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w...... states Department of Agriculture A Structural Economic Research Service Econometric Model of Technical Bulletin Number 1733 the Canadian Wheat Sector Ä Kenneth W. Bailey CONVERSION CHART
1 metric ton (mt) of wheat = 36.743711 bushels (bu) 1 metric ton of barley = 45.929637 bushels 1 metric ton = 2,204.622 pounds 1 hectare (ha) = 2.47 acres
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The Economic Research Service has no copies for free distribution. A Structural Econometric Model of the Canadian Wheat Sector. By Kenneth W. Bailey. Economic Research Service, U.S. Department of Agriculture. Technical Bulletin No. 1733.
ABSTRACT
This improved model of the Canadian wheat sector incorporates the effect of beginning wheat stocks on producer price expectations, predicts Canadian Wheat Board (CWB) behavior in setting various prices, and estimates the mathematical relationships (elasticities) between U.S. grain prices and Canadian wheat exports. The model reveals that a sustained 20-percent decrease in the U.S. wheat loan rate beginning in 1986 would result in a 20-percent decrease in Canadian wheat exports that same year, a A2-percent decrease by 1990, and a 96-percent decrease in the longrun from the baseline, assuming all else remains constant. A similar decrease in the U.S. com loan rate—holding U.S. wheat loan rates and all else constant at 1985 levels—will result in a 5-percent increase in Canadian wheat exports in 1986, a 20-percent increase by 1990, and an 86-percent increase in the longrun from the baseline.
Keywords: Wheat, Canada, econometric, Canadian Wheat Board, dynamic elasticity.
ACKNOWLEDGMENTS
I would like to thank Richard Downey and Eileen Krakar of Agriculture Canada and J. Michael Price, Bob Green, Suchada Langley, Mary Anne Normile, and Pat Weisgerber of the Economic Research Service for their comments and reviews; Florence Singer of the Economic Research Service for her statistical assistance; Sharon Lee of the Economics Management Staff for editorial assistance; and Susan DeGeorge of the Economics Management Staff for graphics assistance.
Washington, DC 20005-4788 September 1987 CONTENTS PaRe
SUMMARY iii
INTRODUCTION 1
CANADIAN WHEAT SECTOR 1 Production Patterns 2 Wheat Exports 2 Canadian Wheat Board 2 Canadian Grain Coitmiission 7
CANADIAN POLICIES SUPPORTING WHEAT 8 Transportation Policies 8 Stabilization Policies 9
CONCEPTUAL MODEL OF THE CANADIAN WHEAT SECTOR 10 Canadian Wheat Supply Block 10 Canadian Wheat Demand Block 13 Canadian Wheat Price Block 14 Other Variables and Data 17
EMPIRICAL ESTIMATES 18 Canadian Supply and Utilization 18 Price Linkage Equations 24 Model Validation 34 Elasticity of Canadian Wheat Excess Supply 44
REFERENCES 50
APPENDIX 1-~DATA IN THE ANALYSIS 53
APPENDIX 2—THEORETICAL SUPPLY MODEL 60
APPENDIX 3~-VARIABLE DESCRIPTION LIST 64
11 SUMMARY
This report develops an econometric model of the Canadian wheat sector. The model, representing an improvement to existing models, incorporates the effect of beginning wheat stocks on producer price expectations, predicts the Canadian Wheat Board (CWB) behavior in setting various prices, and estimates the mathematical relationship (elasticities) between U.S. grain prices and Canadian wheat exports. The model reveals that a sustained 20-percent decrease in the U.S. wheat loan rate beginning in 1986 will result in a 20-percent decrease in Canadian wheat exports that same year, a 42-percent decrease by 1990, and a 96-percent decrease in the longrun from the baseline, assuming all else remains constant. A similar decrease in the U.S. com loan rate—holding U.S. wheat loan rates and all else constant at 1985 levels—will result in a 5-percent increase in Canadian wheat exports in 1986, a 20-percent increase by 1990, and an 86-percent increase in the long- run from the baseline.
The model explains the structure of the Canadian wheat sector and how wheat prices in the United States affect it. The model represents an improvement because it explicitly accounts for the structural and institutional characteristics of the Canadian wheat sector. For example, the model reflects how mounting Canadian wheat stocks lower producer expectations of future CWB returns, thereby reducing wheat plantings.
Trade analysts will find this model useful in developing or improving the Canadian wheat component of world trade models. The model results indicate that the elasticities of Canadian wheat exports with respect to the U.S. wheat and corn loan rates are 0.98 and -0.23 in the shortrun, 2.09 and -1.03 in the intermediate run, and 4.81 and -4.29 in the longrun, respectively. For example, the results indicate that a 10-percent increase in the U.S. wheat price will result in a 9.8-percent increase in Canadian wheat exports in the shortrun. A similar change in the U.S. com price will result in increases in Canadian barley prices causing a 2.3-percent decrease in Canadian wheat exports. Policymakers will find the model useful in analyzing the effects of changes in Canadian and U.S. policy on the Canadian wheat sector.
Ill
A Structural Econometric Model of the Canadian Wheat Sector
Kenneth W. Bailey *
INTRODUCTION
Changes in international competition for wheat trade require a more effective model for assessing world supply and demand for wheat. Most world trade models are empirically weak and inadequate in reflecting changes in foreign policies on the excess demand facing the United States.
This report develops a modeling subsystem of the Canadian wheat sector for use in a nonspatial equilibrium world wheat trade model. The report reviews the structure of the Canadian wheat sector, develops a conceptual model of the sector, and estimates an econometric model. Thompson notes that a major flaw with most world trade models has been their lack of sufficient empirical content (30).!/ This report emphasizes a careful review of the structure of the Canadian wheat sector, a review of existing Canadian wheat sector models, and an improvement in empirical content. The model reflects the behavior of the Canadian Wheat Board (CWB) in setting various production, consumption, and export prices and links these prices to U.S. prices.
The model expands the U.S. Department of Agriculture's Food and Agricultural Policy Simulator (FAPSIM) model to include Canada.2/ The export demand components of the FAPSIM model are improved by the development of structural country and/or region models that more accurately assess the world excess demand facing the United States. Hence, this report is useful to trade analysts interested in developing or improving the Canadian wheat component of world trade models. The model will also be useful to policymakers in analyzing the effect of changes in Canadian and U.S. policy on the Canadian wheat sector.
CANADIAN WHEAT SECTOR
The Canadian wheat belt occupies the lower portion of the Canadian Western Provinces and borders the U.S. north-central wheat belt (Montana, South
^Agricultural economist, U.S. Department of Agriculture, Economic Research Service, Agriculture and Trade Analysis Division. 1/ Underscored numbers in parentheses refer to sources listed in the References. 2/ For more information on the FAPSIM model, see (10) and (24). Dakota, North Dakota, and Minnesota), indicating a similarity of soil and environmental conditions between the two countries (fig. 1). This similarity ends, however, when the crop is harvested due to vast differences in farm policies between the two countries.3/
Production Patterns
In Canada, wheat is the number one field crop in terms of area planted, followed by barley, rapeseed, and oats (fig. 2). Most of Canada's wheat is grown in the three Western Prairie Provinces of Alberta, Saskatchewan, and Manitoba, with small amounts grown in the Peace River Valley on the Alberta-British Columbia border and in Eastern Canada (fig. 1). Wheat yields are extremely volatile from year to year, reflecting the constraints of a short growing season, poorly timed rainfall, drought, and an occasional early freeze. Wheat yields have increased over the last 20 years due to technological improvements in inputs but only at an estimated rate of 0.6 bushels per year. Wheat Exports
Wheat is the leading Canadian grain export, followed by barley, rapeseed, and oats (fig. 3). Most of Canada's wheat is of a hard variety with high protein content and is grown and marketed for export purposes. Between 1971 and 1985, approximately 80 percent of all hectares sown to wheat produced a crop destined for the export market. In 1984/85, Canada exported 17.5 million metric tons (mmt) of wheat, including durum wheat and flour, which was down 19 percent from the 21.8 mmt in 1983/84 (table 1). Canada's top five importers are the Soviet Union, China, Japan, Brazil, and Cuba, which accounted for 69 percent of all Canadian wheat exports in 1984/85. The Soviet Union and Japan historically import No. 1 Canada Western Red Spring (CWRS) grade wheat of 12.5-percent protein and above, with smaller amounts of No. 2 CWRS. China and Brazil import mostly No. 3 CWRS, with smaller amounts of Nos. 1 and 2 CWRS. Cuba imports mostly No. 1 CWRS, with smaller amounts of Canada feed grade wheat. The most significant Canadian wheat importers in terms of volume are the Soviet Union and China, which have averaged almost 39 percent of all Canadian wheat exports over the last 10 years (3, 1986, p. 101).
Canadian Wheat Board
The Canadian Federal Government appointed the Canadian Wheat Board (CWB) in 1919 after closing the futures market because of postwar marketing difficulties. The CWB, terminated in 1920, was reactivated in 1935 under the Canadian Wheat Board Act and has been in operation ever since. The CWB's objective as stated in law is to sell the most grain at the most favorable price on behalf of Canadian producers, while providing equitable opportunity for all producers to deliver grain. The CWB achieves this objective by (1) acting as the sole legal agent for the purchasing and marketing of western grown wheat, barley, and oats, (2) pooling all receipts from the sale of grains, (3) returning the net profits to producers in the form of a realized price that is the same for all producers for each grade of grain delivered, and (4) regulating the movement and transportation of grain in Western Canada via marketing quotas.
3/ For a more detailed discussion of the Canadian wheat sector, see (26) and (32). (/> c o "5) 0) ce O)c ü 3 ■O O
(ü 0 o "<5* c c (O ü c (O (/) Figur* 2 Land Use Patterns, Canada
Million hectares 14 Wheat 12
10
6
Barley / "" .••-"••..... / '""**' 4 Oats IIIIIHUnUHNIMIMu -^ fc...... ^^^'*'^' • ;;;;;'"' »« "'""""".^:\, 2 Rapeseed/canola vX' '^'^'"■'^'^^'V^x^' '''''''''''''''«/..H.MHN.,,.H¡K»^pi*»<«..m, ,
I I I r^ I ■ I j I I \ I \ \ I I \ \ L- 1964 68 72 76 80 84 Crop year
Source: {S).
Figure 3 Exports of Major Grains, Canada
Million metric tons 24
20 -
16 -
12
Barley
^A»* Oats Rapeseed/canola ^■^■■^. 0 i iHlllIlBBBffiíiiiilllÉlllllllllliliiiiii áiiiiiiiiiiil iMii!!l!H'!Mll^''''''''t''''''HH'itiiiii il ml iiiiiiiiiiiiiiiliiii Aiiiiiiiiiiii mil 1964 68 72 76 80 84 Crop year
Source: (J). Table 1—Canadian wheat exports to major markets 1/
Country : 1982/83 2/ : 1983/84 : 1984/85
: 1.000 metric tons
U.S.S.R. 6,959 6,761 6,019 China 4,424 3,514 2,845 Japan 1,341 1,325 1,324 Brazil 1,503 1,363 1,152 Cuba 1,101 1,053 779 United Kingdom 1,109 955 633
Syria : 242 265 580 Algeria : 517 813 508 Egypt, Arab : Republic of : 49 686 468 Iraq : 280 608 367 Italy : 624 702 221 Others 3/ : 3,219 3,680 2,647
Total : 21.368 21.765 17.543 1/ All wheat including wheat flour in whole wheat equivalents. 2/ Includes bagged seed exports. 3/ Preliminary, subject to revision.
Source: (5, 1986, p. 13).
The Canadian Wheat Board Act provides for a board of three to five commissioners appointed by a Federal Minister responsible for the CWB and who is in turn appointed by the Prime Minister. An advisory coiranittee of 11 producers elected from districts in the Western Prairie Provinces advises and assists the CWB.
Board Payments
Producers in the Western Prairie Provinces receive a pooled price from the proceeds of the CWB*s sales (less CWB expenses) generally in the form of two payments. The first payment is called an initial payment and is paid to producers upon delivery of their grain to country elevators after deductions are made for handling costs and transportation charges. Freight deductions are made based on the likely destination of grain to the west coast (Vancouver or Prince Rupert) or east coast (Thunder Bay or St. Lawrence Seaway). Canada's Federal Government establishes initial prices each crop year for the basic grades of wheat, barley, and oats after taking into consideration recommendations given by the CWB. Initial prices are usually announced prior to planting, between March and April. The initial price is set equal to 75 percent of what the Government expects market returns will be. This price is set conservatively since the initial price is guaranteed by the Federal Government and, hence, acts as a floor price. If sales in a particular year are better than anticipated, or if prices strengthen significantly during the crop year, the CWB may make additional payments called adjustment or interim payments. These adjustments are made after the initial prices have been announced and are typically made between October and March of the respective crop year. The final payment is determined after all the grain from the pool has been marketed. Producers receive a final payment if there is money left in the pool after all receipts are pooled and any prior payments and the CWB's expenses have been deducted. The final payment is usually announced 3-6 months after the close of the marketing year, although it has been announced more recently in January. Producers have received a final payment in most years since the early sixties but did not in the 1968/69 crop year and probably will not in 1986/87.
Wheat Marketing
Western Canadian producers market their wheat, barley, and oats either through the CWB, or through offboard markets. All wheat destined either for human consumption or export use must be marketed by law through the CWB. Wheat not sold for these purposes can be sold for livestock feed use. Although producers can market their premium grade wheats through either markets, producers typically choose the CWB because of the price premiums they offer for the higher quality wheats. The offboard markets deal primarily with feed quality grains, with sales both at the local and national levels. Sales at the local level are comprised of farm-to-farm, farm-to-feedlot, and farm-to-feed mill sales. These offboard sales were permitted to take place as long as they were within the Province where the grain was produced. In 1973, the Canadian Federal Government further permitted offboard sales between Provinces but not between the east and west Provinces. This constraint, however, was eliminated the following year when sales were permitted between all Provinces (26, p. 5). Since then, sales made at the national level involved sales made to private grain companies which marketed feed grains to the Eastern Provinces. Prices and sales in the offboard market are determined independently of the CWB, although access of offboard grain to rail and elevator facilities is controlled by the CWB. The CWB also controls all wheat imports into Canada, which in effect prevents any arbitrage between offboard and U.S. wheat prices.
Delivery Quota System
The CWB also regulates the movement of grain in Western Canada. Producers receive the same price for their product no matter when they market their grain. So, the CWB regulates the timing of grain deliveries to (1) avoid congestion at harvest, (2) provide for an equitable sharing of delivery opportunities for all producers, and (3) spread deliveries evenly over the crop year.
