4. Real interest rates. The Excel spreadsheet PS1-data.xls provides data on the

Question

4. Real interest rates. The Excel spreadsheet PS1-data.xls provides data on the monthly Federal Funds rate and the CPI for all urban consumers from 1970:1 to 2010:11. (a) Compute the monthly inflation rate for each month from 1970:2 to 2010:11. For each month, express the inflation rate as a percent change at annual rate. Note that this inflation rate (quoted at an annual rate) is in the same units as the Federal Funds rate, i.e., percent per year. (b) Compute the ex post real interest rate for each month, i.e., the nominal interest rate each month minus the inflation rate (annual rate) for that month. Plot this data series (i.e., plot the real interest rate). (c) What is the real interest rate currently? How does it compare to other periods late in recession or early in recoveries. (The troughs of the last recessions were Nov 1979, Mar 1975, July 1980, Nov 1982, Mar 1991, and Nov 2001.) Excel CPIU FEDFUNDS 1970:01 37.900 8.98 1970:02 38.100 8.98 1970:03 38.300 7.76 1970:04 38.500 8.10 1970:05 38.600 7.94 1970:06 38.800 7.60 1970:07 38.900 7.21 1970:08 39.000 6.61 1970:09 39.200 6.29 1970:10 39.400 6.20 1970:11 39.600 5.60 1970:12 39.800 4.90 1971:01 39.900 4.14 1971:02 39.900 3.72 1971:03 40.000 3.71 1971:04 40.100 4.15 1971:05 40.300 4.63 1971:06 40.500 4.91 1971:07 40.600 5.31 1971:08 40.700 5.56 1971:09 40.800 5.55 1971:10 40.900 5.20 1971:11 41.000 4.91 1971:12 41.100 4.14 1972:01 41.200 3.50 1972:02 41.400 3.29 1972:03 41.400 3.83 1972:04 41.500 4.17 1972:05 41.600 4.27 1972:06 41.700 4.46 1972:07 41.800 4.55 1972:08 41.900 4.80 1972:09 42.100 4.87 1972:10 42.200 5.04 1972:11 42.400 5.06 1972:12 42.500 5.33 1973:01 42.700 5.94 1973:02 43.000 6.58 1973:03 43.400 7.09 1973:04 43.700 7.12 1973:05 43.900 7.84 1973:06 44.200 8.49 1973:07 44.200 10.40 1973:08 45.000 10.50 1973:09 45.200 10.78 1973:10 45.600 10.01 1973:11 45.900 10.03 1973:12 46.300 9.95 1974:01 46.800 9.65 1974:02 47.300 8.97 1974:03 47.800 9.35 1974:04 48.100 10.51 1974:05 48.600 11.31 1974:06 49.000 11.93 1974:07 49.300 12.92 1974:08 49.900 12.01 1974:09 50.600 11.34 1974:10 51.000 10.06 1974:11 51.500 9.45 1974:12 51.900 8.53 1975:01 52.300 7.13 1975:02 52.600 6.24 1975:03 52.800 5.54 1975:04 53.000 5.49 1975:05 53.100 5.22 1975:06 53.500 5.55 1975:07 54.000 6.10 1975:08 54.200 6.14 1975:09 54.600 6.24 1975:10 54.900 5.82 1975:11 55.300 5.22 1975:12 55.600 5.20 1976:01 55.800 4.87 1976:02 55.900 4.77 1976:03 56.000 4.84 1976:04 56.100 4.82 1976:05 56.400 5.29 1976:06 56.700 5.48 1976:07 57.000 5.31 1976:08 57.300 5.29 1976:09 57.600 5.25 1976:10 57.900 5.02 1976:11 58.100 4.95 1976:12 58.400 4.65 1977:01 58.700 4.61 1977:02 59.300 4.68 1977:03 59.600 4.69 1977:04 60.000 4.73 1977:05 60.200 5.35 1977:06 60.500 