/* Nonlinear Consumption Function Example examined in 5th Ed. Greene Econometric Analysis. See example p. 171 and Table 5.1. */ data yc; input Year qtr realgdp realcons realinvs realgovt realdpi cpi_u M1 tbilrate unemp pop infl realint; c = realcons; y = realdpi; datalines; 1950.0 1.0 1610.5 1058.9 198.1 361.0 1186.1 70.6 110.20 1.12 6.4 149.461 0.0000 0.0000 1950.0 2.0 1658.8 1075.9 220.4 366.4 1178.1 71.4 111.75 1.17 5.6 150.260 4.5071 -3.3404 1950.0 3.0 1723.0 1131.0 239.7 359.6 1196.5 73.2 112.95 1.23 4.6 151.064 9.9590 -8.7290 1950.0 4.0 1753.9 1097.6 271.8 382.5 1210.0 74.9 113.93 1.35 4.2 151.871 9.1834 -7.8301 1951.0 1.0 1773.5 1122.8 242.9 421.9 1207.9 77.3 115.08 1.40 3.5 152.393 12.6160 -11.2160 1951.0 2.0 1803.7 1091.4 249.2 480.1 1225.8 77.6 116.19 1.53 3.1 152.917 1.5494 -.0161 1951.0 3.0 1839.8 1103.9 230.1 534.2 1235.8 78.2 117.76 1.63 3.2 153.443 3.0809 -1.4542 1951.0 4.0 1843.3 1110.5 210.6 563.7 1238.5 79.3 119.89 1.65 3.4 153.970 5.5874 -3.9374 1952.0 1.0 1864.7 1113.6 215.6 584.8 1238.5 78.8 121.31 1.64 3.1 154.566 -2.5301 4.1701 1952.0 2.0 1866.2 1135.1 197.7 604.4 1252.0 79.4 122.37 1.68 3.0 155.165 3.0341 -1.3575 1952.0 3.0 1878.0 1140.4 207.8 610.5 1276.1 80.0 123.64 1.83 3.2 155.766 3.0113 -1.1813 1952.0 4.0 1940.2 1180.5 223.3 620.8 1300.5 80.0 124.72 1.92 2.8 156.369 .0000 1.9233 1953.0 1.0 1976.0 1194.9 227.5 641.2 1317.5 79.6 125.33 2.05 2.7 157.009 -2.0050 4.0517 1953.0 2.0 1992.2 1202.5 228.5 655.9 1336.3 80.2 126.05 2.20 2.6 157.652 3.0038 -.8004 1953.0 3.0 1979.5 1199.8 222.8 647.6 1330.2 80.7 126.22 2.02 2.7 158.298 2.4860 -.4627 1953.0 4.0 1947.8 1191.8 205.0 645.4 1325.9 80.5 126.37 1.49 3.7 158.946 -.9926 2.4792 1954.0 1.0 1938.1 1196.2 203.4 627.1 1330.3 80.5 126.54 1.08 5.3 159.675 .0000 1.0800 1954.0 2.0 1941.0 1211.3 203.0 606.1 1327.9 80.7 127.18 .81 5.8 160.407 .9926 -.1792 1954.0 3.0 1962.0 1227.3 213.3 591.2 1344.2 80.4 128.38 .87 6.0 161.142 -1.4898 2.3598 1954.0 4.0 2000.9 1252.6 223.3 587.4 1373.6 80.1 129.72 1.04 5.3 161.881 -1.4953 2.5320 1955.0 1.0 2058.1 1280.1 247.2 586.4 1392.7 80.1 131.07 1.26 4.7 162.669 .0000 1.2567 1955.0 2.0 2091.0 1304.3 262.8 579.9 1423.3 80.1 131.88 1.51 4.4 163.462 .0000 1.5133 1955.0 3.0 2118.9 1320.3 266.4 584.0 1451.1 80.5 132.40 1.86 4.1 164.258 1.9925 -.1292 1955.0 4.0 2130.1 1336.7 272.0 571.3 1468.1 80.4 132.64 2.35 4.2 165.058 -.4972 2.8439 1956.0 1.0 2121.0 1339.2 262.9 570.9 1480.9 80.4 133.11 2.38 4.0 165.808 .0000 2.3800 1956.0 2.0 2137.7 1343.7 260.0 582.6 1497.8 81.4 133.38 2.60 4.2 