Econ problem set

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econ24
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Homework 2
April 20, 2022
Overview
Due date: Friday, April 29
In this exercise, you will make use of the spreadsheet provided on the class website.
The spreadsheet features data with different tabs, corresponding to different exercises in the homework.
We have constructed some simulated data by choosing parameter values and following the Solow model
structure. At the top of tabs 1a and 2a we have specified parameters of the Solow model: depreciation (δ),
the Cobb-Douglas technology parameter (α), the savings rate (s) along with exogenous growth rates for TFP
(x) and population (n). In addition, we have specified initial conditions for the level of technology (A0),
population (L0), and capital (K0) in the initial period (the year 1955). For tabs 1b and 2b you are invited to
adjust the parameter values and compare the model-simulated growth to real life data (which you will find
online). For tabs 3 and 4 we supply growth rate patterns for population and technology that don’t follow the
simple constant growth rate structure, while the other aspects of the Solow model are left unchanged.
Recall that the Solow model specifies a production function of the form:
Yt = AtKαt L
1−α
t
where t indexes the time period in which production takes place.
When asked to fill in values for real wages, rental rates, and income shares you may assume that these values
are pinned down by cost minimization behavior and that all available inputs (labor and capital) are fully
utilized.
Question 1 – Solow Model for US (25 points)
For this questions please use sheets 1a and 1b.
(a) (10 points) In sheet 1a in columns G through M, please construct spreadsheet formulas to calculate
the requested values using the Solow model. Specifically, please calculate: output per efficiency units
(ŷ = Y/ÃL), output per capita, capital-labor ratio, the labor share of income, real wages, the growth
rate of GDP per capita, and the real rental rate of capital.
(b) (10 points) In sheet 1a in cells E2 and E3, please calculate the long-run stable level of capital per
effective worker (k̂ = K/ÃL) and output per effective worker (ŷ = Y/ÃL). In cell H2 enter the first
year in our simulated data when the capital per effective worker is within 1% of its long-run stable
level. For the year in cell H2, how large is the gap between the growth of output per worker in the
simulated data and the growth rate that would prevail on the balanced growth path?
(c) (5 points) Download data on US real GDP based from the Penn World Tables at the link here. Enter
US real GDP (PPP), series rgdpe, into column G of sheet 1b and population, series pop, into column
H, and calculate real GDP per capita growth in column I. How does the simulated data in sheet 1a
compare to this data? Try adjusting any model parameters or initial conditions to better match the
simulated and observed data.
1
https://www.rug.nl/ggdc/productivity/pwt/?lang=en
Question 2 – Solow Model for China (35 points)
For this question, please use sheets 2a and 2b. Relative to the scenario for the US (on sheet 1a) we allow for
faster population growth, a larger initial population, and a smaller initial capital stock. In addition, we freeze
China’s TFP growth for the first 20 years (1955-1975) and then have China’s TFP match the US level from
20 years prior (e.g. Chinese TFP in 2020 equals the US level in 2000).
(a) (10 points) In sheet 2a in columns G through M, please construct spreadsheet formulas to calculate the
requested values using the Solow model using the given data and parameters for the China model.
(b) (10 points) In sheet 2a in cells E2 and E3, please calculate the long-run stable level of capital per
effective worker (k̂ = K/ÃL) and output per effective worker (ŷ = Y/ÃL) for the China model. Are
these values higher or lower than the corresponding values for the US? Explain why the two values
differ. In cells H2 and H3, calculate the long-run stable level of capital per effective worker and output
per effective worker if there is no TFP growth (as we assumed for 1955-1975). Are these values higher
or lower than the values for the scenario with TFP growth? Explain your answer.
(c) (10 points) Given the assumptions in sheet 2a, what is the long-run growth rate of GDP per capita
in China? In our model, is growth in China increasing or decreasing over time? How does growth
change between 1974 and 1976? How does growth evolve after 1976? Explain why the model and other
assumptions generate this pattern.
(d) (5 points) Download data on Chinese real GDP based from the Penn World Tables at the link here.
Enter Chinese real GDP (PPP), series rgdpe, into column G of sheet 2b and population, series pop,
into column H, and calculate real GDP per capita growth in column I. How does the simulated data
in sheet 2a compare to this data? Try adjusting any model parameters or initial conditions to better
match the simulated and observed data.
Question 3 – One Child Policy (20 points)
For this question, please use sheet 3. In addition to liberalizing its economy under the Reform and Opening
Up policies of Deng Xiaoping, China also experienced a profound change in its demographic patterns in part
driven by the imposition of the One Child policy. In this section, we adjust the model from question 2 to
account for these demographic changes.
(a) (5 points) In sheet 3, construct an alternative path for Chinese population (column B, rows 15 to 110)
as follows. For 1955 to 2019, use the population growth data from Penn World tables. Then, from 2019
to 2050, assume a constant growth rate of -1% (n = -0.01). Based on the Penn World tables data what
was the average growth rate of China’s population each of the 20-year periods 1955-1975, 1975-1995,
and 1995-2015? (Note: columns C, D, E, and F should update automatically when you fill in column
B).
(b) (5 points) Construct the deduced variables in columns G through M using the new path for population
growth. How does the new path for population growth affect the growth rate of total output? What
about the growth rate of output per worker? For both variables, is there a permanent (i.e. on the
balanced growth path) effect to the growth rate from this change in population growth?
(c) (10 points) Using the growth accounting procedure, what is the contribution of capital, labor, and
technology growth to Chinese growth in questions 2 and 3. Please fill in these values in columns O, P,
and Q for sheets 2a and 3. Explain the differences.
Question 4 – Technology Catch-Up (20 points)
For this question, please use sheet 4. In addition to China beginning a period of TFP growth, we might
expect that China begins to close the gap in technology relative to the US. In this question we construct an
2
https://www.rug.nl/ggdc/productivity/pwt/?lang=en
alternative path for TFP that allows for a non-constant growth rate of TFP over time in China. Note that
this sheet will automatically pull in the population path you built in sheet 3.
(a) (5 points) Inspect the formula in column C for years 1976 onward (row 36 on). Describe in words what
you think this formula is doing. In questions 2 and 3 what happened to the relative level (ratio) of
TFP in the US and China over time? With this new formula what happens to the relative level of TFP
over time? Will this ratio tend to a particular value in the long run?