5.39 1977:07 60.800 5.42 1977:08 61.100 5.90 1977:09 61.300 6.14 1977:10 61.600 6.47 1977:11 62.000 6.51 1977:12 62.300 6.56 1978:01 62.700 6.70 1978:02 63.000 6.78 1978:03 63.400 6.79 1978:04 63.900 6.89 1978:05 64.500 7.36 1978:06 65.000 7.60 1978:07 65.500 7.81 1978:08 65.900 8.04 1978:09 66.500 8.45 1978:10 67.100 8.96 1978:11 67.500 9.76 1978:12 67.900 10.03 1979:01 68.500 10.07 1979:02 69.200 10.06 1979:03 69.900 10.09 1979:04 70.600 10.01 1979:05 71.400 10.24 1979:06 72.200 10.29 1979:07 73.000 10.47 1979:08 73.700 10.94 1979:09 74.400 11.43 1979:10 75.200 13.77 1979:11 76.000 13.18 1979:12 76.900 13.78 1980:01 78.000 13.82 1980:02 79.000 14.13 1980:03 80.100 17.19 1980:04 80.900 17.61 1980:05 81.700 10.98 1980:06 82.500 9.47 1980:07 82.600 9.03 1980:08 83.200 9.61 1980:09 83.900 10.87 1980:10 84.700 12.81 1980:11 85.600 15.85 1980:12 86.400 18.90 1981:01 87.200 19.08 1981:02 88.000 15.93 1981:03 88.600 14.70 1981:04 89.100 15.72 1981:05 89.700 18.52 1981:06 90.500 19.10 1981:07 91.500 19.04 1981:08 92.200 17.82 1981:09 93.100 15.87 1981:10 93.400 15.08 1981:11 93.800 13.31 1981:12 94.100 12.37 1982:01 94.400 13.22 1982:02 94.700 14.78 1982:03 94.700 14.68 1982:04 95.000 14.94 1982:05 95.900 14.45 1982:06 97.000 14.15 1982:07 97.500 12.59 1982:08 97.700 10.12 1982:09 97.700 10.31 1982:10 98.100 9.71 1982:11 98.000 9.20 1982:12 97.700 8.95 1983:01 97.900 8.68 1983:02 98.000 8.51 1983:03 98.100 8.77 1983:04 98.800 8.80 1983:05 99.200 8.63 1983:06 99.400 8.98 1983:07 99.800 9.37 1983:08 100.100 9.56 1983:09 100.400 9.45 1983:10 100.800 9.48 1983:11 101.100 9.34 1983:12 101.400 9.47 1984:01 102.100 9.56 1984:02 102.600 9.59 1984:03 102.900 9.91 1984:04 103.300 10.29 1984:05 103.500 10.32 1984:06 103.700 11.06 1984:07 104.100 11.23 1984:08 104.400 11.64 1984:09 104.700 11.30 1984:10 105.100 9.99 1984:11 105.300 9.43 1984:12 105.500 8.38 1985:01 105.700 8.35 1985:02 106.300 8.50 1985:03 106.800 8.58 1985:04 107.000 8.27 1985:05 107.200 7.97 1985:06 107.500 7.53 1985:07 107.700 7.88 1985:08 107.900 7.90 1985:09 108.100 7.92 1985:10 108.500 7.99 1985:11 109.000 8.05 1985:12 109.500 8.27 1986:01 109.900 8.14 1986:02 109.700 7.86 1986:03 109.100 7.48 1986:04 108.700 6.99 1986:05 109.000 6.85 1986:06 109.400 6.92 1986:07 109.500 6.56 1986:08 109.600 6.17 1986:09 110.000 5.89 1986:10 110.200 5.85 1986:11 110.400 6.04 1986:12 110.800 6.91 1987:01 111.400 6.43 1987:02 111.800 6.10 1987:03 112.200 6.13 1987:04 112.700 6.37 1987:05 113.000 6.85 1987:06 113.500 6.73 1987:07 113.800 6.58 1987:08 114.300 6.73 1987:09 114.700 7.22 1987:10 115.000 7.29 1987:11 115.400 6.69 1987:12 115.600 6.77 1988:01 116.000 6.83 1988:02 116.200 6.58 1988:03 116.500 6.58 1988:04 117.200 6.87 1988:05 117.500 7.09 1988:06 118.000 7.51 1988:07 118.500 7.75 1988:08 119.000 8.01 1988:09 119.500 8.19 