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DEVELOPMENT OF AN AGGREGATIVE PROGRAMMING MODEL OF AUSTRALIAN AGRICULTURE

Neal Walker and John L. Dillon U n i v h t y of New England (Australia)

This paper describes, in broad terms, an Aggregative Programming Model of Australian Agriculture (APMAA) currently under develop- ment at the University of New England. APMAA will simulate farmer decision-making on more than 500 Representative Farms located in 56 regions. Linear programming is used as the basic tool ,for analysis, though other quantitative techniques such as regression analysis and statistical simulation are used in portions of the model. Special treatment is accorded to farmer behaviour, and production uncertainty is reflected through a weather simulator.

Introduction Development of an Aggregative Programming Model of Australian Agriculture (APMAA) commenced in 1972 at the University of New England. The aim of the model is to simulate the micro and macro effects on agriculture of changing economic conditions and climatic influences, and to experiment with various policies which could be implemented. The model is primarily concerned with the extensive crop and livestock activities which account for the bulk of Australian agricultural production. This paper describes the economic environment which the model is intended to reflect and the model structure and methodology utilised in gaining this end.

I t should be noted that the APMAA model is not complete at this writing and thus this paper deals with the model at an early stage of development. Justification lies in letting others know of the methodology being utilised to reflect a particular set of economic and environmental conditions.

Formulation of AF'MAA APMAA is designed to simulate the type, amount, and spatial distribution of agricultural production and resource use in Australia. Such information is desired on both an aggregate basis and a disaggregate basis by year for a pre-specified period of time. Three aspects of the agricultural sector were con- sidered to be of special importance in structuring the model.

Firstly, since the agricultural sector is basically a family farm private enterprise sub-economy, decisions regarding input use are made at the farm level. Given the decision role of farmers, it was desired to make the model reflect their known tendency towards risk aversion.

Secondly, Australians enjoy a relatively high standard of living. As living standards rise, and as pressures for agricultural adjustment increase, people become concerned about the distribution of income as well as its absolute level.

244 NEAL WALKER AND JOHN L. DILLON

In order to produce information concerning the distributional impact of economic growth and distributional effects of agricultural policy, the model was to be a highly disaggregated one.

The third aspect of Australian agriculture which was deemed deserving of special attention is the high degree of weather uncertainty which exists throughout the continent. This uncertainty can cause a wide divergence between a farmer’s plan and its actual outcome and should be reflected by the model.

A representative-farm (RF) programming approach was adopted as the basic technique of analysis. However, other quantitative techniques such as regression analysis and statistical simulation are also used in portions of the model. The structure of APMAA is presented below, followed by discussion of methodology utilised in handling risk aversion, disaggregation and weather uncertainty.

Structure of APMAA A diagrammatic flow chart showing the structure of APMAA is presented in Figure 1. Representative Farm (RF) plans are generated in a linear program- ming (LP) subroutine. Because the RF plans are generated independently, the

Figure 1 Flow Diagram of the structure of APMAA

Topography

Yield

Spatial Equilibrium

Realized Physical and Financial Results

supply of inputs which are fixed in aggregate but transferrable among farms (notably breeding stock) may not equal the demand for such, either on a regional basis or in aggregate. Two approaches to this problem are being developed. The first involves regional flexibility constraints for the relevant inputs; the second utilises a spatial equilibrium sub-model in which demand for and supply of the input(s) on a regional basis, and input shipping costs between regions, are utilised

DEVELOPMENT OF A N APMAA 245

to allocate available supplies of the input (methodology from Kate, 1972 and Walker, 1975). Once an optimal set of R F plans is obtained, it is assumed that the plans are, in fact, implemented. The rainfall-yield simulator then gener- ates an ‘outcome’ based on the R F plans and a simulated rainfall pattern. The final outcomes (for each RF) are scaled by the number of farms represented. Scaled results can then be aggregated by farm type, by farm size, by commodity group, or by a combination of the above, to a regional, state or national level.

The physical and financial outcome for each RF in Year 1 is carried forward to that farm’s stock of resources in Year 2 through a system of linkage equations. Thus the model may be run sequentially for a specified number of years.

Within this structure, RF decision-making is simulated using a one-year time horizon. Such aspects as farm birth/death/amalgamation and technological change are not treated by the present model. However, long-run aspects enter the decision-making process through the behavioural sector of the LP and through the spatial equilibrium submodel.

Commodity prices are determined exogenously and are discounted for distance from major ports. This treatment of prices is justified by the heavy dependence of the Australian economy on world trade (thus domestic prices depend largely on world economic conditions), and by the high concentration of population along limited stretches of coastline. This second factor means that agricultural output flows to major ports regardless of its ultimate destination (domestic consumption or export).

