RDP 8704: The Role and Consequences of Investment in Recent Australian Economic Growth Appendix A: Estimated Production Functions

Jeffrey Carmichael and Nigel Dews

April 1987

Table A.1
Aggregate Production Function
1967(3) to 1986(2)
  Constant Share Elasticity Technological Progress  
β / B α / γ σ δ R2
Cobb-Douglas:*
1. 378.96
(0.576)		 0.36
(0.057)		 1.00
 		 0.0028
(0.0003)		 0.995
 
CES:
3. 934.93
(241.75)		 0.20
 		 1.09
(0.028)		 0.0028
(0.0003)		 0.984
 
4. 533.37
(147.77)		 0.30
 		 1.03
(0.025)		 0.0028
(0.0003)		 0.984
 
5. 317.31
(91.74)		 0.40
 		 0.98
(0.023)		 0.0028
(0.0003)		 0.984
 
6. 191.05
(56.67)		 0.50
 		 0.95
(0.022)		 0.0028
(0.0003)		 0.984
 
7. 113.92
(34.18)		 0.60
 		 0.91
(0.020)		 0.0028
(0.0003)		 0.984
 
8. 65.70
(19.65)		 0.70
 		 0.87
(0.018)		 0.0028
(0.0003)		 0.984
 
9. 35.28
(10.31)		 0.80
 		 0.84
(0.017)		 0.0028
(0.0003)		 0.984
 
10. 16.03
(4.39)		 0.90
 		 0.79
(0.015)		 0.0028
(0.0003)		 0.984
 
* Estimated without imposing linear homogeneity (assuming δ = .0028) the capital share (α) = 0.355 and the labour share = 0.670.
Table A.2
Private Sector Production Function
1967(3) to 1986(2)
  Constant Share Elasticity Technological Progress  
β / B α / γ σ δ R2
Cobb-Douglas:
1. 278.11
(0.462)		 0.42
(0.049)		 1.00
 		 0.0014
(0.0006)		 0.985
 
CES:
2. 2,091.99
(365.67)		 0.10
 		 1.20
(0.030)		 0.0022
(0.0005)		 0.965
 
3. 1,117.28
(222.42)		 0.20
 		 1.09
(0.025)		 0.0022
(0.0005)		 0.965
 
4. 660.82
(141.31)		 0.30
 		 1.03
(0.022)		 0.0022
(0.0004)		 0.965
 
5. 406.32
(90.86)		 0.40
 		 0.98
(0.020)		 0.0023
(0.0004)		 0.965
 
6. 252.56
(58.06)		 0.50
 		 0.94
(0.019)		 0.0023
(0.0004)		 0.965
 
7. 155.51
(36.24)		 0.60
 		 0.91
(0.017)		 0.0023
(0.0004)		 0.965
 
8. 92.77
(21.60)		 0.70
 		 0.87
(0.016)		 0.0023
(0.0004)		 0.965
 
9. 25.77
(19.42)		 0.80
 		 0.87
(0.054)		 0.0023
(0.002)		 0.532
 
10. 24.64
(5.28)		 0.90
 		 0.78
(0.013)		 0.0023
(0.0004)		 0.965
 
Table A.3
Mining Production Function
1967(3) to 1985(2)
  Constant Share Elasticity Technological Progress  
β / B α / γ σ δ R2
Cobb-Douglas:
1. 120.00
(0.368)		 0.57
(0.034)		 1.00
 		 −0.0066
(0.002)		 0.959
 
CES:
2. 2,747.60
(426.12)		 0.10
 		 1.28
(0.020)		 −0.0074
(0.002)		 0.893
 
3. 1,174.81
(199.65)		 0.20
 		 1.17
(0.017)		 −0.0072
(0.002)		 0.894
 
4. 596.34
(105.44)		 0.30
 		 1.11
(0.015)		 −0.0070
(0.002)		 0.895
 
5. 325.40
(58.44)		 0.40
 		 1.07
(0.014)		 −0.0068
(0.002)		 0.895
 
6. 183.28
(32.89)		 0.50
 		 1.103
(0.013)		 −0.0067
(0.002)		 0.896
 
7. 103.86
(18.35)		 0.60
 		 0.99
(0.012)		 −0.0065
(0.002)		 0.896
 
8. 57.77
(9.88)		 0.70
 		 0.95
(0.011)		 −0.0064
(0.002)		 0.896
 
9. 30.44
(4.92)		 0.80
 		 0.91
(0.010)		 −0.0062
(0.002)		 0.897
 
Table A.4
Manufacturing Production Function
1967(3) to 1985(2)
  Constant Share Elasticity Technological Progress  
β / B α / γ σ δ R2
Cobb-Douglas:
1. 235.46
(0.550)		 0.41
(0.057)		 1.00
 		 0.0064
(0.0003)		 0.923
 
