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w Forecasting supply at the farm level

e ABARE

A U S T R A L I A N

B R O A D A C R E AGRICULTURE

Forecasting supply at the farln level

Philip Kokic Steve Beare

Vernon Topp Vivek Tulpulk

ABARE KESEARCW REPORT 93.7 - e ABARE

0 Commonwealth of Australia 1993

This work is copyright. The Copyright Act 1968 permits fair dealing for study, research, news reporting, criticism or review. Selected passages, tables or diagrams may be reproduced for such purposes provided acknowledgment of the source is included. Major extracts or the entire document may not be reproduced by any process without the written permission of the Executive Director, ABARE.

ISSN 1037-8286 ISBN 0 642 188 18 1

Kokic, P., Beare, S., Topp, V. and TulpulC, V. 1993, Australian Broadacre Agriculture: Forecasting Supply at the Farm Level, ABARE Research Report 93.7, Canberra.

Australian Bureau of Agricultural and Resource Economics GPO Box 1563 Canberra 2601

Telephone (06) 272 2000 Facsimile (06) 272 2001

ABARE is a professionally independent research organisation attached to the Department of Primary Industries and Energy.

ABARE project 1263.101

Foreword

Data from ABARE's Australian agricultural and grazing industries survey are perhaps the most important and extensive source of financial and physical information available on Australian broadacre agriculture. Their potential applications are wide. The data are used in numerous reports released to the general public, in economic research and in government decision making.

However, the usefulness of this survey information has been partially restricted by the lack of appropriate farm level economic models. Such models can be used to assess farm level responses to changes in the economic environment in which broadacre agriculture operates.

In this report, new methods of estimation are used to construct a reliable farm level model of supply response in Australian broadacre agriculture.

The supply model forms the final major link in a fully integrated projection system, which includes ABARE's geographic information system. The system will enable researchers and policy makers to examine in detail the effects of price and policy changes on production costs, farm cash income and farm business profit.

BRIAN FISHER Executive Director, ABARE

April 1993

Acknowledgments

This report was prepared in the Research Resource Unit. The mathematical theory in this paper was motivated by work undertaken by Ken Brewer, formerly of ABARE, now retired.

The authors also wish to thank Ray Chambers of the Australian National University for his valuable input in the early stages of this project and the referees for their comments and suggestions.

Contents

Summary

1 Australia's broadacre industries Broadacre agricultural production in the 1980s Regional information

2 Modelling Australian broadacre agriculture Production elasticities in broadacre agriculture, 1980-8 1 to 1990-91 Regional variations in elasticities Substitution possibilities Three year estimates, 1988-89 to 1990-9 1

3 Using the model to assess the regional impacts of policy and price changes

Appendixes A Model development B Parameter estimation

I C Using the supply model as a forecasting tool

D Own-price and cross-price elasticities, 1980-81 to 1990-91

References

Box I Means and percentiles

Figures A Contributions to total broadacre receipts B Prices for major broadacre commodities C Composition of broadacre receipts, by zone D Own-price elasticity of supply for wool E Own-price elasticity of supply for beef F Own-price elasticity of supply for mutton G Own-price elasticity of supply for lamb H Own-price elasticity of supply for wheat

Maps 1 Broadacre industries survey zones 2 Own-price elasticity for wool, 1980-8 1 to 1990-9 1 3 Own-price elasticity for beef, 1980-8 1 to 1990-91 4 Own-price elasticity for wheat, 1980-81 to 1990-91 5 Elasticity of wool supply with respect to beef price,

1980-81 to 1990-91 6 Elasticity of wool supply with respect to wheat price,

1980-81 to 1990-91 7 Elasticity of beef supply with respect to wheat price,

1980-81 to 1990-91 8 Elasticity of beef supply with respect to wool price,

1980-81 to 1990-91 9 Elasticity of wheat supply with respect to wool price,

1980-81 to 1990-91 10 Elasticity of wheat supply with respect to beef price,

1980-81 to 1990-91 11 Own-price elasticity for wool, 1988-89 to 1990-91 12 Own-price elasticity for beef, 1988-89 to 1990-91 13 Own-price elasticity for wheat, 1988-89 to 1990-91

Tables 1 1989-90 income and production projections using the

supply model 25 2 1990-9 1 income and production projections using the

supply model 26 3 Own-price elasticities, 1980-8 1 to 1990-9 1 45 4 Cross-price elasticities, 1980-8 1 to 1990-9 1 46

vii

Australian farm returns for agricultural commodities are likely to be influenced by a variety of economic factors in the future. Some of the most important influences on the prices of Australian farm commodities may be reforms to agricultural protection in northern hemisphere countries, economic developments in Eastern Europe and the Commonwealth of Independent States (the former Soviet Union), and economic growth in Asia and developing countries. Continued microeconomic reforms in Australia could also have a significant impact on farm costs and revenues. And year to year changes in weather conditions will continue to cause significant fluctuations in production and income.

In such an environment, reliable forecasts of Australian agricultural production and farm incomes generated for a range of alternative market conditions will be important. In this report a modelling framework which provides detailed estimates at the farm level of the responsiveness of Australian agricultural supply to shifts in output prices is developed. Such measures of responsiveness are called 'elasticities'.

Own-price elasticities measure the change in the supply of a commodity in response to a small change in the price of that commodity. For example, an own-price elasticity for wool of 0.46 indicates that supply will increase by 4.6 per cent in response to a price rise of 10 per cent. Cross-price elasticities measure the change in the supply of a commodity in response to a change in the price of other commodities. For example, a cross-price elasticity between the supply of beef and the price of wheat

Returns for Australian farm

products are affected by many economic factors

Reliable forecasts are therefore important to

decision making

Elasticities measure response to price

changes

Forecasting supply at the farm level

Regional level estimates of elasticities are provided for wool, beef, mutton, lamb and wheat

Regional elasticities will improve supply forecasts

Supply responsiveness falls as price rises

-- -

of -0.02 indicates that the supply of beef will fall by 0.2 per cent in response to an increase in the price of wheat of 10 per cent.

In this report, regional estimates of average own- price and cross-price elasticities of supply for the five major Australian broadacre commodities - wool, beef, mutton, lamb and wheat - are presented. These regional elasticities are obtained by aggregating estimates of farm level elasticities for each year. The farm level elasticities are estimated from farm survey data collected each year by ABARE. Formulas for own-price and cross- price elasticities are obtained by assuming that farms in the Australian agricultural and grazing industries survey maximise their annual net farm income subject to the constraint that their changes in production are limited by the amount of land available to them.

Because policy changes or shifts in market conditions can affect farmers in different locations in different ways it is instructive to have estimates of the responsiveness of supply at the regional level rather than just at the national industry level. Regional variations emerge because of differences in land quality and climatic conditions between regions as well as any within-region differences in the composition of output at any given time. The generation of accurate regional supply elasticities will improve aggregate supply forecasts and help to provide more detailed information about the regional impacts of price and policy changes.

In general, the responsiveness of farm supply of a commodity falls as the price of that commodity rises. Also, the own-price elasticity for a commodity is likely to be lower if the amount of land devoted to the production of a unit of that commodity is small relative to other activities, or if the rental rate of the land is high.

ABARE research report 93.7 I

Model development

The analysis of supply responsiveness described in this report is based on a farm level econometric model of farm cash income. Farmers are assumed to maximise their annual farm cash income (defined as total cash receipts less total cash costs) by producing combinations of wool, lamb, mutton, beef or wheat subject to a fixed land area constraint. Farm level own-price and cross-price elasticities are derived from this model. Fundamental to the derivation of these elasticities is the assumption that certain fixed characteristics - for example, soil and climatic conditions and management practices - will determine the profitability of each farm relative to other farms of a similar size.