Risk behaviour The simulation of farmer decision-making using LP models in which profit is maximised without regard to behavioural aspects is often held to be unduly unrealistic. It is a generally held hypothesis that farmers are not only concerned with the income results of farm plans but also with the variability of income. Quadratic programming can be used to specify the set of farm plans that are efficient in terms of maximising expected income for a given level of income variance. However, because of the large number of representative farm matrices in the model, a scarcity of computing time, and a general lack of information on the choice criteria between efficient plans, a simpler approach was desired - preferably using LP.

The initial approach has been to use the focus-loss constrained programming (FLCP) approach of Boussard and Petit (1967). They have shown that it is possible to add constraints to a profit maximising LP model to constrain the variability of profit outcomes. In their formulation, expected total gross margin (E) is maximised subject to some probability level that total gross margin (assumed to follow a normal distribution) will be greater than some minimum total gross margin (MINI). This involves addition of one ‘focus-loss’ constraint for each activity (in the LP matrix) which has an uncertain gross margin.

In incorporating the FLCP concept into APMAA, two modifications were made. The empirical value of each focus-loss constraint was based on the variance of the gross margin of the activity (as suggested by Kennedy and Francisco, 1974), and a trade-off between E and MINI was allowed in each LP matrix (as suggested by Webster and Kennedy, 1975).

Distributional effects Agricultural holdings in Australia range in size from less than 10 acres to over 1 million acres. Climatic conditions range from lush tropical through Mediter- ranean to arid desert. The results of a given policy would be expected to vary

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246 NEAL WALKER AND JOHN L. DILLON

considerably among farms operating under such divergent conditions. In order adequately to reflect the farm structure and to simulate distributional effects of policies, farms are stratified by region, by type and by size.

Delineation of regions follows the Statistical Division classification system of the Australian Bureau of Statistics. The primary reason for using this system was that of data availability. However, Statistical Divisions do conform to broad geographical features.

Farms in each region are further stratified into as many as six farm types and three farm sizes. Farm types are based on the predominant activities which exist on the farm and include sheep, cereal grain, sheep-grain, beef, dairy and multi- purpose farms. Farms are classified by size (within a region) in such a way that 50 per cent of all farm numbers (of a given farm type in a given region) are in- cluded in the medium-size category which is centred on the weighted average acreage.* Once the medium-size farm category is specified, the small and large farm categories are defined by the weighted average acreage of the relevant residual group. A Representative Farm (RF) was constructed for each regional size group of 400 to 600 farms (on average).

Specification of the model for the State of New South Wales includes 135 RFs distributed among 14 regions. The Australian model will contain more than 500 RFs located in 56 regions. This level of disaggregation of the model will allow a given policy to be related to a relatively small, locationally specific group of producers, each of whom has similar resource endowments and production possibilities.

Weather uncertainty Farm plans (for RFs) are generated by APMAA in an LP subroutine and are based on expected yields. A weather simulator then generates a ‘realised’ yield which, in turn, determines the ‘outcome’ of the farm plan.

Many yield correlations based on weather could be considered. For example, wheat yield in Region 1 could be highly correlated with wheat yields in Regions 2, 3 and 8 and also highly correlated with barley and oat yields in various Regions (as well as within Region 1). Similarly the number of climatic variables and their time bases which could be included in a weather simulator is large - temperature, rainfall, wind velocity, evapotranspiration, indices combining several variables, etc. To avoid a highly complex multi-dimensional problem, yields of all activities within a region are based on monthly rainfall within the region and correlations between regions is based on monthly rainfall correlations alone.

A rainfall-yield simulator was developed using the region as the basic geo- graphical unit to be treated. It consists of two parts: a rainfall generator, and a system of equations which generate yields as a function of rainfall.

The rainfall generator output consists of monthly rainfall distributions for each region. The generator takes into account rainfall correlations between regions using multi-variate analysis techniques.

The yield generator output consists of regional yield distributions (by activity) conditional on rainfall. Multi-variate techniques are used to adjust yield distribu- tions to take into account residual correlations between the output of production activities.

* Possible measures of farm size include acreage, capital value, labour availability and gross receipts. In view of the large variation in labour/capital ratios on Australian farms, the difficulties of capital valuation and the large variability in gross receipts (from year to year), acreage was deemed the most consistent and meaningful intraregional measure of farm size.