The CWB was first granted authorization to establish marketing quotas in 1940 with an amendment to the Canadian Wheat Board Act. During the fifties and sixties, the CWB typically announced a general delivery quota shortly after harvest, giving farmers a certain delivery entitlement based on total hectares planted. Farmers could then market a limited tonnage per hectare for the entire area planted to all grains over certain periods during the marketing year. This delivery quota system was general in nature, meaning that specific grains were not targeted for delivery. If a specific grain was needed because of strong market demand, supplementary quotas were announced. In 19 70, separate quotas for each grain replaced the general and supplementary quota system. This new program was modified to complement the wheat "Lower Inventories for Tomorrow" program (Operation LIFT), a 1-year program intended to reduce seeded acreage by half from the 1969 level because of excess stock conditions. This program was carried out by providing wheat producers wheat area reduction incentives and completely excluding land sown to wheat, except for Soft White Spring Wheat, from the quota base. In 1971, operation LIFT was terminated and the quota system was modified to account for separate quotas for each grain, including wheat. Today, the CWB announces delivery quota entitlements for the principal grains prior to harvest. The delivery quota entitlement is still based on total hectares planted plus perennial forage (assignable hectares). Farmers, however, have greater flexibility in reassigning those hectares to specific quota grains they wish to market.
During periods of excess stocks, Canadian farmers are required to store their excess grain, but U.S. farmers who participate in the crop programs have the option of forfeiting their grain to the U.S. Government at the loan rate. Hence, most Canadian farmers have onfarm storage, out of necessity, to store their grain until their marketing quotas come due or for periods in which production plus farm stocks exceed their delivery entitlement.
Wheat Milling Price
Another regulatory capability of the CWB of interest to this report is the setting of the wheat price for end-use by domestic millers and processors. Wheat for food and industrial use is sold exclusively by the CWB directly to millers and processors at a rate set between a floor and ceiling price. The Canadian Government bounded that price, called the milling price, to protect Canadian consumers from highly fluctuating wheat prices. The wheat milling price used in this report is an updated version of that used in Spriggs* report (26). Between 1969 and 1972, the milling price was set at $71.83 per metric ton. Between 1973 and 1978, the price was set at a maximum of $119.42 per metric ton. On December 1, 1978, the CWB began a two-price domestic wheat pricing policy whereby millers were charged the export price of No. 1 CWRS, 13.5 percent. Thunder Bay, within a range of between $146.98 and $183.72 per metric ton. In August 1980, that range was increased to between $183.72 and $257.21 per metric ton. The export price was changed December 1, 1984, and was set equal to a weighted average of the CWB asking prices at Thunder Bay, Vancouver, and Prince Rupert. In 1986, the two-price domestic wheat policy shifted from a stabilization policy to an income supporting policy in response to falling real world prices. The floor price was increased to $220.46 per metric ton and the ceiling price was increased to $404.18 per metric ton.
Canadian Grain Commission
Canadian grains are graded via standards established by the Canadian Grain Commission, which operates under the authority of the Canada Grain Act. The commission, a Government regulatory agency, is responsible for implementing the official grading and inspection system. This system was designed to separate and qualify various lots of wheat with respect to milling quality. The four grades of CWRS wheat are Nos. 1-3 and feed. Each grade is differentiated by (1) test weight, (2) variety, (3) glassy appearance of the kernals, (4) soundness, and (5) foreign matter (32, p. 12). The variety for No. 1 or 2 CWRS wheat must be of a high quality for milling and breadmaking and, hence, must be Marquis or any variety equal to Marquis. Grades can be further qualified by moisture and percentage of protein content, which also affect their prices. For example. No. 1 CWRS 13.5 percent will sell at a higher price than No. 1 CWRS 11 percent because the No. 1 CWRS 13.5 percent has the higher protein content. In terms of marketing, grades Nos. 1, 2, and 3 CWRS and feed wheat can be delivered to the CWB, although feed wheat is usually sold through the offboard markets.
CANADIAN POLICIES SUPPORTING WHEAT
Canadian support policies have developed over time in response to growing, marketing, and political conditions unique to Canada. For example, Scott is a town in the center of Saskatchewan Province, a province where approximately 50 percent of all western grain is produced. This town is 900-1,000 miles from the Lake Superior port of Thunder Bay in the east and 1,100 miles from the Pacific coast in the west (22, p. 2). This distance between the grain producing regions of the Western Prairie Provinces and port facilities makes transportation costs expensive (fig. 1). Also, since the only mode of grain transportation has been the railway, producers have historically demanded legislation to regulate and assist grain transportation. Other conditions special to Canada are (1) severe weather conditions, which, until just recently, limited wheat production to only spring wheat varieties, and (2) reliance on fluctuating export markets. As a result, prairie farmers have historically suffered from unstable prices and incomes. In response to this situation, stabilization programs have been enacted to support and stabilize producer prices and incomes.4/
Transportation Policies
Canadian transportation policies have been enacted to provide subsidies that reduce transportation costs to producers and maintain and provide services that benefit producers. The major elements of Canada's transportation policies are (1) programs that assist in the transportation of grain to various parts of the country, and (2) capital programs that upgrade Canada's grain handling and transportation system.5/
Any understanding of Canadian transportation policy must begin with the Crow's Nest Pass Agreement, which the Canadian Pacific Railway (CPR) and the Canadian Federal Government signed and confirmed by legislation in 1897. The agreement called for the CPR to receive a Federal subsidy to assist in constructing a rail line into southeastern British Columbia in exchange for reducing and fixing freight rates on grain and flour in perpetuity. This agreement worked reasonably well until the sixties when increased costs reduced the profitability of grain transportation to the railway industry. In response to this situation, the Canadian National and Canadian Pacific railways allowed their boxcars and branch lines to deteriorate in the face of continued losses. As a result, the railway system became a constraint to larger export volumes in the late seventies and Canada's share of world wheat exports declined (22^, p. 1). The Canadian Federal Government reacted to this situation in 1972 with the purchasing and leasing of hopper cars, the repairing of boxcars, and branchline rehabilitation programs. Until then, boxcars were used to move grain to export positions and were in short supply. Boxcars were originally designed as multipurpose cars and, hence, did not efficiently move grain. With the export demand growth of the seventies, the
4/ Much of the discussion of Canada's farm policies in this section is from
5/ For more information on Canada's grain handling and transportation system, see (22) need arose for hopper railcars designed specifically for grain handling and which could move grain much faster than boxcars. The Canadian Federal Government also began programs of branchline rehabilitation and subsidization to preserve and maintain this system in Canada. These programs, however, did little to solve the major problems confronting the grain handling and transportation system in Canada and a need arose to modernize the system of rate structures for rail freight.
The Western Grain Transportation Act was passed in 1983 to improve the efficiency of grain movement within Canada and gradually replace the freight structure established by the Crowds Nest Pass Agreement. Under the new legislation, producers will have to pay an increasing share of the cost of transporting grain to port positions. Producer portions of annual rate increases, however, are strictly controlled by the legislation, and the Government pays the difference between the annual rate increases and the maximum allowed producer contributions.
Stabilization Policies
The purpose of Canadian stabilization policies has been to stabilize producer prices and incomes under conditions of rapidly changing weather patterns and export conditions. The major elements of these policies are (1) advance payments, (2) crop insurance plans, (3) the Western Stabilization Act, (4) the Agricultural Stabilization Act, and (5) the CWB two-price wheat policy.
Advance Payments
Canada has two types of advance payments programs: one for wheat, barley, and oats grown in the Western Prairie Provinces by CWB permit holders, and the other for all other crops including wheat, barley, and oats grown outside the Western Prairie Provinces.
The Prairie Grain Advance Payments Program was enacted in 1957 to provide interest-free cash advances to improve the cash flow of western producers while they waited for their delivery quotas from the CWB to open. Advances may be obtained on grain not yet eligible for delivery to the CWB. These cash advances are expected to be paid back by the end of the crop year and are deducted from initial payments made by the CWB.
The Advance Payments for Crops Act was passed in 1977 to provide interest- free loans to producers not eligible for the Prairie Grain Advance Act. The objective of this act was to prevent producers from selling their crops at harvest time at low prices and to improve the orderly marketing of storable crops. The advances cannot exceed half the expected market price for the crop and are guaranteed up to 95 percent by Agriculture Canada.
Crop Insurance Plans
The Crop Insurance Act of 1959 was passed to provide producers protection against crop losses due to natural hazards. These programs are administered at the Provincial level and are funded by the Federal and Provincial governments and by producers. The commodities covered, participation rates, productivity, and production costs determine actual costs of the programs. Western Grain Stabilization Act
This act, passed in 1976, was implemented to protect western grain producers from market risk resulting from drastic changes in producer prices and farm incomes. Given the large percentage of western grain production entering Canadian export markets, producers are highly susceptible to changes in world market conditions. The program covers wheat, barley, oats, rye, flaxseed, rapeseed, and mustard seed. The program is funded by annual contributions made by producers (a third of the total cost) and the Canadian Federal Government (two-thirds of the total cost). The program operates by making payments to producers when their cash flow is below a specified 5-year average. Producers benefit in years when their cash flow is low by receiving income-stabilizing benefits.
Agricultural Stabilization Act
A similar stabilizing program is the Agricultural Stabilization Act of 1958. The Act provides mandatory price supports for cattle, hogs, industrial milk and cream, corn, soybeans, and oats, as well as spring wheat, winter wheat, and barley grown outside the Western Prairie Provinces. Other commodities may be designated for support at the discretion of the Minister of Agriculture. The program operates by making deficiency payments for eligible commodities when the market price, adjusted for cash costs, is below a prescribed level.
CONCEPTUAL MODEL OF THE CANADIAN WHEAT SECTOR
The model structure developed in this section consists of behavioral relations for area planted, domestic use, stocks, and domestic prices. An identity equal to supply less domestic use and stocks determine exports. This identity is essentially a Canadian wheat excess supply equation, which is a function of a world wheat reference price. The U.S. wheat gulf ports price is defined as the world wheat price and is exogenous to the Canadian wheat submodel. The model specifications presented in this section are conditioned on the review of the Canadian wheat sector presented earlier, a review of existing Canadian crop models, and the theoretical supply model presented in appendix 2. The conceptual model is composed of supply and demand blocks, a price block, and a market clearing identity.
Canadian Wheat Supply Block
The supply component of the Canadian wheat submodel consists of a behavioral relation for area planted. Supply is defined as the sum of production, imports, and beginning stocks. Canadian wheat imports have been nonexistent and will be ignored for this analysis. Beginning stocks are recursive in the supply block; ending stocks are determined endogenously in the demand block. Production is defined as area planted times yield per planted hectare. Area planted will be determined endogenously as a behavioral relation. Yield, in contrast, is highly random in nature and will be considered exogenous to the model.
Supply identity:
WSUPCAt = WPRDCA^ + WTBSCAf (1)
10 Production identity:
WPRDCA^ = WAPTCA^ * WYLDCA^. (2)
Area planted:
WAFTCA^ = WAPTCA(EPW^, EPS^, PE^, WAPTt_;,^). (3) where:
EPWt = ElPWt + EFPWt-
Variable descriptions:
WSUPCA^ = Canadian wheat supply, crop year t, WPRDCAt = Canadian wheat production, crop year t, WTBSCA^ = Canadian wheat total beginning stocks, crop year t, WAPTCA^ = Canadian wheat area planted, crop year t, WYLDCAt = Canadian wheat yield per planted hectare, crop year t, EPW|^ = expected CWB total realized price for wheat, crop year t, EPS^ = expected price of a substitute crop, crop year t, PEt = Canadian wheat production expenses, crop year t, EIPW|^ = expected CWB initial price for wheat, crop year t, and EFPW^ = expected CWB final price for wheat, crop year t.
In the supply block, wheat area planted (WAPTCA) is specified as a function of the expected CWB total realized price for wheat (EPW) and a substitute crop (EPS), wheat production expenses (PE), and the lagged dependent variable. The expected total realized price for wheat is equal to the expected initial payment (EIPW) plus the expected final payment for wheat (EFPW).
The price expectations function has been specified numerous ways in previous Canadian wheat area response studies. Schmitz used the latest final price received prior to planting in both a lagged price and distributed lag model (25). Capel used the March average CWB International Wheat Agreement price in a Nerlovian adaptive expectations model (6^). Meilke used both initial and final payments as separate area-inducing variables (21). Jolly and Abel specified an expected CWB total realized price as the sum of the expected initial and final price, which was then reduced to the CWB selling quotation price (17_) . Spriggs, who referenced Jolly and Abel's theoretical model, used the expected offboard price for wheat as the supply inducing price whether quotas were binding or not (26^). Spriggs assumed that producers formed price expectations on both the CWB and offboard markets and that both these prices affected planting decisions. Since most premium quality wheat, however, is marketed through the CWB and only feed quality wheat is marketed through the offboard markets, prices in the offboard markets cannot be expected to affect planting decisions. Producers can market their high grade wheats through the offboard markets as feed wheat, but premiums for the higher quality grades encourage producers to grow the best quality wheat they can and market it through the CWB. Krakar and Paddock used an average initial price less CWB deductions for transportation and handling as one area inducing variable, and the final price lagged two periods as a separate area inducing variable (20). CWB deductions were included in the specification to express the area inducing price as a farmgate price.
11 The expected CWB total realized price for wheat was assumed to be the proper area inducing price for this report. This price is a function of the current initial price, the adjustment and interim price lagged one period, and the final price lagged two periods, which is similar to the specification used by Krakar and Paddock. Canadian wheat producers typically plant in May and harvest in August, after which the marketing year begins. In recent years, initial prices were announced prior to planting, although in earlier years they were announced shortly after planting. Producers know the level of the initial price at planting time; hence, current prices were used in this report. Adjustment and interim prices were also included in the specification and were lagged one period since they were typically announced after planting, between October and March the following year. Final pajanents are also announced well after planting. At planting time in May, the most recent final payment Canadian farmers have typically received has been a final payment for wheat planted 2 crop years earlier. Hence, the final price lagged 2 crop years was used. To summarize, producers at planting time know the level of initial prices but must form expectations of the adjustment, interim, and final prices.
Another item of concern is how to measure the restrictiveness of the CWB*s marketing quotas and reflect its effect on producers* decisions to plant. This variable typically has been represented as a separate variable in previous reports. Schmitz used beginning stocks. Capel used total wheat supply in February divided by a 5-year moving average of wheat production, and Meilke used marketings of wheat divided by farm wheat supply. Spriggs* measure of quota restrictiveness was equal to deliveries to the CWB divided by farm supply. Spriggs, however, used offboard market prices in his area response model and used the quota restrictiveness variable in an offboard-CWB export quotation price link equation. To specify a measure of quota restrictiveness, let us rewrite the area inducing price from the theoretical model derived in appendix 2 in which EP - \ = y, where EP is the expected CWB total realized price, X is a measure of quota restrictiveness, and \i is the area inducing price. Expectations of the CWB total realized price are revised by X, depending on the degree of quota restrictiveness. In this report, farm plus commercial stocks will be used to reflect quota restrictiveness and it will affect farmers* decisions to plant by revising expectations of the adjustment, interim, and final prices.
The specification for the expectation of the CWB total realized price is as follows:
EPW^ = EPW(WIPYCA^, WAPYCA^^;^, WINPCA^^^^, WFPYCA|^„2 • WTESCA^^^), (4) where:
EPW^ = expected CWB total realized price, WIPYCA^ = CWB initial price for wheat, crop year t, WAPYCA^-i = CWB adjustment price for wheat, crop year t-1, WINPCAt-i = CWB interim price for wheat, crop year t-1, WFPYCA^_2 = CWB final price for wheat, crop year t-2, and WTESCAt^i = wheat total ending stocks, crop year t-1.