Uses of the supply model The supply model developed in this study can provide a valuable input into any analysis of the regional impact of changes in prices and in government policy. In particular, it is envisaged that the main use of the model will be as a general and flexible tool for forecasting production, unit costs, net returns and farm cash income on a regional and national basis.

Because this information is forecast at the farm level, regions and industries can, within limits, be defined arbitrarily. Thus, for example, it becomes possible to analyse the effects of government policy decisions on virtually any subpopulation of the broadacre sector.

The full potential of the supply model becomes more apparent when some of its specific applications are considered. Each November ABARE runs a telephone survey of producers who respond to the Australian agricultural and grazing industries survey to determine their physical and financial situation


Own-price and cross-price

elasticities are derived from farm

level models

Models can be used to forecast production and

farm income

Any broadacre region can be

analysed

Additional regional in formation could be used to update

forecasts

- - - -

for the remaining part of the current financial year. To refine these estimates even further and to take into account any changes in a range of influences - for example, climatic conditions - production information could be collected in regular smaller telephone surveys and the supply model used to update estimates of costs and incomes at the regional

. . . thus improving level. In this way, the supply model enables regular the timeliness of updating of estimates so that they accurately forecasts represent the current situation rather than being a

snapshot based on information available in an earlier period.

ABARE research report 93.7

- - - - - - -

Australia 3 broadacre industries

The data used in this analysis are drawn from ABARE's Australian agricultural and grazing industries survey (AAGIS), a large scale farm survey of broadacre agriculture which is conducted annually. From 1980- 81 to 1989-90 the number of sample farms in the survey ranged between 800 and 1100. In 1990-91 the sample size was increased to 1654 to provide more detailed geographic information.

Each sample farm has a designated survey weight, and the sum of these weights is equal to the broadacre farm population. In 1990-91 this population was approximately 82 000 farms. A range of information is collected from each sample farm, covering production and physical characteristics as well as financial performance. The individual farm information is aggregated to provide national, state and regional statistics. A description of how the survey is designed and the sample selected can be found in ABARE (1992a).

Forecasting supply at the farm level 5

- - - - -- - - - -- - - - - - - -- - - - 1 A Contributions to total broadacre receipts E ABARE

1 Other

Broadacre agricultural production in the 1980s Production of four main broadacre commodities - wool, wheat, beef and sheep meat (mutton and lamb) - is estimated to have contributed over 80 per cent of the total receipts from broadacre farms in each year of the decade to 1990-91. From year to year, however, the relative importance of the individual commodities to total industry returns varies according to changes in relative commodity prices and changes in production. During the latter half of the 1980s, real returns from the production of grains relative to total returns declined markedly, while at the same time relative returns from wool production rose significantly (figure A).

Much of the trend toward increased wool production over the 1980s can be attributed to increases in real wool prices and decreases in real wheat

Prices for major broadacre commodities In 1990-91 dollars I

6 ABARE research report 93.7

prices (figure B). However, following the sharp decline in wool demand in the late 1980s and the subsequent abandonment of the Reserve Price Scheme for wool in June 1991, wool prices and production fell significantly, and are expected to remain relatively low over the medium term.

Regional inforrnation The mix of enterprises on broadacre farms varies according to climate and topography. The AAGIS sample farms are divided geographically into the three major broadacre production zones of Australia, shown in map 1 (ABARE 1992a, p. 2).

The pastoral zone, includes the arid and semiarid regions of Australia. It contains mainly large agricultural holdings on which cattle (in the north) or sheep (in the south) are run extensively, typically on native pastures. Such holdings numbered 4136 in 1990-91. By contrast, the wheat-sheep and high rainfall zones, which are located in the wetter areas of the Australian continent, contain smaller agricultural holdings. Such holdings numbered 45 966 and 32 066 respectively in 1990-91. The drier climate and flatter terrain of the wheat-sheep zone favours extensive cropping in association with livestock (mainly sheep). Conditions in the wetter, colder and often more rugged southern regions of the high rainfall zone make it more suitable than the wheat-sheep zone for intensive grazing of livestock and less suitable for producing cereal grains.

The emphasis on livestock production in both the pastoral and high rainfall zones is apparent in figure C, which shows the average proportions

Composition of broadacre receipts, by zone Average for 1981-82 to 1990-91 E ABARE


of gross receipts contributed by the various commodities over the years 1980-81 to 1989-90. In the pastoral zone, beef accounted for around 51 per cent of gross receipts, while in the high rainfall zone its contribution was somewhat smaller, at around 37 per cent. Wool contributed around 35 per cent to gross receipts in the pastoral zone, closely followed by wool's contribution of approximately 33 per cent in the high rainfall zone. The contribution of wool to gross receipts in the wheat-sheep zone was roughly 24 per cent. Sheep meat (lamb and mutton) made only a small contribution in each zone.


Modelling Australian broadacre agriculture

Using the model described in the appendixes, own-price elasticities for five broadacre commodities - wool, beef, mutton, lamb and wheat - are estimated. The estimates are calculated for each year of the period 1980- 81 to 1990-91. Own-price and cross-price elasticities are then averaged over the entire period, as well as over the three most recent years, and these estimates are presented at the national, zone and industry levels. Regional results are also illustrated using mapping techniques. To give an indication of the extent to which the elasticities can vary from year to year, the eleven year average elasticities (1980-81 to 1990-91) are compared with three year averages (1988-89 to 1990-91).

Production elasticities in broadacre agriculture, 1980-8 1 to 1990-9 1 Annual own-price elasticities for the five broadacre commodities are presented graphically in figures D-H. The mean, median, lower quartile and 90th percentile of the distributions of each elasticity are plotted for each year 1980-8 1 to 1990-9 1 (see box 1 for definitions of these measures). In calculating these aggregate statistics, the weight given to each sample farm is a combination of its survey weight and the quantities of output produced by that farm. When calculated in this way the mean elasticity will be an estimate of the broadacre sector's aggregate supply response to a given price change. For example, in calculating the aggregate own-price elasticity for wool in 1990-91, the individual wool elasticity of each sample farm in 1990-91 is weighted by that farm's survey weight (because the sample farm represents a number of wool growers) and its wool production. Weighting the average by the farm's production means that farms producing larger quantities of wool will have a greater impact on the aggregate wool elasticity than farms with lower wool production.

In all years, the mean own-price elasticities of the five major broadacre commodities were greater than the corresponding medians, indicating that the distributions of these values are skewed to the right. That is, elasticities greater than the mean occurred less frequently. But when they were greater, then, on average, they were further from the mean than were those elasticities below the mean. Elasticities above the 90th percentile were in



most cases reasonably large, indicating that a small but significant proportion of farmers changed production readily in response to price movements. However, the lower quartiles of the elasticity distributions were, in most cases, very close to zero, implying that a larger proportion of farmers did not respond readily to the price changes, either because they were unable to do so, they considered other factors to be more important or they produced only a single commodity.

Wool The distribution of the own-price elasticity for wool is shown in figure D. From 1980-81 to 1984-85 wool prices and production were both relatively static, and mean wool elasticities changed little. In 1985-86 sheep stocking

rates increased, implying that the amount of land required to produce a kilogram of wool had fallen. Farmers were then able to react to changes

I

I in wool prices more readily without being adversely constrained by land area requirements. As a consequence there was a general increase in wool elasticities in 1985-86. Record wool prices in 1987-88 and 1988-89 led to increased net returns (profits) to wool production and so wool supply elasticities in those years were relatively low. After 1988-89, however, a combination of falling prices and high production led to an increase in average wool elasticities.

Beef Throughout the 1980s both the beef herd and beef prices remained relatively constant. This is in stark contrast to the previous decade when


E Own-price elasticity of supply for beef I I

E ABAREI I

a substantial increase in beef cattle numbers in the mid-1970s was followed by an equally rapid decline in the latter half of the decade. Beef elasticities over the period varied little and in absolute terms were relatively small (figure E). The increase and subsequent decline in beef elasticities during the late 1980s were caused mainly by changes in the unit land area associated with beef production. This was itself influenced to some extent by the substantial changes in the national sheep flock at that time.

