Production and Long-Term Growth
ConceptualizationThis conceptualization is a way to organize your thinking to understand many complex interrelated economic events.
How does output increase?Key to our analysis of growth will be the production functionCan boost output by increasing factor inputs or using inputs more efficiently
Aggregate Production FunctionAggregate production function for the US:
y = A k.3n.7
y = real output (income) k = physical stock of capitaln = labor input per unit of timeA = level of efficiency or total factor productivity (TFP)
Growth Accounting is Everywhere
Calibrating the Aggregate Production FunctionThe production function is motivated by this fact:
Labor income share is consistently 70% of national incomeCapital income share is 30% of national income
Labor Income Share of GDPDistribution of National Income, 1994Employee Compensation as Percentage of GNP 1959-1999 (very stable over time at 70%)
Grafikon1
0.6820780512
0.6771634615
0.6862697448
0.6867788462
0.6871495327
0.6941781623
0.6953982714
0.6969270467
0.6964243982
0.6912168344
0.6887892377
0.6841761116
0.6850545221
0.6880269815
0.6862622472
0.6838643371
0.6868131868
0.6845261895
0.6840551181
0.6831530139
0.6805293006
0.6839166046
0.6842585829
0.6868121956
0.6785213735
0.6773195876
0.6778433024
0.6773507768
0.6754788666
0.6837419959
0.6891311022
0.6896499698
0.6939784302
0.6971904266
0.697915148
0.6996284653
0.7030379041
0.7029743311
0.70608557
0.7088492115
0.7108156482
0.7160090475
0.7221127801
0.729957291
0.7390089871
0.7367410607
0.7350821222
0.738317757
0.7305021063
0.7294642857
0.7294001318
0.7275954814
0.7293725939
0.7314530963
0.7231912785
0.7171390527
0.7187126437
0.7216615606
0.721464402
0.7173265219
0.726957844
0.7347228012
0.7375857563
0.7395833333
0.73932277
0.7334487916
0.7220295537
0.7223522528
0.7222182974
0.7274307971
0.7290305011
0.7314327583
0.7268154263
0.7223325062
0.7178241574
0.7205701934
0.7255529519
0.7160393243
0.7162783325
0.7160973614
0.7199581507
0.7227059284
0.7251420116
0.7249721397
0.7266832918
0.7440369913
0.7424988804
0.7336942621
0.7306615042
0.7374648117
0.7244409572
0.733346372
0.7421435272
0.7359048167
0.7400473753
0.742765763
0.7385638
0.7321590703
0.7280760666
0.7248545019
0.7160433071
0.71217818
0.7119109254
0.7145053661
0.7139969224
0.7169670566
0.7176653834
0.7219032707
0.7235049477
0.7268937555
0.7304168316
0.7364827046
0.7319123386
0.7259967507
0.720834741
0.7208098645
0.7180609074
0.7188641566
0.717105106
0.7127485762
0.7123142739
0.7149292296
0.719817975
0.7235004386
0.7214313958
0.7199552101
0.7239099739
0.7229146692
0.7237947387
0.725518348
0.7272765369
0.7293853541
0.7245530828
0.7259802155
0.7408753964
0.7281271461
0.7283425575
0.7254534681
0.7293005743
0.7225836518
0.7340704752
0.7231504444
0.7190899041
0.7157018725
0.717425187
0.7163943701
0.7136124062
0.7133226271
0.7083120436
0.7070154424
0.7079722427
0.7079285985
0.7053416955
0.7036418056
0.7028036266
0.7070598459
0.7099256592
0.7118493465
0.7130702262
0.7137674108
0.7113913696
0.7122495992
0.7143749751
Wn/Y
gnp
yearqtr1959gnpcompens
195911959.25402.3274.40.6820780512
195921959.5416281.70.6771634615
195931959.75411.5282.40.6862697448
195941960416285.70.6867788462
196011960.25428294.10.6871495327
196021960.5427.7296.90.6941781623
196031960.75428.1297.70.6953982714
196041961426.3297.10.6969270467
196111961.25427.92980.6964243982
196121961.5437.2302.20.6912168344