Canadian producers have become accustomed to second guessing or forecasting major price and quota decisions made by the CWB. Therefore, the model assumes if total ending stocks are expected to be higher than in the prior year, farmers will anticipate that (1) marketing quotas will be more restrictive
12 over the coming marketing year, and (2) the final payment associated with the CWB marketing receipts from the coming crop year will be lower than from the prior year. Hence, farmers will take their most recent final payment, which is often received early in the calendar year, and discount it accordingly. Farmers will then respond by planting less wheat. In contrast, if total ending stocks are tight at planting, farmers will anticipate that the marketing quota will not be binding in the coming marketing year, and that final payments associated with the coming crop year will be much higher than previous final paynients. Hence, farmers would respond by planting more area to wheat.
Canadian Wheat Demand Block
The demand component of the Canadian wheat submodel consists of behavioral equations for food, feed, seed, and ending stocks. Demand is defined as the sum of domestic demand and ending stocks. Domestic demand is defined as the sum of food use, industrial use, feed use, loss in handling, and seed use.
Food demand:
WFODCA^ = WFODCACRWMILCA^, RPDINCA^). (5)
Feed demand:
WFEDCA^ = WFEDCACRWOFFCA^, RPSFDCA^, LPICA^, LNCA^). (6)
Seed demand:
WSEDCAt_i = WSEDCA(WAPTCAt, TREND^). (7)
Ending stocks:
WTESCA^ = WTESCA(WSUPCA|^, WAPTCA^^^^, RWQUOCA^) . (8)
Variable descriptions:
WFODCA^ = Canadian wheat food and industrial use, crop year t, RWMILCA|^ = real CWB wheat mill price, crop year t, RPDINCAj- = Canadian real personal disposable income, year t, WFEDCAt = Canadian wheat feed use and loss in handling, crop year t, RWOFFCA^ = Candian real wheat offboard price, crop year t, RPSFDCA^ = Canadian real price of wheat feed substitute, crop year t, LPICA^ = Canadian livestock price index, year t, LNCA^ = Canadian livestock numbers, year t, WSEDCA^_3^ = Canadian wheat seed use, crop year t-1, WAPTCA|^ = Canadian wheat area planted, crop year t, TRENDt = trend, 1960=60, WTESCAt = Canadian wheat total ending stocks, crop year t, WSUPCAt = Canadian wheat production plus beginning stocks, crop year t, and RWQUOCAt = CWB real export quotation price for wheat, crop year t.
In the demand block, four behavioral equations are specified. Wheat demand for food and industrial use (WFODCA) is specified as a function of the real milling price of wheat (RWMILCA) and real personal disposable income (RPDINCA) (equation 5). The milling price used in this report is an updated version of that used in Spriggs* report.
13 Wheat demand for feed (WFEDCA) is specified as a function of the real offboard price of wheat (RWOFFCA), the real price of a substitute livestock feed (RPSFDCA), a livestock price index (LPICA), and livestock numbers (LNCA) (equation 6).
Wheat seed demand (WSEDCA) is specified as a function of WAPTCA and TREND (equation 7). At planting time, farmers make simultaneous decisions on a number of inputs to use in the production process. From the theoretical model derived in appendix 2, derived demand functions for inputs such as land and seed were derived simultaneously. Because of the nature of the reported data, however, seed use during crop year t is determined simultaneously with planting decisions for a crop to be harvested in the coming crop year. Therefore, seed demand in period t-l is a function of area planted in period t. Seed use is also a function of TREND, which assumes that farmers have adopted improved varieties over the historical period to improve germination rates. As farmers substituted farm-grown varieties for improved ones, seeding rates concurrently declined to lower costs.
Equation 8 in the demand block is an ending stocks equation that specifies total ending stocks (WTESCA) as a function of current wheat production plus beginning stocks (WSUPCA), wheat area planted for the coming crop year (WAPTCA), and the real export price of wheat (RWQUOCA). As the export price of wheat rises, the CWB is expected to increase the marketing quota for wheat and move more grain into export positions, thus lowering stocks levels. Also, as planting during the last few months of the t crop year increases, the CWB is expected to reduce current stock levels via exports to make room for a larger expected harvest in the t+1 crop year.
Canadian Wheat Price Block
Nonspatial equilibrium models assume the existence of a single world market clearing price. The model assumes U.S. prices for wheat, barley, and livestock as world reference prices. Canadian prices are specified in the supply and demand behavioral equations and are linked to the world reference prices. These price linkages are developed for CWB initial, total realized, offboard, export quotation, and livestock prices.
Wheat offboard price:
WOFFCAt = WOFFCA(WIPYCAt, WGULFP^, ERCAUS^, WSUPCA^). (9)
CWB initial price for wheat:
WIPYCA^ = WIPYCA(WHLRUS^, WTBSUS^, WIPYCA^.^]^, ERCAUS^) . (10)
CWB total realized price for wheat:
WTRPCA^ = WIPYCA^ + WAPYCA^ + WINPCA^. + WFPYCA^., = WTRPCA(WGULFPt, ERCAUSt). (11)
CWB final price for wheat:
WFPYCAt = WTRPCAt " WIPYCA^ - WAPYCA^ - WINPCAf (12)
14 Canadian export price for wheat:
WQUOCAt = WQUOCAiWGULFPt., ERCAUSt) . (13)
Canadian wheat mill price:
WMILCAt = WQUOCAt if LB < WQUOCA^ < UB, (14) = UB if WQUOCAt > UB, and = LB if WQUOCAt < LB, where UB and LB are the upper and lower bounds of the CWB's two-price domestic policy scheme.
Barley offboard price:
BOFFCAt = BOFFCA(BIPYCAt, CRPFUS^, ERCAUS^, BSUFCA^). (15)
CWB initial price for barley:
BIPYCAt = BIPYCA(CRLRUSt, CTBSUS^, BIPYCAt_i, ERCAUS^). (16)
CWB total realized price for barley:
BTRPCAt = BIPYCA^ + BAPYCA^. ■»- BFPYCA^, = BTRPCA(CRPFUSt, ERCAUS^). (17)
CWB final price for barley:
BFPYCA^ = BTRPCA^ - BIPYCA^ - BAPYCA^, (18)
Livestock price index:
LPICAt = LPICA(LPIUSt, ERCAUS^). (19)
Market clearing identity:
WEXPCA|^ = WPRDCA^ -h WTESCA^^^ - WFODCA^ - WFEDCA^^ - WSEDCA^. - WTESCA^^. (20)
Variable descriptions:
WOFFCA^ = Canadian wheat offboard price, crop year t, WIPYCAt = CWB initial price for wheat, crop year t, WGULFPt = U.S. gulf ports season average price for wheat, crop year t, ERCAUS^ = Canadian-U.S. exchange rate, crop year t, WSUPCA^ = Canadian wheat beginning stocks plus production, crop year t, WHLRUS^ = U.S. wheat loan rate, crop year t, WTBSUS^ = U.S. wheat total beginning stocks, crop year t, WTRPCA^ = CWB total realized price for wheat, crop year t, WAPYCAt = CWB adjustment price for wheat, crop year t, WINPCA^ = CWB interim price for wheat, crop year t, WFPYCA^ = CWB final price for wheat, crop year t, WQUOCAt = CWB export quotation price for wheat, crop year t, WMILCA^ = Canadian wheat mill price, crop year t, BOFB'CA^ = Canadian barley offboard price, crop year t, BIPYCA^ = CWB initial price for barley, crop year t, CRPFUS^ = U.S. season average price for corn, crop year t,
15 BSUPCA^ = Canadian barley beginning stocks plus production, crop year t, CRLRUSt = U.S. corn loan rate, crop year t, CTBSUSt = U.S. corn total beginning stocks, crop year t, BTRPCAt = CWB total realized price for barley, crop year t, BAFYCA^^ = CWB adjustment price for barley, crop year t, BFFYCA^ = CWB final price for barley, crop year t, LPICAt = Canadian livestock price index, year t, LPIUS^ = U.S. livestock price index, year t, WEXPCA^ = Canadian wheat exports, crop year t, WPRDCA^ = Canadian wheat production, crop year t, WTESCA^ = Canadian wheat total ending stocks, crop year t, WFODCA^ = Canadian wheat food and industrial use, crop year t, WFEDCAt = Canadian wheat feed use and loss in handling, crop year t, and WSEDCAj^ = Canadian wheat seed use, crop year t.
The third block is a price block which links Canadian domestic prices to world reference prices—defined here as U.S. prices—and describes the behavior of the Canadian Federal Government and the CWB in setting initial, final, and export prices. Equation (9) links the Canadian wheat offboard price (WOFFCA) with the CWB initial price for wheat (WIPYCA), the U.S. wheat price (WGULFP), the Canadian-U.S. exchange rate (ERCAUS), and beginning stocks plus production of Canadian wheat (WSUPCA). The CWB initial price represents a floor price for the offboard market because it is guaranteed by the Canadian Government. The U.S. wheat price and exchange rate are included in the specification as a proxy for the Canadian wheat export price; it is expected that as the export price rises, so also does the offboard price. The supply of wheat is inversely related to the offboard price since the latter is expected to strengthen during periods of short wheat supplies.
The CWB initial price for wheat (WIPYCA) is related to the U.S. wheat loan rate (WHLRUS), U.S. total beginning wheat stocks (WTBSUS), and a lagged dependent variable. The Government sets the initial price prior to spring planting according to what officials think the wheat total realized price will be for the crop that will be harvested that fall. Expectation of the wheat total realized price is in turn according to expectations of the U.S. wheat price for the coming marketing year. The Government's expectation of the wheat total realized price prior to planting is hypothesized to be a function of the U.S. loan rate, which represents a floor price for U.S. wheat, and the level of U.S. wheat carryover stocks. As U.S. wheat stocks fall, expectations of U.S. market prices are expected to rise. The wheat initial price is also conditioned on the level of the initial price in the previous year, and the Canadian Government is hesitant to make drastic changes in the level of the initial price from one year to the next. This was most apparent in the seventies when significant adjustment payments had to be made since the intial price was set at a level far below export returns.
The CWB wheat total realized price (WTRPCA) is defined as the sum of the initial price for wheat, the wheat adjustment price (WAPYCA), the wheat interim price (WINPCA), and the final price for wheat, and is functionally related to the U.S. wheat market price (equation 11). This price is calculated by the CWB by first computing total CWB marketing receipts, and then deducting handling, freight, and board operating expenses. The CWB marketing receipts are equal to cash receipts from both the domestic and export markets. Hence, the wheat total realized price is a weighted average of the Canadian wheat mill and export price. The Canadian wheat mill price (equation 14) is equal to the export price (WQUOCA) as long as it is within
16 bounds set by law. The Canadian export price is a function of the U.S. wheat price and the Canadian-U.S. exchange rate (equation 13). Since the wheat mill price is a function of the Canadian wheat export price and the export price is a function of the U.S. market price, one can then conclude that the CWB total realized price for wheat is functionally related to the U.S. wheat market price.
The CWB barley offboard, initial, final, and total realized prices (equations 15-18) are specified and computed in the same manner as wheat except they are linked to U.S. corn prices. U.S. corn is imported into Canada and competes directly with Canadian barley. Equation (19) specifies the Canadian livestock price index (LPICA) as functionally related to U.S. livestock prices (LPIUS) and the Canadian-U.S. exchange rate.
Equation (20) is the market clearing identity which sets exports equal to excess supply, which is equal to domestic supply less domestic demand and ending stocks. This equation along with the price linkages essentially describes the Canadian wheat submodel developed in this report. This model is called a submodel because it is not a complete modeling system since it does not contain a U.S. component that solves for U.S. prices. The model was developed as a component to a much larger world wheat trade model. The Canadian wheat submodel is a disequilibrium model and can be solved only if U.S. prices, considered exogenous to the model, are supplied.
Other Variables and Data
The majority of data came from primary or secondary Canadian sources. The data source for wheat supply and utilization was the Canada Grains Council and the Agricultural/Natural Resources Division, Statistics Canada (3). The source for the CWB producer payments was the Canada Grains Council and the Canadian Wheat Board (3 and 5). The data source for offboard prices and CWB selling quotations was the Canada Grains Council (3). The wheat milling price source was Spriggs, with updates calculated by the International Economics Division, ERS, USDA (26^). The data source for hog price and numbers, personal disposable income, and population was Statistics Canada (28 and 29). The source for the consumer price indicies and exchange rates for the United States and Canada was the International Monetary Fund (13 and 14).
The U.S. wheat price used in this report is not the gulf port price reported by the U.S. Department of Agriculture because that figure was calculated as a simple calendar year average price (31). Since this report links Canada's prices with U.S. prices, which are both reported on a crop-year basis, the U.S. price was recalculated as follows:
I Pi*EXPi WGULFPt = _J: , I EXPi i where. :
WGULFP = season average export weighted gulf ports price, U.S. dollar per metric ton, P = simple quarterly average gulf ports price for Hard Ordinary Wheat, U.S. dollar per metric ton, and EXP = quarterly wheat exports, million bushels.
17 Quarters used were June-August, September-November, December-February, and March-May. Monthly export prices were available over the historical period, although monthly exports were not. Therefore, monthly prices were averaged simply over quarters and then weighted by quarterly exports to yield the season average gulf ports price.
EMPIRICAL ESTIMATES
The Canadian wheat submodel was estimated via ordinary least squares (OLS) over 1960-85.6/ The OLS estimation technique may lead to inconsistent parameter estimates but was chosen over other techniques for two reasons. First, the model is nonlinear in the variables, which precludes the use of instrumental variables in two-stage least squares (2SLS) and three-stage least squares (3SLS) techniques.2/ Second, other simultaneous or full-information techniques are not guaranteed to represent an improvement over OLS when the model may be incorrectly specified ij). Johnston notes that a necessary condition under which 3SLS is asymptotically more efficient than 2SLS is that the complete modeling system is correctly specified (16, p. 489). The possibility for misspecification increases as a modeling system becomes larger and more detailed. Hence, the possibility of a misspecification would deny any advantage of 3SLS over 2SLS, and a nonlinear specification would preclude the use of 2SLS.
Variables were generally maintained in an equation when **V ratios were statistically significant within a 90-percent confidence interval. The regression results of the Canadian wheat submodel are in tables 2 and 4-16. Six supply and demand behavioral equations, five CWB price behavioral equations, and three price link equations were estimated. All variables have correct a priori signs and most are statistically significant within a 95-percent confidence interval.