Mutton The mean own-price elasticities for mutton varied between 0.2 and 0.4 during the 1980s, but fell to around 0.1 in 1990-91 (figure F). As mutton

I F Own-price elasticity of supply for mutton I I E ABARE I I

12 ABARE rrsearclz report 93.7

production is dictated primarily by changes in the size of the sheep flock - which is itself chiefly driven by wool and lamb prices - mutton elasticities in any single year tend to fluctuate according to the combined influence of prices, costs and unit land areas. The interrelationships between the size of the sheep flock, wool prices, lamb prices and mutton prices make it difficult to generalise about trends in mutton supply response.

Lamb The average lamb elasticities shown in figure G are larger in absolute terms than any of the other commodities analysed. This reflects the smaller unit land areas required to produce lambs, and hence the greater

1 G Own-price elasticity of supply for lamb I

I

sensitivity of production to price movements because land area, in general, I I is not a limiting factor. I

Wheat The estimated own-price elasticity for wheat was also relatively stable over the study period (figure H) despite a steady decline in the price of wheat. The estimated average annual elasticity of supply for wheat ranged between 0.2 and 0.4 over the period. This stability partly reflects the fact that wheat farmers reduced costs at roughly the same rate as the decline in prices (see ABARE 1990, figure I). Any increase in the wheat supply elasticity in response to falling wheat prices was offset by farmers developing more efficient production techniques.


1 H Own-price elasticity of supply for wheat I

Regional variations in elasticities The results obtained in the previous section show that own-price elasticities for the various broadacre commodities can vary substantially from year to year. In large measure this variation is caused by seasonal factors, including changes in prices, weather conditions and stocking rates. To remove some of the effects of seasonal variation, the elasticity estimates have been averaged over time. Average elasticities have been calculated for the eleven year period, 1980-8 1 to 1990-9 1.

The regional variations in own-price and cross-price elasticities over the period 1980-81 to 1990-91 are shown in maps 2-10. These maps were generated using the method of 'local averaging' described in appendix B. Detailed estimates of own-price and cross-price elasticities, by industry and zone for the period 1980-8 1 to 1990-91, are provided in tables 3 and 4 in appendix D. These elasticities indicate the zone or industry aggregate response to a given price change.

Wool The eleven year national average own-price elasticity for wool was estimated to be 0.46. This compares with own-price elasticities for wool of 0.35 and 0.50 used in Beare, Fisher and Sutcliffe (1991). Regional own-price elasticities for wool are shown in map 2.

In Western Australia, wool elasticities are relatively high in the wheat- sheep zone, but fall away toward the south western corner of the state


Own-price elasticity for wool, 1980-81 to 1990-91 2 ,alaverages

E ABARE

below 0.307

0.307 to 0.384 0.384 to 0.408 0.408 to 0.422

0.422 to 0.452 0.452 to 0.491 0.491 to 0.502 0.502 to 0.521 0.521 to 0.549 above 0.549 no data

Own-price elasticity for beef, 1980-81 to 1990-91 3 ,ma, averages - E ABARE

below 0.010 0.010 to 0.032

0.032 to OM0 0.050 to 0.064 0.064 to 0.080 0.080 to 0.103 0.103 to0.133 0.133 to 0.156

11 0.156 to0.187 above 0.187

0 no data


where farms become smaller but where average land values are higher. A band of inelastic wool supply extends from South Australia through Victoria and into Tasmania. In New South Wales, own-price wool elasticities generally increase moving from the south west to the north east of the state, reflecting increased substitution possibilities. Elasticities for wool in Queensland are slightly above the national average for most of the state except in the north west where they are well above average.

Beef The eleven year national average own-price elasticity for beef was estimated to be 0.10. Map 3 for beef shows an inelastic beef supply response throughout the Northern Territory, the Kimberley region of Western Australia and in Queensland. Beef elasticities were above average in the wheat-sheep zones of Western Australia, South Australia, Victoria and New South Wales.

The more obvious differences in regional beef elasticities can be explained by regional variations in the cost structures of beef farms, which are themselves linked to variations in unit land values, unit land areas (or the intensity of operation), and the degree to which the operating area constrains changes in output.

In the high rainfall zone, beef farms are generally smaller and more intensively operated than those in the other zones, and are presumably operating at close to maximum capacity. The high unit land values in this zone relative to the other two zones would imply significant losses in potential income if beef farmers did not operate on all usable land. Under these conditions, the rate at which costs increase with output in this zone is relatively high, and the land area constraint substantially restricts the rate of change in output. Consequently, average elasticities of supply for beef in this zone are relatively low.

Beef farms in the wheat-sheep zone are generally larger than those in the high rainfall zone, and land values generally lower. There is also a greater opportunity for enterprise diversification in this zone. The less intensive nature of production in this zone implies that the rate at which costs increase with output will be lower than that in the high rainfall zone, and that the land constraint will be less restrictive to increased production. As a result, own-price elasticities for beef in the wheat-sheep zone are higher on average than those in the high rainfall zone.


Beef production in the pastoral zone is the least intensive of all the livestock zones and there are only limited (if any) alternative uses for land. Consequently, unit land values are very low throughout most of the zone. Own-price elasticities of supply for beef in the pastoral zone averaged 0.05 over the period, compared with 0.07 in the high rainfall zone and 0.15 in the wheat-sheep zone.

Wheat The eleven year national average own-price elasticity for wheat was estimated to be 0.23. However, as was the case with beef, there is considerable regional variation in elasticity estimates. The own-price elasticities for wheat in map 4 depict an inelastic supply response in south east South Australia, Victoria and southern New South Wales. Regional wheat elasticities increase from south to north through the wheat belts of New South Wales and Queensland.

Wheat elasticities in Western Australia are relatively high throughout the wheat-sheep zone, again reflecting lower costs of increasing output and

4 Own-price elasticity for wheat, 1980-81 to 1990-91 Local averages

below 0.138

0.138 to 0.163 0.163 to 0.177 0.177 to 0.197 0.197 to 0.225 0.225 to 0.253

a 0.253 to 0.277 a 0.277 to 0.280

0.280 to 0.284 above 0.284

0 no data


less restrictive operating area constraints in this region, as well as the importance of competing activities for wheat growing in those areas, such as lupins and barley production and wool growing.

Substitution possibilities The extent of substitution possibilities for different enterprises is reflected in the magnitude of the cross-price elasticities for each commodity. The cross-price elasticities for wool, beef and wheat are shown in maps 5-10, and are consistent with the regional elasticities shown in maps 2, 3 and 4. For example, where the own-price elasticities for beef, wheat and wool are relatively high, say in Western Australia, the cross-price elasticities are also relatively high, reflecting a strong potential in this state for substitution between the relevant commodities.


