The following data and programs were used for Peter Yoo's September/October 1994 REVIEW article, "Boom or Bust? The Economic Effects of the Baby Boom." **************************************************************************** DINC: Disposable income (BQDPICURSAR) billions nominal. Saving: Gross Savings (SVGCURSAR) billions nominal. SavingP: Gross Private Savings (SVPCURSAR) billions nominal. GPDInv: Gross Private Domestic Investment (BQGPDCONSAR) in billions of 87 dollars. Wage: Hourly Compensation deflated by IPDGDP (BQHCOCONSI) in billions of 87 dollars. Consump: Personnal consumption expenditure (BQPCECOSSAR) in billions of 87 dollars. SavingR: saving/DINC. SavingPR: SavingP/DINC. --------------------------------------------------------------------------- NOTE: Annual SavingR and SavingPR are averages of quarterly data and therefore will not equal the ratios of annual data. SOURCE: All data are quarterly from RDAS and are averaged to create annual data. **************************************************************************** Date DINC Saving SavingP GPDInv Wage Consump SavingR SavingPR 1946 159.23 35.48 30.28 ERR ERR ERR 0.22 0.19 1947 169.08 42.50 28.15 198.75 43.58 793.30 0.25 0.17 1948 188.38 51.73 42.35 229.80 44.00 813.00 0.27 0.22 1949 188.15 36.60 39.85 187.38 45.28 831.43 0.19 0.21 1950 207.68 51.43 44.38 256.45 47.90 874.35 0.25 0.21 1951 228.18 58.28 52.75 255.63 49.18 894.75 0.26 0.23 1952 240.20 52.83 56.35 231.58 51.90 923.38 0.22 0.23 1953 255.58 52.18 57.93 240.30 54.53 962.45 0.20 0.23 1954 261.25 51.65 58.88 234.05 56.10 987.35 0.20 0.23 1955 279.85 68.20 65.33 284.80 56.35 1047.00 0.24 0.23 1956 298.83 77.70 72.33 282.18 58.13 1078.68 0.26 0.24 1957 315.25 77.28 76.48 266.90 60.00 1104.45 0.25 0.24 1958 326.35 66.48 77.38 245.75 61.88 1122.20 0.20 0.24 1959 346.68 79.40 82.50 296.38 62.90 1178.93 0.23 0.24 1960 360.50 85.13 81.55 290.83 64.58 1210.73 0.24 0.23 1961 376.20 84.38 87.43 289.40 66.78 1238.35 0.22 0.23 1962 398.63 92.83 95.78 321.20 68.55 1293.28 0.23 0.24 1963 418.35 100.38 98.75 343.28 70.60 1341.93 0.24 0.24 1964 454.68 109.98 111.53 371.83 73.58 1417.18 0.24 0.25 1965 491.03 124.98 123.75 413.03 74.40 1497.03 0.25 0.25 1966 530.73 131.55 132.50 437.98 76.95 1573.85 0.25 0.25 1967 568.65 130.75 144.48 418.63 79.20 1622.35 0.23 0.25 1968 617.78 141.73 146.38 440.08 81.90 1707.50 0.23 0.24 1969 663.80 159.50 149.55 461.30 83.80 1771.18 0.24 0.23 1970 722.05 155.20 165.80 429.73 86.60 1813.48 0.22 0.23 1971 784.85 173.73 192.18 475.70 87.85 1873.73 0.22 0.24 1972 848.48 201.68 204.85 532.15 89.93 1978.40 0.24 0.24 1973 958.13 252.30 245.43 591.68 92.13 2066.70 0.26 0.26 1974 1046.53 