196131961.75446307.20.6887892377
196141962458.8313.90.6841761116
196211962.25467.7320.40.6850545221
196221962.5474.4326.40.6880269815
196231962.75479.7329.20.6862622472
196241963486.5332.70.6838643371
196311963.25491.4337.50.6868131868
196321963.5500.2342.40.6845261895
196331963.75508347.50.6840551181
196341964517.6353.60.6831530139
196411964.255293600.6805293006
196421964.5537.2367.40.6839166046
196431964.75547.6374.70.6842585829
196441965554.3380.70.6868121956
196511965.25570.8387.30.6785213735
196521965.5582394.20.6773195876
196531965.75593.5402.30.6778433024
196541966611.5414.20.6773507768
196611966.25631.7426.70.6754788666
196621966.5640.3437.80.6837419959
196631966.75651.4448.90.6891311022
196641967662.8457.10.6896499698
196711967.25667.6463.30.6939784302
196721967.5672.74690.6971904266
196731967.75685.9478.70.697915148
196741968699.8489.60.6996284653
196811968.25717.6504.50.7030379041
196821968.5736.3517.60.7029743311
196831968.75752.6531.40.70608557
196841969767.3543.90.7088492115
196911969.25782.25560.7108156482
196921969.5795.8569.80.7160090475
196931969.75812.2586.50.7221127801
196941970819.5598.20.729957291
197011970.25823.4608.50.7390089871
197021970.5833.46140.7367410607
197031970.75846.3622.10.7350821222
197041971845.3624.10.738317757
197111971.25878.3641.60.7305021063
197121971.5896653.60.7294642857
197131971.75910.2663.90.7294001318
197141972929.5676.30.7275954814
197211972.25961.17010.7293725939
197221972.5978.6715.80.7314530963
197231972.751009729.70.7231912785
1972419731051.47540.7171390527
197311973.251087.5781.60.7187126437
197321973.51109.8800.90.7216615606
197331973.751136.3819.80.721464402
1973419741174.5842.50.7173265219
197411974.251183.7860.50.726957844
197421974.51199.5881.30.7347228012
197431974.751224.4903.10.7375857563
1974419751238.4915.90.7395833333
197511975.251243.3919.20.73932277
197521975.51270.3931.70.7334487916
197531975.751326.4957.70.7220295537
1975419761367.2987.60.7223522528
197611976.251415.51022.30.7222182974
197621976.51437.81045.90.7274307971
197631976.751468.81070.80.7290305011
1976419771501.31098.10.7314327583
197711977.251550.611270.7268154263
197721977.516121164.40.7223325062
197731977.751667.41196.90.7178241574
1977419781711.71233.40.7205701934
197811978.251749.71269.50.7255529519
197821978.51841.11318.30.7160393243
197831978.751892.71355.70.7162783325
1978419791955.61400.40.7160973614
197911979.252007.21445.10.7199581507
197921979.52044.41477.50.7227059284
197931979.752094.91519.10.7251420116
1979419802153.61561.30.7249721397
198011980.252205.51602.70.7266832918
198021980.52184.31625.20.7440369913
198031980.75223316580.7424988804
1980419812345.81721.10.7336942621
198111981.252427.81773.90.7306615042
198121981.52451.11807.60.7374648117
198131981.7525491846.60.7244409572
1981419822556.51874.80.733346372
198211982.252558.41898.70.7421435272
198221982.52605.51917.40.7359048167
198231982.752617.419370.7400473753
1982419832626.41950.80.742765763
198311983.252677.91977.80.7385638
198321983.52753.520160.7321590703
198331983.752829.12059.80.7280760666
19834198429212117.30.7248545019
198411984.2530482182.50.7160433071
198421984.53138.42235.10.71217818
198431984.753206.32282.60.7119109254
1984419853251.92323.50.7145053661
198511985.253314.32366.40.7139969224
198521985.53351.22402.70.7169670566
198531985.753402.724420.7176653834
1985419863448.82489.70.7219032707
198611986.253486.52522.50.7235049477
198621986.53502.32545.80.7268937555