(b) (5 points) Construct the deduced variables in columns G through M. How does Chinese growth in this
scenario compare to what you saw in questions 2 and 3? Does this do a better or worse job of matching
the observed data?
(c) (10 points) Given the new path for TFP, in the long-run (e.g. 2100 onward) will Chinese living standards
grow faster, slower, or at the same rate as in the US? Will the level of Chinese living standards be
higher, lower, or the same as in the US? Explain your answer.
3
Overview
Question 1 – Solow Model for US (25 points)
Question 2 – Solow Model for China (35 points)
Question 3 – One Child Policy (20 points)
Question 4 – Technology Catch-Up (20 points)
1a – US model
United States
delta 0.1 To fill: kss 1st year kt within 1% of kss:
alpha 0.33333 To fill: yss
savings rate 0.2
pop growth n 0.012
tech growth x 0.035
Initial Condtions
L0 170 (US pop in millions)
K0 600000
A0 100
Model Deduced Variables
Units Million Normalization Millions of Dollars Millions of Real Dollars Millions of Real Dollars
Year Population TFP Capital Output Investment Output per Efficiency Unit Output/Capita Capital/Capita Labor Share Real Wages GDP Per Capita Growth Real Rental Rate
1955 170 100 600000 258823.9964 51764.79928
1956 172.04 103.5 591764.7993 268780.584 53756.11681
1957 174.10448 107.1225 586344.4362 279550.2225 55910.04449
1958 176.1937338 110.8717875 583620.037 291192.1655 58238.4331
1959 178.3080586 114.7523001 583496.4664 303768.736 60753.74719
1960 180.4477553 118.7686306 585900.567 317345.4964 63469.09928
1961 182.6131283 122.9255326 590779.6096 331991.4475 66398.28949
1962 184.8044859 127.2279263 598099.9381 347779.2555 69555.8511
1963 187.0221397 131.6809037 607845.7954 364785.5097 72957.10194
1964 189.2664054 136.2897353 620018.3178 383091.0094 76618.20187
1965 191.5376022 141.0598761 634634.6879 402781.0812 80556.21624
1966 193.8360535 145.9969717 651727.4353 423945.9259 84789.18518
1967 196.1620861 151.1068657 671343.877 446680.9949 89336.19898
1968 198.5160311 156.395606 693545.6883 471087.3955 94217.47911
1969 200.8982235 161.8694522 718408.5985 497272.3259 99454.46518
1970 203.3090022 167.5348831 746022.2039 525349.5389 105069.9078
1971 205.7487102 173.398604 776489.8913 555439.8356 111087.9671
1972 208.2176947 179.4675551 809928.8693 587671.5897 117534.3179
1973 210.7163071 185.7489196 846470.3003 622181.3026 124436.2605
1974 213.2449028 192.2501317 886259.5308 659114.1915 131822.8383
1975 215.8038416 198.9788863 929456.416 698624.8126 139724.9625
1976 218.3934877 205.9431474 976235.7369 740877.7197 148175.5439
1977 221.0142096 213.1511575 1026787.707 786048.1618 157209.6324
1978 223.6663801 220.611448 1081318.569 834322.8225 166864.5645
1979 226.3503766 228.3328487 1140051.276 885900.6029 177180.1206
1980 229.0665812 236.3244984 1203226.269 940993.4517 188198.6903
1981 231.8153801 244.5958559 1271102.333 999827.246 199965.4492
1982 234.5971647 253.1567108 1343957.549 1062642.726 212528.5453
1983 237.4123307 262.0171957 1422090.339 1129696.489 225939.2979
1984 240.2612786 271.1877976 1505820.603 1201262.043 240252.4086
1985 243.144414 280.6793705 1595490.951 1277630.928 255526.1857
1986 246.0621469 290.5031484 1691468.042 1359113.911 271822.7823
1987 249.0148927 300.6707586 1794144.02 1446042.252 289208.4505
1988 252.0030714 311.1942352 1903938.068 1538769.056 307753.8112
1989 255.0271083 322.0860334 2021298.073 1637670.708 327534.1416
1990 258.0874336 333.3590446 2146702.407 1743148.406 348629.6812
1991 261.1844828 345.0266111 2280661.848 1855629.789 371125.9577
1992 264.3186966 357.1025425 2423721.621 1975570.668 395114.1337
1993 267.4905209 369.6011315 2576463.592 2103456.882 420691.3764
1994 270.7004072 382.5371711 2739508.609 2239806.259 447961.2517
1995 273.9488121 395.9259721 2913519 2385170.715 477034.143
1996 277.2361978 409.7833811 3099201.243 2540138.491 508027.6981
1997 280.5630322 424.1257995 3297308.817 2705336.528 541067.3056
1998 283.9297886 438.9702025 3508645.241 2881433.009 576286.6018
1999 287.336946 454.3341595 3734067.319 3069140.054 613828.0108
2000 290.7849894 470.2358551 3974488.598 3269216.605 653843.321
2001 294.2744093 486.6941101 4230883.059 3482471.491 696494.2982
2002 297.8057022 503.7284039 4504289.051 3709766.697 741953.3393
2003 301.3793706 521.3588981 4795813.485 3952020.847 790404.1693
2004 304.995923 539.6064595 5106636.306 4210212.916 842042.5833
2005 308.6558741 558.4926856 5438015.259 4485386.188 897077.2377
2006 312.3597446 578.0399296 5791290.971 4778652.466 955730.4931
2007 316.1080615 598.2713271 6167892.367 5091196.563 1018239.313
2008 319.9013583 619.2108235 6569342.443 5424281.093 1084856.219
2009 323.7401746 640.8832024 6997264.417 5779251.565 1155850.313
2010 327.6250567 663.3141145 7453388.288 6157541.823 1231508.365
2011 331.5565574 686.5301085 7939557.824 6560679.828 1312135.966
2012 335.535236 710.5586623 8457738.007 6990293.84 1398058.768
