Use the government saving and GDP data in Exercise 2.29 to calculate the ratio of government saving to GDP each year from 1990 through 2009. Then use least squares to estimate the model Y = α + βX + ε, where Y is the ratio of government saving to GDP and X is the year.

Exercise 2.29

Table 2.14 shows U.S. federal government saving and GDP (in billions of dollars).

Government saving is government income minus government expenditures; a positive value represents a budget surplus, a negative value a budget deficit. Calculate the government savings as a percentage of GDP each year and display your data in a time series graph. Write a brief paragraph summarizing your graph.

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Table 2.14: Exercise 2.29 Year Saving GDP Year Saving GDP Year Saving GDP 1960 -1.0 526.4 1977 -46.0 2,030.1 1994 -262.3 7,085.2 1961 -8.0 544.8 1978 -31.9 2,293.8 1995 -244.5 7,414.7 1962 -8.3 585.7 1979 -26.7 2,562.2 1996 -179.7 7,838.5 1963 -4.1 617.8 1980 -75.7 2,788.1 1997 -73.8 8,332.4 1964 -7.9 663.6 1981 -73.5 3,126.8 1998 27.0 8,793.5 1965 -5.2 719.1 1982 -161.3 3,253.2 1999 64.4 9,353.5 1966 -8.0 787.7 1983 -201.8 3,534.6 2000 146.6 9,951.5 1967 -21.2 832.4 1984 -190.4 3,930.9 2001 -65.1 10,286.2 1968 -12.1 1969 1.4 1970 -21.5 909.8 1985 -215.5 984.4 1,038.3 4,217.5 2002 -422.4 10,642.3 1986 -238.5 4,460.1 2003 -553.3 11,142.1 1987 -208.4 4,736.4 2004 -531.1 11,867.8 1971 -31.3 1,126.8 1988 -186.7 5,100.4 2005 -418.3 12,638.4 1972 -16.8 1,237.9 1989 -181.7 1975 1976 1973 -3.8 1974 -15.7 -86.7 -62.5 1,382.3 1,499.5 1,637.7 1992 1,824.6 1993 1990 -251.8 1991 -301.3 5,800.5 5,992.1 2008 5,482.1 2006 2007 -291.6 13,398.9 -408.1 14,061.8 -912.3 14,369.1 -373.1 6,342.4 2009 -1,592.7 14,119.0 -338.3 6,667.4 2010 -1,559.1 14,660.4