an empirically implementable integrated multiregional model for australia

Regional Science and Urban Economics 16 (1986) 181-195. North-Holland

AN EMPIRICALLY IMPLEMENTABLE INTEGRATED MULTIREGIONAL MODEL FOR AUSTRALIA

Christine SMITH

Griffith University, Nathan, Queensland 4111, Australia

Received June 1984, final version received August 1985

This paper describes an integrated multiregion model that is empirically implementable for the states of Australia. The model comprises an input-output module, a demographic module, an econometric module and a factor demand (substitution) module. A thorough examination is made of the required data base, and a sequence of steps developed for linking these modules together in a reasonably efficient manner. Finally, consideration is given to further extensions of the model to include a comparative cost-industrial complex module, an interregional programming module and an interdependent policy formation module.

1. Introduction

Over the past 25 years, a feature common to the regional science literature in many different countries has been the development of operational methods of regional analysis. Two recent trends in this literature are

(1) an emphasis on multiregion rather than single-region model building,’

and (2) an emphasis on integrated model building efforts, as a result of recog-

nition that each type of multiregional model has different strengths and weaknesses and hence that benefits can be obtained from complementary rather than competitive use of such alternative types of models.2

This paper describes an integrated multiregion model whose component modules are each capable of implementation given the nature of the data available in the Australian context, and develops a sequence of steps that are considered both reasonable and feasible for achieving the necessary linkages between these modules. As depicted in fig. 1, the model has seven components: (1) an interregional input-output module, (2) a comparative cost-

‘For general reviews of recent multiregional model building efforts, see Adams and Glickman (1980), Bolton (1980a, 1980b, 1982a, 1982b), Courbis (1982b), Glickman (1982), Issaev et al. (1982), Nijkamp and Rietveld (1980, 1982a, 1982b), Nijkamp et al. (1982), Rietveld (1981, 1982a, 1982b), and Snickars (1982).

‘For further discussion of this type of philosophy, see Isard et al. (1960) Isard et al. (1981) Isard and Anselin (1982) Isard and Smith (1983c, 1984, 1986), Lakshmanan (1982) Smith (1983) Treyz (1980) and Treyz and Stevens (1980).

01660462/86/$3.50 0 1986, Elsevier Science Publishers B.V. (North-Holland)

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industrial complex module, (3) an interregional programming module, (4) a demographic module, (5) a regional econometric module, (6) a factor demand (substitution) module, and (7) a conflict management-multipolicy formation

module. In section 2, an outline is provided of the structure of the input-output,

demographic, econometric and factor demand modules. In section 3, we present a sequence of steps via which these four modules could be success- fully integrated. In section 4, we discuss how these steps would be revised when the remaining non-policy modules are included in the model. In section 5, a rationale is provided for extension to include a conflict management- multipolicy formation module. Finally, some concluding remarks are made in section 6.

2. Operational components of the integrated model

The core component of the integrated model is the one which determines (projects) the level of economic activity in each region. An interregional input- output module is to be constructed to serve this purpose, and procedures have been developed for deriving the required (a) technical and trade coefficients, and (b) base year output, primary input, and final demand estimates. These procedures make use of available secondary data, however allowance has been made for supplementary surveys to be conducted to improve the accuracy of those cells which have the most significant impact on the multipliers derived from the ‘next to final’ version of the table.3

Since improved projections of economic activity can be obtained from utilisation of a combined economic-demographic model, a demographic module is included as the next component of the integrated model.4 As indicated in fig. 1 this module contains natural increase, overseas migration and interregional migration submodules. The natural increase submodule employs projections of demographic class specific birth and death rates published by the Australian Bureau of Statistics (ABS). The overseas migration submodule takes the national level of net foreign immigration fd to be predetermined by policy for each demographic class (d = 1,. . . ,12). It then allocates these given magnitudes among regions (J, L = 1,. . ,6) via the use of

3For details, see Smith (1983, 52-164 and 6022632). Unless superior data exists to suggest otherwise, each region’s technical coefficients are assumed to be usefully approximated by the corresponding national coefficients. For some sectors, Isard ideal-type trade coefficients can be estimated. For others, a combination of the commodity balance and location quotient methods are used to estimate Moses-type trade coefficients. Finally, a variant of the RAS procedure is employed to achieve the required row-column total consistency.