Canadian Supply and Utilization
Canadian wheat area planted (WAPTCA) was estimated as a function of the wheat initial price less CWB deductions (RWCWBCA), the expected wheat final price (EFFYCA), the expected total realized price of barley less CWB barley deductions (RBCWBCA), variables reflecting the ''Lower Inventories for Tomorrow'' program (DUM69, DUM70), and a lagged dependent variable (table 2, fig. 4). All price variables were deflated by a lagged fertilizer price index (FIPFER). The producer knows the initial price at planting and forms expectations of the adjustment, interim, and final prices. The model specifies the expectation of the total realized less initial price (EFPYCA) as the sum of the adjustment and interim prices lagged one period (WAPYCA, WINPCA) and the final price lagged two periods (WFPYCA), deflated by the lagged fertilizer price index and a wheat stock index (WSI). The wheat stock index is equal to total beginning stocks (WTBSCA) divided by the mean of stocks over the estimation period. Barley enters the model as a competing crop for wheat production resources. The barley expected net realized price
6/ Unless otherwise noted, years are in crop years; that is, 1960 = 1960/61. 7_/ There are estimators that apply 2SLS and 3SLS to nonlinear systems. Fair and Parke successfully used a full-information maximum likelihood estimator and nonlinear 2SLS and 3SLS estimators to estimate a nonlinear macroeconometric model (9).
18 Table 2—Canadian wheat area planted
Ordinary least squares estimates
Dependent variable WAPTCA Ntimber of observations 17 Sample period 1968-1984 1/ Standard error of regres s ion 578.048 Sum of squared residuals 3,341,400 R - squared .95413 Adjusted R - squared .92661 Durbin - Watson statistic 2.1891 Durbin h statistic -.40860 Estimated autocorrelation (Rho) -.09454
Standard Signifi- Mean Variable Coefficient error T-ratio cance level elasticity
ONE 3,521.59 1,477 2.385 0.03828 RWCWBCA 1,612.08 851.6 1.893 .08762 0.27 EFPYCA 856.916 289.6 2.959 .01430 .06 RBCWBCA -2,016.66 505.6 -3.989 .00256 -.28 DUM69 -1,880.67 628.2 -2.994 .01348 — DÜM70 -5,855.19 616.6 -9.495 0 — WAPTCA[-1] .666569 .07269 9.170 0 —
Calculated variables:
RWCWBCA = (WIPYCA - HCWH3C[-1] - CR0W)/FIPFER[-1] EFPYCA = (WAPYCA[-1] + WINPCA[-1] + WFPYCA[-2])/(FIPFER[~l]*WSI WSI = WTBSCA/13,352.09 2/ RBCWBCA = (BIPYCA + BAPYCA[-1] + BFPYCA[-2] - HCBA3C[-1] - CR0W)/FIPFER[-1]
Variable descriptions:
WAPTCA Canadian wheat, total area planted, August-July 1,000 ha WIPYCA CWB wheat initial price. No. 1 CWRS C$/mt HCWH3C Handling costs for wheat. Western Canada C$/mt CROW Transportation costs, Scott, Saskatchewan, to Thunder Bay C$/mt FIPFER Farm price index for fertilizer, Canada, August/July index:1981=100 WAPYCA CWB wheat adjustment price. No. 1 CWRS C$/mt WINPCA CWB wheat interim price. No. 1 CWRS C$/mt WFPYCA CWB wheat final price. No. 1 CWRS C$/mt WTBSCA Canadian wheat, total beginning stocks, August-July 1,000 mt BIPYCA CWB barley initial price. No. 1 feed C$/mt BAPYCA CWB barley adjustment price. No. 1 feed C$/mt BFPYCA CWB barley final price. No. 1 feed C$/mt HCBA3C Handling costs for barley. Western Canada C$/mt DÜM69 Dummy variable, equals 1 in 1969, 0 elsewhere DUM70 Dummy variable, equals 1 in 1970, 0 elsewhere
1/ Crop year, that is, 1968-84 = 1968/69-1984/85. 2/ The wheat stock index (WSI) was computed by dividing wheat beginning stocks by the mean of beginning stocks over the historical period.
19 Figure 4 Wheat Area Planted, Canada
Million hectares 14
/!^ 12 r % ^X>y^ J/^ 10 - ^^ Predicted ^.^gfa^
^>^ Actual y
V/ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1968 72 76 80 84 Crop year
(RBCWBCA) is equal to the sum of the initial price (BIPYCA), the adjustment price lagged one period (BAPYCA), and the final price lagged two periods (BFPYCA), less CWB deductions, and deflated by the lagged fertilizer price index. An alternative specification would be to deflate the barley prices by a barley stock index to account for the effect of barley stocks on producer price expectations. Another area response specification might involve the expected price of canola since canola is another competitor for wheat production resources.
The wheat area response specification involved the use of a lagged dependent variable and was therefore tested for autocorrelation. A Durbin h statistic of x-0.41 was computed from the statistical results, which fails to reject the hypothesis of a nonautocorrelated error structure.8/ Hence, the OLS estimates were retained. Wheat price elasticities for the initial and final prices were calculated at the mean from the model and are 0.29 and 0.02, respectively, compared with 0.46 and 0.06 from the Krakar and Paddock report, and 0.53 and 0.08 from the Meilke report (table 3). The barley cross-price elasticities for the initial and final prices estimated at the mean from the model are -0.25 and -0.03, respectively, compared with -0.69 and -0.05 from the Meilke report. These cross-price elasticities are significantly different from the results of the Krakar and Paddock report that found -0.06 for the barley initial price. The expected final price variable (EFPYCA) containing the beginning stocks index has the correct sign and is statistically significant.
8/ For more information on the Durbin h statistic, see (1_6, p. 318).
20 This variable supports the hypothesis that as carry-in stocks get large» farmers revise their expectations of final payments and marketing quota*s downward and reduce their plantings to wheat. The statistical results suggest that a 10-percent increase in beginning stocks will reduce wheat plantings by 0.3 percent. The coefficient for the lagged dependent variable is significant and confirms Nerlove's partial adjustment hypothesis; farmers do not instantaneously adjust their area planted to changes in prices, rather, they adjust to the optimum level over time. The coefficient for the lagged dependent variable estimated in this report is 0.6 7 compared with 0.42 calculated in the Devadoss report and 0.48-0.49 in the Meilke report. This result suggests that we have estimated Canadian wheat producers to be less responsive to price signals than did the other studies. Overall, the elasticities estimated in this report compare favorably with those presented in the literature. For more comparisons of area response elasticities, see table 3.
Table 3—Comparisons of Canadian wheat area response elasticities 1/
Krakar : Devadoss: and and Bailey Paddock others ' Spriggs Meilke Item : 1968-84 1968-83 1964-77 : 1949-74 (20) (8) (26) (21)
Area inducing prices: :
Wheat— : CWB initial price : 0.2881 0.4597 — — 0.53 CWB final price : .0227 .0612 — — .08 CWB initial plus : final price : — — 0.38 — .35 Offboard price — — — 0.43 —
Barley— CWB initial price -.2527 -.0564 — -.69 CWB final price -.0311 — — — -.05 CWB initial plus offboard price : — -.30 CWB initial plus final price : — — — -.40 Offboard price : — -.0548 — -.22 —
Handling costs: Wheat : -.0090 -.0126 — — — Barley : .0140 .0030 — — —
Freight rate : .0036 -0.0163 — — —
Wheat beginning stocks : -.0345 — — — — — = not applicable. CWB = Canadian Wheat Board.
1/ Shortrun elasticities evaluated at the mean.
21 Canadian wheat yield (WYLDCA) was estimated as a function of TREND (table 4, fig. 5). Yield in this model is assumed to be exogenous, although this equation can be used to simulate yields under favorable, average, and poor weather conditions by moving the trend line up or down one or two standard deviations.
Wheat for food and industrial use was estimated in table 5. WHFOOD represents the wholesale demand for wheat and shifts with respect to the retail demand for wheat products (bread and bakery goods). A strict interpretation of consumer demand theory suggests that the demand for wheat for food use should be estimated for a representative wheat miller and then summed across all millers. Data on the consumption and number of wheat millers in Canada, however, are not available. Wheat food use was then specified on a per capita basis; however, the statistical results did not support this specification. Hence, WHFOOD was estimated in an aggregate form as a function of the real wheat milling price (RMILL) and real personal disposable income (RPDINCA) (table 5, fig. 6). Dummy variables were incorporated into the specification to account for unexplained outliers. The real milling price elasticity was estimated to be -0.06, compared with -0.03 frbm the Spriggs report. The elasticity of real personal disposable income was calculated to be 0.23, which when compared with the real milling price elasticity indicates that food use is more responsive to aggregate real income than to the real milling price. One explanation for the magnitude of this elasticity is that real aggregate income is highly correlated with population, which is included in the dependent variable.
Wheat for feed use (WHFEED) was estimated as a function of the real offboard price of wheat (RWOFFCA) and barley (RBOFFCA), the real price of hogs (RPHOGCA), and the number of hogs on farms (HOGNCA) (table 6, fig. 7). Dummy variables were included in the specification to account for unexplained outliers. The results indicate a direct-price elasticity of -1.03 for the real price of offboard wheat and cross-price elasticities of 0.62 and 0.73 for the real prices of offboard barley and hogs, respectively. The results also indicate the dependent variable is sensitive to the number of hogs on farms, suggesting a 10-percent increase in hog numbers will increase the demand for feed wheat by 7.1 percent. Hogs and poultry are the major consumers of feed wheat in Canada. A futura report should incorporate poultry prices and numbers in the feed demand specification.
Wheat for seed use (WSEDCA) in period t was estimated as a function of wheat area planted in period t+1 (WAPTCA) and TREND (table 7, fig. 8). The statistical results indicate that farmers used an average 95.5 kilograms of wheat per hectare per year for seeding. The results also indicate that use per hectare decreased 0.21 kilograms per year over the historical period.
Wheat total ending stocks (WTESCA) were estimated as a function of the CWB selling quotations for wheat (WQUOCA), wheat total beginning stocks plus production (WSUPCA), and wheat area planted for the coming crop year (WAPTCA[+1]) (table 8, fig. 9). Dummy variables were included in the specification to account for an unprecedented 56-percent rise in the export price of wheat in 1972, and the enormous buildup in wheat stocks prior to the imposition of the LIFT program in 1967 and 1968. Attempts to deflate the export price by the Canadian consumer price index resulted in a statistically insignificant coefficient; hence, the nominal price was retained. The statistical results indicate that a 10-percent increase in the export price of wheat will reduce stocks by 2.5 percent. A similar increase in WSUPCA will
22 Table 4—Canadian wheat yield
Ordinary least squares estimates
Dependent variable WYLDCA Number of observations 26 Mean of dependent variable 1.68793 Sample period 1960-1985 Standard error of regression .23207 Sum of squared residuals 1.3464 R - squared .37918 Adjusted R - squared .37918 Durbin - Watson statistic 1.7971 Estimated autocorrelation (Rho) .10145
Standard Signifi- •iable Coefficient error T-ratio canee level
TREND 0.023286 0.0006244 37.293
Variable descriptions:
WYLDCA Canadian wheat, yield per planted hectare, August-July mt/ha TREND Year: 1960=60, 1985=85
Figure 6 Wheat Yield, Canada
tons per hectare
23 increase ending stocks by 11.6 percent. The elasticity for area planted indicates that as wheat plantings in May for the coming crop year increase by 10 percent, the CWB responds by reducing current year end inventories by 9.3 percent.
Price Linkage Equations
The equations describing (1) the behavior of the Canadian Federal Government and the CWB in setting prices and (2) price transmission equations are in tables 9-16. The wheat offboard price (WOFFCA) was estimated as a function of the wheat initial price (WIPYCA), the U.S. wheat price in Canadian dollars per
Table 5—Canadian wheat food use
Ordinary least squares estimates
Dependent variable WHFOOD Number of observations 23 Sample period 1963-85 Standard error of regression 32.937 Sum of squared residuals 19,527 R - squared .95537 Adjusted R - squared .94545 Durbin - Watson statistic 2.6535 Estimated autocorrelation (Rho) -.32676
Standard Signifi- Mean Variable Coefficient error T-ratio cance level elasticity
ONE 1,533.98 62.35 24.602 0 ^ RMILL -.640336 .3047 -2.101 .04996 -0.06 RPDINCA .002771 .00015 18.255 0 .23 D7479 98.3272 25.42 3.868 .00113 DUM76 -84.6457 34.21 -2.474 .02355 — —
Calculated variables:
WHFOOD = WFODCA + WINUCA RMILL = WMILCA/(CPICA/100) RPDINCA = PDINCA/(CPICA/100)
Variable descriptions:
WFODCA Canadian wheat, human food use, August-July 1,000 mt WINUCA Canadian wheat, industrial use, August-July 1,000 mt WMILCA Canadian wheat, domestic milling price, August-July C$/mt CPICA Canadian consumer price index index:1980=100 PDINCA Canadian personal disposable income million C$ D7479 Dummy variable, equals 1 in 1974 and 1979, 0 elsewhere DUM76 Dummy variable, equals 1 in 1976, 0 elsewhere
24 metric ton (WGULFCA), and Canadian wheat beginning stocks plus production (WSUPCA) (table 9, fig. 10). The statistical results suggest that a 10-percent increase in the Canadian wheat floor price (WIPYCA) would increase the wheat offboard price 3.4 percent. A 10-percent increase in the U.S. wheat price (WGULFCA) would increase the wheat offboard price 5.9 percent, and a similar increase in Canadian wheat beginning stocks plus production would decrease the offboard price 8.2 percent.
Table 6—Canadian wheat feed use
Ordinary least squares estimates
Dependent variable WHFEED Number of observations 23 Sample period 1963-85 Standard error of regression 150.27 Sum of squared residuals 383,880 R - squared .83995 Adjusted R - squared .79287 Durbin - Watson statistic 1.5808 Estimated autocorrelation (Rho) .20961
Standard Signifi- Mean Variable Coefficient error T-ratio cance level elasticity
RWOFFCA -16.3333 4.488 -3.639 0.00203 -1.03 RBOFFCA 12.0854 5.058 2.389 .02874 .62 RPHOGCA .206156 .0208 9.900 0 .73 HOGNCA ,189313 .0121 15.651 0 .71 DÜM65 -467.172 161.2 -2.899 .00999 -__>. D8284 -452.188 130.7 -3.459 .00300
Calculated variables:
WHFEED = WFEDCA + WLIHCA RWOFFCA = WOFFCA/(CPICA/100) RBOFFCA = B0FFCA/(CPICA/100) RPHOGCA = PHOGCA/(CPICA/100)
Variable descriptions:
WFEDCA Canadian wheat, feed use, August-July 1,000 mt WLIHCA Canadian wheat, loss in handling, August-July 1,000 mt WOFFCA Canadian wheat, offboard price C$/mt BOFFCA Canadian barley, offboard price C$/mt PHOGCA Canadian price index 100 hogs, dress basis, Winnipeg C cents/cwt CPICA Canadian consumer price index, index:1980=100 HOGNCA Canadian hog numbers, on farm, July 1 1,000 head DUM65 Dummy variable, equals 1 in 1965, 0 elsewhere D8284 Dummy variable, equals 1 in 1982 and 1984, 0 elsewhere
25 Figure 6 Wheat Food and Industrial Use, Canada
Million metric tons 2.2
2.1
2.0
1.9
1.8
1.7
1.6 J \ I i L 1963 65 70 75 80 85 Crop year
Figure 7 Wheat Feed Use, Canada
Million metric tons 2.6
1.2 J L I I I I I I I I I \ L J L J L 1963 65 70 75 80 85 Crop year
26 The CWB initial price for wheat (WIPYCA) was estimated as a function of the U.S. wheat loan rate (WHLRUS), U.S. wheat beginning stocks (WTBSUS), and a lagged dependent variable (table 10, fig. 11). It was hypothesized that the Canadian Government sets initial prices according to a fixed percent of its expectation of the total realized price associated with the coming pool crop year. The total realized price is a weighted average of domestic and export prices and is a function of world market prices. The model, therefore, specifies the expected total realized price of wheat as a function of the U.S. wheat loan rate and U.S. wheat beginning stocks. The U.S. wheat beginning stocks variable WTBSUS is statistically significant and suggests that the Canadian Government revises expectations of world wheat market prices downward when U.S. wheat stocks are high and lowers the wheat initial price accordingly. The estimated coefficient.for the lagged dependent variable is also statistically significant in the initial price specification and suggests that the Canadian Government considers the level of the previous period's initial price when setting the current price. Attempts to convert the U.S. wheat loan rate into Canadian dollars via the Canadian-U.S. exchange rate resulted in a statistically insignificant coefficient. The exchange rate, therefore, was left out of the specification. The statistical results suggest that a 10-percent increase in WHLRUS and WTBSUS results in a 7.7- and -3.6-percent change, respectively, in the wheat initial price. The coefficient for the lagged dependent variable is 0.46, and the associated elasticity suggests that a 10-percent increase in last period's wheat initial price will increase the current period's price 4.4 percent.