198631986.753536.22582.90.7304168316
1986419873573.22631.60.7364827046
198711987.253664.12681.80.7319123386
198721987.53754.72725.90.7259967507
198731987.753847.92773.70.720834741
1987419883941.428410.7208098645
198811988.254022.52888.40.7180609074
198821988.54106.22951.80.7188641566
198831988.754185.33001.30.717105106
1988419894284.43053.70.7127485762
198911989.254347.830970.7123142739
198921989.54373.33126.60.7149292296
198931989.7543953163.60.719817975
1989419904446.33216.90.7235004386
199011990.254552.23284.10.7214313958
199021990.54643.93343.40.7199552101
199031990.754674.23383.70.7239099739
1990419914693.533930.7229146692
199111991.254702.33403.50.7237947387
199121991.54736.23436.20.725518348
199131991.754772.634710.7272765369
1991419924810.935090.7293853541
199211992.254933.83574.80.7245530828
199221992.54993.83625.40.7259802155
199231992.754950.936680.7408753964
1992419935096.53710.90.7281271461
199311993.255149.53750.60.7283425575
199321993.55231.93795.50.7254534681
199331993.755258.63835.10.7293005743
1993419945364.53876.30.7225836518
199411994.255372.13943.50.7340704752
199421994.55524.33994.90.7231504444
199431994.755608.24032.80.7190899041
1994419955719.74093.60.7157018725
199511995.255774.44142.70.717425187
199521995.55833.14178.80.7163943701
199531995.755919.64224.30.7136124062
1995419965977.84264.10.7133226271
199611996.256067.14297.40.7083120436
199621996.56177.84367.80.7070154424
199631996.756254.24427.80.7079722427
1996419976341.64489.40.7079285985
199711997.256473.64566.10.7053416955
199721997.56581.94631.30.7036418056
199731997.756694.94705.20.7028036266
1997419986789.14800.30.7070598459
199811998.256887.24889.40.7099256592
199821998.56977.649670.7118493465
199831998.757087.15053.60.7130702262
1998419997193.85134.70.7137674108
199911999.257334.55217.70.7113913696
199921999.57423.15287.10.7122495992
199937522.15373.60.7143749751
5449.7
gnp
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
US Production Function: Measurementy, k, measured in billions of 1992 dollars.n measured in millions of workers.A is computed by using the production function
y
k
n
A
% A
1980
4612
4491
99.3
14.80
1981
4725
4655
100.4
14.89
0.6
1982
4624
4765
99.5
14.56
-2.2
1983
4810
4849
100.8
14.93
2.5
1984
5138
5004
105.0
15.35
2.8
1985
5330
5189
107.2
15.53
1.1
1986
5490
5328
109.6
15.62
0.6
1987
5648
5445
112.4
15.69
0.4
1988
5863
5572
115.0
15.92
1.5
1989
6060
5708
117.3
16.11
1.2
1990
6139
5830
117.3
16.11
1.2
1991
6079
5892
116.9
16.04
-0.7
1992
6244
5979
117.6
16.34
1.8
1993
6384
6094
119.3
16.44
0.6
1994
6609
6258
123.1
16.52
0.5
1995
6743
6473
124.9
16.52
0.0
1996
6995
6566
126.7
16.80
1.7
1997
7270
6716
129.6
17.16
2.1
1998
7560
6815
131.5
17.59
2.5
1999
7862
6917
133.5
18.01
2.4
Growth Accountingand Efficiency of the EconomyGrowth-accounting equation:
The labor contribution to growth:0.7 * % growth of labor
Capital contribution to growth:0.3 * % growth in capital
Growth during 1950-73: TFP has been importantlabor input also important for US and Japan. Examples of Growth Accounting
Growth slowed down dramatically during 1973-92Examples of Growth Accounting
Understanding efficiency Higher A implies that the economy is more efficient
More output can be produced with the same inputs (labor and capital)
Innovation and TFP Growth
Learning by doing and TFP growthIn New Economy same effect is achieved by using computers and other IT --- this also raises y/n.