40ther multiregional models which involve the linkage of economic and demographic modules include: Ballard et al. (1980) Beaumont et al. (1982) Courbis (1979, 1980, 1982a), Evans and Baxter (1980), Harris (1973, 1980) Hollenbeck (1980) Isserman (1982) Ledent (1982), Madden and Batey (1980), Milne et al. (1980, 1980a), and Olsen et al. (1977).

184 C. Smith, Multiregional mod&for Austrulia

share coefficients IID: derived from ABS base year data. Finally, the interregional migration submodule includes

(4

(b)

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a set of demographic class specific econometric equations for projecting gross regional inmigration rates (M;f&) by members of the labour force.

+ a2 F add,((d.E~,I,E:)I(d,Ed,I,Ed,)) i I 1 add,((.E~,l,E:,)I(.Ed,IsEd,)) d'

( W Y$/,Ei,)/( W Y,./,E,.) = wage income W Kc per member of demographic class d’ in region J relative to the nation (a proxy for potential gains from migration into .I),

(dnE~./&.)/(d &,,/,E,.) = change in employment demand .E,, for members of d’ in region J compared with the nation (a proxy for change in employment opportunities in J relative to elsewhere),

(DE~,/sE~,)/(.Ed./,Ed.) = ratio of employment demand relative to labour supply sEdf for members of d’ in region J compared with the nation (a proxy for the probability of obtaining employment in J relative to elsewhere),

odd,= weight attached to conditions prevailing for members of d’ by current members of d when making migration decisions, and

p1 =a stochastic error term;

a set of demographic class specific econometric equations for projecting gross regional outmigration rates (Mi ./sEi) by members of the labour force;5 a gravity model for projecting the interregional pattern of net labour force migration flows &ii” subject to the constraints on total movements suggested by the above-mentioned econometric equations; and a set of fixed migration rate coefficients <i” derived from base year ABS data for projecting net interregional migration flows by non-labour force members.”

‘The problem of ensuring that the sum of regional outmigration projections is equivalent to the sum of regional inmigration projections must also be resolved. We do so by taking a simple average of these two sums as a binding control total, and then proportionally adjusting the individual regional projections until this constraint is met.

‘For a full presentation and discussion of the equations comprising this module, see Smith (1983, 278-358).


The third component of the integrated model is a regional econometric module which, as indicated in fig. 1, contains household income and

consumption expenditure, labour market, private investment expenditure and government expenditure submodules. Its role is to provide employment demand, labour supply and wage rate estimates for each region, and to give projections of the consumption, investment and government expenditure components of final demand required for operation of the interregional input-output module. The household income and consumption expenditure submodule contains equations for determining household disposable income HDYJ, wage income WY: by demographic class, non-wage income by type N WY; (k= 1,. . ,6), and household consumption expenditure by type HCE; (q=l,..., 5)’ For example, for per capita expenditure on durable goods we have

+b4(HCE~,,~,/P:_,)+~z, where

(HD Y:/P:) = household disposable income per capita in region J, UN: =unemployment level in region J,

8 =indicator of national credit conditions, and (HCEi,,- ,/Pf_ 1) = lagged dependent variable, included to reflect a partial

adjustment mechanism.

The labour market submodule includes equations for projecting, for each demographic class, employment demand by sector i (i = 1,. . . , n), labour force

participation rates (and hence labour supply sE,), and wage rates by sector (i=l,..., 4)’ For example, wage rates are determined by a system of equations

which distinguishes between

(a) a basic wage component SW$ which is set by the arbitration courts

when national and state wage decisions are handed down. Changes in this component are treated as a linear function of change in the consumer price index (lagged), and change in labour productivity in sector i (lagged); and

‘The data required for implementing this submodule are derived from the national accounts, population census, economic census and public finance statistics published by the ABS. For further details on equation forms and data sources, see Smith (1983, 3577365). Other multiregional econometric modules which contain household income and/or consumption expenditure equations include Ballard et al. (1980) Ballard and Glickman (1980) Crow (1973), Harris (1973, 19X0), and Mime et al. (1980, 1980a).

‘The data required for implementing this submodule are derived from the national accounts, labour force survey, economic census and population census statistics published by the ABS. For further details on equation forms and data sources, see Smith (1983, 365-375). Other multiregional econometric modules which contain labour market equations include Ballard et al. (1980), Ballard and Glickman (1977) Courbis (1979, 1980, 1982b), Fromm et al. (1980) and Mime et al. (1980, 1980a).

186 C. Smith, Multiregional model for Australia

(b) an above award wage component, which is estimated for each region as a function of local labour market conditions.