CES:
2. 1,346.69
(296.35)		 0.10
 		 1.23
(0.036)		 0.0064
(0.0003)		 0.970
 
3. 697.84
(172.44)		 0.20
 		 1.12
(0.030)		 0.0064
(0.0003)		 0.970
 
4. 404.98
(106.42)		 0.30
 		 1.05
(0.027)		 0.0064
(0.0003)		 0.970
 
5. 166.88
(60.18)		 0.40
 		 1.04
(0.033)		 0.0063
(0.0004)		 0.946
 
6. 151.34
(42.08)		 0.50
 		 0.96
(0.022)		 0.0064
(0.0003)		 0.970
 
7. 60.23
(92.55)		 0.60
 		 0.95
(0.119)		 0.0064
(0.0017)		 0.04
 
8. 55.16
(15.30)		 0.70
 		 0.89
(0.019)		 0.0064
(0.0003)		 0.970
 
9. 30.83
(8.309)		 0.80
 		 0.85
(0.017)		 0.0064
(0.0003)		 0.970
 
10. 14.86
(3.72)		 0.90
 		 0.79
(0.015)		 0.0064
(0.0003)		 0.970
 
Table A.5
Finance, Property and Business Production Function
1967(3) to 1985(2)
  Constant Share Elasticity Technological Progress  
β / B α / γ σ δ R2
Cobb-Douglas:
1. 79.88
(0.756)		 0.64
(0.073)		 1.00
 		 −0.0449
(0.010)		 0.753
 
CES:
2. 2,707.62
(84.91)		 0.10
 		 1.35
(0.005)		 −0.0858
(0.007)		 0.973
 
3. 897.13
(26.32)		 0.20
 		 1.26
(0.004)		 −0.1051
(0.008)		 0.975
 
4. 377.47
(10.47)		 0.30
 		 1.21
(0.003)		 −0.1232
(0.009)		 0.977
 
5. 171.55
(4.73)		 0.40
 		 1.17
(0.002)		 −0.1426
(0.010)		 0.978
 
6. 88.74
(2.30)		 0.50
 		 1.14
(0.002)		 −0.165
(0.010)		 0.979
 
7. 45.79
(1.17)		 0.60
 		 1.12
(0.002)		 −0.1942
(0.011)		 0.980
 
8. 23.87
(0.613)		 0.70
 		 1.09
(0.001)		 −0.235
(0.013)		 0.981
 
9. 14.91
(5.53)		 0.80
 		 0.99
(0.044)		 −0.076
(0.037)		 0.921
 
10. 22.04
(6.91)		 0.90
 		 0.84
(0.020)		 −0.031
(0.005)		 0.921
 
Table A.6
Other Industries Production Function
1967(3) to 1985(2)
  Constant Share Elasticity Technological Progress  
β / B α / γ σ δ R2
Cobb-Douglas:
1. 47.83
(1.46)		 0.62
(0.162)		 1.00
 		 0.0034
(0.0003)		 0.982
 
CES:          
2. 700.38
(484.45)		 0.10
 		 1.42
(0.155)		 0.0034
(0.0003)		 0.917
 
3. 353.63
(261.21)		 0.20
 		 1.26
(0.121)		 0.0034
(0.0003)		 0.917
 
4. 205.83
(155.80)		 0.30
 		 1.17
(0.105)		 0.0034
(0.0003)		 0.917
 
5. 127.30
(96.80)		 0.40
 		 1.11
(0.094)		 0.0034
(0.0003)		 0.917
 
6. 80.95
(60.96)		 0.50
 		 1.06
(0.085)		 0.0034
(0.0003)		 0.917
 
7. 51.85
(38.15)		 0.60
 		 1.01
(0.077)		 0.0034
(0.0003)		 0.917
 
8. 32.82
(23.21)		 0.70
 		 0.96
(0.070)		 0.0034
(0.0003)		 0.917
 
9. 19.99
(13.25)		 0.80
 		 0.91
(0.063)		 0.0034
(0.0003)		 0.917
 
10. 11.02
(6.48)		 0.90
 		 0.84
(0.054)		 0.0034
(0.0003)		 0.917
 

Cobb-Douglas:

CES:

where: Q = the appropriate measure of GDP for the 4 quarters ended the current quarter in 1979/80 prices, consistent with ABS (1986);
  L = the average number of people employed over the 4 quarters up to and including the current quarter;
  K = the average 1979/80 price value of the appropriate measure of the capital stock (excluding dwellings) over the 4 quarters ended:
  • 6 quarters prior to the current quarter for aggregate, private sector, and other industries;
  • 8 quarters prior to the current quarter for mining;
  • 4 quarters prior to the current quarter for manufacturing;
  • 2 quarters prior to the current quarter for finance, etc.; and
  t = time.

Figures in parentheses are standard errors.

Quarterly estimates of private sector output, employment and output by industry have been constructed using a number of assumptions. Details are contained in Appendix B; as are the sources, definations and copies of all data used in this study.