249.48 255.95 542.98 92.30 2053.80 0.24 0.24 1975 1150.88 241.43 306.28 437.63 92.50 2097.48 0.21 0.27 1976 1263.98 284.78 323.03 520.63 95.25 2207.25 0.23 0.26 1977 1391.25 338.20 354.98 600.43 96.85 2296.58 0.24 0.25 1978 1567.75 415.73 412.80 664.58 97.48 2391.83 0.26 0.26 1979 1752.98 468.45 457.88 669.73 98.05 2448.33 0.27 0.26 1980 1952.95 465.45 499.58 594.43 99.00 2447.05 0.24 0.26 1981 2174.45 556.63 585.90 631.10 98.30 2476.93 0.26 0.27 1982 2319.55 508.38 616.95 540.48 100.03 2503.65 0.22 0.27 1983 2493.75 501.55 641.35 599.50 100.43 2619.38 0.20 0.26 1984 2759.55 633.93 742.70 757.50 100.60 2746.08 0.23 0.27 1985 2942.98 610.38 735.65 745.93 101.78 2865.83 0.21 0.25 1986 3131.48 574.63 721.40 735.08 104.60 2969.13 0.18 0.23 1987 3289.55 618.98 730.68 749.30 105.58 3052.23 0.19 0.22 1988 3548.20 704.03 802.30 773.38 106.38 3162.40 0.20 0.23 1989 3787.00 741.83 819.38 783.98 105.48 3223.33 0.20 0.22 1990 4050.55 722.68 861.13 746.78 107.10 3272.60 0.18 0.21 1991 4230.55 733.75 929.93 675.68 108.35 3258.55 0.17 0.22 1992 4500.18 717.80 986.93 732.83 111.33 3341.80 0.16 0.22 1993 4706.73 780.85 1005.20 820.35 112.90 3453.25 0.17 0.21 ************** Graph Data: *********************************************** ************** Total population growth rate = ln differences of total * 100 Working age population growth = ln differences of 18-64 *100 Real Wages = ln differences of wages *100 Real returns to capital = r long gov National saving rate= nat saving Per capita consumption = ln differences of consumer ************************************************************* Date total 18-64 wage rlong natsav consumer 1900 76.09 42.28 1901 77.58 43.27 1902 79.16 44.32 1903 80.63 45.33 1904 82.17 46.38 1905 83.82 47.51 1906 85.45 48.63 1907 87.01 49.71 1908 88.71 50.88 1909 90.49 52.09 1910 92.41 53.36 1911 93.86 54.30 1912 95.34 55.22 1913 97.23 56.37 1914 99.11 57.51 1915 100.55 58.36 1916 101.96 59.21 1917 103.27 59.93 1918 103.21 59.27 1919 104.51 60.52 1920 106.46 61.91 1921 108.54 63.07 1922 110.05 63.87 1923 111.95 65.05 1924 114.11 66.43 1925 115.83 67.54 1926 117.40 68.66 1927 119.04 69.85 1928 120.51 71.03 1929 121.77 72.15 1930 123.08 73.36 1931 124.04 74.28 1932 124.84 75.15 1933 125.58 76.03 1934 126.37 76.97 1935 127.25 77.89 1936 128.05 78.76 1937 128.83 80.82 1938 129.83 81.80 1939 130.88 83.00 1940 132.12 84.11 1941 133.40 85.20 1942 134.86 86.25 1943 136.74 87.29 1944 138.40 88.23 1945 139.93 89.01 1946 141.39 89.90 6.75 1947 144.13 90.88 43.58 14.41 5504.21 1948 146.63 91.91 44.00 22.03 5544.53 1949 149.19 92.70 45.28 13.94 5573.00 1950 151.68 93.32 47.90 0.30 15.87 5764.29 1951 154.29 93.92 49.18 -2.52 18.32 5799.26 