Thus we have

+~,(wR:,,-,lBw:,,-,)+~~, where

=ratio of the total wage rate to basic wage rate for members of d in sector i, region J,

=ratio of employment demand to labour supply for members of d in region J, and

( WR$, f _ 1/B Wf& _ 1) = lagged dependent variable, included to reflect a partial adjustment mechanism due to inertia in the labour market.

The private investment expenditure submodule includes equations for deter-

mining fixed capital (investment) expenditure KPRf by sector i (i = 1,. . . , 20).9 For example, for non-service sectors we have

KPR;=g,+g,((VA;- WY;)-(VA;,_,- WY:,_,))

+gz( WRitIUCCit) +g3(K%/KSit)

+g4KPRi,_1 +p4, where

(V/A:-- WYi)-(VA{,_l - WY:,_,)=change in gross operating surplus for firms in sector i, region J,

(WR,JUCC,) = wage rates relative to user cost of capital in sector i,

(KSQKSit) =subsidies available to help finance investment expenditure in region J relative to elsewhere, and

KPR;,_l = lagged dependent variable, included to reflect a partial

adjustment mechanism.

The government expenditure submodule distinguishes between three levels of government (E = 1,. . . , 3), eight categories of current expenditure programs (p=l,..., S), and seven categories of capital expenditure programs (k = 1,. . . ,7). It takes national expenditure by the federal government (I= 1) to be exogenous, and allocates these expenditures among regions via use of a set of constants !Pi, and Qif derived from base year data. On the other hand, a set

‘Other multiregional econometric modules which contain investment expenditure equations include Crow (1979), Harris (1973, 1980) and Lakshmanan (1980). The data required for implementing this submodule are derived from national accounts and economic census data published by the ABS. For further details on equation forms, see Smith (1983, 375-378).


of econometric equations are included for determining current GCONS,, and capital GINI&,, expenditures for the remaining levels of government.”

When using an input-output module for projecting the level of economic activity, it is important to permit the underlying technical-trade coefficients to change over time in response to relative price changes. It is for this reason that a factor demand (substitution) module is included as the next component of the integrated model.” Following Halvorsen and Ford (1978) and Lakshmanan et al. (1984), this module employs a translog cost function for estimating the level of demand for four broad classes of factor inputs (capital K, labour L, energy E, and materials M) for each sector i and region J. That is

S,Ji = a,i + 2 B,,, i In c + ~,i, r, s = K, L, E, M, where

Sri =share of factor I in total production costs of sector i, P, =cost (price) per unit of factor s, and pri =a stochastic error term.

3. Proposed linkage procdure re: Operational compmeats

The following steps are suggested for use at this stage.”

3.1. Step 1: Natural increase and overseas migration components of

demographic module

The demographic module is used first to estimate non-interregional movements from one demographic class to another over the projection period. Variables considered include births, deaths and net foreign immigration, and the final result is a set of crude population estimates for each region.

3.2. Step 2: Interregional input-output module (round 1)

In -order to facilitate integration with the factor demand module, each region’s economy is next divided into four broad categories of sectors - energy inputs E, material inputs M, labour inputs L, and capital inputs K.

“Other multiregional econometric modules which contain government expenditure equations are Crow (1973), Ballard and Glickman (1977) and Ballard et al. (1980). For further details on equation forms and data sources for this submodule, see Smith (1983, 378-384).

“Because of data limitations in the Australian context, this module is applied to manufacturing sectors only. For further details, see Smith (1983, 418473).

“These steps are tentative, and would undoubtedly be improved upon once experience was gained in the operation of the model.

An initial set of final demand estimates is then derived for each sector (i=l,..., n) by allocating national projections of these magnitudes among regions on the basis of past trends and/or the crude population estimates derived in step l.13

Assuming base year coefficients remain unchanged, standard interregional input-output procedures can then be employed to yield projections of output levels by sector (i = 1,. . . , n) for each region.

3.3. Step 3: Labour market component of regional econometric module (round 1)

The output projections derived in step 2 can next be employed in the labour market component of the regional econometric module to yield projections of

I; (4

3.4.

employment demand by demographic class by sector, labour force participation rates (and hence labour supply, by demographic class), and wage rates (and hence wage income) by demographic class by sector.14

Step 4: Interregional migration component of demographic module (round I)

The employment demand, labour supply and wage income projections derived in step 3 represent inputs to the interregional migration component of the demographic module. Operation of the latter yields projections of interregional migration rates (and hence levels) for each demographic class. These projections can then be employed to revise the regional population estimates derived at the end of step 1.

