Question 3.12: To study the relationship between capacity utilization in manufacturing and inflation in the United States, we obtained the data shown bellow. In this table, Y= inflation rate as measured by the % change in GDP implicit price deflator and X= capacity utilization rate in manufacturing as measured by output as a percent of capacity for years 1960 - 2007.

a. A priori, what would you expect to be the relationship between inflation rate and capacity utilization rate? What is the economic rationale behind your expectation ?

b. Regress Y and X and present your result in the format of : se= (estimated regression coefficients from standard errors), t= (estimated t values), p value= (of computed t values)

c. Is the estimated slope coefficient statistically significant?

d. Is it statistically different from unity?

e. The natural rate of capacity utilization is defined as the rate at which Y is zero. What is this rate for the period under the study?

Year Capacity Inflation
1960 80.1 1.7
1961 77.3 1.0
1962 81.4 1.0
1963 83.5 1.3
1964 85.6 1.3
1965 89.5 1.6
1966 91.1 2.9
1967 87.2 3.1
1968 87.1 4.2
1969 86.6 5.5
1970 79.4 5.7
1971 77.9 4.4
1972 83.3 3.2
1973 87.6 6.2
1974 84.4 11.0
1975 73.5 9.1
1976 78.2 5.8
1977 82.4 6.5
1978 84.3 7.6
1979 84.2 11.3
1980 78.7 13.5
1981 77 10.3
1982 71 6.2
1983 73.5 3.2
1984 79.4 4.3
1985 78.3 3.6
1986 78.4 1.9
1987 80.9 3.6
1988 83.9 4.1
1989 83.1 4.8
1990 81.6 5.4
1991 78.3 4.2
1992 79.4 3.0
1993 80.3 3.0
1994 82.8 2.6
1995 83.1 2.8
1996 81.9 3.0
1997 83 2.3
1998 81.7 1.6
1999 80.8 2.2
2000 80.1 3.4
2001 73.9 2.8
2002 73 1.6
2003 74.2 2.3
2004 76.6 2.7
2005 78.8 3.4
2006 80.4 3.2
2007 80.1 2.8