1988:10 119.900 8.30 1988:11 120.300 8.35 1988:12 120.700 8.76 1989:01 121.200 9.12 1989:02 121.600 9.36 1989:03 122.200 9.85 1989:04 123.100 9.84 1989:05 123.700 9.81 1989:06 124.100 9.53 1989:07 124.500 9.24 1989:08 124.500 8.99 1989:09 124.800 9.02 1989:10 125.400 8.84 1989:11 125.900 8.55 1989:12 126.300 8.45 1990:01 127.500 8.23 1990:02 128.000 8.24 1990:03 128.600 8.28 1990:04 128.900 8.26 1990:05 129.100 8.18 1990:06 129.900 8.29 1990:07 130.500 8.15 1990:08 131.600 8.13 1990:09 132.500 8.20 1990:10 133.400 8.11 1990:11 133.700 7.81 1990:12 134.200 7.31 1991:01 134.700 6.91 1991:02 134.800 6.25 1991:03 134.800 6.12 1991:04 135.100 5.91 1991:05 135.600 5.78 1991:06 136.000 5.90 1991:07 136.200 5.82 1991:08 136.600 5.66 1991:09 137.000 5.45 1991:10 137.200 5.21 1991:11 137.800 4.81 1991:12 138.200 4.43 1992:01 138.300 4.03 1992:02 138.600 4.06 1992:03 139.100 3.98 1992:04 139.400 3.73 1992:05 139.700 3.82 1992:06 140.100 3.76 1992:07 140.500 3.25 1992:08 140.800 3.30 1992:09 141.100 3.22 1992:10 141.700 3.10 1992:11 142.100 3.09 1992:12 142.300 2.92 1993:01 142.800 3.02 1993:02 143.100 3.03 1993:03 143.300 3.07 1993:04 143.800 2.96 1993:05 144.200 3.00 1993:06 144.300 3.04 1993:07 144.500 3.06 1993:08 144.800 3.03 1993:09 145.000 3.09 1993:10 145.600 2.99 1993:11 146.000 3.02 1993:12 146.300 2.96 1994:01 146.300 3.05 1994:02 146.700 3.25 1994:03 147.100 3.34 1994:04 147.200 3.56 1994:05 147.500 4.01 1994:06 147.900 4.25 1994:07 148.400 4.26 1994:08 149.000 4.47 1994:09 149.300 4.73 1994:10 149.400 4.76 1994:11 149.800 5.29 1994:12 150.100 5.45 1995:01 150.500 5.53 1995:02 150.900 5.92 1995:03 151.200 5.98 1995:04 151.800 6.05 1995:05 152.100 6.01 1995:06 152.400 6.00 1995:07 152.600 5.85 1995:08 152.900 5.74 1995:09 153.100 5.80 1995:10 153.500 5.76 1995:11 153.700 5.80 1995:12 153.900 5.60 1996:01 154.700 5.56 1996:02 155.000 5.22 1996:03 155.500 5.31 1996:04 156.100 5.22 1996:05 156.400 5.24 1996:06 156.700 5.27 1996:07 157.000 5.40 1996:08 157.200 5.22 1996:09 157.700 5.30 1996:10 158.200 5.24 1996:11 158.700 5.31 1996:12 159.100 5.29 1997:01 159.400 5.25 1997:02 159.700 5.19 1997:03 159.800 5.39 1997:04 159.900 5.51 1997:05 159.900 5.50 1997:06 160.200 5.56 1997:07 160.400 5.52 1997:08 160.800 5.54 1997:09 161.200 5.54 1997:10 161.500 5.50 1997:11 161.700 5.52 1997:12 161.800 5.50 1998:01 162.000 5.56 1998:02 162.000 5.51 1998:03 162.000 5.49 1998:04 162.200 5.45 1998:05 162.600 5.49 1998:06 162.800 5.56 1998:07 163.200 5.54 1998:08 163.400 5.55 1998:09 163.500 5.51 1998:10 163.900 5.07 1998:11 164.100 4.83 1998:12 164.400 4.68 1999:01 164.700 4.63 1999:02 164.700 4.76 1999:03 164.800 4.81 1999:04 165.900 4.74 1999:05 166.000 4.74 1999:06 166.000 4.76 1999:07 166.700 4.99 1999:08 167.100 5.07 1999:09 167.800 5.22 1999:10 168.100 5.20 1999:11 168.400 5.42 1999:12 