2013 339.5616589 735.4282154 9010022.974 7448118.983 1489623.797
2014 343.6363988 761.168203 9598644.474 7936004.258 1587200.852
2015 347.7600356 787.8090901 10225980.88 8455920.009 1691184.002
2016 351.933156 815.3824082 10894566.79 9009965.877 1801993.175
2017 356.1563539 843.9207925 11607103.29 9600379.281 1920075.856
2018 360.4302301 873.4580203 12366468.82 10229544.45 2045908.89
2019 364.7553929 904.029051 13175730.82 10900002.06 2180000.411
2020 369.1324576 935.6700677 14038158.15 11614459.46 2322891.892
2021 373.5620471 968.4185201 14957234.23 12375801.66 2475160.333
2022 378.0447916 1002.313168 15936671.14 13187102.94 2637420.588
2023 382.5813291 1037.394129 16980424.61 14051639.25 2810327.85
2024 387.1723051 1073.702924 18092710 14972901.49 2994580.298
2025 391.8183728 1111.282526 19278019.3 15954609.55 3190921.909
2026 396.5201932 1150.177414 20541139.28 17000727.36 3400145.472
2027 401.2784356 1190.433624 21887170.82 18115478.9 3623095.78
2028 406.0937768 1232.098801 23321549.52 19303365.24 3860673.047
2029 410.9669021 1275.222259 24850067.62 20569182.7 4113836.539
2030 415.8985049 1319.855038 26478897.39 21918042.25 4383608.45
2031 420.889287 1366.049964 28214616.1 23355390.13 4671078.026
2032 425.9399584 1413.861713 30064232.52 24887029.83 4977405.966
2033 431.0512379 1463.346873 32035215.23 26519145.54 5303829.107
2034 436.2238528 1514.564013 34135522.82 28258327.09 5651665.417
2035 441.458539 1567.573754 36373635.95 30111596.59 6022319.319
2036 446.7560415 1622.438835 38758591.68 32086436.78 6417287.356
2037 452.117114 1679.224195 41300019.87 34190821.21 6838164.242
2038 457.5425194 1737.997041 44008182.12 36433246.46 7286649.292
2039 463.0330296 1798.826938 46894013.2 38822766.44 7764553.288
2040 468.5894259 1861.785881 49969165.17 41369028.94 8273805.788
2041 474.212499 1926.948387 53246054.44 44082314.59 8816462.918
2042 479.903049 1994.39158 56737911.91 46973578.37 9394715.674
2043 485.6618856 2064.195285 60458836.4 50054493.83 10010898.77
2044 491.4898283 2136.44212 64423851.52 53337500.22 10667500.04
2045 497.3877062 2211.217595 68648966.41 56835852.74 11367170.55
2046 503.3563587 2288.61021 73151240.32 60563676.02 12112735.2
2047 509.396635 2368.711568 77948851.49 64536021.18 12907204.24
2048 515.5093946 2451.616473 83061170.58 68768926.58 13753785.32
2049 521.6955073 2537.423049 88508838.84 73279482.59 14655896.52
2050 527.9558534 2626.232856 94313851.47 78085900.56 15617180.11
1b – US modeldata
United States
delta 0.1
alpha 0.33333
savings rate 0.2
pop growth n 0.012
tech growth x 0.035
Initial Condtions
L0 170 (US pop in millions)
K0 600000
A0 100
Model Data
Units Million Normalization Millions of Dollars Millions of Real Dollars Millions of Real Dollars
Year Population TFP Capital Output Investment Real GDP (PPP) Population Growth of Real GDP per capita
1955 170 100 600000 258823.9964 51764.79928
1956 172.04 103.5 591764.7993 268780.584 53756.11681
1957 174.10448 107.1225 586344.4362 279550.2225 55910.04449
1958 176.1937338 110.8717875 583620.037 291192.1655 58238.4331
1959 178.3080586 114.7523001 583496.4664 303768.736 60753.74719
1960 180.4477553 118.7686306 585900.567 317345.4964 63469.09928
1961 182.6131283 122.9255326 590779.6096 331991.4475 66398.28949
1962 184.8044859 127.2279263 598099.9381 347779.2555 69555.8511
1963 187.0221397 131.6809037 607845.7954 364785.5097 72957.10194
1964 189.2664054 136.2897353 620018.3178 383091.0094 76618.20187
1965 191.5376022 141.0598761 634634.6879 402781.0812 80556.21624
1966 193.8360535 145.9969717 651727.4353 423945.9259 84789.18518
1967 196.1620861 151.1068657 671343.877 446680.9949 89336.19898
1968 198.5160311 156.395606 693545.6883 471087.3955 94217.47911
1969 200.8982235 161.8694522 718408.5985 497272.3259 99454.46518
1970 203.3090022 167.5348831 746022.2039 525349.5389 105069.9078
1971 205.7487102 173.398604 776489.8913 555439.8356 111087.9671
1972 208.2176947 179.4675551 809928.8693 587671.5897 117534.3179
1973 210.7163071 185.7489196 846470.3003 622181.3026 124436.2605
1974 213.2449028 192.2501317 886259.5308 659114.1915 131822.8383
1975 215.8038416 198.9788863 929456.416 698624.8126 139724.9625
1976 218.3934877 205.9431474 976235.7369 740877.7197 148175.5439
1977 221.0142096 213.1511575 1026787.707 786048.1618 157209.6324
1978 223.6663801 220.611448 1081318.569 834322.8225 166864.5645
1979 226.3503766 228.3328487 1140051.276 885900.6029 177180.1206
1980 229.0665812 236.3244984 1203226.269 940993.4517 188198.6903
1981 231.8153801 244.5958559 1271102.333 999827.246 199965.4492
1982 234.5971647 253.1567108 1343957.549 1062642.726 212528.5453
1983 237.4123307 262.0171957 1422090.339 1129696.489 225939.2979
1984 240.2612786 271.1877976 1505820.603 1201262.043 240252.4086
1985 243.144414 280.6793705 1595490.951 1277630.928 255526.1857
1986 246.0621469 290.5031484 1691468.042 1359113.911 271822.7823