Table 7—Canadian wheat seed use
Ordinary least squares estimates
Dependent variable WSEDCA[-1] Number of observations 25 Sample period 1960-84 Standard error of regression 20.034 Sum of squared residuals 8,829.7 R - squared .98879 Adjusted R - squared .9877 7 Durbin - Watson statistic 1.1502 Estimated autocorrelation (Rho) .42488
Standard Signifi- Variable Coefficient error T-ratio cance level
ONE 129.436 42.21 3.066 0.00565 WAPTCA .095498 .00222 42.963 0 TREND -2.28910 .5839 -3.921 .00073
Variable descriptions:
WSEDCA Canadian wheat, seed use, August-July 1,000 mt WAPTCA Canadian wheat, total area planted, August-July 1,000 ha TREND Year: 1960=60, ... , 1985=85
27 The next equation estimated the wheat total realized price (WTRPCA) as a function of the U.S. wheat price in Canadian dollars (WGULFCA) (table 11, fig. 12). WTRPCA is a weighted average of the Canadian mill and export price of wheat and is hypothesized to be a function of the U.S. wheat market price in Canadian dollars. WTRPCA is computed by the CWB from marketing receipts over the pool crop year, which runs from November 1 to October 31. Since the U.S. wheat crop year is from June to May, WTRPCA was estimated as a function of the U.S. wheat price in Canadian dollars during the t and t-i-1 periods. Only the current variable, however, was statistically significant. The statistical results indicate that a ID-percent increase in the U.S. wheat market price will result in an 8.5-percent increase in the wheat total realized price.
Table 8—Canadian wheat total ending stocks
Ordinary least squares estimates
Dependent variable WTESCA Number of observations 24 Sample period 1961-84 Standard error of regression 1,439.6614 Sum of squared residuals 35,235,000 R - squared .9386 7 Adjusted R - squared .91702 Durbin - Watson statistic 2.6488 Estimated autocorrelation (Rho) -.32438
Standard Signifi- Mean Variable Coefficient error T-ratio cance level elasticity
ONE 13,039.4 3,082 4.230 0.00056 WQUOCA -24.4174 5.265 -4.638 .00024 -0.25 WSUPCA .481747 .07100 6.785 0 1.16 WAPTCA[+1] -1.12304 .17620 -6.375 .00001 -.93 DUM6 7 5,115.72 1,548 3.305 .00419 — DUM68 5,898.84 1,535 3.842 .00131 — DUM72 -4,629.86 1,499 -3.089 .00666 —
Calculated variables:
WSUPCA = WTESCA[-1] + WAPTCA^WYLDCA
Variable descriptions:
WTESCA Canadian wheat, total ending stocks, August-July 1,000 mt WQUOCA CWB wheat selling quotations, basis in storage Thunder Bay or St. Lawrence C$/mt WAPTCA Canadian wheat, total area planted, August-July 1,000 ha WYLDCA Canadian wheat. yield per planted hectare, August-July mt/ha DUM6 7 Dummy variable. equals 1 in 196 7, 0 elsewhere DUM68 Dummy variable, equals 1 in 1968, 0 elsewhere DUM72 Dunmiy variable. equals 1 in 1972, 0 elsewhere
28 Figure 8 Wheat Seed Use, Canada
Million metric tons 1.3
J \ I I L 1960 64 68 72 76 80 84 Crop year
Figure 0 Wheat Total Ending Stocks, Canada
Million metric tons 28
24
20
16
12
1961 64 68 72 76 80 84 Crop year
29 The barley offboard, initial, and total realized prices were specified in a manner similar to that of wheat, although U.S. corn prices are hypothesized to affect these prices. The barley offboard price (BOFFCA) was estimated as a function of the barley initial price (BIPYCA), the U.S. corn market price in Canadian dollars (CRPFCA), and the sum of Canadian barley beginning stocks and production (BSUPCA) (table 12, fig. 13). The results indicate that the off board price is much more responsive to the U.S. corn price than to either the Canadian barley initial price or supply. A 10-percent increase in the barley initial price and the U.S. corn price in Canadian dollars will result in a 2.4- and 8.9-percent increase, respectively, in the barley offboard price. A similar increase in the supply of Canadian barley will result in a 2.3-percent decrease in the barley offboard price.
Table 9—Canadian wheat offboard price
Ordinary least squares estimates
Dependent variable WOFFCA Number of observations 25 Sample period 1963-85 Standard error of regression 10.056 Sum of squared residuals 1,921.3 R - squared .95157 Adjusted R - squared .94393 Durbin - Watson statistic 1.6028 Estimated autocorrelation (Rho) .19860
Standard Signifi- Mean Variable Coefficient error T-ratio cance level elasticity
ONE 79.0320 25.54 3.094 0.00597 _ WIPYCA .29938 .13940 2.148 .04486 0.34 WGULFCA .40977 .1094 3.746 .00137 .59 WSUPCA -.00225 .00076 -2.943 .00834 -.82
Calculated variables:
WGULFCA = (WGULFP - EXSBUS*36.744)*ERCAUS WSUPCA = WTBSCA + WAPTCA^WYLDCA
Variable descriptions:
WOFFCA Western Canadian feed wheat, offboard price C$/mt WIPYCA CWB wheat initial price. No. 1 CWRS C$/mt WGULFP U.S. season average wheat price, gulf ports, June-May US$/mt EXSBUS U.S. wheat export subsidy US$/bu ERCAUS Canadian-U.S. exchange rate, Canadian dollar per U.S. dollar, end of period Index WTBSCA Canadian wheat, total beginning stocks, August-July 1,000 mt WAPTCA Canadian wheat, total area planted, August-July 1,000 ha WYLDCA Canadian wheat, yield per planted hectare, August-July mt/ha
30 The barley initial price (BIPYCA) was estimated as a function of the U.S. corn loan rate (CRLRUS), U.S. corn beginning stocks (CTBSUS), and a lagged dependent variable (table 13, fig. 14). Duirany variables were included in the specification to account for unexplained sharp price increases in 1973 and 1980. The statistical significance of these variables suggests that (1) U.S. corn beginning stocks significantly affect the Canadian Government's expectations of the barley total realized price associated with the coming pool crop year, and (2) the level of the barley initial price in any year is strongly influenced by the level in the previous year. The mean elasticities computed from the statistical results suggest that a 10-percent decrease in the U.S. corn loan rate will result in a 2.3-percent decrease in BIPYCA and that a 10-percent increase in U.S. corn beginning stocks will result in a 1.6-percent decrease in BIPYCA. The coefficient for the lagged dependent variable is 0.82, and the corresponding elasticity suggests that a 10-percent increase in last period's BIPYCA will result in a 7.8-percent increase in this period's BIPYCA.
The next equation estimated the barley total realized price (BTRPCA) as a function of the U.S. corn price in Canadian dollars (CRPFCA) (table 14, fig. 15). Dummy variables were included in the specification to account for unexplained price increases similar to those in the initial price. The elasticity computed from the results indicates that a 10-percent increase in
Table 10—Canadian wheat initial price
Ordinary least squares estimates
Dependent variable WIPYCA Number of observations 25 Sample period 1961-85 Standard error of regression 6.55022 Sum of squared residuals 901.01 R - squared .98290 Adjusted R - squared .98046 Durbin - Watson statistic 2.0067 Durbin h statistic -.01954 Estimated autocorrelation (Rho) -.00335
Standard Signifi- Mean Variable Coefficient error T-ratio canee level elasticity
ONE 14.2850 4.220 3.385 0.00279 WHLRUS 36.3393 6.106 5.952 .00001 0.77 WTBSUS -0.03501 0.006 -6.128 0 -.36 WIPYCA[-1] .46080 .103 4.490 .00020 .44
Variable descriptions:
WIPYCA CWB wheat initial price, No. 1 CWRS C$/mt WHLRUS U.S. wheat loan rate US$/bu WTBSUS U.S. wheat, total beginning stocks, June-May million bu
31 Figure 10 Wheat Offboard Price, Western Canada
Canadian dollars per metric ton 160
140 Actual 120
100
80
60
40
20 J I I L 1963 65
Figure 11 CWB Initial Wlieat Price, NQ. 1 CWRS'
Canadian dollars per metric ton 190 170 - ^'^•S 150
130 -
110 -
90 3 /'"r 70 Pf^dicted ^^
50
30 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1961 64 68 72 76 80 84 Pool account
1/ Canada Western Red Spring Wheat, basis In storage. Thunder Bay or Vancouver.
32 the U.S. corn price results in a 9-percent increase in BTRPCA. The Canadian price of hogs (PHOGCA) was estimated as a function of the U.S. seven-market barrows and gilts price in Canadian dollars (BGPM7CCA) in table 15 (fig. 16). A price transmission elasticity of 0.86 was computed from the statistical results, indicating a less-than-perfect degree of price transmission between the two hog sectors.
The last equation estimated the CWB selling quotations price for wheat (WQUOCA) as a function of the U.S. wheat price (WGULFCA) (table 16, fig. 17). An elasticity of price transmission from the United States to the Canadian border was calculated from the statistical results to be 0.91. The CWB wheat export quotation price does not represent a true Canadian export price, since it is a benchmark price announced by the CWB and does not represent actual negotiated prices. The wheat export quotation price can be considered a
Table 11—Canadian wheat total realized price
Ordinary least squares estimates
Dependent variable WTRPCA Number of observations 25 Sample period 1960-84 Standard error of regression 9.0309 Sum of squared residuals 1,875.8 R - squared .97652 Adjusted R - squared .97550 Durbin - Watson statistic 1.1583 Estimated autocorrelation (Rho) .42083
Standard Signifi- Mean Variable Coefficient error T-ratio canee level elasticity
ONE 17.1006 3.730 4.585 0.00013 WGULFCA 0.885728 02864 30.930 0 0.85
Calculated variables:
WTRPCA = WIPYCA -H WAPYCA -H WINPCA -f WFPYCA WGULFCA = (WGULFP - EXSBUS^36.744)*ERCAUS
Variable descriptions:
WTRPCA CWB wheat total realized price. No. 1 CWRS C$/mt WIPYCA CWB wheat initial price. No. 1 CWRS C$/mt WAPYCA CWB wheat adjustment price. No. 1 CWRS C$/mt WINPCA CWB wheat interim price. No. 1 CWRS C$/mt WFPYCA CWB wheat final price. No, 1 CWRS C$/mt WGULFP U.S. season average wheat priée, gulf ports, June-May US$/mt EXSBUS U.S. wheat export subsidy US$/bu ERCAUS Canadian-U.S. exchange rate, Canadian dollar per U.S. dollar, end of period Index
33 ceiling price for the export market, however, since importing nations would never pay above the CWB announced export price. Other studies have computed unit value export price by dividing the value of Canadian wheat exports by export volume. One problem with this approach, however, is that the unit value export price cannot account for changes in the proportions of various grades of wheat and their respective prices from one year to the next.
Model Validation
The goodness of fit of single equation models can be judged or validated by noting if they have correct a priori signs and by analyzing regression statistics such as the R^ and t-statistics. This validation process is far too simple in the case of multi-equation models in which the statistical fit of the complete modeling system and its dynamic structure must be evaluated.
Table 12—Canadian barley offboard price
Ordinary least squares estimates
Dependent variable BOFFCA Number of observations 22 Sample period 1963-84 Standard error of regression 12.1004 Sum of squared residuals 2,635.6 R - squared .89070 Adjusted R - squared .87248 Durbin - Watson statistic 1.0038 Estimated autocorrelation (Rho) .49810
Standard Signifi- Mean Variable Coefficient error T-ratio cance level elasticity
ONE 7.39031 10.06 0.735 0.47208 BIPYCA .245221 .2082 1.178 .25425 0.24 CRPFCA 28.3644 6.533 4.342 .00039 .89 BSUPCA -.00129 .0009 -1.355 .19208 -.23
Calculated variable:
CRPFCA = CRPFUS*ERCAUS BSUPCA = BTBSCA + BPRDCA
Variable descriptions:
BOFFCA Western Canadian feed barley, offboard price C$/mt BIPYCA CWB barley initial price, No. 1 feed C$/mt CRPFUS U.S. corn, season average farm price, October-September US$/bu ERCAUS Canadian-U.S. exchange rate, Canadian dollar per U.S. dollar, end of period Index BTBSCA Canadian barley, total beginning stocks, August-July 1,000 mt BPRDCA Canadian barley, production, August-July 1,000 mt
34 Figure 12 CWB Total Realized Wheat Price, No. 1 CWRS^
Canadian dollars per metric ton 225
200
J 1 1 \ I I L 1960 64 68 72 76 80 84 Pool account
1/ Canada Western Red Spring Wheat, basis in storage, Thunder Bay or Vancouver.
Figure 13 Barley Offboard Price, Western Canada
Canadian dollars per metric ton 140
120 -
Actual 100 -
80
60
40 -
20 1963 Crop year
35 The simultaneous system of equations developed in this report is validated by linking all behavioral equations and identities, dynamically simulating the linked system over the historical period, and graphically and quantitatively evaluating the results.9/ The system is dynamically simulated over the historical period by first using historical values of the lagged endogenous variables in the initial year and then using previous-year model solutions for the lagged endogenous variables in the remaining years. Historical values of the exogenous variables are used throughout the historical simulation period. Once the model has been dynamically simulated, the actual and simulated results are plotted over the historical period to visually inspect the performance of the complete model. Appropriate validation statistics are next computed for the supply and demand behavioral equations to quantitatively assess the complete model's goodness of fit.
9/ See (24, p. 6) for a definition of dynamic simulation and (23, pp. 354-466) for a general discussion of simultaneous models.