166.561 4.9444 -2.3478 1956.0 3.0 2135.3 1346.8 257.1 577.3 1504.1 82.0 133.48 2.60 4.1 167.318 2.9376 -.3409 1956.0 4.0 2170.4 1365.3 254.4 592.5 1526.5 82.7 134.09 3.06 4.1 168.078 3.4001 -.3368 1957.0 1.0 2182.7 1374.2 250.0 604.0 1527.5 83.3 134.29 3.17 3.9 168.848 2.8916 .2784 1957.0 2.0 2177.7 1376.5 249.9 600.6 1538.6 84.3 134.36 3.16 4.1 169.621 4.7733 -1.6167 1957.0 3.0 2198.9 1387.7 255.6 605.5 1548.7 84.9 134.26 3.38 4.2 170.398 2.8369 .5431 1957.0 4.0 2176.0 1388.8 234.1 616.6 1543.1 85.2 133.48 3.34 4.9 171.178 1.4109 1.9324 1958.0 1.0 2117.4 1370.1 216.7 609.6 1524.7 86.4 133.72 1.84 6.3 171.917 5.5945 -3.7578 1958.0 2.0 2129.7 1380.9 211.3 625.0 1534.1 86.7 135.22 1.02 7.4 172.659 1.3865 -.3665 1958.0 3.0 2177.5 1402.3 228.4 628.4 1568.1 86.7 136.64 1.71 7.3 173.404 .0000 1.7100 1958.0 4.0 2226.5 1418.8 249.6 641.5 1588.0 86.7 138.48 2.79 6.4 174.153 .0000 2.7867 1959.0 1.0 2273.0 1445.2 263.0 651.5 1599.5 86.7 139.70 2.80 5.8 174.894 .0000 2.8000 1959.0 2.0 2332.4 1468.2 286.2 663.9 1629.6 87.3 141.20 3.02 5.1 175.638 2.7586 .2614 1959.0 3.0 2331.4 1483.8 266.6 668.1 1627.0 87.7 141.00 3.53 5.3 176.385 1.8286 1.7048 1959.0 4.0 2339.1 1485.6 275.6 662.2 1639.2 88.0 140.00 4.30 5.6 177.136 1.3660 2.9340 1960.0 1.0 2391.0 1499.2 305.3 648.8 1657.7 88.0 139.80 3.95 5.1 177.841 .0000 3.9467 1960.0 2.0 2379.2 1518.1 274.0 657.4 1666.5 88.7 139.60 3.09 5.2 178.548 3.1692 -.0759 1960.0 3.0 2383.6 1512.1 272.4 665.9 1667.7 88.8 141.20 2.39 5.5 179.259 .4507 1.9426 1960.0 4.0 2352.9 1513.5 239.5 673.1 1667.2 89.3 140.70 2.36 6.3 179.972 2.2459 .1174 1961.0 1.0 2366.5 1512.8 245.0 680.4 1680.6 89.3 141.90 2.38 6.8 180.718 .0000 2.3767 1961.0 2.0 2410.8 1535.2 263.3 687.2 1705.4 89.4 142.90 2.33 7.0 181.468 .4477 1.8790 1961.0 3.0 2450.4 1542.9 285.5 694.0 1729.4 89.9 143.80 2.32 6.8 182.220 2.2309 .0924 1961.0 4.0 2500.4 1574.2 290.2 711.1 1764.4 89.9 145.20 2.48 6.2 182.976 .0000 2.4767 1962.0 1.0 2544.0 1590.6 307.3 723.4 1777.9 90.3 146.00 2.74 5.6 183.663 1.7758 .9675 1962.0 2.0 2571.5 1609.9 304.5 731.7 1799.3 90.5 146.60 2.72 5.5 184.352 .8850 1.8350 1962.0 3.0 2596.8 1622.9 310.0 740.8 1811.4 91.2 146.30 2.86 5.6 185.044 3.0820 -.2253 1962.0 4.0 2603.3 1645.9 299.5 744.2 1825.5 91.0 147.80 2.80 5.5 185.739 -.8782 3.6815 1963.0 1.0 2634.1 1657.1 315.4 740.0 1838.9 91.3 149.20 2.91 5.8 186.409 1.3165 1.5935 1963.0 2.0 2668.4 1673.0 320.8 744.3 1857.2 91.7 150.40 2.94 5.7 187.082 1.7486 1.1947 1963.0 3.0 2719.6 1695.7 331.5 765.9 1879.2 92.1 152.00 3.28 5.5 187.757 1.7410 