1987 249.0148927 300.6707586 1794144.02 1446042.252 289208.4505
1988 252.0030714 311.1942352 1903938.068 1538769.056 307753.8112
1989 255.0271083 322.0860334 2021298.073 1637670.708 327534.1416
1990 258.0874336 333.3590446 2146702.407 1743148.406 348629.6812
1991 261.1844828 345.0266111 2280661.848 1855629.789 371125.9577
1992 264.3186966 357.1025425 2423721.621 1975570.668 395114.1337
1993 267.4905209 369.6011315 2576463.592 2103456.882 420691.3764
1994 270.7004072 382.5371711 2739508.609 2239806.259 447961.2517
1995 273.9488121 395.9259721 2913519 2385170.715 477034.143
1996 277.2361978 409.7833811 3099201.243 2540138.491 508027.6981
1997 280.5630322 424.1257995 3297308.817 2705336.528 541067.3056
1998 283.9297886 438.9702025 3508645.241 2881433.009 576286.6018
1999 287.336946 454.3341595 3734067.319 3069140.054 613828.0108
2000 290.7849894 470.2358551 3974488.598 3269216.605 653843.321
2001 294.2744093 486.6941101 4230883.059 3482471.491 696494.2982
2002 297.8057022 503.7284039 4504289.051 3709766.697 741953.3393
2003 301.3793706 521.3588981 4795813.485 3952020.847 790404.1693
2004 304.995923 539.6064595 5106636.306 4210212.916 842042.5833
2005 308.6558741 558.4926856 5438015.259 4485386.188 897077.2377
2006 312.3597446 578.0399296 5791290.971 4778652.466 955730.4931
2007 316.1080615 598.2713271 6167892.367 5091196.563 1018239.313
2008 319.9013583 619.2108235 6569342.443 5424281.093 1084856.219
2009 323.7401746 640.8832024 6997264.417 5779251.565 1155850.313
2010 327.6250567 663.3141145 7453388.288 6157541.823 1231508.365
2011 331.5565574 686.5301085 7939557.824 6560679.828 1312135.966
2012 335.535236 710.5586623 8457738.007 6990293.84 1398058.768
2013 339.5616589 735.4282154 9010022.974 7448118.983 1489623.797
2014 343.6363988 761.168203 9598644.474 7936004.258 1587200.852
2015 347.7600356 787.8090901 10225980.88 8455920.009 1691184.002
2016 351.933156 815.3824082 10894566.79 9009965.877 1801993.175
2017 356.1563539 843.9207925 11607103.29 9600379.281 1920075.856
2018 360.4302301 873.4580203 12366468.82 10229544.45 2045908.89
2019 364.7553929 904.029051 13175730.82 10900002.06 2180000.411
2020 369.1324576 935.6700677 14038158.15 11614459.46 2322891.892
2021 373.5620471 968.4185201 14957234.23 12375801.66 2475160.333
2022 378.0447916 1002.313168 15936671.14 13187102.94 2637420.588
2023 382.5813291 1037.394129 16980424.61 14051639.25 2810327.85
2024 387.1723051 1073.702924 18092710 14972901.49 2994580.298
2025 391.8183728 1111.282526 19278019.3 15954609.55 3190921.909
2026 396.5201932 1150.177414 20541139.28 17000727.36 3400145.472
2027 401.2784356 1190.433624 21887170.82 18115478.9 3623095.78
2028 406.0937768 1232.098801 23321549.52 19303365.24 3860673.047
2029 410.9669021 1275.222259 24850067.62 20569182.7 4113836.539
2030 415.8985049 1319.855038 26478897.39 21918042.25 4383608.45
2031 420.889287 1366.049964 28214616.1 23355390.13 4671078.026
2032 425.9399584 1413.861713 30064232.52 24887029.83 4977405.966
2033 431.0512379 1463.346873 32035215.23 26519145.54 5303829.107
2034 436.2238528 1514.564013 34135522.82 28258327.09 5651665.417
2035 441.458539 1567.573754 36373635.95 30111596.59 6022319.319
2036 446.7560415 1622.438835 38758591.68 32086436.78 6417287.356
2037 452.117114 1679.224195 41300019.87 34190821.21 6838164.242
2038 457.5425194 1737.997041 44008182.12 36433246.46 7286649.292
2039 463.0330296 1798.826938 46894013.2 38822766.44 7764553.288
2040 468.5894259 1861.785881 49969165.17 41369028.94 8273805.788
2041 474.212499 1926.948387 53246054.44 44082314.59 8816462.918
2042 479.903049 1994.39158 56737911.91 46973578.37 9394715.674
2043 485.6618856 2064.195285 60458836.4 50054493.83 10010898.77
2044 491.4898283 2136.44212 64423851.52 53337500.22 10667500.04
2045 497.3877062 2211.217595 68648966.41 56835852.74 11367170.55
2046 503.3563587 2288.61021 73151240.32 60563676.02 12112735.2
2047 509.396635 2368.711568 77948851.49 64536021.18 12907204.24
2048 515.5093946 2451.616473 83061170.58 68768926.58 13753785.32
2049 521.6955073 2537.423049 88508838.84 73279482.59 14655896.52
2050 527.9558534 2626.232856 94313851.47 78085900.56 15617180.11
2051 534.2913237 2718.151006 100499646.4 83207586.4 16641517.28
2052 540.7028195 2813.286291 107091199.1 88665218.88 17733043.78
2053 547.1912534 2911.751311 114115122.9 94480833.16 18896166.63
2054 553.7575484 3013.662607 121599777.3 100677909.7 20135581.94
2055 560.402639 3119.140798 129575381.5 107281469.2 21456293.84
2a – China model
China
delta 0.1 kss (tech growth) kss (no tech growth)
alpha 0.33333 yss (tech growth) yss (no tech growth)
savings 0.2
pop growth n 0.025
tech growth x 0.035
Initial Condtions
L0 600 (China pop in millions)
K0 100000
A0 —> 20 years behind US
Model Deduced Variables Growth Accounting (real GDP)
Units Million Normalization Millions of Dollars Millions of Real Dollars Millions of Real Dollars