1952 156.95 94.50 51.90 1.51 14.44 5883.09 1953 159.57 95.16 54.53 0.90 14.26 6031.71 1954 162.39 95.76 56.10 1.78 15.01 6080.08 1955 165.28 96.47 56.35 -0.23 16.66 6334.90 1956 168.22 97.21 58.13 -0.22 17.39 6412.25 1957 171.27 97.79 60.00 0.19 18.73 6448.44 1958 174.14 98.59 61.88 1.55 16.17 6444.20 1959 177.83 98.53 62.90 1.12 14.64 6629.51 1960 180.67 99.47 64.58 2.33 17.19 6701.27 1961 183.69 100.81 66.78 3.11 15.13 6741.48 1962 186.54 101.96 68.55 1.76 16.12 6933.04 1963 189.24 103.04 70.60 2.68 15.81 7091.05 1964 191.89 104.08 73.58 2.48 16.07 7385.39 1965 194.30 106.12 74.40 1.50 17.34 7704.59 1966 196.56 107.91 76.95 1.25 17.42 8006.97 1967 198.71 109.71 79.20 1.90 17.29 8164.33 1968 200.71 111.45 81.90 0.57 14.46 8507.47 1969 202.68 113.23 83.80 1.29 18.85 8738.90 1970 204.88 115.09 86.60 1.44 17.21 8851.44 1971 207.66 116.46 87.85 0.54 16.16 9023.00 1972 209.90 118.85 89.93 1.29 15.53 9425.62 1973 211.91 121.07 92.13 0.73 18.56 9752.77 1974 213.85 123.30 92.30 -0.73 16.29 9603.75 1975 215.97 125.60 92.50 -1.25 16.63 9711.75 1976 218.04 128.04 95.25 1.51 14.88 10123.37 1977 220.24 130.41 96.85 0.84 15.72 10427.65 1978 222.59 132.82 97.48 0.60 16.13 10745.67 1979 225.06 135.33 98.05 0.55 17.67 10878.79 1980 227.23 137.83 99.00 1.85 16.15 10769.28 1981 229.47 140.03 98.30 2.96 17.33 10794.30 1982 231.66 142.07 100.03 6.27 15.66 10807.25 1983 233.79 143.87 100.43 7.03 13.14 11203.87 1984 235.83 145.46 100.60 7.69 15.03 11644.55 1985 237.92 146.88 101.78 6.98 13.31 12045.13 1986 240.13 148.26 104.60 5.29 11.76 12364.50 1987 242.29 149.61 105.58 5.46 13.19 12597.46 1988 244.50 151.13 106.38 5.08 13.34 12934.20 1989 246.82 152.68 105.48 3.90 12.68 13059.47 1990 249.42 154.01 107.10 4.30 11.56 13121.10 1991 252.18 155.28 108.35 4.10 11.76 12921.68 1992 254.92 156.52 111.33 4.57 11.75 13109.11 1993 257.93 158.19 112.90 11.79 13388.48 1994 260.71 159.46 1995 263.43 160.75 1996 266.10 162.16 1997 268.70 163.67 1998 271.26 165.38 1999 273.77 167.26 2000 276.24 169.13 2001 278.68 170.97 2002 281.10 172.83 2003 283.51 174.61 2004 285.90 176.41 2005 288.29 178.19 2006 290.68 179.93 2007 293.09 181.68 2008 295.51 183.38 2009 297.96 184.96 2010 300.43 186.71 2011 302.93 188.33 2012 305.45 189.96 2013 307.99 190.59 2014 310.55 191.43 2015 313.12 192.24 2016 315.69 192.95 2017 318.26 193.61 2018 320.83 194.10 2019 323.39 194.51 2020 325.94 194.82 2021 328.47 195.04 2022 330.98 195.24 2023 333.46 195.28 2024 335.91 195.35 2025 338.34 195.46 2026 340.73 195.54 2027 343.09 195.72 2028 345.42 195.95 2029 347.72 196.30 2030 349.99 196.78 2031 352.24 197.43 2032 354.45 198.32 2033 356.65 199.34 2034 358.82 200.43 2035 360.98 201.51 2036 