Elasticity of wool supply with respect to beef price, 1980-81 to 1990-91 Local averages

above -0.014 -0.014 to -0.015

-0.015 to -0.026

-0.026 to -0.029 -0.029 to -0.031 -0.031 to -0.033 -0.033 to -0.038

-0.038 to -0.046 -0.046 to -0.058 below -0.058 no data

1

Elasticity of wool supply with respect to wheat price, 1980-81 to 1990-91 Local averages 1

E ABARE

above -0.003 -0.003 to -0.017

-0.017 to -0.024 -0.024 to -0.035

0 -0.035 to -0.047 -0.047 to -0.059 -0.059 to -0.070

8% -0.070 to -0.085 rn -0.085 to -0.1 19

below -0.11 9

no data

above -0.003 -0.003 to -0.017

- - - - - - -


7 Elasticity of beef supply with respect to wool price, 1980-81 to 1990-91 Local averages

above -0.005 -0.005 to -0.016 -0.016 to -0.026 -0.026 to -0.036 -0.036 to -0.045 -0.045 to -0.053 -0.053 to -0.060 -0.060 to -0.069 -0.069 to -0.080 below -0.080 no data

Elasticity of beef supply with respect to wheat price, 1980-81 to 1990-91 Local averages


Elasticity of wheat supply with respect to wool price, 1 9 Local averages

above -0.039 -0.039 to -0.041

-0.041 to -0.048 -0.048 to -0.061 -0.061 to -0.079 -0.079 to -0.082 -0.082 to -0.087

-0.087 to -0.092

-0.092 to -0.096 below -0.096 no data

1


Three year estimates, 1988-89 to 1990-91

Average own-price elasticities for wool, beef and wheat are shown in maps 11, 12 and 13. On balance, the elasticities during this period were higher for each of the three commodities than those obtained over the eleven year period. This reflects lower unit returns during 1990-91, particularly for wool.

While the absolute level of the elasticities has varied between the periods, the regional distribution has remained relatively stable. This is because the key determinants of the distribution - namely the relative magnitudes of unit prices, costs and land values - are likely to have remained roughly constant between the periods.

Own-price elasticity for wool, 1988-89 to 1990-91 1 1 h a 1 averages

below 0.494

0.494 to 0.567

0.567 to 0.653 0.653 to 0.713 0.713 to 0.759

0.759 to 0.791

0.791 to 0.809 0.809 to 0.829 0.829 to 0.852 above 0.852 no data

I


Own-price elasticity for beef, 1988-89 to 1990-91 Local averages

below 0.032

0.032 to 0.103 0.103 to 0.126 0.126 to 0.161 0.161 to 0.196 0.196 to 0.227

0.227 to 0.251 0.251 to 0.304

81 0.304 to 0.340 above 0.340 no data

1 3 Own-price elasticity for wheat, 1988-89 to 1990-91 Local averages

below 0.188

0.188 to 0.193 0.193 to 0.207 0.207 to 0.221 0.221 to 0.239 0.239 to 0.275

0.275 to 0.283 0.283 to 0.285 0.285 to 0.288 above 0.288

no data


Using the model to assess the regional impacts of policy and price changes

The supply model developed in this study can provide a valuable input to the analysis of government policy and assessments of the regional impacts of price changes. In particular, it is envisaged that the main use of the model will be as a general and flexible tool for forecasting production, unit costs, net returns and farm cash income on a regional and national basis.

The model can be used to forecast commodity production and farm income on the basis of either predicted changes in commodity prices or assumptions about the impact of policy changes on commodity prices. ABARE currently produces commodity price forecasts a number of years ahead (see, for example, ABARE 1992b). By using these aggregate price projections, farm level prices for each of the commodities may be indexed forward. Farm level forecasts of production, prices and incomes can then be produced.

Of course, because of breeding limitations, there is a limit to how quickly a farm's supply will respond to price changes. Provided the estimated elasticities are not too large and price changes not too dramatic the breeding limitations will not apply. In addition, the lamb and wheat production elasticities may be viewed as referring to a relatively short time period, with full adjustments for these commodities being made within one year. For mutton and wool production, however, adjustments may take up to two years, and for beef up to three years.

The projection techniques described in appendix C assume that production changes occur within the breeding constraints.

Using the approach described in appendix C, production and farm cash income were forecast for 1989-90 using 1988-89 AAGIS data, and for 1990-91 using 1989-90 data. Weighted means of the projections were then computed, by industry. Comparisons of the means of forecast and actual production figures and farm cash income are summarised in tables 1 and 2. The aggregate commodity prices used to index individual farm prices are shown at the foot of each table.


1 1989-90 income and production projections using the supply model a Average per farm

1988-89 1989-90 Actual 1989-90 Predicted actual actual change predicted change

Wool production kg kg % kg %

All broadacre 8 787 10 137 Wheat and other crops 2 333 2 672 Mixed livestock-crops 10722 12569

BeefL Sheep-beef

Beef production no. no. % no. %

All broadacre 82 90 10 85 4 Wheat and other crops 21 17 -19 22 5 Mixed livestock-crops 22 29 32 24 9 Sheep 27 31 15 29 7 Beef 239 252 5 239 0 Sheep-beef 101 121 20 108 7

Mutton production no. no. % no. %

All broadacre 415 390 -6 354 -15 Wheat and other crops 189 175 -7 137 -28 Mixed livestock-crops 495 497 0 391 -2 1 Sheep 694 636 -8 642 -7 Beef 12 8 -33 9 -25 - -

Sheepbeef 496 447 -10 389 -22

Lamb production no. no. % no. %

All broadacre 182 204 12 195 7 Wheat and other crops 68 72 6 74 9 Mixed livestock-crops 18 1 212 17 196 8 Sheep 311 33 1 6 333 7 Beef 9 5 4 4 9 0 Sheep-beef 285 355 25 303 6

Wheat production t t % t %

All broadacre 163 169 4 166 2 Wheat and other crops 543 597 10 546 1 Mixed livestock-crops 398 397 0 408 3

;=?' 18 19 6 19 6 9 17 89 9 0

Sheepbeef 20 11 -45 2 1 5 I 1 Farm cash income $ $ % $ %

All broadacre 51 200 47 700 -7 39 800 -22 Wheat and other crops 74 400 78 300 5 63 300 -15 Mixed livestock-crops 67 400 64 500 -4 50 000 -26 Sheep 56 200 45 800 -19 38 000 -3 2 Beef 22 700 25 900 14 25 000 10 Sheep-beef 40 100 34 400 -14 31700 -2 1

a The commodity prices used to index farm prices were:

Wool Beef Mutton Lamb Wheat

c k c k cflcg cflcs $It

1988-89 1 026 210 57 134 214 1989-90 911 216 28 139 195


2 1990-91 income and production projections using the supply model a Average per farm

1989-90 1990-91 Actual 1990-91 Predicted actual actual change predicted change

Wool production kg kg % kg %

All broadacre 10453 10339 -1 9 760 -7

Beef production no.

113

no. no.

All broadacre Wheat and other crops Mixed livestock-crops

EZ?' Sheep-beef

Mutton production no. no. no.


EP?' Sheep-beef

Lamb production no. no.

188 60

239 239

7 37 1

no.

21 1 94

243 308

10 360

t

119 524 342

19 8

14

$

26 500 46 100 26 800 19 100 34 200 19 600


EZ?' Sheepbeef

Wheat production

All broadacre Wheat and other crops Mixed livestock-crops Sheep Beef Sheep-beef

Farm cash income

All broadacre Wheat and other crops Mixed livestock-crops Sheep Beef Sheepbeef

a The commodity prices used to index farm prices were:



Wool The prediction of an average 3 per cent increase in wool production on 'all broadacre' farms in 1989-90 compares with an actual increase of 15 per cent. While the fall in wool prices placed downward pressure on the estimate of production, the decline in the prices of all other commodities - in particular, mutton prices - contributed to the increase in wool production through cross-price effects. Wool production was predicted to fall by 7 per cent in 1990-91 compared with an actual fall in that year of 1 per cent.

The underestimate of the change in wool production in 1989-90 partly reflects the inability to incorporate dynamic effects. For example, while wool prices in 1989-90 were forecast to fall from 1026ckg to 91 lckg, the absolute level of wool prices in 1989-90 was still significantly higher than the long term average. Given the high wool prices at the time, it might have been unrealistic to expect wool producers to reduce production simply on the basis of the decline in the expected wool price for a single period. Indeed, it could be argued that growers would have had an incentive to continue with their expansion of the wool producing sheep flock at the time, albeit at a lower rate than in the previous year.