Year Population TFP Capital Output Investment Output per Efficiency Unit Output/Capita Capital/Capita Labor Share Real Wages GDP Per Capita Growth Real Rental Rate TFP Contribution Capital Contribution Labor Contribution
1955 600 100 100000 330187.0941 66037.41881
1956 615 100 156037.4188 389330.3993 77866.07986
1957 630.375 100 218299.7568 442665.0897 88533.01795
1958 646.134375 100 285002.7991 491838.8055 98367.7611
1959 662.2877344 100 354870.2803 537912.8524 107582.5705
1960 678.8449277 100 426965.8227 581614.7702 116322.954
1961 695.8160509 100 500592.1945 623468.9023 124693.7805
1962 713.2114522 100 575226.7555 663868.725 132773.745
1963 731.0417385 100 650477.8249 703119.458 140623.8916
1964 749.317782 100 726053.934 741464.5056 148292.9011
1965 768.0507265 100 801741.4418 779102.5963 155820.5193
1966 787.2519947 100 877387.8168 816199.309 163239.8618
1967 806.9332945 100 952888.897 852895.0717 170579.0143
1968 827.1066269 100 1028179.022 889310.8647 177862.1729
1969 847.7842926 100 1103223.292 925552.3834 185110.4767
1970 868.9788999 100 1178011.44 961713.1395 192342.6279
1971 890.7033724 100 1252552.924 997876.8159 199575.3632
1972 912.9709567 100 1326872.995 1034119.082 206823.8163
1973 935.7952306 100 1401009.511 1070509.014 214101.8029
1974 959.1901114 100 1475010.363 1107110.227 221422.0455
1975 983.1698642 100 1548931.372 1143981.776 228796.3553
1976 1007.749111 103.5 1622834.59 1222520.155 244504.031
1977 1032.942839 107.1225 1705055.162 1307676.476 261535.2953
1978 1058.76641 110.8717875 1796084.941 1399971.983 279994.3966
1979 1085.23557 114.7523001 1896470.844 1499968.001 299993.6003
1980 1112.366459 118.7686306 2006817.36 1608269.286 321653.8571
1981 1140.17562 122.9255326 2127789.481 1725527.619 345105.5239
1982 1168.680011 127.2279263 2260116.057 1852445.692 370489.1384
1983 1197.897011 131.6809037 2404593.589 1989781.271 397956.2543
1984 1227.844437 136.2897353 2562090.485 2138351.697 427670.3394
1985 1258.540547 141.0598761 2733551.776 2299038.714 459807.7428
1986 1290.004061 145.9969717 2920004.341 2472793.682 494558.7364
1987 1322.254163 151.1068657 3122562.643 2660643.182 532128.6364
1988 1355.310517 156.395606 3342435.015 2863695.059 572739.0118
1989 1389.19328 161.8694522 3580930.526 3083144.933 616628.9865
1990 1423.923112 167.5348831 3839466.46 3320283.213 664056.6427
1991 1459.521189 173.398604 4119576.456 3576502.668 715300.5336
1992 1496.009219 179.4675551 4422919.344 3853306.577 770661.3153
1993 1533.40945 185.7489196 4751288.725 4152317.529 830463.5058
1994 1571.744686 192.2501317 5106623.358 4475286.91 895057.3821
1995 1611.038303 198.9788863 5491018.405 4824105.14 964821.0279
1996 1651.314261 205.9431474 5906737.592 5200812.707 1040162.541
1997 1692.597117 213.1511575 6356226.374 5607612.087 1121522.417
1998 1734.912045 220.611448 6842126.154 6046880.594 1209376.119
1999 1778.284846 228.3328487 7367289.658 6521184.248 1304236.85
2000 1822.741967 236.3244984 7934797.542 7033292.742 1406658.548
2001 1868.310517 244.5958559 8547976.336 7586195.595 1517239.119
2002 1915.018279 253.1567108 9210417.821 8183119.574 1636623.915
2003 1962.893736 262.0171957 9925999.954 8827547.511 1765509.502
2004 2011.96608 271.1877976 10698909.46 9523238.598 1904647.72
2005 2062.265232 280.6793705 11533666.23 10274250.29 2054850.059
2006 2113.821863 290.5031484 12435149.67 11084961.97 2216992.394
2007 2166.667409 300.6707586 13408627.1 11960100.42 2392020.085
2008 2220.834094 311.1942352 14459784.47 12904767.42 2580953.484
2009 2276.354947 322.0860334 15594759.51 13924469.41 2784893.882
2010 2333.26382 333.3590446 16820177.44 15025149.62 3005029.925
2011 2391.595416 345.0266111 18143189.62 16213222.67 3242644.533
2012 2451.385301 357.1025425 19571515.19 17495611.91 3499122.382
2013 2512.669934 369.6011315 21113486.05 18879789.8 3775957.96
2014 2575.486682 382.5371711 22778095.41 20373821.39 4074764.279
2015 2639.873849 395.9259721 24575050.15 21986411.34 4397282.268
2016 2705.870696 409.7833811 26514827.4 23726954.56 4745390.912
2017 2773.517463 424.1257995 28608735.57 25605590.99 5121118.198
2018 2842.855399 438.9702025 30868980.21 27633264.63 5526652.926
2019 2913.926784 454.3341595 33308735.12 29821787.27 5964357.454
2020 2986.774954 470.2358551 35942219.06 32183907.31 6436781.463
2021 3061.444328 486.6941101 38784778.62 34733384 6946676.801
2022 3137.980436 503.7284039 41852977.56 37485067.56 7497013.512
2023 3216.429947 521.3588981 45164693.31 40454985.69 8090997.137
2024 3296.840696 539.6064595 48739221.12 43660436.88 8732087.376
2025 3379.261713 558.4926856 52597386.38 47120091.21 9424018.242
2026 3463.743256 578.0399296 56761665.99 50854099.03 10170819.81
2027 3550.336837 598.2713271 61256319.19 54884208.36 10976841.67
2028 3639.095258 619.2108235 66107528.95 59233891.49 11846778.3
2029 3730.07264 640.8832024 71343554.35 63928481.74 12785696.35
2030 3823.324456 663.3141145 76994895.26 68995320.95 13799064.19