3.5. Step 5: Household income, consumption, investment and government expenditure components of’ regional econometric module (round 1)

The household consumption, investment and government expenditure components of final demand can now be revised via operation of the

13These initial final demand estimates need to be derived from outside the model - for example, from the operation of existing national econometric models. For further discussion, see Smith (1983, 208-210).

“% deriving these projections, we also need exogenous’ projections of a number of other variables. For example, for each demographic class we need estimates for each region of the median number of years of school completed, the participation rate in full-time educational institutions and the average number of hours worked by each member of the workforce. For further discussion, see Smith (1983, chapter 7).

C. Smith, Multiregional model,for Australia 189

remaining components of the regional econometric module. In so doing, use is made of

(a) the regional output estimates derived in step 2, (b) the regional employment demand, labour supply and wage rate

estimates derived in step 3, and (c) the revised regional population estimates derived in step 4.”

The interregional input-output module requires estimates of final demand by sector (i= l,..., n) while the regional econometric module yields projections of final demand by type. l6 In order to utilise the results of the latter in subsequent steps, use is next made of appropriately defined transformation matrices containing parameters derived from base year data.”

3.6. Step 6: Factor demand (substitution) module (round 1)

Given exogenous projections of capital P,, material P,, and energy P, prices and the wage rate P, estimates derived in step 3, the factor demand (substitution) module can now be run. This yields projections of cost shares Sfi (r = K, M, E, L) for each region’s manufacturing sectors. Comparison with

the corresponding base year cost shares in these sectors gives an indication of the magnitude of adjustments required within the broad categories of technical input-output coefficients identified, and subsequently utilised, in step 2.”

3.7. Step 7: Interregional input-output module (round 2)

The revised final demand estimates derived in step 5 and the revised input output coefficients derived in step 6 can now be employed in a rerun of

the interregional input-output module.

l5In addition, exogenous projections are required for a number of other variables - for example, national credit conditions, the level of urbanisation in each region, and the average user cost of capital in manufacturing sectors. For further discussion, see Smith (1983, chapter 7).

16For example, as discussed above, household final demand is estimated for four broad categories of consumption expenditure only; while government tinal demand is estimated for eight broad categories of capital goods expenditure only.

“For example, for household final demand we make use of a set of transformation matrices Ti whose typical element shows the proportion of region J’s household consumption expenditure of type 4 (q= 1,. ,4) which is purchased from sector i (i= 1, , n) in region L (L= 1,. ,6); while for private investment final demand we make use of a set of transformation matrices Ti whose typical element shows the proportion of capital expenditure made by sector k (k = 1,. . I;) in region J which is allocated to purchases from sector i in region L. For further discussion on these and other transformation matrices, see Smith (1983, 385-392).

IsThese adjustments can be made across-the-board for input-output coefficients within each broad category, or the analyst may consider applying constraints such that the corresponding physical quantity coefficients do not vary by more than a certain percentage. For further details on these procedural rules for adjusting input-output coefficients, see Smith (1983, 436447).


3.8. Step 8: Rerun of other components of integrated model (rounds 2-n)

Steps 3-7 are then repeated until the integrated model converges on a reasonable set of results - that is until all major discrepancies are eliminated and the magnitude of revisions being made in key variables (output, employment, etc) are deemed insignificant.lg

4. Extensions to include other non-policy modules

4.1. Comparative cost-industrial complex module

For those industries (or parts of industries) whose regional distributions are heavily influenced by transport costs, energy costs and other Weberian- type locational factors the output projections derived from an interregional input-output module can be improved upon. In particular, the locational patterns of these industries - primarily export-based mining and/or mineral processing industries in the Australian context - can be projected more accurately via the use of a comparative cost-industrial complex module.20

When a module of this type is included steps 2 and 7 of the linkage procedure described in section 3 would need to be revised from ‘operation of the input-output module’ to ‘combined operation of the input-output and comparative cost-industrial complex modules’. The revised step 2 would then involve the following phases:

(a) the cost-sensitive mineral-based sectors are removed from the standard input-output transactions table, and placed within a set of non- traditional final demand columns (and corresponding primary input rows),21

(b) initial final demand estimates are then derived for those sectors remaining in the structural matrix,

(c) initial projections are then made of the total market demand (intermediate and final) for those sectors placed in the non-traditional final demand section of the table,

(d) comparative cost-industrial complex analysis is then performed to determine what proportion of the total market demand estimated in (c) will be allocated to each region within Australia,

(e) the results of (d) are then used to modify the input-output type coefficients included in the non-traditional final demand section of the input-output table,

“For further discussion on the convergence procedure, see Isard and Smith (1986). “For a detailed outline of the comparative cost and industrial complex techniques of analysis,

see Isard et al. (1959, 1960) and Smith (1983, 166208). ‘iIn so doing, the partitioning of coefficients into the capital K, labour L, energy E and

material M categories required for operation of the factor demand module would be retained.