What determines TFP?
Relationship between Income and Growth
Open Countries Tend to ConvergeOpen: (1) effective protection rates < 40%, (2) quotas on < 40% of imports, (3) no currency controls or currency black markets, (4) no export marketing board, and (5) not socialist.
Technology Adoption Rates Differ Dramatically Across Countries
The Speed of Technology Adoption is Rising Over TimePercent of U.S. HouseholdsYear
Productivity growth rates in the USWhere is the US productivity growth coming from since the mid 90s?
Recent Productivity in the US
Why Care About TFP?Sustained Growth not possible without TFP growth
Incentive to invest related to return to capital---this falls rapidly to zero without TFP growth
Without TFP growth income will stop growing
Soviet Union had no TFP growthreturn to capital fell to zero
International Differences in Labor Productivity
Output per workerLabor productivity is output per worker
Living standard is determined byA: efficiency (or TFP)k/n: capital per worker
International Differences in Output per Worker Residual TFP x Education = TFP
Sheet1
(All figures are relative to the United States.)
CapitalEducationResidual TFPOutput per Worker
Canada1.000.901.030.93
Italy1.060.651.210.83
France1.090.671.130.82
UK0.890.811.010.73
Spain1.020.611.110.68
Japan1.120.800.660.59
Mexico0.870.540.930.43
Korea0.860.760.580.38
Iran0.980.470.640.30
Chile0.990.660.400.26
Peru0.940.620.410.24
Egypt0.450.580.720.19
Pakistan0.580.390.570.13
India0.710.450.270.09
Sudan0.840.340.230.07
Lesotho0.680.480.190.06
Kenya0.750.460.170.06
Rwanda0.440.340.290.04
Uganda0.360.390.220.03
Source: Hall and Jones, QJE (1999)
Sheet2
Sheet3
International DifferencesOutput Per Worker is higher in economies with Higher EducationHigher Residual TFP (other than education)More Physical Capital
Economies with higher TFP = Residual TFP x Education also have more capital
Convergence of Economies
Does TFP growth explain convergence?
TFP relative to the US
Sheet1
YearsCanadaFranceGermanyItalyJapanKoreaUnited Kingdom
19470.812
19480.793
19490.800
19500.8200.5310.462
19510.8040.5210.493
19520.8400.5260.5220.5900.434
19530.8410.5520.5310.6150.443
19540.8170.5700.5710.6210.463
19550.8320.5670.6090.6410.4820.668
19560.8760.5860.6310.6700.4940.673
19570.8590.6010.6520.6740.5070.687
19580.8600.6000.6600.6980.4960.686
19590.8410.6060.6810.7050.5050.678
19600.8430.6430.7370.7160.5510.2400.700
19610.8380.6540.7480.7400.6010.2390.701
19620.8360.6580.7420.7400.5640.2350.677
19630.8460.6670.7400.7300.5880.2460.677
19640.8510.6790.7680.7310.6210.2520.689
19650.8590.6850.7850.7620.6130.2450.677
19660.8640.6920.7700.7700.6310.2650.678
19670.8590.7130.7520.8010.6580.2710.699
19680.8730.7190.8100.8080.7080.2750.706
19690.8680.7570.8690.8510.7400.3030.704
19700.9140.7880.9090.8760.7790.3160.742
19710.9160.7890.9000.8300.7680.3130.769
19720.9090.7910.8920.8270.7730.3100.770
19730.9070.8060.9060.8490.7720.3480.775
Source: Productivity, Vol. 2, by Dale W. Jorgenson, MIT Press, 1995.
Sheet1
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
Canada
France
Germany
Italy
Japan
Korea
United Kingdom
Year
Total Factor Productivity Relative to US
Sheet2
Sheet3
Growth from 1,000,000 BC to now Pre-Industrial Revolution stagnation in per-capita income Industrial Revolution and TFP Growing Income Inequality 21st Century may be the Century of Convergence
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