2031 3918.907567 686.5301085 83094469.93 74463918.75 14892783.75
2032 4016.880256 710.5586623 89677806.68 80366124.38 16073224.88
2033 4117.302263 735.4282154 96783250.89 86736312.22 17347262.44
2034 4220.234819 761.168203 104452188.2 93611581.92 18722316.38
2035 4325.74069 787.8090901 112729285.8 101031974.5 20206394.9
2036 4433.884207 815.3824082 121662752.1 109040705.6 21808141.11
2037 4544.731312 843.9207925 131304618 117684416.9 23536883.38
2038 4658.349595 873.4580203 141711039.6 127013448.1 25402689.63
2039 4774.808335 904.029051 152942625.3 137082130 27416426
2040 4894.178543 935.6700677 165064788.7 147949100.5 29589820.11
2041 5016.533007 968.4185201 178148130 159677646.8 31935529.36
2042 5141.946332 1002.313168 192268846.3 172336073.3 34467214.66
2043 5270.49499 1037.394129 207509176.4 185998099.8 37199619.96
2044 5402.257365 1073.702924 223957878.7 200743290.7 40148658.13
2045 5537.313799 1111.282526 241710749 216657518.2 43331503.63
2046 5675.746644 1150.177414 260871177.7 233833462.7 46766692.54
2047 5817.64031 1190.433624 281550752.5 252371152.4 50474230.48
2048 5963.081318 1232.098801 303869907.7 272378545.7 54475709.13
2049 6112.158351 1275.222259 327958626.1 293972160.1 58794432.01
2050 6264.96231 1319.855038 353957195.5 317277750.6 63455550.12
2b – China modeldata
China
delta 0.1
alpha 0.33333
savings 0.2
pop growth n 0.025
tech growth x 0.035
Initial Condtions
L0 600 (China pop in millions)
K0 100000
A0 —> 20 years behind US
Model Data
Units Million Normalization Millions of Dollars Millions of Real Dollars Millions of Real Dollars
Year Population TFP Capital Output Investment Real GDP (PPP) Population Growth of Real GDP per capita Population growth
1955 600 100 100000 330187.0941 66037.41881
1956 615 100 156037.4188 389330.3993 77866.07986
1957 630.375 100 218299.7568 442665.0897 88533.01795
1958 646.134375 100 285002.7991 491838.8055 98367.7611
1959 662.2877344 100 354870.2803 537912.8524 107582.5705
1960 678.8449277 100 426965.8227 581614.7702 116322.954
1961 695.8160509 100 500592.1945 623468.9023 124693.7805
1962 713.2114522 100 575226.7555 663868.725 132773.745
1963 731.0417385 100 650477.8249 703119.458 140623.8916
1964 749.317782 100 726053.934 741464.5056 148292.9011
1965 768.0507265 100 801741.4418 779102.5963 155820.5193
1966 787.2519947 100 877387.8168 816199.309 163239.8618
1967 806.9332945 100 952888.897 852895.0717 170579.0143
1968 827.1066269 100 1028179.022 889310.8647 177862.1729
1969 847.7842926 100 1103223.292 925552.3834 185110.4767
1970 868.9788999 100 1178011.44 961713.1395 192342.6279
1971 890.7033724 100 1252552.924 997876.8159 199575.3632
1972 912.9709567 100 1326872.995 1034119.082 206823.8163
1973 935.7952306 100 1401009.511 1070509.014 214101.8029
1974 959.1901114 100 1475010.363 1107110.227 221422.0455
1975 983.1698642 100 1548931.372 1143981.776 228796.3553
1976 1007.749111 103.5 1622834.59 1222520.155 244504.031
1977 1032.942839 107.1225 1705055.162 1307676.476 261535.2953
1978 1058.76641 110.8717875 1796084.941 1399971.983 279994.3966
1979 1085.23557 114.7523001 1896470.844 1499968.001 299993.6003
1980 1112.366459 118.7686306 2006817.36 1608269.286 321653.8571
1981 1140.17562 122.9255326 2127789.481 1725527.619 345105.5239
1982 1168.680011 127.2279263 2260116.057 1852445.692 370489.1384
1983 1197.897011 131.6809037 2404593.589 1989781.271 397956.2543
1984 1227.844437 136.2897353 2562090.485 2138351.697 427670.3394
1985 1258.540547 141.0598761 2733551.776 2299038.714 459807.7428
1986 1290.004061 145.9969717 2920004.341 2472793.682 494558.7364
1987 1322.254163 151.1068657 3122562.643 2660643.182 532128.6364
1988 1355.310517 156.395606 3342435.015 2863695.059 572739.0118
1989 1389.19328 161.8694522 3580930.526 3083144.933 616628.9865
1990 1423.923112 167.5348831 3839466.46 3320283.213 664056.6427
1991 1459.521189 173.398604 4119576.456 3576502.668 715300.5336
1992 1496.009219 179.4675551 4422919.344 3853306.577 770661.3153
1993 1533.40945 185.7489196 4751288.725 4152317.529 830463.5058
1994 1571.744686 192.2501317 5106623.358 4475286.91 895057.3821
1995 1611.038303 198.9788863 5491018.405 4824105.14 964821.0279
1996 1651.314261 205.9431474 5906737.592 5200812.707 1040162.541
1997 1692.597117 213.1511575 6356226.374 5607612.087 1121522.417
1998 1734.912045 220.611448 6842126.154 6046880.594 1209376.119
1999 1778.284846 228.3328487 7367289.658 6521184.248 1304236.85
2000 1822.741967 236.3244984 7934797.542 7033292.742 1406658.548
2001 1868.310517 244.5958559 8547976.336 7586195.595 1517239.119
2002 1915.018279 253.1567108 9210417.821 8183119.574 1636623.915
2003 1962.893736 262.0171957 9925999.954 8827547.511 1765509.502
2004 2011.96608 271.1877976 10698909.46 9523238.598 1904647.72
2005 2062.265232 280.6793705 11533666.23 10274250.29 2054850.059
2006 2113.821863 290.5031484 12435149.67 11084961.97 2216992.394
2007 2166.667409 300.6707586 13408627.1 11960100.42 2392020.085
