship do you expect between the two indexes? Why?
TABLE 5.10 CPI AND WPI, UNITED STATES, 1960-1999
|
Year
|
CPI
|
WPI
|
Year
|
CPI
|
WPI
|
|
1960
|
29.8
|
31.7
|
1980
|
86.3
|
93.8
|
|
1961
|
30.0
|
31.6
|
1981
|
94.0
|
98.8
|
|
1962
|
30.4
|
31.6
|
1982
|
97.6
|
100.5
|
|
1963
|
30.9
|
31.6
|
1983
|
101.3
|
102.3
|
|
1964
|
31.2
|
31.7
|
1984
|
105.3
|
103.5
|
|
1965
|
31.8
|
32.8
|
1985
|
109.3
|
103.6
|
|
1966
|
32.9
|
33.3
|
1986
|
110.5
|
99.70
|
|
1967
|
33.9
|
33.7
|
1987
|
115.4
|
104.2
|
|
1968
|
35.5
|
34.6
|
1988
|
120.5
|
109.0
|
|
1969
|
37.7
|
36.3
|
1989
|
126.1
|
113.0
|
|
1970
|
39.8
|
37.1
|
1990
|
133.8
|
118.7
|
|
1971
|
41.1
|
38.6
|
1991
|
137.9
|
115.9
|
|
1972
|
42.5
|
41.1
|
1992
|
141.9
|
117.6
|
|
1973
|
46.2
|
47.4
|
1993
|
145.8
|
118.6
|
|
1974
|
51.9
|
57.3
|
1994
|
149.7
|
121.9
|
|
1975
|
55.5
|
59.7
|
1995
|
153.5
|
125.7
|
|
1976
|
58.2
|
62.5
|
1996
|
158.6
|
128.8
|
|
1977
|
62.1
|
66.2
|
1997
|
161.3
|
126.7
|
|
1978
|
67.7
|
72.7
|
1998
|
163.9
|
122.7
|
|
1979
|
76.7
|
83.4
|
1999
|
168.3
|
128.0
|
Source: Economic Report of the President, 2000, pp. 373 and 379.
b. Suppose you want to predict one of these indexes on the basis of the other index. Which will you use as the regressand and which as the regressor? Why?
c. Run the regression you have decided in b. Show the standard output. Test the hypothesis that there is a one-to-one relationship between the two indexes.
d. From the residuals obtained from the regression in c, can you enter- tain the hypothesis that the true error term is normally distributed? Show the tests you use.