(4

and the input-output type technology constraints governing substitution possibilities,

finally, the output projections derived for non-agricultural sectors in (b) are checked for consistency against those derived for agricultural sectors in (d). Where discrepancies arise, modifications are made to the final demand estimates employed for the non-agricultural sectors in (b) and the input-output and programming modules successively rerun until the analyst is satisfied with the internal consistency of the results.26

5. Rationale for inclusion of an interdependent policy formation module

The final module depicted at the centre of fig. 1 is a conflict management - multipolicy formation module (designated INPOL). Its role is to assist in

(a) the identification of the joint or interdependent impacts of a given set of governmental policies on key economic and demographic variables for each region, and/or

(b) the identification of the set of policy changes which are most likely to be adopted over a given time period (for example, between the years 1985 and 2000) given the pressures being exerted upon it from the various sections of society.

Efforts have only just begun to develop systematically and comprehensively the tools required to make this module comparable to the other modules in terms of rigour of supporting theory, depth of operational analysis and quality of empirically testable hypotheses.*’ Nevertheless present indications suggest that this module, if allowed to develop, should become an increasingly valuable component of the model.

6. Conclusion

In this paper, an integrated system of multiregional modules has been proposed for eventual implementation in the Australian context, It could be that some or all of these modules do not yield reasonable results when confronted with actual data. In addition, for many purposes it may be that only some of the modules need be employed for reasonably accurate results to be obtained. Nevertheless, it is claimed that the complete model represents a realistic ‘ideal’ to which future generations of Australian regional scientists might aim if they are to be as effective as possible in assisting political leaders, decision-makers and others in the formulation of appropriate policies to be employed at federal or state levels of government.

Z6For further detailed discussion of the joint operation of input-output and programming modules for Australian agriculture, see Smith (1983, 634-638).

27See for example Isard and Smith (1983a, b,c, and 1984) and Smith (1983, 478-571).


(f) the input-output module is then operated, and output level projections derived for the sectors remaining in the structural matrix,

(g) finally, the output projections derived for non-traditional sectors in (d) are checked for consistency against those derived for traditional sectors in (f). Where discrepancies arise, modifications are made in (b) and (c) and the comparative cost-industrial complex and input-output modules successively rerun until the analyst is satisfied with the internal consistency of the results.

The remaining steps of the linkage procedure remain unchanged except that steps 5 and 6 now involve, respectively, the revision of final demand and input-output type coefficients for both the traditional and non-traditional sections within the input-output table.22

4.2. Interregional programming module

Another set of industries for which input-output projections can be improved upon are those characterized by input and/or output substitution. In the Australian context, some agricultural sectors fall into this category since farmers in these sectors are able to adjust their output mixes (and hence input requirements) as a function of their expectations regarding relative output prices. In order to handle such sectors adequately, consideration may be given to inclusion of an interregional programming module.23

Two linear programming models of Australia’s agricultural sectors are already in operation,24 and with minor modifications either could be fused with the interregional input-output module.25 Such in essence requires

(a) removal of the relevant agricultural sectors from the input-output structural matrix,

(b) operation of the ‘revised’ input-output module to generate initial estimates of output levels for each non-agricultural sector,

(c) definition of a set of agricultural end-products, and the use of the results of (b) in the derivation of an initial estimate of intermediate and final demands for these end products,

(d) operation of the interregional programming module to determine the pattern of agricultural sector production patterns that maximize returns to farmers given prevailing price and demand levels for end products,

*‘For further detailed discussion of the joint operation of the input-output and comparative cost-industrial complex modules, see Smith (1983, 208-218).

23For a detailed outline of the various forms of interregional programming modules that could be employed here, see Isard et al. (1960), and Smith (1983, 225-257).

‘%ee Longmire et al. (1979), Moneypenny (1975), and Mandeville (1976). 25Steps 2 and 7 of the linkage procedure described in section 3 would then become ‘combined

operation of the input-output and programming modules’.

C. Smith, Multire~ional model for Australia 193

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an empirically implementable integrated multiregional model for australia

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