2008 2220.834094 311.1942352 14459784.47 12904767.42 2580953.484
2009 2276.354947 322.0860334 15594759.51 13924469.41 2784893.882
2010 2333.26382 333.3590446 16820177.44 15025149.62 3005029.925
2011 2391.595416 345.0266111 18143189.62 16213222.67 3242644.533
2012 2451.385301 357.1025425 19571515.19 17495611.91 3499122.382
2013 2512.669934 369.6011315 21113486.05 18879789.8 3775957.96
2014 2575.486682 382.5371711 22778095.41 20373821.39 4074764.279
2015 2639.873849 395.9259721 24575050.15 21986411.34 4397282.268
2016 2705.870696 409.7833811 26514827.4 23726954.56 4745390.912
2017 2773.517463 424.1257995 28608735.57 25605590.99 5121118.198
2018 2842.855399 438.9702025 30868980.21 27633264.63 5526652.926
2019 2913.926784 454.3341595 33308735.12 29821787.27 5964357.454
2020 2986.774954 470.2358551 35942219.06 32183907.31 6436781.463
2021 3061.444328 486.6941101 38784778.62 34733384 6946676.801
2022 3137.980436 503.7284039 41852977.56 37485067.56 7497013.512
2023 3216.429947 521.3588981 45164693.31 40454985.69 8090997.137
2024 3296.840696 539.6064595 48739221.12 43660436.88 8732087.376
2025 3379.261713 558.4926856 52597386.38 47120091.21 9424018.242
2026 3463.743256 578.0399296 56761665.99 50854099.03 10170819.81
2027 3550.336837 598.2713271 61256319.19 54884208.36 10976841.67
2028 3639.095258 619.2108235 66107528.95 59233891.49 11846778.3
2029 3730.07264 640.8832024 71343554.35 63928481.74 12785696.35
2030 3823.324456 663.3141145 76994895.26 68995320.95 13799064.19
2031 3918.907567 686.5301085 83094469.93 74463918.75 14892783.75
2032 4016.880256 710.5586623 89677806.68 80366124.38 16073224.88
2033 4117.302263 735.4282154 96783250.89 86736312.22 17347262.44
2034 4220.234819 761.168203 104452188.2 93611581.92 18722316.38
2035 4325.74069 787.8090901 112729285.8 101031974.5 20206394.9
2036 4433.884207 815.3824082 121662752.1 109040705.6 21808141.11
2037 4544.731312 843.9207925 131304618 117684416.9 23536883.38
2038 4658.349595 873.4580203 141711039.6 127013448.1 25402689.63
2039 4774.808335 904.029051 152942625.3 137082130 27416426
2040 4894.178543 935.6700677 165064788.7 147949100.5 29589820.11
2041 5016.533007 968.4185201 178148130 159677646.8 31935529.36
2042 5141.946332 1002.313168 192268846.3 172336073.3 34467214.66
2043 5270.49499 1037.394129 207509176.4 185998099.8 37199619.96
2044 5402.257365 1073.702924 223957878.7 200743290.7 40148658.13
2045 5537.313799 1111.282526 241710749 216657518.2 43331503.63
2046 5675.746644 1150.177414 260871177.7 233833462.7 46766692.54
2047 5817.64031 1190.433624 281550752.5 252371152.4 50474230.48
2048 5963.081318 1232.098801 303869907.7 272378545.7 54475709.13
2049 6112.158351 1275.222259 327958626.1 293972160.1 58794432.01
2050 6264.96231 1319.855038 353957195.5 317277750.6 63455550.12
3 – China with Pop Growth Chng
China
delta 0.1
alpha 0.33333
savings 0.2
pop growth n -0.02
tech growth x 0.035
Initial Condtions
L0 600 (China pop in millions)
k0 100000
A0 —> 20 years behind US
Model Deduced Variables Growth Accounting (real GDP)
Units Million Normalization Millions of Dollars Millions of Real Dollars Millions of Real Dollars
Year Population TFP Capital Output Investment Output per Efficiency Unit Output/Capita Capital/Capita Labor Share Real Wages GDP Per Capita Growth Real Rental Rate TFP Contribution Capital Contribution Labor Contribution
1955 100 100000 0 0
1956 100 90000 0 0
1957 100 81000 0 0
1958 100 72900 0 0
1959 100 65610 0 0
1960 100 59049 0 0
1961 100 53144.1 0 0
1962 100 47829.69 0 0
1963 100 43046.721 0 0
1964 100 38742.0489 0 0
1965 100 34867.84401 0 0
1966 100 31381.05961 0 0
1967 100 28242.95365 0 0
1968 100 25418.65828 0 0
1969 100 22876.79245 0 0
1970 100 20589.11321 0 0
1971 100 18530.20189 0 0
1972 100 16677.1817 0 0
1973 100 15009.46353 0 0
1974 100 13508.51718 0 0
1975 100 12157.66546 0 0
1976 103.5 10941.89891 0 0
1977 107.1225 9847.709022 0 0
1978 110.8717875 8862.93812 0 0
1979 114.7523001 7976.644308 0 0
1980 118.7686306 7178.979877 0 0
1981 122.9255326 6461.081889 0 0
1982 127.2279263 5814.9737 0 0
1983 131.6809037 5233.47633 0 0
1984 136.2897353 4710.128697 0 0
1985 141.0598761 4239.115828 0 0
1986 145.9969717 3815.204245 0 0
1987 151.1068657 3433.68382 0 0
1988 156.395606 3090.315438 0 0
1989 161.8694522 2781.283894 0 0
1990 167.5348831 2503.155505 0 0
1991 173.398604 2252.839954 0 0
1992 179.4675551 2027.555959 0 0
1993 185.7489196 1824.800363 0 0
1994 192.2501317 1642.320327 0 0
1995 198.9788863 1478.088294 0 0
1996 205.9431474 1330.279465 0 0
1997 213.1511575 1197.251518 0 0
1998 220.611448 1077.526366 0 0
1999 228.3328487 969.7737298 0 0
2000 236.3244984 872.7963568 0 0
2001 244.5958559 785.5167211 0 0
2002 253.1567108 706.965049 0 0
2003 262.0171957 636.2685441 0 0
2004 271.1877976 572.6416897 0 0
2005 280.6793705 515.3775207 0 0
2006 290.5031484 463.8397687 0 0
2007 300.6707586 417.4557918 0 0
2008 311.1942352 375.7102126 0 0