The distorting effects of the Reserve Price Scheme for wool, which was suspended during the 1990-91 financial year, would also have influenced outcomes in 1989-90. The high minimum reserve price is likely to have encouraged the production of wool in 1989-90. Since it would have taken some time for farmers to adjust their production mixture after the suspension of the scheme, wool production in 1990-91 was still slightly higher than the levels predicted by the model in that year.

Beef Beef production was predicted to increase by 4 per cent in 1989-90 at the national level, compared with an actual increase in that year of 10 per cent. Production on beef specialist farms was predicted to remain unchanged compared with the actual result of a 5 per cent increase, while for sheepbeef farms the model underestimated the increase in production. In general, the model predicted the direction of change in total beef production at the national level reasonably well. In 1990-91, however, the change in average beef production at the industry level was not accurately forecast - a slight increase was predicted rather than the actual small fall.

Forecasting supply at the farm level 2 7

Mutton and lamb Mutton production was predicted to fall in 1989-90 but at a greater rate than actually occurred. Lamb production was predicted to increase by 7 per cent, which compares favourably with an actual increase of 12 per cent. Predictions of mutton and lamb production in 1990-91 were in the right direction at both the national and industry levels, although the magnitudes of change were consistently underestimated.

Wheat The increase in wheat production at the national level in 1989-90 was forecast accurately. However, for 1990-9 1, wheat production at the national level was predicted to fall by 3 per cent but actually rose by 4 per cent.

One factor which helps to explain the divergence between actual and predicted output in the case of wheat is that, at the time planting decisions for the 1990-91 wheat crop were being made, the expected wheat price was still relatively high, and did not fall until after much of the wheat crop was already in the ground. Also, it is likely that ideal weather conditions resulting in near record production in certain regions in 1990-91 would have distorted the accuracy of these forecasts.

This example highlights the importance of using the most accurate and up-to-date information on prices and other market conditions available when using the model to make forecasts.

Farm cash income In general, the supply model appears to have forecast farm cash income well in both 1989-90 and 1990-91. The predictions of farm cash income in 1989-90 combine the predicted outputs of the individual commodities along with the expected commodity price changes. As shown in table 1, the 1989-90 income predictions at both the national and industry levels were generally in the right direction, but overstated the magnitude of the change. Predictions of farm incomes in 1990-91 are accurate at both the national and industry levels.


Appendix

Model development

The analysis of supply responsiveness reported in this study is based on a farm level econometric model of farm cash income. Farmers are assumed to maximise annual farm cash income (defined as total cash receipts less total cash costs) by producing combinations of wool, lamb, mutton, beef or wheat subject to a fixed land area constraint. For a general treatment of applications of profit maximising models and an exhaustive list of references, see Chambers (1988).

Because of the complexity of modelling the time series cross-sectional data from ABARE's Australian agricultural and grazing industries survey, dynamic specifications have not been attempted at this stage. As a result, livestock inventory changes over time are not modelled.

The farm cash income model A generalised farm cash income maximisation problem for an individual farmer producing m commodities subject to a given production technology and land area constraint may be written as follows:

m

(A) Maximise zi = 8, Q, - Xi j=l

such that for some function GG:

where zi is the farm cash income of farm i; Pij is the unit price received for commodity j by farm i; Qij is the quantity of commodity j sold by farm i; Wi is the vector of variable input prices faced by farm i; Xi is the vector of variable inputs used by farm i; and Vi is the total land available to farm i.

The constraints I and 2 define the production possibilities set available to the farmer. It is assumed that this set is strictly convex and that the solution to the problem is unique.


In order to obtain supply response equations, it is convenient to construct the dual cost minimisation problem to the profit maximisation problem. Define the unrestricted cost function for farm i, Ci(Wi, Qil, . . . , Qim) by the minimand for the following optimisation problem:

(B) Minimise Ci = W,Xi

such that: G..(X)=Q[~, v j = 1, . . . , m,

where

Replacing WiXi in optimisation problem A with Ci(Wi, Qi1, . . . , Qim) and eliminating the constraint that GG(X) = aj yields the following maximisation problem:

such that:

It can be shown that the unique levels of output obtained as maximisers in problem A and in problem C are identical.

To reflect rising unit costs, the form of the unrestricted cost function used is:

where ai, bij and pij > 1 are unknown constants. These parameters can be regarded as functions of input prices and factors affecting each farm individually, such as soil type or managerial ability. The operating area function was approximated by a single-term Taylor series and its form is therefore linear. Specifically:

where ci and dij are also unknown constants. The parameter dij may be interpreted as the land area associated with the production and sale of a single unit of commodity j in a given year.


To simplify the notation, in the rest of this subsection the subscript i will be removed from all mathematical symbols. All results, however, continue to hold at the farm level.

To maximise a farm's overall profitability the farmer must produce an optimal mixture of commodities. Because farmers are assumed to be constrained in the amount they can produce by the total amount of land available, the optimisation problem corresponds to finding the maximum of the function:

where A is a Lagrange multiplier and V = v is fixed.

The partial derivative of function 5 is:

Since pj > 1, the matrix of second order partial derivatives off is negative definite for Qj > 0, and so the profit is maximised when $1 6Qj = 0. From equation 6, this occurs when:

Substituting equation 7 into expression 3 it follows that, at the optimum, total cash costs equal:

I

where:

(9) pj = (Pj +Adj)lpj.

The value pj may be interpreted as the average variable cost of producing a single unit of commodity j. It may also be derived from the equation for profit in optimisation problem C:


where U j = (5 - P j ) represents the net return from producing one unit of commodity j. It will be assumed that all farms are operating at their optimum output levels, and so it will be possible to use equation 10 to estimate a farm's unit net returns and hence the unit costs. A technique for estimating these and other farm level parameters in the profit and operating area models are described in appendix B.

Derivation of supply elasticities The optimality condition (equation 7) relates output quantities to prices. Supply responsiveness is measured by the elasticities derived from equation 7. To derive these elasticities we proceed as follows.

Equation 7 implies that:

and hence the (own-price) elasticities are:

where:

(I3) ak = Pk fak. Likewise, the cross-price elasticities, for j # k, are:

Equations 12 and 14 involve the derivative of A. This unknown quantity will be eliminated from the elasticity formulas. Note that, for j # k:

Consequently, by substituting expressions 12 and 14 into 15 we find:


Differentiating equation 4 with respect to Pj, and noting that V = v remains fixed, then:

Substituting equation 16 into this expression implies, after some simple algebraic manipulations, that:

where:

Also, on substituting expression 18 into 16, it follows that, for j + k:

Likewise, by equating expressions 12 and 18:

Expressions 18, 20 and 21 are a set of simultaneous differential equations which define the farm level supply equations - that is, the function relating change in f a ~ m output to change in price. The elasticities are expressed as functions of the unit cost of and unit return to production, and the unit land area used to produce each of the m commodities.

Notice that farm cash income is the total return to land capital including fixed improvements, non-land capital and depreciation. If the final term in expression 5 is treated as a potential cost item, the Lagrange multiplier k may be interpreted as the additional annual cost per hectare a farmer would pay for additional land, non-land capital and depreciation on a per hectare basis; in other words, it is the shadow annual unit rental rate for land capital and non-land capital including depreciation.

Interpretation In equation 3, pk is a scale parameter which represents the rate at which costs increase with output. From equation 18 it can be seen that the greater the rate of increase in costs, the lower the supply elasticity.


From equations 9 and 18 it can be seen that higher prices (other things being constant) will lead to lower supply elasticities - that is, the response to price changes declines as price increases. In this sense the price response is asymmetrical. Also, from equations 13 and 18, the own- price elasticity for a commodity is likely to be lower if the amount of land devoted to the production of a unit of that commodity is small relative to other activities, or if the rental rate of land is high.