Table 13—Canadian barley initial price
Ordinary least squares estimates
Dependent variable BIPYCA Number of observations 21 Sample period 1964-84 Standard error of regression 4.02616 Sum of squared residuals 243.15 R - squared .98664 Adjusted R - squared .98219 Durbin - Watson statistic 1.7363 Durbin h statistic .65476 Estimated autocorrelation (Rho) .13187
Standard Signifi- Mean Variable Coefficient error T-ratio canee level elasticity
ONE 7.24441 2.533 2.860 0.01191 CRLRUS 10.3418 4.214 2.454 .02683 0.23 CTBSUS -.01024 .002 -5.851 .00003 -.16 BIPYCA[-1] .82198 .084 9.723 0 .78 DUM73 20.9770 4.232 4.956 .00017 — DUMBO 43.9840 4.477 9.825 0 —
Variable descriptions:
BIPYCA CWB barley initial price. No. 1 feed C$/mt CRLRUS U.S. corn loan rate, October-September US$/bu CTBSUS U.S. corn total beginning stocks, October-September million bu DUM73 Dummy variable, equals 1 in 1973, 0 elsewhere DUMBO Dummy variable, equals 1 in 1980, 0 elsewhere
36 The excess supply of Canadian wheat was simulated over the historical period by first simulating the endogenously determined price equations (tables 9-16) over the historical period 1968-84 and feeding these prices into the supply and utilization equations (tables 2 and 4-8) and e5q)ort identity (equation 20), which was in turn simulated over the same historical period. The endogenous simulated variables were then plotted against historical data over the simulation period and are presented in figures 18-21. The graphic results reveal that simulated supply and ending stocks track well over the historical period (figs. 18 and 20). Domestic use appears to have rather large errors and tracks poorly over the historical period, but its volume is small relative to that of total supply and ending stocks (fig. 19). Hence, the simulated export identity appears to track reasonably well over the historical period
Table 14—Canadian barley total realized price
Ordinary least squares estimates
Dependent variable BTRPCA Number of observations 22 Sample period 1963-84 Standard error of regression 7.51116 Sum of squared residuals 1,015.5 R - squared .96344 Adjusted R - squared .95734 Durbin - Watson statistic 1.2979 Estimated autocorrelation (Rho) .35105
Standard Signifi- Mean Variable Coefficient error T-ratio cance level elasticity
ONE 6.14688 4.036 1.523 0.14509 CRPFCA 34.7864 1.721 20.210 0 0.90 DUM73 24.5805 7.729 3.180 .00518 ___ DUM81 21.7903 7.829 2.783 .01227
Calculated variables:
BTRPCA = BIPYCA + BAPYCA + BFPYCA CRPFCA = CRPFUS^ERCAUS
Variable descriptions:
BTRPCA CWB barley total realized price. No. 1 feed C$/mt BIPYCA CWB barley initial price, No. 1 feed C$/mt BAPYCA CWB barley adjustment price. No. 1 feed C$/mt BFPYCA CWB barley final price. No. 1 feed C$/mt CRPFUS U.S. corn, season average farm price, October-September US$/bu ERCAUS Canadian-U.S. exchange rate, Canadian dollar per U.S. dollar, end of period Index DUM73 Dummy variable, equals 1 in 1973, 0 elsewhere DUM81 Dun\my variable, equals 1 in 1981, 0 elsewhere
37 Figure 14 CWB Initial Barley Price, No. 1 Feed Barley'
Canadian dollars per metric ton 130
110
90
Actual 70
50 - ^___^ Predicted
30 I I I I I I I I I I L 1964 68 72 76 80 84 Pool account
1/ Baals In stomge. Thunder Bay.
Figure 1S CWB Total Realized Barley Price, No. 1 Feed Barley'
Canadian dollars per metric ton 150
130
110
90
70
50
30 1963 Pool account
1/ Basis In storage. Thunder Bay.
38 due to the good fit and dynamic properties of the price equations and the area response and ending stocks equations.
The next step in the validation process is to analyze statistical measures of the model's ability to duplicate economic and institutional relationships over the historical period. Validation statistics for the mean absolute relative error (MARE) and the percentage turning point error (FTPE) were computed for the model under dynamic simulation.10/ The FTPE was computed with the following formula:
If (AC^^i ~ ACt)/(PR^^;^ - PR^) > 0, TPEt = 0,
else TPEt = 1, for all t = 1,..., n,
PTPE = I (TPEt)/n. t=l
10/ See (18), (23, pp. 360-74), and (24) for indepth discussions on the historical validation of simultaneous equations econometric models.
Table 15—Canadian hog price
Ordinary least squares estimates
Dependent variable PHOGCA Number of observations 26 Sample period 1960-86 Standard error of regression 296.698 Sum of squared residuals 2,112,700 R - squared .9 7695 Adjusted R - squared .97599 Durbin - Watson statistic .89089 Estimated autocorrelation (Rho) .55455
Standard Signifi- Mean Variable Coefficient error T-ratio cance level elasticity
ONE 622.384 135.8 4.582 0.00012 BGPM7CCA 108.373 3.398 31.891 0 0.86
Calculated variables:
BGPM7CCA=BGPM7C'«fERCAüS
Variable descriptions:
PHOGCA Canadian price index 100 hogs, dress basis, Winnipeg C cents/cwt BGPM7C U.S. barrows and gilts price, seven markets US$/cwt ERCAUS Canadian-U.S. exchange rate, Canadian dollar per U.S. dollar, end of period Index
39 where:
AC = historical observation, PR = predicted value, TPE = turning point error, and PTPE = percentage turning point errors.
The statistical results of the MARE and PTPE for the supply, demand, export, and price equations are presented in table 17. Food use has the lowest MARE of 0 01, and wheat exports and the barley offboard price have the highest MARE'S of 0.13 and 0.15, respectively. The PTPE statistics indicate that the Canadian pork price, the wheat and barley offboard prices, and the barley total realized price have the lowest PTPE's, between 11.8 and 17.6 percent, whereas wheat exports and wheat initial, total realized, and export prices have the highest PTPE, between 41.2 and 58.8 percent. These results reveal that wheat exports have the highest combined MARE and PTPE. The export equation reflects the combined effects of the area planted, domestic use, and ending stocks equations, which are in turn affected by the price equations.
Table 16—Canadian wheat export price
Ordinary least squares estimates
Dependent variable WQUOCA Number of observations 25 Sample period 1960-84 Standard error of regression 9.65845 Sum of squared residuals 2,145.6 R - squared .98046 Adjusted R - squared .97961 Durbin - Watson statistic 1.4100 Estimated autocorrelation (Rho) .29502
Standard Signifi- Mean Variable Coefficient error T~i catio canee level elasticity
ONE 12.3618 3.989 3 .099 0.00506 _-.. WGULFCA 1.0A053 .03063 33 .975 0 0.91
Calculated variables:
WGULFCA = (WGULFP - EXSBUS*36.744)*ERCAUS
Variable descriptions:
WQUOCA CWB wheat selling quotations, basis in storage Thunder Bay or St. Lawrence C$/mt WGULFP U.S. season average wheat price, gulf ports, June-May US$/mt EXSBUS U.S. wheat export subsidy US$/bu ERCAUS Canadian-U.S. exchange rate, Canadian dollar per U.S. dollar, end of period Index
40 Figure 16 Hog Price Index, Winnipeg, Canada
Canadian dollars per hundredweight 85
75
65 Actual
55
45
35
25 r.
15 I I J L J \ I I J L J \ L 1960 65 70 75 80 85 Year 1/ Average price, dreesed. Index 100.
Figure 17 CWB Wlieat Export Quotations^
Canadian dollars per metric ton 250
200
J J \ \ I L J L 1960 64 68 72 76 80 84 Crop year
1/ Averege. No. 1 Canada Western Red Spring. 13.5 percent. Basis In storage. Thunder Bay or Vancouver.
41 Rgure 16 Simulated Wheat Supply, Canada^
Million metric tons 42
38 -
34
30
26 -
22 1968
1/ Predicted values determined under dynamic simulation.
Figure 19 Simulated Wheat Domestic Use, Canada^
Million metric tons 6.0
5.5
5.0
4.5
4.0 1968
1/ Predicted values determined under dynamic simulation.
42 20 Simulated Wheat Ending Stoclcs, Canada^
Million metric tons 30
26
22
18
14
10
1968
1/ Predicted values determined under dynamic simulation.
Figure 21 Simuiated Wlieat Exports, Canada^
Million metric tons 22
1/ Predicted values determined under dynamic simulation.
43 Improvements in any of these equations should improve the performance of the export identity. Additional improvements should be directed toward the wheat initial, total realized, and export prices, and the barley offboard price.
Elasticity of Canadian Wheat Excess Supply
An important concern of U.S. policyniakers is estimates of the elasticity of excess supply of export competing countries with respect to U.S. prices. For example, an empirical estimate of such an elasticity for Canadian wheat could provide policymakers with the response of Canadian wheat exports to the recent drop in U.S. crop loan rates. Several methods can be used to compute excess supply and demand elasticities (11). Bredahl and others calculated the elasticity of export demand facing the United States by using differential calculus (2). Problems with this methodology are that the elasticities are either point elasticities or are computed at the mean of the historical data and ignore the dynamics of simultaneous equation modeling systems. Dynamic elasticities were computed in this report for Canadian wheat exports using the complete Canadian wheat excess supply model.11/
Dynamic elasticities were computed by dynamically simulating the model from 1985 and forward under, alternative assumptions. All exogenous and the initial
11/ For an interesting discussion on dynamic elasticities and multipliers, see (16, pp. 8-11) and (23, pp. 391-401).
Table 17—Validation statistics, 1968-84
Variable : MARE 1/ PIPE 2/ description
Wheat area planted : 0.095 0.294 Wheat food use : .010 .235 Wheat feed use : .107 .235 Wheat seed use : .093 .235 Wheat total ending stocks : .083 .235 Wheat exports ; .125 .412 Wheat offboard price .091 .176 Wheat initial payment .054 .588 Wheat total real- ized price : .069 .412 Barley offboard price : .146 .176 Barley initial : payment : .060 .353 Barley total real- : ized price : .090 .176 Pork price : .047 .118 Wheat export price : .056 .412 1/ MARE is the mean absolute relative error. 2/ PTPE is the percentage of times the model misses turning point in the historical data.
44 level of lagged endogenous variables were fixed at 1985 levels. U.S. price linkages were developed that linked the U.S. loan rates to U.S. season average farm prices and the wheat gulf ports price. The following equation was used to link the U.S. wheat gulf ports price to the U.S. wheat season average farm price:
WGULFP^. = 4.99131 + 42. 7953*WHPFUS,
where:
WGULFP = U.S. wheat price, gulf ports, and WHPFUS = U.S. wheat season average farm price.
U.S. wheat and corn farm prices were assumed to be a fixed percentage of the respective loan rates as existed in 1985. This assumption was made to avoid the possibility of U.S. market prices falling below the loan rate. The inclusion of a U.S. wheat component that endogenously determines U.S. wheat prices should solve this problem and allow for a more complete price adjustment. The inclusion of this component, however, is beyond the scope of this report.
The price linkages were incorporated, and the initial lagged endogenous variables were fed into the Canadian wheat submodel. An export baseline was computed by allowing the endogenous variables to solve dynamically through time. The Canadian wheat export baseline declined from 14.6 mmt and settled to 6.2 mmt over the 40-year simulation period (table 18). Three alternative simulations were then made under sustained shocks for U.S. wheat and corn loan rates and the Canadian-U.S. exchange rate. Dynamic elasticities were then computed by dividing the percentage change in exports under the shocked simulations from the baseline by the percentage change in the respective shocked exogenous variable. The effect of the three shocked exogenous variables on the Canadian wheat submodel is complex because of the dynamic and recursive nature of the linked system of equations. Therefore, the quantitative effect of the shocked exogenous variables on prices, supply, demand, and exports will be explained via a graphic presentation of the conceptual model presented earlier in this report. Table 18 presents the time paths for exports resulting from the shocks and the computed elasticities.