363.11 202.48 2037 365.23 203.47 2038 367.34 204.71 2039 369.43 206.18 2040 371.51 207.70 2041 373.57 209.15 2042 375.63 210.65 2043 377.69 212.03 2044 379.74 213.38 2045 381.78 214.64 2046 383.82 215.75 2047 385.87 216.88 2048 387.92 217.94 2049 389.97 219.03 2050 392.03 220.17 ************************************************************************** Figures for the Ramsey Model, Dependency Ratio Model and Overlapping Generations Model are simulations generated by the GAUSS (version 3.01) programs provided below. ------------------------------------------------ Overlapping Generations Model: GAUSS simulation ************************************************************************** library nlsys.l32, pgraph.l32; /* Parameters */ delta = 0.01; @ subjective discount rate @ rho = 2; @ risk aversion @ T = 60; @ life span @ Tp = 45; @ years in labor force @ n = 0.010; @ population growth rate @ mu = 0.010; @ change in pop growth rate @ tau = 15; @ duration of mu @ w = 1; @ real wage @ fin = 100; @ number of periods @ alpha = 0.33; @ Cobb-Douglas parameter @ popu = zeros(fin+T,2); /* Population */ Y = zeros(fin,2); /* Aggregate Output */ sY = zeros(fin,2); /* Savings as % of Output */ C = zeros(fin,2); /* Per Capita Consumption */ k = zeros(fin,2); /* Capital to Labor Ratio */ w = zeros(fin,2); /* Wages */ r = zeros(fin,2); /* Interest Rates */ /* Calculate Population */ popu[.,1] = (1 + n) ^ seqa(-(T-1),1,fin+T); popu[1:T,2] = popu[1:T,1]; popu[T+1:T+tau,2] = popu[T,2] * (1 + n + mu) ^ seqa(1,1,tau); popu[T+tau+1:fin+T,2] = popu[T+tau,2] * (1 + n) ^ seqa(1,1,fin-tau); /* Solve for Original Steady State */ x0 = 0.10 | 23; g = n | n; L = Labor(g[1],g[2],Tp,0); { xf, fvp, jc, tcode } = nlsys(&f12,x0); r[.,1] = xf[1] * ones(fin,1); k[.,1] = (r[.,1] / alpha) ^ (1 / (alpha - 1)); w[.,1] = k[.,1] ^ alpha - r[.,1] .* k[.,1]; c0 = w[1,1] * ((r[1,1] - delta) / rho - r[1,1]) * (1 - exp(-r[1,1] * Tp)) / (r[1,1] * (exp(((r[1,1] - delta) / rho - r[1,1]) * T) - 1)); a = zeros(T,2); /* Individual's Assets */ na = zeros(T,2); /* Temporary Hold for Individual's Assets */ ci = zeros(T,2); /* Consumption of Individuals */ cap = zeros(1,2); /* Aggregate Capital */ /* Consumption */ mess = ((1 + r[1,1]) / (1 + delta)) ^ (seqa(1,1,T-1) / rho); linc = w[1,1] ./ (1 + r[1,1]) ^ seqa(0,1,Tp); i = 1; do while i <= T-1; ti = 1 / (1 + sumc(mess[1:T-i,1]))'; if i == 1; ci[i,1] = ti .* sumc(linc[1:Tp,1])'; a[1,1] = w[1,1] - ci[1,1]; elseif i > 1 and i <= Tp; ci[i,1] = ti .* (sumc(linc[1:Tp-i+1,1])'+ (1 + r[1,1]) .* a[i-1,1]); a[i,1] = (1 + r[1,1]) .* a[i-1,1] + w[1,1] - ci[i,1]; elseif i > Tp and i < T; ci[i,1] = ti .* (1 + r[1,1]) .* a[i-1,1]; a[i,1] = (1 + r[1,1]) .