In different time periods the factors affecting regional supply elasticities are likely to be influenced heavily by weather conditions. For example, if unfavourable weather conditions in one year reduce the yield of a commodity, this would tend to increase the apparent supply responsiveness for that commodity. At the same time, however, unit costs for the commodity will typically be higher as total cash costs are spread over a reduced output. Unless unit prices increase sufficiently to offset the higher costs, net returns will be lower, and this will lead to higher measured supply responsiveness. It is the net effect of these factors which will determine the overall impact of a change in seasonal conditions in any one year.

Changes in input costs can also be expected to influence supply elasticities from year to year. For example, if interest rates were to rise and farmers maintained the same level of output then the shadow annual unit rental value of the land and non-land capital including depreciation, A, would increase. This, in turn, would lower the elasticity of supply in that year.

Finally, it is important to note from equation 19 that if a farm receives all of its income from producing one commodity, then the farm's supply elasticity for that commodity is equal to zero. This result occurs because any change in output price leads to an offsetting change in the shadow rental price of land and non-land capital including depreciation, A, and consequently the farmer has no incentive to alter production. By the same token, a farm which produces a large range of commodities is likely to have a higher own-price supply elasticity than a similar farm producing a smaller range of commodities.


Appendix

Parameter estimation

To obtain estimates of own-price and cross-price elasticities for each farm in a particular year, the model developed in appendix A is estimated using cross-sectional data from the Australian agricultural and grazing industries survey (AAGIS) for that year. In order to generate farm level estimates using a single year of cross-sectional data, the approach used here involves the application of M-quantile regression techniques (see Breckling and Chambers 1988). This method is similar to that used by ABARE (1990) to derive unit costs and returns from farm level data.

Estimating elasticities It would be preferable to estimate elasticities using farmers' expectations of prices rather than the prices they actually received for the various commodities. However, information on expected prices is not collected in AAGIS. Furthermore, there would be considerable difficulty in estimating their values at the farm level, because the time when production decisions are made varies considerably from farm to farm as do farmers' opinions of expected prices. Of course, this problem is not of concern in years when expected and realised prices are similar, or when farm level elasticities are averaged over several years. However, evidence presented in chapter 3 and appendix C suggests that the estimated elasticities are still accurate for predicting supply. Further investigations are currently under way to assess the effect of this measurement problem.

As mentioned in the previous section, it is necessary to assume that all farms are operating close to their optimal level of output. When this is assumed, it is possible to use equation 10 to estimate farm level unit net returns.

n n Let ii = n - ' x ai and qi = np1C qii be the average unit net return for

i = l i=l

commodity j. Then expression 10 implies that:


where is a residual error term for farm i. Expression 22 is a multiple regression model, and provided reasonable assumptions can be made about the behaviour of the residual term, ordinary least squares regression will provide reliable estimates of rl j . These estimates, however, may be quite inaccurate for estimating an individual farm's net return, qij, unless the farm's profit, x i , lies close to the regression plane. That is, given the farm's level of output, its profit is close to average. To circumvent this problem the approach given in ABARE (1990) was used.

The approach in that study was to estimate functions p + a(p) and p + qj(p) from the unit interval [0,1] onto the real line. The value pi of p was then found so that:

The value qj(pi) is a farm level estimate of the unit net return, qij, for commodity j. The functions a(p) and q j (p) were defined via the quantiles of the conditional distribution of the profit, z, given Ql, . . . , Q,. That is:

The underlying motivation behind the estimates qj(pi) is as follows. The function x(p) represents the conditional pth quantile of x given the level of output Ql, . . . , Q,,,. In this study it is assumed that this function is linear in Ql, . . . , Q,. A particular farm's profit may be close to n(p) for either or both of two reasons:

- random variation or

- certain fixed characteristics - for example, soil and climatic conditions or management practices - that determine the farm's profitability relative to other farms of a similar size.

If it is assumed that the second cause is the dominant one, it would be expected that if the same farm had produced slightly different amounts of output, it would still be close to the same quantile plane, x(p). Hence, true unit net returns for the farm should be well approximated by VI(P), - - - 2 Vm(p).

In practice, the functions ql (p) , . . . , q,(p) are not known exactly, but must be estimated from survey data. M-quantile regression (Breckling


and Chambers 1988) provides a technique for estimating these functions. A detailed description of how M-quantile regression may be used to estimate qj(p) is given in ABARE (1990), and so only a brief outline of the technique is presented here.

In M-quantile regression the parameters in equation 24 are estimated from the data as follows. Let:

and

2py(r) , if r > 0, (26) P) =

2(1- p)y(r), otherwise,

where 0 I p I 1. The probability in equation 24 results when finding the minimum of the expectation:

where (I?f l &)p(r, p) = ~ ( r , p) . (The estimate of n(p) that is obtained when minimising the sample version of expression 27 is called the pth conditional sample quantile. The function p(r ,p) is often referred to as the loss function for estimating quantiles of a distribution and y(r ,p) as the corresponding influence function which is obtained by differentiating expression 27 to find its minimum. Therefore, estimates of the unit net returns corresponding to the pth conditional sample quantile are found by solving the equations:

where:

(29)

Although expression 25 is the preferred influence function to use, numerical problems arise in trying to solve equation 28 due to the discontinuity in

at r = 0. This problem is related to the fact that sample quantiles are


sometimes not unique. The approach used here is to replace expression 25 with a smooth approximation. The Huber influence function given in ABARE (1990, p. 13) was used.

The final step in estimating the unit net returns is to smooth the values obtained from equation 28. This smoothing step is required since qj(p) can only be estimated for a few values of p, and to solve expression 23 an estimate of the whole function is required. The method used was to calculate fij(p) for p = 0.05, 0.10, . . . , 0.95. Smoothed values Gj(p) were then produced by fitting cubic polynomials in p to each fij(p). Finally, farm-specific estimates of unit net returns were produced by using the smoothed functions Gj(p) in expression 23. From now on let fiij represent the estimate of unit net return for commodity j and farm i obtained in this way.

An estimate of the unit cost of commodity j on farm i is then simply:

where Pij is the total cash receipts for commodity j received during the financial year on the farm divided by the quantity sold.

The method used to estimate the unit land areas, dg in equation 4, was analogous to the way Gij were obtained, with some slight difference. To introduce extra stability in the estimation process, where possible, several years data were combined and a quantile model of the form:

was fitted. Here, the subscript t represents the financial year, and the intercept term, c,(p), depends on t, whereas the quantile regression coefficients do not. The purpose of a varying intercept term was to absorb any temporal variation in the data. The terms lilt, Ii2t, . . . , Iirt are inventories of stock held on the land. It was necessary to include inventories in the model since land is not only being used to produce the various commodities, but to support stock. In practice, due to their high correlations with output quantities, it is often necessary to adjust the inventory variables in expression 31. The adjustment method used for AAGIS data is described in more detail in the next section. From now on, to simplify this exposition, the subscript t will be dropped.


The final step in producing elasticity estimates was to specify the value of the Lagrange multiplier, Ai. Recall the interpretation of Li given in appendix A. A raw figure was first calculated using interest rate times the price of land, non-land capital and depreciation on a per hectare basis. For the purposes of this paper a long term average interest rate of 10 per cent was used.

Estimates of Ai were then produced by geographically smoothing these raw figures. The technique for smoothing is referred to as 'local averaging', and is described in ABARE (1992a, p. 25). Essentially, farms close to the given farm where the local average is being estimated contribute most to the average while farms further away contribute less. It was necessary to perform this smoothing because if a particular farm expands the size of its operations then it is likely to purchase or rent land from a neighbouring property and possibly rent or purchase additional non-land capital. The value of this land and the additional non-land capital is more likely to be closer to the average in that region rather than to the actual value of these quantities for the given farm.

