The following table gives data on imports, GDP, and the Consumer Price Index (CPI) for the United States over the period 1975€“2005. You are asked to consider the following model:

ln Importst = β₁ + β₂ lnGDP_t + β₃ ln CPI_t + u_t

a. Estimate the parameters of this model using the data given in the table.

b. Do you suspect that there is multicollinearity in the data?

c. Regress: (1) ln Importst = A₁ + A₂ ln GDP_t

(2) ln Importst = B₁ + B₂ ln CPI_t

(3) ln GDPt = C₁ + C₂ ln CPI_t

On the basis of these regressions, what can you say about the nature of multicollinearity in the data?

d. Suppose there is multicollinearity in the data but β̂₂ and β̂₃ are individually significant at the 5 percent level and the overall F test is also significant. In this case should we worry about the collinearity problem?

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Year CPI GDP Imports Year CPI GDP Imports 5,995.9 6,337.7 6,657.4 7,072.2 7,397.7 7,816.9 8,304.3 8,747.0 9,268.4 9,817.0 10,128.0 10,469.6 10,960.8 11,712.5 12,455.8 1975 53.8 1,638.3 1,825.3 2,030.9 2,294.7 2,563.3 2,789.5 3,128.4 3,225.0 3,536.7 3,933.2 4,220.3 4,462.8 4,739.5 5,103.8 5,484.4 5,803.1 98185 1991 136.2 491020 56.9 1976 124228 1992 140.3 536528 151907 1977 60.6 1993 144.5 589394 1978 65.2 176002 1994 148.2 668690 749374 1979 72.6 152.4 212007 1995 1980 82.4 249750 1996 156.9 803113 1997 1998 160.5 1981 90.9 265067 876470 1982 96.5 247642 163.0 917103 268901 1983 99.6 1999 166.6 1029980 1984 103.9 332418 2000 172.2 1224408 1985 107.6 338088 2001 177.1 1145900 1986 109.6 368425 2002 179.9 1164720 2003 184.0 1987 113.6 409765 1260717 447189 188.9 1988 118.3 2004 1472926 124.0 1989 477665 2005 195.3 1677371 1990 130.7 498438