* a[i-1,1] - ci[i,1]; endif; i = i + 1; endo; a[.,2] = a[.,1]; p = rev(popu[1:T,1]); s = 1; do while s <= fin; cls; print "Period " s "of " fin; /* Aggregate Capital */ cap = diag(p' * a[.,.])'; p = rev(popu[s+1:s+T,.]); /* Labor Force */ lab = sumc(p[1:Tp,.])'; /* Production Function */ k[s,.] = cap ./ lab; Y[s,.] = cap ^ alpha .* lab ^ (1 - alpha); r[s,.] = alpha * k[s,.] ^ (alpha - 1); w[s,.] = k[s,.] ^ alpha - r[s,.] .* k[s,.]; /* Consumption */ mess = ((1 + r[s,.]) / (1 + delta)) ^ (seqa(1,1,T-1) / rho); linc = w[s,.] ./ (1 + r[s,.]) ^ seqa(0,1,Tp); i = 1; do while i <= T-1; ti = 1 / (1 + sumc(mess[1:T-i,.]))'; if i == 1; ci[i,.] = ti .* sumc(linc[1:Tp,.])'; elseif i > 1 and i <= Tp; ci[i,.] = ti .* (sumc(linc[1:Tp-i+1,.])'+ (1 + r[s,.]) .* a[i-1,.]); elseif i > Tp; ci[i,.] = ti .* (1 + r[s,.]) .* a[i-1,.]; endif; i = i + 1; endo; ci[T,.] = (1 + r[s,.]) .* a[T-1,.]; C[s,.] = diag(p' * ci)' ./ sumc(p)'; /* Asset */ na[1,.] = w[s,.] - ci[1,.]; na[2:Tp,.] = (1 + r[s,.]) .* a[1:Tp-1,.] + w[s,.] - ci[2:Tp,.]; na[Tp+1:T,.] = (1 + r[s,.]) .* a[Tp:T-1,.] - ci[Tp+1:T,.]; a = na; /* Saving */ sY[s,.] = (Y[s,.] - diag(p' * ci)') ./ Y[s,.]; s = s + 1; endo; end; proc f12(var); local x1, x2, eqns; x1 = var[1]; x2 = var[2]; eqns = K1(g[1],g[2],Tp,0,x1) + K2(g[1],g[2],T,Tp,x1) - x2 | (alpha / (1 - alpha)) / x1 - x2; retp(eqns); endp; proc K1(b1, b2, t2, t1, r); local AK, a1, a2, a3, rdr, c0; rdr = (r - delta) / rho; a1 = (1 + (1 - exp(-r*Tp)) / (exp((rdr-r)*T) - 1)) / (r * (r - b2)); a2 = 1 / (r * b2); a3 = (1 - exp(-r*Tp)) / (r * (exp((rdr-r)*T) - 1) * (rdr - b2)); AK = exp(b1) * (a1 * (exp((r-b2)*t2) - exp((r-b2)*t1)) + a2 * (exp(-b2*t2) - exp(-b2*t1)) - a3 * (exp((rdr-b2)*t2) - exp((rdr-b2)*t1))) / L; retp(AK); endp; proc K2(b1, b2, t2, t1, r); local AK, a1, a2, a3, rdr, c0; rdr = (r - delta) / rho; a1 = (1 - exp(-r*Tp)) / (r * (exp((rdr-r)*T) - 1)); a2 = exp((rdr-r)*T) / (r - b2); a3 = 1 / (rdr - b2); AK = exp(b1) * a1 * (a2 * (exp((r-b2)*t2) - exp((r-b2)*t1)) - a3 * (exp((rdr-b2)*t2) - exp((rdr-b2)*t1))) / L; retp(AK); endp; proc Labor(b1, b2, t2, t1); local AL; AL = exp(b1) * (exp(-b2*t1) - exp(-b2*t2)) / b2; retp(AL); endp; Ramsey and Dependency Ratio Model: GAUSS simulations /* Parameters */ delta = 0.01; @ subjective discount rate @ rho = 4; @ risk aversion @ T = 60; @ life span @ Tp = 45; @ years in labor force @ n = 0.010; @ population growth rate @ mu = 0.010; @ change in pop growth rate @ tau = 15; @ duration of mu @ w = 1; @ real wage @ fin = 100; @ number of periods @ alpha = 0.33; @ Cobb-Douglas parameter @ /* Calculate Population & Age Distributions */ pop0 = zeros(fin,T); pop1 = pop0; pop0[.,1] = (1 + n) ^ seqa(1,1,fin); pop0[1,2:T] = pop0[1,1] / (1 + n) ^ seqa(1,1,T-1)'; pop1[1:tau,1] = (1 + n + mu) ^ seqa(1,1,tau); pop1[tau+1:fin,1] = pop1[tau,1] * (1 + n) ^ seqa(1,1,fin-tau); pop1[1,2:T] = pop0[1,2:T]; i = 2; do while i <= fin; pop0[i,2:T] = pop0[i-1,1:T-1]; pop1[i,2:T] = pop1[i-1,1:T-1]; i = i + 1; endo; gamma1 = sumc(pop1') ./ sumc(pop1[.,1:Tp]'); s = zeros(fin,2); /* Savings as % of Output */ c = zeros(fin,2); /* Per Capita Consumption */ k = zeros(fin,2); /* Capital to Labor Ratio */ w = zeros(fin,2); /* Wages */ r = zeros(fin,2); /* Interest Rates */ /* Ramsey Model*/ k0 = ((delta + n) / alpha) ^ (1 / (alpha -1)); k1 = ((delta + n + mu) / alpha) ^ (1 / (alpha -1)); c0 = k0 ^ alpha - n * k0; c1 = k1 ^ alpha - (n + mu) * k1; beta = - alpha * (alpha - 1) * k1 ^ (alpha - 2) * c1 / rho; lambda = delta - sqrt(delta^2+4*beta) / 2; print beta lambda k0 k1; wait; k[1:tau,1] = k1 + (k0 - k1) * exp(lambda*seqa(1,1,tau)); beta = - alpha * (alpha - 1) * k0 ^ (alpha - 2) * c0 / rho; lambda = delta - sqrt(delta^2+4*beta) / 2; print beta lambda; k[tau+1:fin,1] = k0 + (k[tau,1] - k0) * exp(lambda*seqa(1,1,fin-tau)); c[1,1] = k[1,1] ^ alpha - (k[1,1] - k0) - (n + mu) * k[1,1]; c[2:fin,1] = k[2:fin,1] ^ alpha - (k[2:fin,1] - k[1:fin-1,1]); c[2:tau,1] = c[2:tau,1] - (n + mu) * k[2:tau,1]; c[tau+1:fin,1] = c[tau+1:fin,1] - n * k[tau+1:fin,1]; s[.,1] = (k[.,1] ^ alpha - c[.,1]) ./ k[.,1] ^ alpha; @ normalizations @ s[.,1] = s[.,1] / ((k0^ alpha - c0) / k0 ^ alpha); c[.,1] = c[.,1] / c0; k[.,1] = k[.,1] / k0; w[.,1] = k[.,1] ^ alpha; r[.,1] = k[.,1] ^ (alpha - 1); /* Solve for Original Steady State */ x0 = 0.10 | 23; g = n | n; L = Labor(g[1],g[2],Tp,0); { xf, fvp, jc, tcode } = nlsys(&f12,x0); r[.,1] = xf[1] * ones(fin,1); k[.,1] = (r[.,1] / alpha) ^ (1 / (alpha - 1)); w[.,1] = k[.,1] ^ alpha - r[.,1] .* k[.,1]; c0 = w[1,1] * ((r[1,1] - delta) / rho - r[1,1]) * (1 - exp(-r[1,1] * Tp)) / (r[1,1] * (exp(((r[1,1] - delta) / rho - r[1,1]) * T) - 1)); a = zeros(T,3); /* Individual's Assets */ na = zeros(T,3); /* Temporary Hold for Individual's Assets */ ci = zeros(T,3); /* Consumption of Individuals */ cap = zeros(1,3); /* Aggregate Capital */ /* Consumption */ mess = ((1 + r[1,1]) / (1 + delta)) ^ (seqa(1,1,T-1) / rho); linc = w[1,1] ./ (1 + r[1,1]) ^ seqa(0,1,Tp); i = 1; do while i <= T-1; ti = 1 / (1 + sumc(mess[1:T-i,1]))'; if i == 1; ci[i,1] = ti .* sumc(linc[1:Tp,1])'; a[1,1] = w[1,1] - ci[1,1]; elseif i > 1 and i <= Tp; ci[i,1] = ti .* (sumc(linc[1:Tp-i+1,1])'+ (1 + r[1,1]) .* a[i-1,1]); a[i,1] = (1 + r[1,1]) .* a[i-1,1] + w[1,1] - ci[i,1]; elseif i > Tp and i < T; ci[i,1] = ti .* (1 + r[1,1]) .* a[i-1,1]; a[i,1] = (1 + r[1,1]) .