1.5390 1963.0 4.0 2739.4 1710.0 335.2 759.2 1910.5 92.5 153.30 3.50 5.6 188.434 1.7335 1.7632 1964.0 1.0 2800.5 1743.8 348.9 763.1 1947.6 92.6 154.50 3.54 5.5 189.093 .4322 3.1045 1964.0 2.0 2833.8 1775.0 347.5 772.9 1999.4 92.9 155.60 3.48 5.2 189.755 1.2938 2.1862 1964.0 3.0 2872.0 1807.8 355.7 766.4 2027.8 93.2 158.70 3.51 5.0 190.419 1.2896 2.2170 1964.0 4.0 2879.5 1812.8 358.3 766.1 2052.6 93.6 160.30 3.69 5.0 191.085 1.7131 1.9736 1965.0 1.0 2950.1 1852.5 394.9 765.5 2071.8 93.7 161.50 3.90 4.9 191.675 .4271 3.4729 1965.0 2.0 2989.9 1873.2 394.6 781.3 2096.4 94.7 162.20 3.88 4.7 192.267 4.2463 -.3663 1965.0 3.0 3050.7 1905.3 408.4 800.3 2155.3 94.8 164.90 3.86 4.4 192.861 .4222 3.4378 1965.0 4.0 3123.6 1959.3 410.1 817.2 2200.4 95.4 167.80 4.16 4.1 193.457 2.5237 1.6330 1966.0 1.0 3201.1 1988.6 444.1 832.5 2219.3 96.3 170.50 4.63 3.9 193.965 3.7559 .8774 1966.0 2.0 3213.2 1994.0 436.5 857.8 2224.6 97.1 171.60 4.60 3.8 194.475 3.3092 1.2874 1966.0 3.0 3233.6 2016.6 432.7 870.1 2254.0 98.1 172.00 5.05 3.8 194.986 4.0984 .9516 1966.0 4.0 3261.8 2025.1 435.8 888.0 2280.5 98.6 172.00 5.25 3.7 195.499 2.0336 3.2131 1967.0 1.0 3291.8 2037.3 424.9 925.6 2312.6 98.9 174.80 4.54 3.8 195.966 1.2152 3.3215 1967.0 2.0 3289.7 2064.6 405.0 921.3 2329.9 99.7 177.00 3.66 3.8 196.435 3.2226 .4374 1967.0 3.0 3313.5 2075.2 415.2 926.8 2351.4 100.7 180.70 4.34 3.8 196.904 3.9920 .3513 1967.0 4.0 3338.3 2087.9 423.6 934.8 2367.9 101.6 183.30 4.79 3.9 197.375 3.5591 1.2276 1968.0 1.0 3406.2 2136.2 433.8 951.4 2409.5 102.8 185.50 5.07 3.7 197.857 4.6967 .3699 1968.0 2.0 3464.8 2169.6 451.8 956.0 2451.2 104.0 189.40 5.51 3.6 198.341 4.6422 .8711 1968.0 3.0 3489.2 2210.7 437.3 958.3 2457.9 105.1 192.70 5.22 3.5 198.826 4.2086 1.0148 1968.0 4.0 3504.1 2220.4 442.2 960.5 2474.3 106.4 197.40 5.58 3.4 199.312 4.9173 .6660 1969.0 1.0 3558.3 2244.8 470.8 956.9 2477.5 108.0 200.00 6.14 3.4 199.807 5.9703 .1697 1969.0 2.0 3567.6 2258.8 467.1 956.0 2501.5 109.7 201.30 6.24 3.4 200.303 6.2473 -.0039 1969.0 3.0 3588.3 2269.0 477.2 954.1 2550.2 111.2 202.10 7.05 3.6 200.800 5.4324 1.6176 1969.0 4.0 3571.4 2286.5 452.6 943.1 2568.1 112.9 203.90 7.32 3.6 201.298 6.0688 1.2512 1970.0 1.0 3566.5 2300.8 438.0 936.2 2581.9 114.5 205.70 7.26 4.2 201.920 5.6289 1.6344 1970.0 2.0 3573.9 2312.0 439.4 927.3 2626.0 116.3 207.60 6.75 4.8 202.545 6.2393 .5107 1970.0 3.0 3605.2 2332.2 446.5 930.9 2661.1 117.5 211.90 6.37 5.2 203.171 4.1061 2.2672 1970.0 4.0 3566.5 2324.9 421.0 929.9 2650.9 119.1 214.30 5.36 5.8 203.799 5.4101 -.0501 1971.0 1.0 3666.1 2369.8 475.9 918.6 2703.5 119.8 218.70 3.87 5.9 204.549 2.3441 1.5226 1971.0 2.0 3686.2 2391.4 490.2 915.2 2742.6 121.5 223.60 4.21 5.9 205.303 5.6362 -1.4296 1971.0 3.0 3714.5 2409.8 496.5 911.9 2752.9 122.2 226.60 5.05 6.0 206.059 2.2979 2.7554 1971.0 4.0 3723.8 2449.8 480.6 909.4 2782.1 123.1 228.20 4.23 5.9 206.818 2.9352 1.2981 1972.0 1.0 3796.9 2482.2 513.6 920.8 2797.6 124.0 234.20 3.44 5.8 207.429 2.9138 .5229 1972.0 2.0 3883.8 2527.5 544.9 921.9 2822.9 125.0 236.80 3.75 5.7 208.043 3.2129 .5338 1972.0 3.0 3922.3 2565.9 554.1 907.6 2883.6 126.2 243.30 4.24 5.6 208.658 3.8217 .4183 1972.0 4.0 3990.5 2626.3 559.4 909.1 2993.0 127.3 249.10 4.85 5.4 209.275 3.4714 1.3819 1973.0 1.0 4092.3 2674.2 595.2 914.5 3031.9 129.8 251.50 5.64 4.9 209.792 7.7793 -2.1393 1973.0 2.0 4133.3 2671.4 618.2 911.5 3059.6 132.4 256.90 6.61 4.9 210.309 7.9331 -1.3231 1973.0 3.0 4117.0 2682.5 597.5 898.5 3079.3 135.5 258.00 8.39 4.8 210.829 9.2576 -.8676 1973.0 4.0 4151.1 2675.6 615.3 908.4 3118.3 138.5 262.70 7.47 4.8 211.349 8.7595 -1.2928 1974.0 1.0 4119.3 2652.4 579.2 920.0 3072.1 143.1 266.50 7.60 5.1 211.844 13.0693 -5.4660 1974.0 2.0 4130.4 2662.0 577.3 927.8 3045.5 146.9 268.60 8.27 5.2 212.339 10.4834 -2.2134 1974.0 3.0 4084.5 2672.2 543.4 924.2 3053.3 151.7 271.30 8.29 5.6 212.836 12.8611 -4.5711 1974.0 4.0 4062.0 2628.4 547.0 927.4 3036.7 155.4 274.00 7.34 6.6 213.334 9.6390 -2.3024 1975.0 1.0 4010.0 2648.8 450.8 940.8 3015.0 157.8 276.20 5.88 8.3 213.862 6.1304 -.2537 1975.0 2.0 4045.2 2695.4 436.4 938.3 3156.6 160.6 282.70 5.40 8.9 214.392 7.0354 -1.6320 1975.0 3.0 4115.4 2734.7 474.9 941.8 3114.9 163.6 286.00 6.34 8.5 214.924 7.4030 -1.0664 1975.0 4.0 4167.2 2764.6 486.8 949.1 3147.6 166.3 286.80 5.68 8.3 215.457 6.5476 -.8643 1976.0 1.0 4266.1 2824.7 535.1 952.5 3201.9 167.5 292.40 4.95 7.7 215.979 2.8760 2.0773 1976.0 2.0 4301.5 2850.9 559.8 943.3 3229.0 170.1 296.40 5.17 7.6 216.503 6.1613 -.9879 1976.0 3.0 4321.9 2880.3 561.1 938.9 3259.7 172.6 300.00 5.17 7.7 217.028 5.8361 -.6661 1976.0 4.0 4357.4 2919.6 565.9 938.6 3283.5 174.3 305.90 4.70 7.8 217.554 3.9205 .7795 1977.0 1.0 4410.5 2954.7 595.5 945.3 3305.4 178.2 313.60 4.62 7.5 218.104 8.8514 -4.2281 1977.0 2.0 4489.8 2970.5 635.0 955.1 3326.8 181.8 319.00 4.83 7.1 218.655 8.0003 -3.1736 1977.0 3.0 4570.6 2999.1 670.7 956.0 3376.5 184.0 324.90 5.47 6.9 219.207 4.8114 .6586 1977.0 4.0 4576.1 3044.0 656.4 954.5 3433.8 186.1 330.50 6.14 6.7 219.761 4.5394 1.5973 1978.0 1.0 4588.9 3060.8 667.2 956.7 3466.3 