2009 322.0860334 338.1391914 0 0
2010 333.3590446 304.3252722 0 0
2011 345.0266111 273.892745 0 0
2012 357.1025425 246.5034705 0 0
2013 369.6011315 221.8531234 0 0
2014 382.5371711 199.6678111 0 0
2015 395.9259721 179.70103 0 0
2016 409.7833811 161.730927 0 0
2017 424.1257995 145.5578343 0 0
2018 438.9702025 131.0020509 0 0
2019 454.3341595 117.9018458 0 0
2020 470.2358551 106.1116612 0 0
2021 486.6941101 95.50049508 0 0
2022 503.7284039 85.95044557 0 0
2023 521.3588981 77.35540101 0 0
2024 539.6064595 69.61986091 0 0
2025 558.4926856 62.65787482 0 0
2026 578.0399296 56.39208734 0 0
2027 598.2713271 50.75287861 0 0
2028 619.2108235 45.67759075 0 0
2029 640.8832024 41.10983167 0 0
2030 663.3141145 36.9988485 0 0
2031 686.5301085 33.29896365 0 0
2032 710.5586623 29.96906729 0 0
2033 735.4282154 26.97216056 0 0
2034 761.168203 24.2749445 0 0
2035 787.8090901 21.84745005 0 0
2036 815.3824082 19.66270505 0 0
2037 843.9207925 17.69643454 0 0
2038 873.4580203 15.92679109 0 0
2039 904.029051 14.33411198 0 0
2040 935.6700677 12.90070078 0 0
2041 968.4185201 11.6106307 0 0
2042 1002.313168 10.44956763 0 0
2043 1037.394129 9.40461087 0 0
2044 1073.702924 8.464149783 0 0
2045 1111.282526 7.617734805 0 0
2046 1150.177414 6.855961324 0 0
2047 1190.433624 6.170365192 0 0
2048 1232.098801 5.553328673 0 0
2049 1275.222259 4.997995805 0 0
2050 1319.855038 4.498196225 0 0
4 – China Catching Up
China
delta 0.1
alpha 0.33333
savings 0.2
pop growth n
tech growth x 0.035
Initial Condtions
L0 600 (China pop in millions)
k0 100000
A0
Model Deduced Variables Growth Accounting (real GDP)
Units Million Normalization Millions of Dollars Millions of Real Dollars Millions of Real Dollars
Year Population TFP Capital Output Investment Output per Efficiency Unit Output/Capita Capital/Capita Labor Share Real Wages GDP Per Capita Growth Real Rental Rate TFP Contribution Capital Contribution Labor Contribution
1955 100 100000 0 0
1956 100 90000 0 0
1957 100 81000 0 0
1958 100 72900 0 0
1959 100 65610 0 0
1960 100 59049 0 0
1961 100 53144.1 0 0
1962 100 47829.69 0 0
1963 100 43046.721 0 0
1964 100 38742.0489 0 0
1965 100 34867.84401 0 0
1966 100 31381.05961 0 0
1967 100 28242.95365 0 0
1968 100 25418.65828 0 0
1969 100 22876.79245 0 0
1970 100 20589.11321 0 0
1971 100 18530.20189 0 0
1972 100 16677.1817 0 0
1973 100 15009.46353 0 0
1974 100 13508.51718 0 0
1975 100 12157.66546 0 0
1976 106.2555554 10941.89891 0 0
1977 112.7541997 9847.709022 0 0
1978 119.5010638 8862.93812 0 0
1979 126.50156 7976.644308 0 0
1980 133.7613992 7178.979877 0 0
1981 141.2866072 6461.081889 0 0
1982 149.0835402 5814.9737 0 0
1983 157.1589001 5233.47633 0 0
1984 165.5197483 4710.128697 0 0
1985 174.1735203 4239.115828 0 0
1986 183.1280387 3815.204245 0 0
1987 192.3915263 3433.68382 0 0
1988 201.9726198 3090.315438 0 0
1989 211.8803819 2781.283894 0 0
1990 222.1243145 2503.155505 0 0
1991 232.7143711 2252.839954 0 0
1992 243.6609702 2027.555959 0 0
1993 254.9750079 1824.800363 0 0
1994 266.6678712 1642.320327 0 0
1995 278.7514514 1478.088294 0 0
1996 291.2381584 1330.279465 0 0
1997 304.1409342 1197.251518 0 0
1998 317.4732679 1077.526366 0 0
1999 331.2492109 969.7737298 0 0
2000 345.4833924 872.7963568 0 0
2001 360.1910355 785.5167211 0 0
2002 375.387974 706.965049 0 0
2003 391.0906703 636.2685441 0 0
2004 407.3162329 572.6416897 0 0
2005 424.0824358 515.3775207 0 0
2006 441.4077377 463.8397687 0 0
2007 459.311303 417.4557918 0 0
2008 477.8130223 375.7102126 0 0
2009 496.9335351 338.1391914 0 0
2010 516.6942529 304.3252722 0 0
2011 537.1173824 273.892745 0 0
2012 558.2259514 246.5034705 0 0
2013 580.0438339 221.8531234 0 0
2014 602.5957775 199.6678111 0 0
2015 625.9074313 179.70103 0 0
2016 650.0053751 161.730927 0 0
2017 674.9171494 145.5578343 0 0
2018 700.671287 131.0020509 0 0
2019 727.2973458 117.9018458 0 0
2020 754.8259425 106.1116612 0 0
2021 783.2887878 95.50049508 0 0
2022 812.7187229 85.95044557 0 0
2023 843.1497576 77.35540101 0 0
2024 874.6171096 69.61986091 0 0
2025 907.1572448 62.65787482 0 0
2026 940.8079205 56.39208734 0 0
2027 975.6082285 50.75287861 0 0
2028 1011.598641 45.67759075 0 0
2029 1048.821057 41.10983167 0 0
2030 1087.318854 36.9988485 0 0
2031 1127.136933 33.29896365 0 0
2032 1168.321777 29.96906729 0 0
2033 1210.921502 26.97216056 0 0
2034 1254.985915 24.2749445 0 0
2035 1300.566571 21.84745005 0 0
2036 1347.716833 19.66270505 0 0
2037 1396.491938 17.69643454 0 0
2038 1446.949058 15.92679109 0 0
2039 1499.14737 14.33411198 0 0
2040 1553.148122 12.90070078 0 0
2041 1609.014711 11.6106307 0 0
2042 1666.812752 10.44956763 0 0
2043 1726.610156 9.40461087 0 0
2044 1788.477216 8.464149783 0 0
2045 1852.48668 7.617734805 0 0
2046 1918.713845 6.855961324 0 0
2047 1987.236643 6.170365192 0 0
2048 2058.13573 5.553328673 0 0
2049 2131.494588 4.997995805 0 0
2050 2207.399616 4.498196225 0 0

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