* a[i-1,1] - ci[i,1]; endif; i = i + 1; endo; a[.,2] = a[.,1]; a[.,3] = a[.,1]; p = rev(popu[1:T,1]); s = 1; do while s <= fin; cls; print "Period " s "of " fin; /* Aggregate Capital */ cap = diag(p[.,.]' * a[.,.])'; p = rev(popu[s+1:s+T,.]); /* Labor Force */ lab = sumc(p[1:Tp,.])'; /* Production Function */ k[s,.] = cap ./ lab; Y[s,.] = cap ^ alpha .* lab ^ (1 - alpha); r[s,.] = alpha * k[s,.] ^ (alpha - 1); w[s,.] = k[s,.] ^ alpha - r[s,.] .* k[s,.]; /* Consumption */ mess = ((1 + r[s,.]) / (1 + delta)) ^ (seqa(1,1,T-1) / rho); linc = w[s,.] ./ (1 + r[s,.]) ^ seqa(0,1,Tp); i = 1; do while i <= T-1; ti = 1 / (1 + sumc(mess[1:T-i,.]))'; if i == 1; ci[i,.] = ti .* sumc(linc[1:Tp,.])'; elseif i > 1 and i <= Tp; ci[i,.] = ti .* (sumc(linc[1:Tp-i+1,.])'+ (1 + r[s,.]) .* a[i-1,.]); elseif i > Tp; ci[i,.] = ti .* (1 + r[s,.]) .* a[i-1,.]; endif; i = i + 1; endo; ci[T,.] = (1 + r[s,.]) .* a[T-1,.]; C[s,.] = diag(p' * ci)' ./ sumc(p)'; /* Asset */ na[1,.] = w[s,.] - ci[1,.]; na[2:Tp,.] = (1 + r[s,.]) .* a[1:Tp-1,.] + w[s,.] - ci[2:Tp,.]; na[Tp+1:T,.] = (1 + r[s,.]) .* a[Tp:T-1,.] - ci[Tp+1:T,.]; a = na; /* Saving */ sY[s,.] = (Y[s,.] - diag(p' * ci)') ./ Y[s,.]; s = s + 1; endo; /* Cutler et al. */ gamma0 = sumc((1+n)^seqa(1,-1,T)) / sumc((1+n)^seqa(1,-1,Tp)); k0 = (delta / alpha) ^ (1 / (alpha - 1)); c0 = (k0 ^ alpha - n * k0) / gamma0; c[1:tau,2] = (k0 ^ alpha - (n + mu) * k0) / gamma1[1:tau]; c[tau+1:fin,2] = (k0 ^ alpha - n * k0) / gamma1[tau+1:fin]; s[.,2] = (k0 ^ alpha - gamma1 .* c[.,2]) / k0 ^ alpha; @ normalization @ s[.,2] = s[.,2] / ((k0 ^ alpha - gamma0 * c0) / k0 ^ alpha); c[.,2] = c[.,2] ./ c0; k[.,2] = ones(fin,1); w[.,2] = ones(fin,1); r[.,2] = ones(fin,1); end; proc f12(var); local x1, x2, eqns; x1 = var[1]; x2 = var[2]; eqns = K1(g[1],g[2],Tp,0,x1) + K2(g[1],g[2],T,Tp,x1) - x2 | (alpha / (1 - alpha)) / x1 - x2; retp(eqns); endp; proc K1(b1, b2, t2, t1, r); local AK, a1, a2, a3, rdr, c0; rdr = (r - delta) / rho; a1 = (1 + (1 - exp(-r*Tp)) / (exp((rdr-r)*T) - 1)) / (r * (r - b2)); a2 = 1 / (r * b2); a3 = (1 - exp(-r*Tp)) / (r * (exp((rdr-r)*T) - 1) * (rdr - b2)); AK = exp(b1) * (a1 * (exp((r-b2)*t2) - exp((r-b2)*t1)) + a2 * (exp(-b2*t2) - exp(-b2*t1)) - a3 * (exp((rdr-b2)*t2) - exp((rdr-b2)*t1))) / L; retp(AK); endp; proc K2(b1, b2, t2, t1, r); local AK, a1, a2, a3, rdr, c0; rdr = (r - delta) / rho; a1 = (1 - exp(-r*Tp)) / (r * (exp((rdr-r)*T) - 1)); a2 = exp((rdr-r)*T) / (r - b2); a3 = 1 / (rdr - b2); AK = exp(b1) * a1 * (a2 * (exp((r-b2)*t2) - exp((r-b2)*t1)) - a3 * (exp((rdr-b2)*t2) - exp((rdr-b2)*t1))) / L; retp(AK); endp; proc Labor(b1, b2, t2, t1); local AL; AL = exp(b1) * (exp(-b2*t1) - exp(-b2*t2)) / b2; retp(AL); endp;