189.8 336.60 6.41 6.3 220.343 7.8747 -1.4647 1978.0 2.0 4765.7 3127.0 709.7 982.1 3513.0 195.3 347.10 6.48 6.0 220.926 11.4264 -4.9431 1978.0 3.0 4811.7 3143.1 728.8 990.3 3548.1 199.3 352.70 7.32 6.0 221.512 8.1098 -.7898 1978.0 4.0 4876.0 3167.8 746.3 999.6 3582.6 202.9 356.90 8.68 5.9 222.098 7.1608 1.5192 1979.0 1.0 4888.3 3188.6 746.0 990.6 3620.7 209.1 362.10 9.36 5.9 222.713 12.0397 -2.6797 1979.0 2.0 4891.4 3184.3 745.7 1000.5 3607.1 216.6 373.60 9.37 5.7 223.330 14.0959 -4.7226 1979.0 3.0 4926.2 3213.9 732.1 1002.4 3628.8 223.4 379.70 9.63 5.9 223.948 12.3646 -2.7313 1979.0 4.0 4942.6 3225.7 717.8 1010.8 3657.8 229.9 381.40 11.80 6.0 224.569 11.4722 .3311 1980.0 1.0 4958.9 3222.4 711.7 1025.6 3678.5 239.8 388.10 13.46 6.3 225.230 16.8643 -3.4010 1980.0 2.0 4857.8 3149.2 647.4 1028.7 3612.2 247.6 389.40 10.05 7.3 225.893 12.8037 -2.7537 1980.0 3.0 4850.3 3181.2 599.8 1015.4 3637.6 251.7 405.40 9.24 7.7 226.558 6.5693 2.6673 1980.0 4.0 4936.6 3219.4 662.2 1013.9 3703.8 258.4 408.10 13.71 7.4 227.225 10.5083 3.2017 1981.0 1.0 5032.5 3233.1 726.3 1027.5 3713.5 265.1 418.70 14.37 7.4 227.783 10.2393 4.1340 1981.0 2.0 4997.3 3235.5 693.4 1030.1 3696.6 271.3 425.50 14.83 7.4 228.342 9.2472 5.5795 1981.0 3.0 5056.8 3250.5 733.9 1027.8 3777.0 279.3 427.50 15.09 7.4 228.903 11.6245 3.4622 1981.0 4.0 4997.1 3225.0 708.8 1034.8 3777.2 281.5 436.20 12.02 8.2 229.466 3.1384 8.8849 1982.0 1.0 4914.3 3244.3 634.8 1033.6 3769.4 283.1 442.40 12.89 8.8 230.013 2.2671 10.6262 1982.0 2.0 4935.5 3253.4 631.6 1039.5 3791.4 290.6 447.90 12.36 9.4 230.562 10.4590 1.9010 1982.0 3.0 4912.1 3274.6 623.5 1046.8 3799.4 293.3 457.50 9.71 9.9 231.113 3.6993 6.0107 1982.0 4.0 4915.6 3329.6 571.1 1064.0 3806.4 292.4 474.30 7.94 10.7 231.664 -1.2293 9.1660 1983.0 1.0 4972.4 3360.1 590.7 1069.8 3831.2 293.4 490.20 8.08 10.4 232.195 1.3657 6.7143 1983.0 2.0 5089.8 3430.1 650.7 1078.2 3857.8 298.1 504.40 8.42 10.1 232.726 6.3569 2.0631 1983.0 3.0 5180.4 3484.7 691.4 1097.0 3928.6 301.8 513.40 9.19 9.4 233.258 4.9342 4.2525 1983.0 4.0 5286.8 3542.2 762.2 1078.8 4010.2 303.5 520.80 8.79 8.5 233.792 2.2468 6.5465 1984.0 1.0 5402.3 3579.7 845.0 1091.0 4103.0 307.3 530.80 9.01 7.9 234.299 4.9771 4.0362 1984.0 2.0 5493.8 3628.3 873.2 1115.2 4182.4 310.7 540.50 9.84 7.4 234.806 4.4013 5.4420 1984.0 3.0 5541.3 3653.5 890.7 1123.1 4258.8 314.5 543.90 10.34 7.4 235.315 4.8625 5.4808 1984.0 4.0 5583.1 3700.9 876.9 1144.2 4286.1 315.5 551.20 8.97 7.3 235.825 1.2698 7.7035 1985.0 1.0 5629.7 3756.8 848.9 1157.6 4287.6 