Simulation I involved a 20-percent drop in the U.S. wheat loan rate from $3.30 per bushel to $2.40. The result was a time path for exports that originated at a lower level and declined more rapidly than the baseline. The effect of a change in the U.S. wheat price on the Canadian wheat submodel is illustrated by the conceptual model presented in figure 22. The world market is shown in the upper left panel where U.S. wheat excess supply ES^g is equated with the excess demand from the rest-of-the-world ED^^^ at the world market clearing price P^s- This component is exogenous to the Canadian wheat submodel, which is shown in the lower and upper right panels. Canadian wheat excess supply ES(P^.)^ is equal to Canadian wheat supply S^ less domestic demand D^ at the Canadian price P^. The U.S. wheat price P^g is defined as the world wheat reference price and is transmitted into the Canadian wheat sector via price transmission equations which, when substituted into ES(P^) yields a Canadian excess supply function in U.S. dollars ESCP^g)^. A decrease in the U.S. wheat price from P^s to P^g» will result in a decrease in Canadian wheat prices from P^. to P^* and a decrease in area planted and, hence, supply from Ob to Oa. Feed use and stocks increase in response to the lower wheat prices, resulting in an increase in domestic use
45 Table 18—Computation of the dynamic elasticities of Canadian wheat exports \J
: Simulation I 2/ : Simulation II 1/ : Simulation III 4/ : Canadian wheat export elasticity ¡Canadian : U.S. ¡Canadian : U.S. : Canadian : Export : wheat : wheat : wheat : corn : wheat : Exchange :U.S. wheat : U.S. corn : Exchange Year : baseline ! >/:exports : loan : exports : loan : exports : rate : loan rate : loan rate : rate
1,000 mt 1,000 mt C$/mt 1,000 mt C$/mt 1,000 mt C$/mt
1985 : 14,570 11,716 2.64 15,248 2.04 13,704 1.118 0.979 -0.233 0.297 1986 : 14,425 10,856 2.64 15,535 2.04 13,468 1.118 1.237 -.385 .332 1987 : 13,992 9,698 2.64 15,601 2.04 12,668 1.118 1.534 -.575 .473 1988 : 13,363 8,493 2.64 15,479 2.04 11,651 1.118 1.822 -.792 .641 1989 : 12,629 7,346 2.64 15,223 2.04 10,597 1.118 2.092 -1.027 .805 1990 : 11,863 6,300 2.64 14,888 2.04 9,598 1.118 2.345 -1.275 .955
1991 : 11,116 5,370 2.64 14,520 2.04 8,695 1.118 2.585 -1.531 1.089 1992 : 10,419 4,557 2.64 14,149 2.04 7,901 1.118 2.813 -1.790 1.209 1993 : 9,790 3,856 2.64 13,797 2.04 7,215 1.118 3.031 -2.046 1.315 1994 9,234 3,256 2.64 13,475 2.04 6,631 1.118 3.237 -2.296 1 .410 1995 8,752 2,748 2.64 13,188 2.04 6,136 1.118 3.430 -2.534 1.494 1996 8,339 2,320 2.64 12,938 2.04 5,721 1.118 3.609 -2.757 1.570 1997 7,989 1,962 2.64 12,722 2.04 5,374 1.118 3.772 -2.963 1.636 1998 7,693 1,662 2.64 12,539 2.04 5,085 1.118 3.920 -3.150 1.695 1999 7,446 1,413 2.64 12,385 2.04 4,845 1.118 4.051 -3.317 1.746 2000 7,239 1,206 2.64 12,255 2.04 4,646 1.118 4.167 -3.465 1.791
2001 7,067 1,035 2.64 12,147 2.04 4,482 1.118 4.268 -3.594 1.829 2002 . 6,925 893 2.64 12,057 2.04 4,345 1.118 4.355 -3 .705 1.862 2003 : 6,807 776 2.64 11,982 2.04 4,233 1.118 4.430 -3.801 1.891 2004 : 6,710 680 2.64 11,920 2.04 4,140 1.118 4.494 -3.883 1.915 2005 : 6,629 600 2.64 11,869 2.04 4,064 1.118 4.548 -3.952 1.935 2006 : 6,563 534 2.64 11,827 2.04 4,001 1.118 4.593 -4.011 1.952 2007 : 6,508 480 2.64 11,792 2.04 3,949 1.118 4.631 -4.060 1.966 2008 : 6,463 436 2.64 11,764 2.04 3,907 1.118 4.663 -4.101 1.978 2009 : 6,426 399 2.64 11,740 2.04 3,871 1.118 4.689 -4.135 1.988 2010 : 6,396 369 2.64 11,721 2.04 3,843 1.118 4.711 -4.163 1.996
2011 : 6,371 344 2.64 11,705 2.04 3,819 1.118 4.730 -4.187 2.003 2012 : 6,350 324 2.64 11,692 2.04 3,799 1.118 4.745 -4.206 2.008 2013 : 6,333 307 2.64 11,681 2.04 3,783 1.118 4.757 -4.222 2.013 2014 : 6,319 293 2.64 11,672 2.04 3,770 1.118 4.768 -4.235 2.017 2015 : 6,308 282 2.64 11,665 2.04 3,759 1.118 4.776 -4.247 2.020 2016 : 6,298 273 2.64 11,659 2.04 3,750 1.118 4.783 -4.256 2.023 2017 : 6,290 265 2.64 11,654 2.04 3,743 1.118 4.789 -4.263 2.025 2018 : 6,284 259 2.64 11,650 2.04 3,737 1.118 4.794 -4.269 2.027 2019 : 6,279 254 2.64 11,646 2.04 3,732 1.118 4.798 -4.274 2.028 2020 : 6,274 249 2.64 11,644 2.04 3,728 1.118 4.801 -4.278 2.029
2021 : 6,271 246 2.64 11,641 2.04 3,724 1.118 4.804 -4.282 2.030 2022 : 6,268 243 2.64 11,639 2.04 3,722 1.118 4.806 -4.285 2.031 2023 : 6,266 241 2.64 11,638 2.04 3,719 1.118 4.808 -4.287 2.032 2024 : 6,264 239 2.64 11,637 2.04 3,717 1.118 4.809 -4.289 2.033 2025 : 6,262 237 2.64 11.636 2.04 3,716 'l .118 4.811 -4.291 2.033 mt = metric tons; C$ = Canadian dollar. 1/ Elasticities of Canadian wheat exports with respect to the U.S. wheat and corn loan rates and the Canadian-U.S. exchange rate. 2/ Simulation of a sustained 20-percent drop in the 1985 U.S. wheat loan rate, holding all other exogenous variables constant at 1985 levels. 3/ Simulation of a sustained 20-percent drop in the 1985 U.S. corn loan rate, holding all other exogenous variables constant at 1985 levels. 4/ Simulation of a sustained 20-percent drop in the 1985 Canadian-U.S. exchange rate, holding all other exogenous variables constant at 1985 levels. 5/ Simulated Canadian wheat export baseline holding all exogenous variables constant at 1985 levels.
46 from Oc to Od. The combined effects of supply and domestic demand result in a decrease in Canadian wheat exports from Of to Oe. The empirical results of simulation I reveal that a decrease in the U.S. wheat loan rate results in a decrease in U.S. market prices and a decrease in Canadian wheat offboard, initial, total realized, and export prices. This results in a longrun contraction in Canadian wheat exports relative to the baseline. Hence, the elasticity of Canadian wheat exports with respect to the U.S. wheat loan rate is positive and is 1.0 in the shortrun, 2.1 in the intermediate run (5 years), and 4.8 in the longrun.
The second simulation, noted simulation II in table 18, involves a 20~percent drop in the U.S. corn loan rate from $2.55 per bushel to $2.04. The results indicate an expansion in the export time path from the baseline. These results are interpreted via the conceptual model presented in figure 23. U.S. corn prices are linked to Canadian barley prices in the model. A drop in U.S. corn prices is transmitted into the Canadian crop sector, resulting in a drop in barley prices. A decrease in barley prices causes an expansion in area planted to wheat as producers shift from barley to wheat production on the
Figure 22 Effect of Lower U.S. Wheat Prices on the Canadian Wheat Submodei
World market Canadian market ES(Pc)c
Price transmission
ES(Pc)c
0 a b Q 0 cd 1/ Price transmission from U.S. to Canadian wheat prices.
47 margin. Canadian wheat supply then shifts from S^ to S^'. Feed demand decreases as feed use is substituted away from wheat to barley, resulting in a shift in domestic wheat demand from D^ to D^'. The combined effect of shifts in the supply and demand curves is a shift in the Canadian wheat excess supply curve from ES(Pe)c ^o ES(Pe)c* and an expansion in Canadian wheat exports from Oa to Ob. The empirical results of simulationll indicate that a decrease in the U.S. corn loan rate results in a decrease in the U.S. corn market price, a decrease in Canadian barley offboard, initial, and total realized prices, no change in Canadian wheat prices, and a longrun expansion in Canadian wheat exports relative to the baseline. The elasticity of Canadian wheat exports with respect to the U.S. com loan rate is negative and is -0.2 in the shortrun, -1.0 in the intermediate run (5 years), and -4.3 in the longrun. The third simulation, noted simulation III in table 18, involves a 20-percent drop in the Canadian-U.S. exchange rate. This drop appreciates the Canadian dollar (C$) relative to the U.S. dollar (US$) since more U.S. dollars can be
Figure 23 Effect of Lower U.S. Corn Prices on the Canadian Wheat Submodel
U.S. corn-Canadian barley price transmission^
ES(Pp)c^c
1/ Price transmission from U.S. corn to Canadian barley prices.
48 purchased from the sale of each Canadian dollar.12/ The effect of an appreciation of the Canadian dollar relative to the U.S. dollar on the Canadian wheat submodel is conceptualized in figure 24. The Canadian wheat excess supply function ES(P^)^ in the lower panel is a function of the Canadian price P^.. When the price transmission equation is substituted into ES(Pc)c» the result is a Canadian wheat excess supply function in U.S. dollars ES(Pus)c- ^ appreciation in the Canadian dollar relative to the U.S. dollar results in a decrease in the Canadian-U.S. exchange rate which lowers Canadian prices relative to U.S. prices. This results in a shift from ^^^^us^c ^o ^Si^us^c*- T^® effect of this change on the Canadian wheat sector is a drop in Canadian wheat prices from P^ to P^', a decrease in area planted and, hence, supply from Ob to Oa, and an increase in domestic use and ending stocks from Oc to Od. The combined effect of changes in domestic supply and demand is to decrease Canadian wheat exports from Of to
12/ For a discussion of the relation between exchange rates and trade, see Houck (12. pp. 158-73).
Figure 24 Effect of an Appreciation in the Canadian Doliar Relative to tlie U.S. Doiiar on tlie Canadian Wlieat Submodel
World market Canadian market us$
Price transmission^
ES(Pc)c
0 a b Q 0 c 1/ Price transmission from U.S. to Canadian wlieat prices.
49 Oe. The empirical results from simulation III confirm the conceptual presentation in figure 24. All prices declined from the baseline as a result of the change in the exchange rate. The exception is the wheat and barley initial prices which were not found statistically related to the exchange rate. The combined effect of a drop in the Canadian-U.S. exchange rate then was to reduce exports in the longrun from the baseline. The elasticities computed from the results in table 18 are 0.3 in the shortrun, 0.8 in the intermediate run, and 2.0 in the longrun.
The elasticities computed under dynamic simulation are summarized below in table 19.
Table 19—Dynamic elasticities of Canadian wheat exports 1/
Elasticity of Canadian wheat exports
U.S. wheat U.S. com Canadian-U.S. Item loan rate loan rate exchange rate
Shortrun 2/ 0.979 -0.233 0.297
Intermediate run 3/ 2.092 -1.027 .805
LonRrun 4/ 4.811 -4.291 2.033 1/ Elasticities of Canadian wheat exports with respect to the U.S. wheat and com loan rates and the Canadian-U.S. exchange rate. 2/ One year. 3/ Five years. 4/ A sufficient time period for the solution to stabilize.
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(32) Wilson, Charles F. Canadian Grain Marketing. Winnipeg: Canadian International Grains Institute, 1979.
52 t- ON vo T- ^ t— o OO CM o t^ CM OO t^ CM OO vo vo ^ t- CM CM o OO ON o ■í3 c\i vo on in in OO in C7N C7N in t- <7N o o ON r- vo t- in o ▼- r- in OO 00 in 4> ^ C\J o ONOO vo C7NVO CTN^ jn- en ^ tr- OO t- in T- CM t- o OO-^ ^ oooo O H o ^ vo CNJ OO r- OO t- in t- vo ^ o vo OO in t- OO OO CM o OO vo vo o r- 00 CM oj OO oj on OO OO m -=3" OO OO OO CM CM CM OO OO OO OO OO OO OO OO OO 00
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Sources: (3_) and Agriculture/Natural Resources Division, Statistics Canada. 54 Appendix table 3—Canadian all wheat ending stocks, 1960-85 • Crop : On : Commercial • year y : farms ¡ ' positions : Total • : J ,000 metric tons 1960/61 i 4,652.5 11,903.9 16,556.5 1961/62 : 1,610.4 9,032.6 10,643.0 1962/63 : 1,760.9 11,500.0 13,260.8 1963/64 : 3,283.3 9.,220.7 12,504.0 1964/65 : 2,969.2 10,993.1 13,962.4 1965/66 : 2,721.6 8,712.4 11,434.0 1966/67 : 5,443.2 10,117.5 15,560.6 1967/68 : 6,613.4 11,689.5 18,302.9 1968/69 : 10,129.7 13,053.5 23,183.2 1969/70 : 14,770.0 12,682.3 27,452.3 1970/71 : 10,745.3 9,235.2 19,980.6 1971/72 !; 8,477.7 7,409.7 15,887.4 1972/73 : 3,129.8 6,814.9 9,944.7 1973/74 ! 2,204.5 7,884.5 10,089.0 1974/75 ! 1,632.9 6,404.7 8,037.6 1975/76 : 1,578.3 6,400.7 7,979.0 1976/77 : 7,157.6 6,160.5 13,318.1 1977/78 : 5,007.5 7,107.7 12,115.2 1978/79 : 8,953.8 5,956.9 14,910.7 1979/80 : 4,272.7 6,448.2 10,720.9 1980/81 : 1,585.0 6,925.2 8,510.2 1981/82 : 3,560.0 6,152.8 9,712.8 1982/83 : 2,010.0 7,973.3 9,983.3 1983/84 : 1,735.0 7,454.7 9,189.7 1984/85 : 1,080.0 6,518.0 7,598.0 1985/86 2/ : 770.0 7.681.0 8,451.0 1/ August-July crop year. 2/ Agriculture/Natural Resources Division, Statistics Canada. Source: (27)* 55 Appendix table 4—Schedule of Canadian Viheat Board payments for wheat, 1960-85 1/ : Initial ! Adjust- :: plus ! Total Pool : Initial : ment : :adjustment ! , Interim : Final !: realized account : payment : payment ,! payment ! payment : payment : price Canadian dollars per metric ton 1960/61 : 51.44 0 51.44 3.67 10.84 65.95 1961/62 : 51.44 3. 67 55.11 0 15.07 70.18 1962/63 : 55.12 0 55.12 0 13.74 68.86 1963/64 : 55.12 0 55.12 0 17.42 72.54 1964/65 : 55.12 0 55.12 0 14.22 69.34 1965/66 : 55.12 0 55.12 0 18.26 73.38 1966/67 : 55.12 0 55.12 0 17.89 73.01 1967/68 ! 62.46 0 62.46 0 4.19 66.65 1968/69 : 62.46 0 62.46 0 0 62.46 1969/70 ! 55.12 0 55.12 2.68 3.93 61.73 1970/71 :. 55.12 0 55.12 0 6.28 61.40 1971/72 ! 53.65 0 53.65 0 4.99 58.64 1972/73 ! : 53.65 11. 02 64.67 0 14.47 79.14 1973/74 !: 82.67 55. 12 137.79 0 30.42 168.21 1974/75 : 82.67 55. 12 137.79 0 26.60 164.39 1975/76 : 82.67 55. 12 137.79 0 8.49 146.28 1976/77 : 110.23 0 110.23 0 6.92 117.15 1977/78 : 110.23 0 110.23 0 10.07 120.30 1978/79 : 110.23 18.37 128.60 0 31.93 160.53 1979/80 : 128.60 27. 56 156.16 0 40.27 196.43 1980/81 : 156.16 40.34 196.50 0 25.62 222.12 1981/82 : 174.50 0 174.50 0 25.12 199.62 1982/83 : 174.50 0 174.50 0 17.84 192.34 1983/84 : 170.00 0 170.00 0 23.98 193.98 1984/85 : 170.00 0 170.00 0 16.37 186.37 1985/86 : 160.00 0 160.00 0 NA NA 1986/87 : 130.00 0 130.00 0 NA NA NA = Not available. 1/ Canada Western Red Spring Viheat, basis in storage, Thunder Bay or Vancouver. Sources: (3_) and (5.). 