RDP 8401: The Equations of the RBA82 Model of the Australian Economy Appendix 1: RBII Specification[1]

J.G. Fahrer, R.W. Rankin and J.C. Taylor

August 1984

1. Household Expenditure

2. Rate of Growth of Business Fixed Capital Stock

3. Stock of Dwellings

4. Exports of Goods and Services

5. Imports of Goods and Services

6. Domestic Production

7. Price of Domestic Production

8. Price of Exports of Goods and Services

9. Price of Government Current Expenditure

10. Average Weekly Earnings

11. Rate of Growth of Employment

12. Labour Supply

13. Non-Bank Holdings of Government Securities

14. Net Australian Private Capital Owned by Overseas Residents

15. Bank Advances

16. Personal Income Taxes

17. Bank Bill Rate

18. Bank Advances Rate

19. Money Rate

20. Bond Rate

21. ($A/$US) Exchange Rate

22. Foreign Reserves

23. Domestic Credit

24. Volume of Money

25. Inventories

26. Expected Sales

27. Private Expected Sales

28. Business Fixed Capital Stock

29. Employment

VARIABLES USED IN RBII
A bank advances to private sector
B government bonds held by private non-bank groups
C* real cash benefits to persons
C domestic credit
CTB* effective company tax base
d real household consumption expenditure
E exchange rate ($A/$US)
F net Australian private capital owned by overseas residents
Fg* net Australian government capital owned by overseas residents
F net Australian private capital owned by overseas residents
g1* real government current expenditure
g2* real government capital expenditure
g3* real public authorities capital expenditure
h* required liquidity ratio of the banking sector
i real imports of goods and services
I* interest payments on government debt
k proportionate change in the real stock of business fixed capital
k1 proportionate change in the real stock of non-mining business fixed capital
k2 Proportionate change in the stock of mining business fixed capital
K real stock of business fixed capital
Kh real stock of dwellings
Kmlnv* stock of mining capital
ℓ proportionate change in employment
L employment
m real stock of money (M/P)
mpk marginal product of capital
mpℓ marginal product of labour
M stock of money (M3)
Mt* target stock of money (M3)
MISC* miscellaneous items in the money supply identity
N labour supply
P price of domestic output
Pbt price of domestic output net of indirect taxes
Pd consumption deflator
Pg price of government consumption expenditure
Pi* Australian import prices ($US)
Pw* world prices ($US)
PWl* price of wool ($US)
Px price of exports
QA* synthetic variable for growth of bank advances, 1973
QOS* synthetic variable for U.S. dock strike, 1969
QE* synthetic variable for expectations about the exchange rate, 1972-6
QER* synthetic variable for timing of exchange rate changes, 1972, 1793, 1974, 1976
QF* synthetic variable for capital inflow during “resources boom”, 1980
Qi* synthetic variable for growth of imports, 1974–1980
Ql* dummy variable for shake-out effect in labour market, 1974-6
Q60* synthetic variable for period of fixed exchange rate, 1959–1971
Qrb1* dummy variable for increases in commercial bill rate, 19
Qrm* synthetic variable for rise in rm, 1973
QS* synthetic variable for increases in official Interest rates, 1961, 1973
QSB* dummy variable for the introduction of Australian Saving Bonds 1976(1)–(2)
QUS* dummy varlable for devaluation of $US, 1973
ra interest rate on bank advances
rb interest rate on 10 year government bonds
rbe expected next-period interest rate on 10 year government bonds
rb1 interest rate on 90 day commercial bills
reu* interest rate on 90 day Eurodollar bills
rk real marginal cost of capital
rm interest rate on trading bank fixed deposits
rw* interest rate on 10 year US government bonds
R gold and foreign exchange reserves
s sales
se expected sales
Inline Equation private expected sales
sd* real statistical discrepancy
t* time trend starting in 1959(3)
t11* index of income tax rate schedule
t2* average rate of tax on consumption
t3* average rate of tariffs
t4* average rate of payroll tax
t5* statutory company tax rate
t6* average rate of tax on expenditure
T1 receipts of direct taxes
T11 receipts of personal income tax
T12 receipts of company tax
T2 receipts of indirect taxes
T21 receipts of sales tax
T22 receipts of payroll tax
v real stock of inventories of goods
wa* index of real award wages