DEVELOPMENT OF AN APMAA 247

Concluding remarks This paper has described, in general terms, the early stages of development of an aggregative programming model of Australian agriculture. Development to date has proceeded on three model aspects simultaneously; data preparation, com- puter software, and the rainfall-yield simulator. A prototype model including all (Australian) States is expected to be operational in late 1976.

More detailed information on APMAA is available in a series of APMAA Reports (see References) which deal either with the progress of the project, or with research work which has developed as a result of technical problems encountered in the project. Individual copies of these reports may be obtained upon request from the authors of this paper.

Acknowledgements The authors are indebted to John W. B. Guise, Richard Monypenny and Emilio Francisco for helpful comments on earlier drafts. Financial support for the project has been provided by the Australian Wool Corporation and the Reserve Bank of Australia.

References APMAA Research Team (1974). Progress Report on a Programming Model of Australian

Agriculture, APMAA Report No. 3. Department of Agricultural Economics and Business Management, University of New England, Armidale, N.S. W., Australia.

Boussard, J. M. and Petit, M. (1967). Representation of Farmers’ Behaviour Under Uncertainty with a Focus-Loss Constraint, J. Fm Econ. 49,869-880.

Francisco, E. M. and Kennedy, J. 0. S. (1975). A Note on the Use of Tchebycheffs Inequality in Linear Programming, J. agric. Econ. 26, 265-267. (Also available as APMAA Report No. 4).

Kate, A. Ten (1972). Decomposition of Linear Programming by Direct Distribution, Econo- metrica 40, 883-889.

Kennedy, J. 0. S. (1972). On Using Aggregative Programming to Model Agriculture in New South Wales, APMAA Report No. 1.

Kennedy, J. 0. S. (1975). Using Regression Analysis to Reduce Aggregation Bias in Linear Programming Supply Models, Aust. J . agric. Econ. 19, 1-11. (Also available as APMAA Report No. 5 . )

Kennedy, J. 0. S. and Francisco, E. M. (1974). On the Formulation of Risk Constraints for Linear Programming, J. agric. Econ. 25, 129-146. (Also available as APMAA Report NO: 2.)

Mandeville, T. M. (1976). Linking APMAA to Representative Regional Input-Output Submodels, APMAA Report No. 8.

Monypenny, J. R. (1975). APMAA ’74: Model, Algorithm, Testing and Application, APMAA Report No. 7.

Walker, Neal (1975). A Spatial Equilibrium Model for Equating Sub-Regional Input Supply and Demand. (Paper presented to the Annual Conference of the Australian Agricultural Economics Society, La Trobe University, Melbourne.)

Webster, J. P. G. and Kennedy, J. 0. S. (1975). Measuring Farmer’s Trade-offs Between Expected Income and Focus-Loss Income, Am. J . agric. Econ. 57,97-105. (Also available as APMAA Report No. 6.)

R6sm6 MISE AU POINT D’UN MODELE DE PROGRAMMATION AGRGGEABLE DE L’AGRICULTURE AUSTRALIENNE

L’article dkcrit, en termes gkndraux, un modgle de programmation agrkgeable de l’agriculture australienne (APMAA), actuellement en cows d’daboration a I’universitb de New England. L’APMAA doit simuler les decisions en matigre de gestion agricole surplus de

248 NEAL WALKER AND JOHN L. DILLON

500 exploitations reprksentatives situtes dans 56 regions. Laprogram- mation linkaire est utiliske comme instrument de base de I’analyse, bien que d’autres techniques quantitatives comme I’analyse de regres- sion et la simulation statistique soient employees partiellement dans le modile. Un traitement sptcial est accordk au comportement des agriculteurs et les incertitudes de production sont reJktPes h I’aide d‘un simulateur atmosphkrique.

Zusammenfassung DIE ENTWICKLUNG EINES AGGREGATIVEN PROGRAMMIERUNGSMODELLS FOR DIE AUSTRALISCHE LANDWIRTSCHAFT

Dieser Artikel beschreibt in grossen Zugen ein aggregatives Programmierungsmodell fur die australische Landwirtschaft (APMAA), das im Augenblick an der Universitat von Neil England entwickelt wird. APMAA simuliert, dafs Farmer auf mehr als 500 reprasentativen Farmen, die in 56 Regionen liegen, Entschei- dungen trefen. Lineare Programmierung wird als Grundinstrument fur die Analyse gebraucht, aber auch andere quantitative Verfahren wie Regressionsanalysen undstatistische Simulation werden in Teilen des Modells angewandt. Das Verhalten der Farmer wird gesondert behandelt, und Produktionsunpewissheit wird durcli einen Wetter- simulator widergespiegelt.