56 Appendix table 5—Canadian wheat and barley wholesale prices, 1960-85 Víheat : Barley : Wheat : Víheat Crop : Offboard : offboard ! : mill :: export year 1/ ! feed price 2/ : feed price 2/ .: price 4/.: price 5/ Canadian dollars per metric ton 1960/61 ¡: 38.25 NA 61.73 61.73 1961/62 !; 45.03 NA 69.81 69.81 1962/63 :: 47.97 NA 72.02 72.02 1963/64 ! 48.50 36.91 74.58 74.59 1964/65 : 48.50 38.81 72.75 72.75 1965/66 ! : 47.40 40.97 73.49 73.49 1966/67 : 52.54 43.27 77.90 77.90 1967/68 : 52.54 42.26 71.65 71.65 1968/69 : 41.89 35.57 71.65 71.65 1969/70 : 33.07 26.47 71.65 66.51 1970/71 : 35.27 30.45 71.65 65.77 1971/72 : 35.27 30.42 71.65 61.91 1972/73 : 53.65 45.31 110.23 96.50 1973/74 : 117.58 96.06 119.42 201.86 1974/75 : 121.25 109.22 119.42 193.41 1975/76 : 126.00 101.00 119.42 172.14 1976/77 : 93.00 82.00 119.42 123.83 1977/78 : 81.00 65.00 119.42 137.20 1978/79 : 91.00 67.00 151.54 177.32 1979/80 : 116.00 102.00 183.72 215.38 1980/81 : 155.00 130.00 240.41 246 .62 1981/82 : 147.00 108.00 217.18 214.31 1982/83 : 126.00 83.00 204.05 204.64 1983/84 : 145.00 107.00 213.16 215.29 1984/85 : 143.00 114.00 235.31 235.31 1985/86 : 111.00 94.00 249.12 249.12 NA = Not available. 1/ August-July crop year. 2/ Weighted average price farmers received for nonboard feed wheat, Western Canada. 3/ Weighted average price farmers received for nonboard feed barley, Western Canada. 4/ Sources: (26.) and Mary Anne Normile, ATAD, ERS, USDA. 5/ Canadian Wheat Board selling quotations. No. 1 Canada Western Red Spring Wheat, 13.5 percent, average, basis in storage. Thunder Bay or St. Lawrence. Sources: (2_) and (26). 57 Appendix table 6—Schedule of Canadian Wheat Board payments for barley, 1960-86 U • «* :Initial plus: : Total Pool : Initial : :Adjustment : adjustment : Final : realized account : payment :: payment : payment : payment ! price Canadian dollars per metric tons 1963/64 ! 39.96 0 39.96 10.47 50.43 196V65 : 39.96 0 39.96 14.47 54.43 1965/66 : 39.96 0 39.96 15.11 55.07 1966/67 ! : 39.96 0 39.96 15.52 55.48 1967/68 : 44.55 0 44.55 1.75 46.30 1968/69 : 44.55 0 44.55 0 44.55 1969/70 : 37.20 0 37.20 1.01 38.21 1970/71 : 37.20 4.59 41.79 0 41.79 1971/72 : 37.20 0 37.20 0 37.20 1972/73 : 39.50 4.13 43.63 23.63 67.26 1973/74 : 64.30 34.45 98.75 20.31 119.06 1974/75 : 71.19 27.56 98.75 8.30 107.05 1975/76 : 73.49 13.78 87.27 16.79 104.06 1976/77 : 80.38 0 80.38 11.12 91.50 1977/78 : 80.38 0 80.38 8.01 88.39 1978/79 : 76.00 3.67 79.67 11.41 91.08 1979/80 : 80.38 9.19 89.57 17.90 107.47 1980/81 : 124.01 6.99 131.00 15.55 146.55 1981/82 : 124.00 0 124.00 7.07 131.07 1982/83 : 110.00 0 110.00 0 110.00 1983/84 : 95.00 15.00 110.00 28.02 138.02 1984/85 : 110.00 15.00 125.00 6.30 131.30 1985/86 : 110.00 0 110.00 NA NA 1986/87 : 80.00 NA NA NA NA NA = Not available 1/ No. 1 Canada Western Feed Barley, basis in storage, Thunder Bay or Vancouver. Sources: (3_) and (5.). 58 Appendix table 7—Canadian macroeconomic data, 1960-84 Personal : : Canadian-U.S. ¡ disposable : Population ! exchange ;! Consumer Year ¡ income : i/ : rate 2/ ; price index : Million Canadian Canadian 1,000 dollar per Idex: dollars people U.S. dollar 1980=100 I960 : 26,567 17,870 0.9960 35.3 1961 ! ! 26,904 18,238 1.0434 35.6 1962 : 29,340 18,583 1.0772 36.0 1963 : 31,168 18,931 1.0806 36.6 1964 : 33,049 19,290 1.0738 37.3 1965 ;: 36,263 19,644 1.0750 38.2 1966 : 39,901 20,015 1.0838 39.6 1967 : 43,123 20,378 1.0806 41.1 1968 : 46,820 20,701 1.0728 42.7 1969 : 50,911 21,001 1.0728 44.7 1970 : 54,009 21,297 1.0112 46.1 1971 : 59,943 21,568 1.0022 47.5 1972 : 68,100 21,802 .9956 49.7 1973 :: 79,719 22,043 .9958 53.5 1974 : 94,545 22,364 .9912 59.3 1975 !: 110,996 22,697 1.0164 65.7 1976 : 125,309 22,993 1.0092 70.7 1977 : 138,307 23,273 1.0944 76.3 1978 : 156,070 23,517 1.1860 83.2 1979 : 175,956 23,747 1.1681 90.7 1980 : 199,740 24,043 1.1947 100.0 1981 : 237,682 24,342 1.1859 112.5 1982 ! 262,785 24,632 1.2294 124.6 1983 ! 275,806 24,885 1.2444 131.9 1984 : 299,903 25,124 1.3214 137.6 1985 : 323,401 25,360 1.3975 143.1 jy As of June 1 . 2/ End of period. Sources: (12.), ( 1Ü_), and (21). 59 APPENDIX 2—THEORETICAL SUPPLY MODEL A theoretical model of crop supply will be derived in this section for the Canadian wheat submodel. The primary objective will be to capture the decisionmaking process of crop producers so a static or timeless analysis will be made via a neoclassical model. Supply response is a relation between quantity and prices. For agricultural crops, supply can be approximated via area and yield response functions. Land is an input in the production process and, hence, an input demand function for land will be derived in this section for a representative crop producer under conditions of profit maximization. First, let us define the following production function: F^Cx^^-j , . . . , Xi„^; Zi^,..., Ziq; a^) = q^, (21) where: F¿= production of crop i, xj^j = the level of input j used in the production of crop i that is under the producers control, ^ik " ^^^ level of input k used in the production of crop i that is not under the producers control, a¿ = hectares planted to crop i, and i = l,...,n; j = l,...,m; k = l,...,q. Inputs Xj^j and a¿ are assumed to be under the direct control of the producer and represent decisionmaking variables whose levels are determined under profit-maximizing conditions. An example of inputs xij would be fuel, fertilizer, chemicals, and seed. Variables such as Zi]^, however, are not under the control of the producer and are assumed exogenous. Examples of ^ik would be rainfall, évapotranspiration, pests, and soil drainage. The following assumptions are made concerning F^: (i) there is a smooth causal relation between outputs F^ and inputs x^j , z^^ç, and a^, or rather F^ is continuously differentiable for all i = 1,...,n, (ii) F^ is concave in XJ^J, ZJ^^^, and a^^, and (iii) Xij > 0, a^ > 0. Given equation (21), one can define the objective of the profit-maximizing Canadian wheat producer who faces perfectly competitive input markets as follows: n n m n Max ir = J: EPi^Mi -II Wj*Xij*ai - r I a^, (22) i=l i=l j=l i=l s.t. Mi - Fi(*) - INVi < 0, Mi < DEi, for all i = l,...,n; j = l,...,m. 60 where: EPi = expected CWB initial plus final payments, or stated alternatively, the expected realized price of crop i, WJ = price of a unit of input j, r = rate of land rent per hectare, M^ = deliveries of crop i to the CWB, INVi = beginning farm stocks of crop i, and DEi = expected CWB delivery entitlement of crop i. The first restriction implies that the producer cannot market more than production plus beginning stocks. The second restriction implies that marketings cannot exceed the producer's expected marketing quota. Hence, the producer maximizes profits subject to the 2n constraints by choosing levels of n inputs ai and m inputs x^j, which implicitly determines levels of the n outputs Fi- The model suggests that if the marketing quota is expected to be nonbinding (DE > M = F + INV), input levels are determined under profit- maximizing conditions. If the marketing quota is, in fact, binding (DE = M = F + INV) then input levels may differ from those under profit-maximizing conditions. The model also suggests that as beginning stocks increase and the marketing quota decreases, input and, hence, output levels would adjust downward to meet the two marketing constraints. Next, the following Lagrangian function is formed: n n m n n L = I EPi^Mi -II Wj*Xij ~ r X ai + I yi^[Fi(*) + INVi - Mi] (23) i=l i=l j=l i=l i=l + I Xi*[DEi - Mi], for all i = 1,...,n; j = 1,...,m. i=l The Kuhn-Tucker conditions are derived as follows (15, pp. 49-62): aL aF(*)i - r + Pi*- < 0, (24) daj aa4 aL aF(*)i r + pi*- *ai = 0, (25) aa^ da; aL aF(*)i = - wj + pi*^ < 0, (26) ax ax ij aL aF(*)i _*Xij - W4 -f Pi*, *xij = 0, (27) ix ij ax ij aL = EPi - Pi - \i < 0, (28) aM¡ 61 dL _*Mi = [EPi - Mi - Xi]*Mi = 0. (29) dL = F(*)i + INVi - Mi > O. (30) dL —-*Vi = [F(*)i + INVi - ^0*Vi = O, (31) opi dL = DEi - Mi > O (32) 3XÏ dL _-*Xi = tDEi - Mi3*Xi = 0. (33) ai, Xij, Mi, Vi, and Xi > O for all i = 1,...,n; j = l,...,m. These conditions, equations (24)-(33), are necessary and sufficient for a local maximum if and only if the Lagrangian function, equation (23), is concave with respect to ai, x^2 and H^.l/ This condition is guaranteed since Fi is concave by assumption (ii) and the objective function and the second constraint are linear. From equation (28) and the complimentary slackness conditions, the following holds strictly if Mi>0 for all i = l,...,n: EPi - Xi = Pi, (3^j where y i is the minimum price needed by the producer to expand production of crop i by one unit, otherwise known as the supply inducing price, and Xi is the shadow price on the expected delivery entitlement quota (25). Relevant conclusions can be drawn from equation (34) concerning the supply inducing price. From equations (32) and (33) and the complimentary slackness conditions one can conclude that: (1) the expected delivery entitlement DEi ^^ binding, or DEi = M-, if Xi > 0 for all i = l,...,n. Therefore, the supply inducing price would be less than the observed CWB price (EP) by the amount Xi and EP4 > 114 . and -^ -^ (2) Xi = 0 if the expected delivery entitlement DEi ^^ not binding, or Mi < DEi ^^^ all i = l,...,n. The CWB price then equals the supply inducing price or EPi = ^i. 1/ A further requirement is that vectors a and x exists that satisfies the Slater conditions (15, pp. 57-58). 62 Next, assuming a^, x^j and Mj^ are strictly greater than zero for all i = l,...,n and j = l,...m, substituting equation (34) into equations (24) anda (26) yields: aFi(*) (EPi - \i)* = r, (35) dai aFi(*) (EPi - X^)* = WJ, for all i = l,...,n; j = l,...,m. (36) axij Equation (35) implies that the profit-maximizing producer will employ hectares of crop i up to where the value marginal product of an additional hectare planted equals the cost of renting the hectare of land. Equation (36) suggests that the profit-maximizing producer will employ input j in the production of crop i up to where the value marginal product of an additional unit of input i equals the cost of that input. From the Kuhn-Tucker conditions, selecting any two equations from (35) and dividing one by the other yields: 3Fi 3ai aajç = .„ , =r (37) aPk aai EPi - Xi aa^ Equation (37) suggests that the rate at which land is substituted between crop enterprises is equal to the ratio of the supply inducing prices. Hence, if the price of crop k rises relative to the price of crop i, the profit- maximizing conditions will dictate that land will be substituted away from production of crop i to production of crop k. Also, let us derive the input demand functions. Solving equations (24)-(33) simultaneously yields the following, a* = ai[EP, w, r, INV, DE, z] and (38) ^ij = Xij[EP, w, r, INV, DE, z], (39) where EP is an nxl vector of expected CWB prices, w is an mxl vector of input prices, INV is an nxl vector of beginning stocks, DE is an nxl vector of expected delivery quota's, and z is a qxl vector of inputs z^. Hence, equations (38) and (39) represent the profit-maximizing levels of inputs a^ and x^j for our representative producer. These inputs vary with product and input prices, land rent, beginning stocks, and expected delivery quotas, given some fixed level of z^j^. The aggregate level input demand functions for a particular market is determined by summing equations (38) and (39) over all c producers in the market as follows: 63 = c*a 1» or Ai = Ai(EP, w, r, INV, DE, z) and (40) Xij = c*x*j, or ^ij = Xij(EP, w, r, INV, DE, z), (Al) APPENDIX 3~VARIABLE DESCRIPTION LIST EndoRenous variables BIPYCA CWB barley initial price. No. 1 feed C$/mt BFPYCA CWB barley final price, No. 1 feed C$/mt BOFFCA Canadian barley, offboard price C$/mt BTRPCA CWB barley total realized price, No. 1 feed C$/mt PHOGCA Canadian price index 100 hogs, dress basis, Winnipeg C cents/cwt WAPTCA Canadian wheat, total area planted, August-July 1,000 ha WEXPCA Canadian wheat, total exports, August-July 1,000 mt WFPYCA CWB wheat final price. No. 1 CWRS C$/mt WHFEED Canadian wheat, feed use and loss in handling, August-July 1,000 mt WHFOOD Canadian wheat, food and industrial use, August-July 1,000 mt WIPYCA CWB wheat initial price. No. 1 CWRS C$/mt WOFFCA Canadian wheat, offboard price C$/mt WSEDCA Canadian wheat, seed use, August-July 1,000 mt WTESCA Canadian wheat, total ending stocks, August-July 1,000 mt WTRPCA CWB wheat total realized price. No. 1 CWRS C$/mt WQUOCA CWB wheat selling quotations, basis in storage Thunder Bay or St. Lawrence C$/mt WYLDCA Canadian wheat, yield per planted hectare, August-July mt/ha Exogenous variables BAPYCA CWB barley adjustment price. No. 1 feed C$/mt BGPM7C U.S. barrows and gilts price, seven markets US$/cwt BPRDCA Canadian barley, production, August-July 1,000 mt BTBSCA Canadian barley, total beginning stocks, August-July 1,000 mt CPICA Canadian consumer price index index 1980=100 CRLRUS U.S. com loan rate, October-September US$/bu CROW Transportation costs, Scott, Saskatchewan, to Thunder Bay C$/mt CRPFUS U.S. com, season average farm price, October-September US$/bu CTBSUS U.S. com total beginning stocks, October-September million bu ERCAUS Canadian-U.S. exchange rate, Canadian dollar per U.S. dollar, end of period Index EXSBUS U.S. wheat export subsidy US$/bu FIPFER Farm input price index for fertilizer, Canada, August/July 1981=100 HCBA3C Handling costs for barley. Western Canada C$/mt HCWH3C Handling costs for wheat. Western Canada C$/mt H06NCA Canadian hog numbers, onfarm, July 1 1,000 head PDINCA Canadian personal disposable income million C$ TREND Year: 1960=60, ... , 1985=85 WAPYCA CWB wheat adjustment price. No. 1 CWRS C$/mt WGULFP U.S. season average wheat price, gulf ports, June-May US$/mt WHLRUS U.S. wheat loan rate US$/bu WINPCA CWB wheat interim price. No. 1 CWRS C$/mt WMILCA Canadian wheat, domestic milling price, August-July C$/mt WTBSUS U.S. wheat, total beginning stocks million bu 64 UNITED STATES DEPARTMENT OF AGRICULTURE ECONOMIC RESEARCH SERVICE 1301 NEW YORK AVENUE, NW. WASHINGTON, D. C. 20005-4788