Having obtained the smoothed unit land values, equation 9 was used to estimate pij and elasticity estimates were obtained.

The approach described above gave unrealistic elasticity estimates for only a small proportion of farms. These farms are identified by the fact that their unit cost, &, for commodity j may exceed the price received. In this case, according to expression 9, pij may be less than 1, which violates one of the basic assumptions of the model. In such cases, elasticities could approach infinity or become negative. There are two possible reasons why this might occur:

- the farm's production of this commodity may be relatively small compared with its overall production (for example, when the commodity is produced in small quantities as a means of diversifying income in some years) or

- the farm may be producing a significant amount of the commodity, but most likely because of unsuitable weather conditions or because the commodity is used on the farm (for example, in the case of feed) its profitability may appear to be low.

Of the farms with potentially unrealistic elasticity estimates for commodity j - that is, pij less than 1 . 1 - the majority were classified to the


first category. When pg was less than 1.1, no elasticity for that commodity was calculated.

The farm level estimates of unit cost, unit land value and ilij were substituted into formulas 18 and 20 to obtain elasticity estimates. The elasticity estimates for farm i will be denoted by iUk.

Application to AAGIS data The techniques described in the previous section for estimating supply elasticities were applied to AAGIS data spanning the period 1980-81 to 1990-91. Data for the years 1980-81 to 1989-90 are 'final' survey data, and 1990-91 are 'preliminary'. For an explanation of the differences between these data qualities refer to ABARE (1992a, p. 5).

In calculating the elasticities, wool production is measured in kilograms sold, wheat production in tonnes sold, and beef, lamb and mutton production in numbers of animals sold. Farm receipts from activities other than the five major broadacre commodities were referred to as 'other'. This made a total of m = 6 commodities that were used in fitting the supply model.

The M-quantile regressions for farm cash income were perfo~~lled separately for each year, whereas for total area operated, data from the two closest years and the reference year were combined and a model of the form given in expression 3 1 was fitted. In fitting these regressions the data for each farm were weighted according to the value of that farm's survey weight. That is, in place of equation 28, the equations:

(32) w i ~ ( 5 , P) = 0, and wiv(q, p)eik = 0, k = 1, . . , rn i ~ s i ~ s

were used to estimate regression parameters, where wi is the survey weight for farm i in the sample of farms. It was necessary to weight the data in order to adjust for the unbalanced nature of the sample against known population characteristics.

M-quantile regression is a robust procedure for estimating regression parameters. That is, it provides estimates which are not unduly influenced by unusual or extreme observations. However, it becomes increasingly unstable as p approaches either 0 or 1. To overcome this problem observations less than the 2nd percentile and beyond the 95th percentile


of the farm cash income distribution were removed when estimating the farm cash income M-quantiles, but the resulting estimates of v j ( p ) were used in constructing unit net return estimates for all farms. An analogous approach was used in the operating area M-quantile regressions.

As mentioned previously, the M-quantile regressions were performed for p = 0.05, 0.10, . . . , 0.95. A second stage of smoothing was then undertaken in which the M-quantile regression estimates i j j ( p ) were fitted with cubic polynomials in p using ordinary least squares regression. In most cases these polynomials fitted very well, with an R~ above 95 per cent. In the few cases where they did not fit well it was found that instability at the extreme values of p was the cause. In this case it was necessary to remove either the estimates corresponding to p = 0.05 or p = 0.95 from the smoothing process.

When performing the land area M-quantile regressions at expression 31 beef and sheep inventories, the current and two closest years data were used. Using these data, estimates of the current year's unit land values, do, were produced. Due to colinearity problems, it was necessary to remove the effect of the quantity of mutton and lamb sold from the sheep inventory and the quantity of beef sold from the beef inventory before including these variables in the model at expression 31. This adjustment was performed by regressing the inventories against the corresponding quantities sold and using the residuals instead. In expression 31 the residual for sheep inventory is denoted by Iil and for beef inventory by Ii2. In fitting expression 31 the correlation between the same farm in different years was ignored. This should result in only a slight loss in the

I

I efficiency of estimation. Again the quantile regression coefficients were smoothed and, using a similar approach to that described in expression 23, estimates zq of the unit land areas were produced.

Forecasting supply at the farnz level 41

Appendix

Using the supply model as a forecasting

Throughout the following the subscript t will be used to indicate the current year, and t+l to denote the forecast year. To simplify the notation, the subscript i will not be used in this appendix. All expressions, however, continue to hold at the farm level.

Formulas 18, 20 and 21 in appendix A are in fact a set of simultaneous differential equations. They define the supply function - that is, how output is related to price. For small changes in price the supply function is almost linear in P I , . . . , P,. Therefore, the following approach for forecasting production was used. For j = 1, . . . , m, let:

Then production is forecast as:

where

Expressions 9 and 21 are used to forecast unit costs. Again, using a first order linear approximation, from expression 21:

m

(36) &+, = a, - ~ , L ? ; ~ A P $ . j=l

The dj values in expression 4 are the same at t+l as at t because it is assumed that the farm's operating area remains fixed. It is also assumed that the form of the cost function is the same at t+l. Thus, on substituting the appropriate terms into expression 9 it follows that the unit costs are:


while the unit net returns are forecast as:

With these basic quantities determined it is possible to forecast several other key variables. These include:

expected cash receipts for commodity j:

total cash receipts:

total cash costs:

and farm cash income as the difference between expressions 40 and 41.

When projecting more than one year ahead the process becomes more involved. This is because the elasticities will now change with time. When projecting to year t+2, the technique that is used to project from year t to year t+l is applied as before. As a result, new values of quantity of output, new unit costs and il are obtained in the projection process to t+l. These

I projected values are substituted into elasticity formulas 18 and 20 to obtain projected elasticities in t+l, and these elasticities are subsequently used when making output projections to year t+2.

It is possible for an elasticity at t+l to differ significantly from the corresponding value at t. For example, the own-price elasticity for commodity j at time t may be large because the price is close to the unit cost for this commodity. However, this ratio may increase dramatically if the price is projected to increase at t+l, resulting in a significant decline in the elasticity.


Validating the supply model as a forecasting tool using historical AAGIS data The validity of the model can be assessed using historical AAGIS information. Differences between the results obtained from the model and actual outcomes emerge because supply in broadacre agriculture in any one year depends not only on output prices but on other factors as well, such as weather conditions, degree of aversion to risk, and any other factors that individual farmers deem to be important.

Since a large proportion of farms remain in the AAGIS sample from one year to the next (usually around 80 per cent) it is possible to use the common subsample over two earlier survey years to check the accuracy of the forecasting method. For example, predicted values for the year 1989-90 can be calculated using 1988-89 data and the techniques described above, and checked against the actual values achieved on farms in that year.

The price differential, APijt, for farm i and commodity j was determined by apply the relative average price change between years t and t+l to the actual farm level prices in year t. For the years chosen in this analysis, the relative average price changes calculated in this manner were close to the forecast price changes prevailing at the time, and on which farmers would have based their production decisions.