real marginal cost of labour

index of average earnings

real exports of goods and services

real demand for exports of goods and services

real supply of exports of goods and services

real world exports of goods and services

real domestic output (net of depreciation)

real normal domestic output (net or depreciation)

real disposable income

real farm output (net of depreciation)

real non-farm output (net of depreciation)

population of working age

expected rate of depreciation

TABLE A1.1 PARAMETER ESTIMATES[2]
Parameter Estimate Asymptotic
Standard Error
α1 0.112 0.027
α2 0.688 0.141
α3 0.024 0.002
α4 0.834 0.158
α5 0.207 0.060
α6 0.900 0.145
α7 0.413 0.093
α8 0.538 0.098
α9 1.435 0.257
α10 0.232 0.048
α11 2.169 0.351
α12 0.130 –
α13 0.101 0.025
α14 0.056 0.014
α15 0.206 0.020
α16 0.415 0.105
α17 0.225 0.057
α18 0.219 0.025
α19 0.447 0.051
α20 0.272 0.024
α21 0.048 0.016
α22 0.500 –
α23 0.500 –
β1 −0.029 0.013
β2 −5.775 1.554
β3 0.200 –
β4 14.642 6.457
β5 −18.807 6.981
β6 −6.470 2.595
β7 0.934 0.024
β8 0.489 0.072
β9 −0.391 0.063
β10 0.400 –
β11 0.009 0.007
β12 −1.019 0.254
β13 −0.117 0.183
β14 0.061 0.057
β15 0.214 0.061
β16 −0.333 0.067
β17 0.645 0.147
β18 −1.065 0.173
β19 0.015 0.003
β20 0.188 0.061
β21 0.928 0.009
β22 −0.079 0.031
β23 0.180 0.046
β24 0.019 0.154
β25 0.231 0.048
β26 0.718 0.014
β27 −0.130 0.024
β28 0.005 0.001
β29 0.200 0.026
β30 0.048 0.025
β31 0.381 0.057
β32 −0.044 0.017
β33 0.258 0.057
β34 0.081 0.014
β35 1.56611 –
β36 0.139 0.028
β37 −0.327 0.079
β38 −0.065 0.035
β39 −0.051 0.009
β40 7.348 8.489
β41 −19.606 6.755
β42 −83.331 17.666
β43 −0.503 0.059
β44 −0.113 0.024
β45 0.250 0.155
β46 6.765 2.501
β47 −0.500 –
β48 0.163 0.016
β49 0.057 0.009
β50 0.172 0.042
β51 0.029 0.003
β52 −7.605 0.890
β53 0.558 0.191
β54 0.5436 –
β55 0.043 0.003
β56 0.500 –
β57 0.050 –
β58 0.022 0.015
β59 −0.027 0.015
β60 0.530 0.083
β61 0.050 0.005
β63 0.200 –
β63 0.127 0.025
β64 −0.012 0.001
β65 −0.019 0.003
β66 0.002 0.001
β67 0.293 0.022
β68 −0.082 0.056
β69 0.098 0.012
β70 0.084 0.006
β71 0.018 0.006
IMPOSED STEADY STATE GROWTH RATES
Variable[3] Notation Growth Rate
Inline Equation (.012)
Inline Equation    
Inline Equation λ2 – λ1 (.009)
Pg, W λ2 – λ1 + λ4 (.0165)
N, L, Z* λ1 – λ4 (.0045)
Trend rate of technical progress λ3 (.0045)
Trend rate of growth of labour productivity λ4 = λ3/(1 – β10) (.0075)
wa λ5 (.0040)
B, F, A, T11, R, C, M, CTB*, Inline Equation, λ2 (.021)
MISC* Mt*, I*, Inline Equation    
Inline Equation – (0.0)
Inline Equation    

Footnotes

A subscript of zero (0) indicates a constant. A bar (–) above a parameter indicates that it is set prior to the estimation of the other parameters of the system. 0 is the differential operation d/dt, e is the exponential operator, and log is the logarithmic (to base e) operator. A variable with a hat (^) above it indicates the desired value of the variable. [1]

Estimation period is 1959(3) – 1980(4). Parameters without a standard error are imposed prior to estimation. [2]

An asterisk (*) next to a variable indicates that it is exogenous. [3]