The following table gives data on private fixed investment in information processing and equipment (Y, in billions of dollars), sales in total manufacturing and trade (X2, in millions of dollars), and interest rate (X3, Moody€™s Aaa corporate bond rate, percent); data on Y and X2 are seasonally adjusted.

a. Test for bilateral causality between Y and X₂, paying careful attention to the lag length.

b. Test for bilateral causality between Y and X₃, again paying careful attention to the lag length.

c. To allow for the distributed lag effect of sales on investment, suppose you decide to use the Almon lag technique. Show the estimated model, after paying due attention to the length of the lag as well as the degree of the polynomial.

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Observation Sales Observation Sales Investment Interest Investment Interest 60,827 61,159 65,662 68,995 73,682 80,283 87,187 90,820 96,685 105,690 108,221 116,895 131,081 153,677 177,912 182,198 204,150 229,513 260,320 297,701 4.41 4.35 1960 4.9 1980 1981 69.6 327,233 355,822 347,625 369,286 410,124 422,583 430,419 457,735 497,157 527,039 545,909 542,815 567,176 595,628 639,163 684,982 718,113 753,445 779,413 833,079 11.94 1961 5.2 82.4 14.17 5.7 1962 1963 4.33 4.26 1982 88.9 13.79 6.5 1983 100.8 12.04 1964 7.3 4.40 1984 121.7 12.71 1965 8.5 4.49 1985 130.8 11.37 10.6 9.02 1966 5.13 1986 137.6 1967 11.2 5.51 1987 141.9 9.38 1968 11.9 6.18 1988 155.9 9.71 7.03 173.0 1969 14.6 1989 9.26 1970 1971 16.7 8.04 1990 176.1 9.32 17.3 7.39 1991 181.4 8.77 7.21 1992 1972 19.3 197.5 8.14 215.0 7.22 1973 23.0 7.44 1993 7.96 1974 26.8 8.57 1994 233.7 1975 28.2 8.83 1995 262.0 7.59 1976 8.43 32.4 1996 287.3 7.37 1997 1998 325.2 1977 38.6 8.02 7.26 6.53 1978 48.3 8.73 367.4 1979 58.6 9.63 1999 433.0 7.04