A Simulation Model of Technical Change and Income Distribution
6.2. The model and solution procedure
6.2.1. Solution procedure
The model is implemented using the GEMPACK software package (Codsi and Pearson 1988). GEMPACK employs the Johansen procedure to approximate nonlinear
relationships as a set of linear equations in variables which are percentage changes of the variables in the underlying model. The model solved by GEMPACK is exactly that specified by the user, since equations are entered in algebraic form. This feature of GEMPACK yields an attractive level of interpretive transparency: all comparative static solutions arrived at are readily explained in terms of relationships between the variables in the model. GEMPACK forms the basis of the well-known ORANI model of the Australian economy (see Dixon et al. 1982).
3The omission of government expenditures from the model is not to deny the actual and potential role of the state in redirecting income flows. Studies cited in Mangahas and Barros (1980) indicate that the pattern of government expenditures has had a small positive effect on income distribution. None of those studies, however, incorporate the value of implicit subsidies to the industry sector in their calculations.
Table 6-1: Equations in the Model
Expressiona Number o f Equations
1. Factor demand and product supply
V = ß > ' + f t / + f t / Y + K A ' + V (s)
k ; = ß > ' + ß i / / + ß i/>; + ß Itaz ; + £ fa' (s)
* v = ß > ' + ß ; / + ß ; / / + ß ; Ä ' + E / (s) 2. Factor supply
L ' = epv'+L' (1)
K ' = E / + K ' (1) 3 . Household income and expenditure
M h = 5 * a + e > / + s AJk( i+ e hky + 2 X ( z / + z / ) 5=1 + 5a/L ' + (h) ( h ) RM„' = M h' - P h' ( h ) C h i ~ ^> hl^l + ^ h l ^ h (h ) C"l - X W-013 h (1)
4. Price setting and market clearing
P s = S l s W ' +V + S zsz s ' r - = 1,2) ■P3 = sl3w +sk3r +sz3z3 1 (ri P i’ = s l4w'+sk4r '+sl4z4 l U) 1 o II o (i) o 5 (i) k' - L V C ' = o s (i)
Total number o f equations 4 5+4/2 +6
a Variable and parameter definitions are listed in Table 6-2. Sectors are indexed by s, households by h. The subscripts l, k, and y denote labour, capital and output respect ively. Numerical subscripts refer to individual sectors.
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Table 6-2: Variables and Parameters in the Model
Symbol Definition
Endogenous Variables
L s Labour demand in sector 5 (s)
Capital demand in sector s ( S )
y . Product supply in sector 5 ( S )
L Aggregate labour supply (1)
K Aggregate capital supply (1)
M h Income of household group h (h)
Pk Expenditure share-weighted price index
of household group h (h)
RM h Real income of household group h (M JP h) (h)
C h 3 Demand for good 3 by household group h (h)
c,
Aggregate demand for good 3 (1)W Price of labour (1)
r Price of capital (1)
Zs Return to specific factor in sector s (s)
p , Price of non-traded good (good 3) (1)
Total endogenous variables 4s + Ah + 6
Exogenous variables
z . Endowment of fixed factor specific to sector s (s)
L Aggregate labour endowment (1)
K Aggregate capital endowment (1)
P , s Technical change shifter* for labour
in agricultural sector s (2)
P y s Technical change shifter* for capital
in agricultural sector 5 (2)
E s Technical change shifter* for output
in agricultural sector s (2)
Ts Overall rate of technical change* in
agricultural sector s (2)
P* Price of manufactured good (1)
Total exogenous variables s + 12
Total number o f variables 5s + 4/z + 1 8
Numeraire price
p i Price of agricultural good
continued...
Table 6-2 (continued)
Symbol Definition
Parameters
ßf Elasticity of demand for factor i with respect to factor price j in sector s
ß* Elasticity of demand for factor i with respect to output price y in sector s
ß^z Elasticity of demand for factor i with respect to fixed factor z in sector 5
ß*f Elasticity of supply of good y with respect to factor price i in sector s
ß* Elasticity of supply of good y with respect to own price in sector s psyz Elasticity of supply of good y with respect to specific factor z in sector 5
Xis Employment share of factor i in sector s sis Distributive share of factor i in sector s
Ehi Own-price elasticity of supply of factor i from household group h
£• Aggregate own-price supply elasticity of factor i
bhi Share of income of household group h derived from earnings of mobile factor i
Share of income of household group h derived from earnings of specific factor Zs
Expenditure share of household group h on good 3
r\h3 Expenditure elasticity of demand for good 3 by household group h
<j)Ai Share of household group h in ownership of factor i
\j/A3 Share of household group h in consumer demand for good 3 5/,3 Price elasticity of demand for good 3 by household group h
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GEMPACK employs the familiar principle that equations linearised by Johansen’s method (i.e. expressed in percentage changes of the variables) can be written in the form
Cz = 0 ,
where C is an nxm matrix (in n equations and m variables, with m > n), and z is an mxl vector of variables in percentage change form. Closure is achieved by selecting any m - n
variables to be exogenous, yielding a system in which the number of equations equals that of endogenous variables. The equation system can then be rewritten in the form
Azl + Dz2 = 0 ,
where zx and z2 are the vectors of endogenous and exogenous variables respectively, and
A and D are the corresponding columns of the matrix C. As long as A is invertible, the elements of zx can be expressed in terms of the parameters and exogenous variables of the model as
zx = -A~lDz2 .
The effects of shocks to the values of exogenous variables in z2 on z1 can then be evaluated as long as the matrix A~lD is not singular (Codsi and Pearson 1988).
In Table 6-1 the complete model is shown to consist of (4s + 4/z + 6) equations and
(5s + 4h+ 18) variables. Closure is achieved by specifying as exogenous the technical change shifters E ' and E \ the price of the manufactured commodity P4', and the endowments of capital, labour and fixed factors K \ L', and Z x to Z4'. This leaves (45 + 4/2 + 6) = 50 endogenous variables and the same number of equations, ensuring that the model’s solutions are just identified. The closure is exactly that employed in the analytical model of Chapter Four, with the addition of one sector and one specific factor.