168.800 5.30 2000:01 169.300 5.45 2000:02 170.000 5.73 2000:03 171.000 5.85 2000:04 170.900 6.02 2000:05 171.200 6.27 2000:06 172.200 6.53 2000:07 172.700 6.54 2000:08 172.700 6.50 2000:09 173.600 6.52 2000:10 173.900 6.51 2000:11 174.200 6.51 2000:12 174.600 6.40 2001:01 175.600 5.98 2001:02 176.000 5.49 2001:03 176.100 5.31 2001:04 176.400 4.80 2001:05 177.300 4.21 2001:06 177.700 3.97 2001:07 177.400 3.77 2001:08 177.400 3.65 2001:09 178.100 3.07 2001:10 177.600 2.49 2001:11 177.500 2.09 2001:12 177.400 1.82 2002:01 177.700 1.73 2002:02 178.000 1.74 2002:03 178.500 1.73 2002:04 179.300 1.75 2002:05 179.500 1.75 2002:06 179.600 1.75 2002:07 180.000 1.73 2002:08 180.500 1.74 2002:09 180.800 1.75 2002:10 181.200 1.75 2002:11 181.500 1.34 2002:12 181.800 1.24 2003:01 182.600 1.24 2003:02 183.600 1.26 2003:03 183.900 1.25 2003:04 183.200 1.26 2003:05 182.900 1.26 2003:06 183.100 1.22 2003:07 183.700 1.01 2003:08 184.500 1.03 2003:09 185.100 1.01 2003:10 184.900 1.01 2003:11 185.000 1.00 2003:12 185.500 0.98 2004:01 186.300 1.00 2004:02 186.700 1.01 2004:03 187.100 1.00 2004:04 187.400 1.00 2004:05 188.200 1.00 2004:06 188.900 1.03 2004:07 189.100 1.26 2004:08 189.200 1.43 2004:09 189.800 1.61 2004:10 190.800 1.76 2004:11 191.700 1.93 2004:12 191.700 2.16 2005:01 191.600 2.28 2005:02 192.400 2.50 2005:03 193.100 2.63 2005:04 193.700 2.79 2005:05 193.600 3.00 2005:06 193.700 3.04 2005:07 194.900 3.26 2005:08 196.100 3.50 2005:09 198.800 3.62 2005:10 199.100 3.78 2005:11 198.100 4.00 2005:12 198.100 4.16 2006:01 199.200 4.29 2006:02 199.400 4.49 2006:03 199.700 4.59 2006:04 200.600 4.79 2006:05 201.400 4.94 2006:06 201.900 4.99 2006:07 202.900 5.24 2006:08 203.700 5.25 2006:09 202.900 5.25 2006:10 201.800 5.25 2006:11 202.000 5.25 2006:12 203.100 5.24 2007:01 203.372 5.25 2007:02 204.258 5.26 2007:03 205.312 5.26 2007:04 205.959 5.25 2007:05 206.850 5.25 2007:06 207.202 5.25 2007:07 207.651 5.26 2007:08 207.671 5.02 2007:09 208.503 4.94 2007:10 209.073 4.76 2007:11 210.740 4.49 2007:12 211.434 4.24 2008:01 212.225 3.94 2008:02 212.703 2.98 2008:03 213.543 2.61 2008:04 214.106 2.28 2008:05 215.287 1.98 2008:06 217.279 2.00 2008:07 219.102 2.01 2008:08 218.779 2.00 2008:09 218.846 1.81 2008:10 216.832 0.97 2008:11 212.923 0.39 2008:12 211.339 0.16 2009:01 211.959 0.15 2009:02 212.877 0.22 2009:03 212.643 0.18 2009:04 212.810 0.15 2009:05 213.050 0.18 2009:06 214.558 0.21 2009:07 214.774 0.16 2009:08 215.566 0.16 2009:09 215.911 0.15 2009:10 216.357 0.12 2009:11 216.859 0.12 2009:12 217.224 0.12 2010:01 217.587 0.11 2010:02 217.591 0.13 2010:03 217.729 0.16 2010:04 217.579 0.20 2010:05 217.224 0.20 2010:06 216.929 0.18 2010:07 217.597 0.18 2010:08 218.150 0.19 2010:09 218.372 0.19 2010:10 218.879 0.19 2010:11 219.146 0.19

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