Use the data in Exercise 13.28.To familiarize yourself with recursive least squares, estimate the savings functions for 1970€“1981, 1970€“1985, 1970€“1990, and 1970€“1995. Comment on the stability of estimated coefficients in the savings functions.

Data from exercise 12.28

Refer to the following table, which gives data on personal savings (Y) and personal disposable income (X) for the period 1970€“2005. Now consider the following models:

How would you choose between these two models? State clearly the test procedure(s) you use and show all the calculations. Suppose someone contends that the interest rate variable belongs in the savings function. How would you test this? Collect data on the 3-month treasury bill rate as a proxy for the interest and demonstrate your answer.

Model A: Y+ + a X_1+u Model B: - + , X + Y +u, Year Savings Income 1970 69.5 735.7 1971 80.6 801.8 1972 869.1 77.2 102.7 113.6 1973 978.3 1,071.6 1,187.4 1,302.5 1,435.7 1,608.3 1,793.5 2,009.0 2,246.1 2,421.2 2,608.4 2,912.0 3,109.3 3,285.1 3,458.3 3,748.7 4,021.7 4,285.8 4,464.3 4,751.4 4,911.9 5,151.8 5,408.2 5,688.5 5,988.8 6,395.9 6,695.0 7,194.0 7,486.8 7,830.1 8,162.5 8,681.6 9,036.1 1974 1975 125.6 122.3 1976 1977 125.3 1978 142.5 1979 159.1 1980 201.4 1981 244.3 1982 270.8 1983 233.6 1984 314.8 1985 280.0 1986 268.4 1987 241.4 1988 272.9 1989 287.1 1990 299.4 1991 324.2 1992 366.0 1993 284.0 1994 249.5 1995 250.9 1996 228.4 1997 218.3 1998 276.8 1999 158.6 2000 168.5 2001 132.3 2002 184.7 2003 174.9 2004 174.3 2005 34.8