318.8 565.70 8.17 7.2 236.348 4.1621 4.0046 1985.0 2.0 5673.8 3791.5 862.8 1180.5 4368.7 322.3 582.90 7.52 7.3 236.872 4.3675 3.1558 1985.0 3.0 5758.6 3860.9 854.1 1209.2 4346.6 324.5 604.40 7.10 7.2 237.397 2.7211 4.3822 1985.0 4.0 5806.0 3874.2 887.8 1214.7 4388.3 327.4 619.10 7.15 7.0 237.924 3.5589 3.5878 1986.0 1.0 5858.9 3907.9 886.2 1224.0 4444.5 326.0 632.60 6.89 7.0 238.474 -1.7141 8.6008 1986.0 2.0 5883.3 3950.4 868.3 1248.0 4489.3 327.9 661.20 6.13 7.2 239.026 2.3245 3.8055 1986.0 3.0 5937.9 4019.7 838.0 1277.4 4507.9 330.2 688.40 5.53 7.0 239.579 2.7959 2.7374 1986.0 4.0 5969.5 4046.8 838.2 1271.5 4504.5 331.1 724.00 5.34 6.8 240.133 1.0888 4.2512 1987.0 1.0 6013.3 4049.7 863.4 1278.4 4556.9 335.9 732.80 5.53 6.6 240.670 5.7572 -.2239 1987.0 2.0 6077.2 4101.5 863.9 1289.1 4512.7 340.1 743.50 5.73 6.3 241.208 4.9705 .7629 1987.0 3.0 6128.1 4147.0 860.5 1292.4 4600.7 344.4 748.50 6.03 6.0 241.748 5.0256 1.0077 1987.0 4.0 6234.4 4155.3 929.3 1310.0 4659.6 345.7 749.40 6.00 5.8 242.289 1.5070 4.4963 1988.0 1.0 6275.9 4228.0 884.6 1300.1 4724.1 349.0 761.10 5.76 5.7 242.840 3.8002 1.9598 1988.0 2.0 6349.8 4256.8 902.5 1302.4 4758.9 353.5 778.80 6.23 5.5 243.391 5.1246 1.1054 1988.0 3.0 6382.3 4291.6 907.5 1300.3 4801.9 358.9 784.60 6.99 5.5 243.945 6.0641 .9292 1988.0 4.0 6465.2 4341.4 916.7 1327.2 4851.4 360.9 786.10 7.70 5.3 244.499 2.2228 5.4805 1989.0 1.0 6543.8 4357.1 952.7 1319.3 4903.5 366.2 782.70 8.53 5.2 245.077 5.8315 2.7018 1989.0 2.0 6579.4 4374.8 941.1 1340.6 4891.0 371.7 773.90 8.44 5.2 245.656 5.9630 2.4770 1989.0 3.0 6610.6 4413.4 929.3 1353.5 4902.7 374.6 782.00 7.85 5.2 246.237 3.1087 4.7413 1989.0 4.0 6633.5 4429.4 922.9 1360.4 4928.8 377.6 792.10 7.64 5.4 246.819 3.1907 4.4493 1990.0 1.0 6716.3 4466.0 934.0 1381.2 5001.6 385.5 800.80 7.76 5.3 247.478 8.2823 -.5256 1990.0 2.0 6731.7 4478.8 933.0 1384.7 5026.6 389.1 809.70 7.77 5.3 248.138 3.7181 4.0486 1990.0 3.0 6719.4 4495.6 912.6 1384.8 5032.7 397.5 821.10 7.49 5.7 248.800 8.5434 -1.0501 1990.0 4.0 6664.2 4457.7 849.6 1398.6 4995.8 400.9 823.90 7.02 6.1 249.464 3.4068 3.6165 1991.0 1.0 6631.4 4437.5 815.1 1404.7 4999.5 404.3 838.00 6.05 6.6 250.134 3.3781 2.6753 1991.0 2.0 6668.5 4469.9 808.8 1408.9 5033.3 407.3 857.40 5.59 6.8 250.805 2.9571 2.6362 1991.0 3.0 6684.9 4484.3 829.8 1403.0 5045.4 411.1 871.20 5.41 6.9 251.478 3.7146 1.6921 1991.0 4.0 6720.9 4474.8 864.2 1397.0 5053.8 413.0 895.90 4.58 7.1 252.153 1.8444 2.7389 1992.0 1.0 6783.3 4544.8 843.8 1407.6 5138.8 417.2 935.80 3.91 7.4 252.869 4.0473 -.1373 1992.0 2.0 6846.8 4566.7 901.8 1405.7 5172.5 419.9 954.50 3.72 7.6 253.587 2.5803 1.1430 1992.0 3.0 6899.7 4600.5 912.1 1413.1 5174.2 423.2 988.70 3.13 7.6 254.307 3.1313 -.0013 1992.0 4.0 6990.6 4665.9 941.6 1413.7 5271.5 425.2 1024.00 3.08 7.4 255.030 1.8859 1.1908 1993.0 1.0 6988.7 4674.9 964.8 1396.4 5181.2 430.1 1038.10 2.99 7.1 255.715 4.5832 -1.5899 1993.0 2.0 7031.2 4721.5 967.0 1398.0 5258.6 432.4 1075.30 2.98 7.1 256.402 2.1333 .8500 1993.0 3.0 7062.0 4776.9 964.1 1398.4 5266.8 434.7 1105.20 3.02 6.8 257.092 2.1220 .8980 1993.0 4.0 7168.7 4822.3 1015.6 1402.2 5338.5 436.8 1129.20 3.08 6.6 257.783 1.9277 1.1523 1994.0 1.0 7229.4 4866.6 1057.3 1388.0 5293.2 441.1 1140.00 3.25 6.6 258.416 3.9185 -.6685 1994.0 2.0 7330.2 4907.9 1118.5 1390.4 5381.2 443.3 1145.60 4.04 6.2 259.052 1.9901 2.0466 1994.0 3.0 7370.2 4944.5 1101.8 1417.5 5420.9 447.5 1152.10 4.51 6.0 259.689 3.7719 .7381 1994.0 4.0 7461.1 4993.6 1150.5 1404.5 5493.4 448.4 1149.80 5.28 5.6 260.327 .8037 4.4797 1995.0 1.0 7488.7 5011.6 1162.4 1407.3 5515.4 453.5 1146.50 5.78 5.5 260.944 4.5238 1.2562 1995.0 2.0 7503.3 5059.6 1128.5 1414.0 5509.0 456.7 1144.10 5.62 5.7 261.562 2.8126 2.8107 1995.0 3.0 7561.4 5099.2 1119.1 1410.8 5546.6 459.0 1141.90 5.38 5.7 262.182 2.0094 3.3706 1995.0 4.0 7621.9 5132.1 1152.4 1393.5 5585.3 459.9 1126.20 5.27 5.6 262.803 .7835 4.4865 1996.0 1.0 7676.4 5174.3 1172.3 1404.8 5622.0 466.5 1122.00 4.95 5.5 263.408 5.6996 -.7496 1996.0 2.0 7802.9 5229.5 1233.4 1430.4 5649.4 469.5 1115.00 5.04 5.5 264.013 2.5641 2.4759 1996.0 3.0 7841.9 5254.3 1281.4 1422.0 5709.7 472.7 1095.80 5.14 5.3 264.620 2.7171 2.4196 1996.0 4.0 7931.3 5291.9 1283.7 1430.6 5729.9 475.0 1080.50 4.97 5.3 265.229 1.9415 3.0285 1997.0 1.0 8016.4 5350.7 1325.4 1434.6 5771.8 479.3 1072.00 5.06 5.2 265.865 3.6048 1.4586 1997.0 2.0 8131.9 5375.7 1400.6 1457.0 5821.2 480.2 1066.20 5.07 5.0 266.503 .7504 4.3229 1997.0 3.0 8216.6 5462.1 1408.6 1464.8 5877.3 483.0 1065.30 5.06 4.9 267.143 2.3256 2.7311 1997.0 4.0 8272.9 5507.1 1438.5 1465.3 5947.5 483.2 1073.40 5.09 4.7 267.784 .1656 4.9211 1998.0 1.0 8396.3 5576.3 1543.3 1456.1 6064.5 485.8 1080.30 5.08 4.6 268.398 2.1465 2.9301 1998.0 2.0 8442.9 5660.2 1516.8 1482.6 6153.6 488.2 1077.60 5.01 4.4 269.013 1.9713 3.0354 1998.0 3.0 8528.5 5713.7 1559.7 1489.9 6209.9 490.1 1076.20 4.88 4.5 269.630 1.5537 3.3263 1998.0 4.0 8667.9 5784.7 1612.1 1504.8 6246.6 491.0 1097.00 4.31 4.4 270.248 .7339 3.5795 1999.0 1.0 8733.5 5854.0 1641.8 1512.3 6268.2 494.4 1102.20 4.42 4.3 