Appendix

Own-price and cross-price elasticities, 1980-81 to 1990-91

3 Own-price elasticities, 1980-81 to 1990-91


All broadacre 0.46 0.10 0.24 2.08 0.23

Wheat and other crops 0.34 0.29 0.29 1.99 0.17 Mixed livestock-crops 0.45 0.22 0.26 2.20 0.29 Sheep 0.45 0.30 0.18 1.97 0.34 Beef 0.57 0.01 0.3 1 2.03 0.42 Sheep-beef 0.61 0.20 0.34 2.16 0.34

Pastoral zone 0.57 0.05 0.53 1.37 0.31 Wheat-sheep zone 0.45 0.15 0.23 2.02 0.23 High rainfall zone 0.45 0.07 0.17 2.17 0.26

Pastoral zone

Wheat and other crops 0.58 0.54 0.63 2.85 0.14 Mixed livestock-crops 0.60 0.20 0.36 0.84 0.37 Sheep 0.44 0.5 1 0.38 1.45 0.85 Beef 0.50 0.00 0.01 0.29 1.26 Sheep-beef 0.91 0.35 0.97 1.35 1.07

Wheat-sheep zone

Wheat and other crops 0.33 0.30 0.29 2.00 0.17 Mixed livestock-crops 0.46 0.24 0.26 2.18 0.29 Sheep 0.45 0.31 0.13 1.74 0.39 Beef 0.48 0.03 0.43 1.90 0.44 Sheep-beef 0.52 0.23 0.21 1.64 0.36

1 High rainfall zone

Wheat and other crops 0.49 0.14 0.16 1.56 0.17 Mixed livestock-crops 0.34 0.08 0.21 2.61 0.32 Sheep 0.45 0.25 0.15 2.08 0.13 Beef 0.75 0.01 0.25 2.16 0.32 Sheep-beef 0.50 0.16 0.21 2.29 0.19


4 Cross-price elasticities, 1980-81 to 1990-91

Production variable Wool Lamb Wool Wheat

Price variable Lamb Wool Wheat Wool

All broadacre -0.02

Wheat and other crops -0.01 Mixed livestock-crops -0.02 Sheep -0.02 Beef -0.01 Sheep-beef -0.02

Pastoral zone Wheat-sheep zone High rainfall zone

Pastoral zone

Wheat and other crops 0.00 Mixed livestock-crops 0.00 Sheep 0.00 Beef 0.00 Sheep-beef 0.00

Wheat-sheep zone

Wheat and other crops -0.01 Mixed livestock-crops -0.02 Sheep -0.02 Beef -0.02 Sheepbeef 4 . 0 1

High rainfall zone

Wheat and other crops -0.01 Mixed livestock-crops -0.02 Sheep -0.03 Beef -0.01 Sheep-beef -0.03

(Continued on next page)


Production variable Beef Mutton

Price variable Mutton Beef

All broadacre -0.02 -0.07

Wheat and other crops -0.01 -0.02 Mixed livestock-crops -0.03 -0.03 Sheep -0.07 -0.05 Beef 0.00 -0.41 Sheep-beef -0.04 -0.22


Pastoral zone

Wheat and other crops -0.09 -0.67 Mixed livestock-crops -0.04 -0.07 Sheep -0.20 -0.07 Beef 0.00 -0.23 Sheep-beef -0.13 -0.32

Wheat-sheep zone

Wheat and other crops -0.01 -0.02 Mixed livestock-crops -0.03 -0.03 Sheep -0.04 -0.06 Beef 0.00 -0.34

I

I Sheepbeef -0.03 -0.19

I High rainfall zone

Wheat and other crops 0.00 -0.03 Mixed livestock-crops -0.01 -0.01 Sheep -0.06 -0.04 Beef 0.00 -0.52 Sheep-beef -0.03 -0.20


Beef

Lamb

Lamb

Beef


Production variable Beef Wheat Mutton Lamb

Price variable Wheat Beef Lamb Mutton

All broadacre -0.02 -0.03 -0.02 4 . 0 1

Wheat and other crops -0.21 -0.02 -0.01 0.00 Mixed livestock-crops -0.09 -0.04 -0.02 -0.01 Sheep -0.01 -0.07 -0.03 -0.01 Beef 0.00 -0.35 -0.02 0.00 Sheep-beef 0.00 -0.23 -0.03 -0.01


pastoral zone

Wheat and other crops -0.32 0.00 0.00 0.00 Mixed livestock-crops -0.08 -0.02 -0.01 4 .01 Sheep 0.00 0.00 0.00 -0.01 Beef 0.00 -0.44 0.00 0.00 Sheep-beef 0.00 -0.11 0.00 0.00

Wheat-sheep zone

Wheat and other crops -0.22 -0.02 -0.01 0.00 Mixed livestock-crops -0.10 -0.04 -0.01 -0.01 Sheep -0.02 -0.09 -0.02 -0.01 Beef -0.01 -0.27 -0.03 -0.01 Sheep-beef -0.01 -0.24 -0.02 -0.01

High rainfall zone

Wheat and other crops -0.05 -0.05 -0.02 0.00 Mixed livestock-crops -0.03 -0.05 -0.02 -0.0 1 Sheep 0.00 -0.02 -0.04 -0.01

I

I Beef 0.00 -0.77 -0.01 0.00 Sheep-beef 0.00 -0.14 -0.04

(Continued on next page) ! 48 ABARE research report 93.7 I

Production variable Mutton

Price variable Wheat

All broadacre -0.10

Wheat and other crops -0.34 Mixed livestock-crops -0.20 Sheep -0.01 Beef -0.01 Sheep-beef 0.00


Pastoral zone

Wheat and other crops -0.40 Mixed l ives tock~ops -0.29 Sheep 0.00 Beef 0.00 Sheep-beef 0.00

Wheat-sheep zone

Wheat and other crops -0.34 Mixed livestock-crops -0.22 Sheep -0.02 Beef -0.03 Sheepbeef -0.01

High rainfall zone

Wheat and other crops -0.14 Mixed livestock-crops -0.06 Sheep 0.00 Beef 0.00 Sheep-beef 0.00

Wheat

Mutton

Lamb Wheat

Wheat Lamb

-0.01 0.00 -0.01 -0.01

0.00 -0.05 0.00 0.00 0.00 -0.04



Production variable Wool Beef Wool Mutton

Price variable Beef Wool Mutton Wool

Australia

All broadacre -0.04

Wheat and other crops -0.01 Mixed -0.02 Sheep -0.03 Beef -0.28 Sheep-beef -0.14


Pastoral zone


Wheat-sheep zone


High rainfall zone



References

ABARE 1990, Costs and Returns to Australian Broadacre Enterprises, ABARE Technical Paper 90.1, AGPS, Canberra.

- 1992a, Farm Suweys Report, 1992, Canberra.

- 1992b, Agriculture and Resources Quarterly, vol. 4, no. 4, December.

Beare, S.C., Fisher, B.S. and Sutcliffe, A.G. 1991, Managing the Disposal of Australia's Wool Stockpile, ABARE Technical Paper 91.2, AGPS, Canberra.

Breckling, J. and Chambers, R. 1988, 'M-quantiles', Biometrika, vol. 75, pp. 761-7.

Chambers, R.G. 1988, Applied Production Analysis: A Dual Approach, Cambridge University Press, England.


Recent related ABARE publications

Technical papers ABARE 1990, Costs and Returns to Australian Broadacre

Enterprises, ABARE Technical Paper 90.1, AGPS, Canberra. $12

Beare, S.C., Fisher, B.S., and Sutcliffe, A.G. 1991, Managing the Disposal of Australia's Wool Stockpile, ABARE Technical Paper 9 1.2, AGPS, Canberra.

Research reports Clark, J., Lembit, M. and Warr, S. 1992, A Regional Model

of Australian Beef Supply, ABARE Research Report 92.8, Canberra.

Connolly, G.P. 1992, World Wool Trade Model, ABARE Research Report 92.12, Canberra.

(This report, ABARE Research Report 93.7, is priced at $20)

Regular reports ABARE, Farm Surveys Report.

ABARE, Agriculture and Resources Quarterly, 1993. - 4 issues $60 - single issue $20

To order publications, contact Denise Flamia on (06) 272 221 1 or write to: Publications Officer. ABARE, GPO Box 1563, Canberra 2601.


BROADACRE

The econometric model of

farm level supply response

presented in this report

provides researchers and

policy makers with a tool for

examining in detail the

regional effects of price and

policy changes on the

production, costs and incomes

of Australian broadacre

farmers.

ABARE RESEARCH REPORT 93.7 - e ABARE

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