270.857 2.7603 1.6630 1999.0 2.0 8771.2 5936.1 1617.4 1516.8 6300.0 497.9 1099.80 4.46 4.3 271.467 2.8217 1.6383 1999.0 3.0 8871.5 6000.0 1655.8 1533.2 6332.4 502.9 1093.40 4.70 4.2 272.078 3.9968 .6998 1999.0 4.0 9049.9 6083.6 1725.4 1564.8 6379.2 504.1 1124.80 5.06 4.1 272.691 .9533 4.1067 2000.0 1.0 9102.5 6171.7 1722.9 1560.4 6431.6 512.8 1113.70 5.54 4.0 274.848 6.8445 -1.3012 2000.0 2.0 9229.4 6226.3 1801.6 1577.2 6523.7 516.5 1105.30 5.78 4.0 277.022 2.8758 2.9009 2000.0 3.0 9260.1 6292.1 1788.8 1570.0 6566.5 520.3 1096.00 6.03 4.1 279.213 2.9321 3.0979 2000.0 4.0 9303.9 6341.1 1778.3 1582.8 6634.9 521.1 1088.10 6.03 4.0 281.422 .6146 5.4154 ; /* Use OLS to get starting values for Nonlinear Least Squares. */ proc reg data=yc; model c = y; run; /* Use the Gauss-Newton Method and LS estimates as starting point to obtain Nonlinear LS Estimates */ proc nlin data=yc maxiter=150; parms alpha=-80.35475 beta=0.92169 gamma=1.0; model c = alpha + beta*y**gamma; der.alpha=1; der.beta=y**gamma; der.gamma=beta*(y**gamma)*log(y); output out=ycfit p=predict r=resid; run; /* Plot Fitted vs. Actual Values */ proc plot data=ycfit; plot c*year predict*year='p' /overlay; plot resid*year / vref=0; run; /* Use several starting points and the Gauss-Newton Method. Using several starting points allows us to check the robustness of the NLS result. */ proc nlin data=yc maxiter=150 best=8; parms alpha=-85 to -75 by 2 beta=0.5 to 1.5 by 0.5 gamma=0 to 2 by 0.5; model c = alpha + beta*y**gamma; der.alpha=1; der.beta=y**gamma; der.gamma=beta*(y**gamma)*log(y); output out=ycfit p=predict r=resid; run; /* Plot Fitted vs. Actual Values */ proc plot data=ycfit; plot c*year predict*year='p' /overlay; plot resid*year / vref=0; run; /* If we leave out the derivatives in proc nlin the method of estimation is by the secant (DUD) method. See the SAS/STAT guide for further information on this method. Let's see if we get roughly the same results using the DUD method as we got using the Gauss-Newton Method. */ proc nlin data=yc maxiter=200; parms alpha=-80.35475 beta=0.92169 gamma=1.0; model c = alpha + beta*y**gamma; output out=ycfit p=predict r=resid; run; proc plot data=ycfit; plot c*year predict*year='p' /overlay; plot resid*year / vref=0; run; proc nlin data=yc maxiter=200 best=8; parms alpha=-85 to -75 by 2 beta=0.5 to 1.5 by 0.5 gamma=0 to 2 by 0.5; model c = alpha + beta*y**gamma; output out=ycfit p=predict r=resid; run; proc plot data=ycfit; plot c*year predict*year='p' /overlay; plot resid*year / vref=0; run;