r ~ I:;iW I:.iW 1.0 w lil. 1.0 w W wW J wW .2 11111 W w ~ Ii£ I.r.: W a.: II: ::: w .0 ~ ~ 1.1 ......"" . 1.1 ...""..... I 111111.8 ·1111'1.25 ""'1.4 111111.6 111111.25 11",1.4 111111.6 MICROCOPY RESOLUTION TEST CHART MICROCOPY ~ESOLUTION TEST CHART NATIONAL BUREAU Of STANDAROS-J963-A NATIONAL BUREAU OF STANDAROS-J963-A t~ ~;;;~ms Analysis of Grain Reserves David J. Eaton United States Economics, Technical Bulletin Department of Statistics, and No, 1611 Agriculture Cooperatives ~ervice A SYSTEMS ANALYSIS OF GRAIN RESERVES. By David J. Eaton. International Economics Division; Econumics, Statistics, and Cooperati-.res Service; U.S. Department of Agriculture. Technical Bulletin No. 1611. ABSTRACT The author develops techniques (1) to size and operate grain reserves to achieve multiple public objectives, (2) to assess buffer stock requirements to stabilize supplies, and (3) to evaluate buffer stock reliability. World grain supplies could fall as much as 5.5 percent below trend in 1975-2000 if: there is no grain reserve and if production patterns mimic recent history. There is a tradeoff between the size of a reserve and its ability to provide grain in shortfall years -the more stability desired, the more grain needed in the buffer stock. There is no "optimal" grain reserve; the desired buffer stock will reflect judgments based on the importance of competing public objectives. Keywords: Grain, grain reserves, world food security, systems analysis, demand, time series, mathematical programming, agricultural policy. Washington, D.C. January 1980 FOREWORD The uncertainty of crop production has meant that control of a food reserve could change the stability of prices or even governments. Management of buffer stocks by institutions in a democracy must acco1mt for the interests of many groups. This report develops methods to incorporate production fluctuations and public objectives into grain reserve management techniques. The report is part of a continuing effort of the International Economics Division to assess the impact of w~ather instability and production fluctuations on world grain supply and demand. David Eaton conducted the research under contract with the Economics, Statistics, and Cooperatives Service while at The Johns Hopkins University (he has since moved to the LBJ School of Public Affairs, The University of Texas at Austin). Jared L. Cohon and Charles S. ReVelle, The Johns Hopkins University, and W. Scott Steele, Office of the Secretary of Agriculture, provided general super­ vision of this study. John Murray, formerly with ESCS, provided reviews. i CONTENTS Page StnnIllary iv I. INTRODUCTION 1 Early Grain Reserves .• ~ •....•.•..••••.•.•.. 2 Joseph and the Pharaoh's Dreams ••••••• 2 Li K'o and the Principles of Confucius 3 Issues in Grain Reserves ••••..•.•.......••• 4 The Production Variation Problem ••••••••••• 7 Multiple Goals in Buffer Stock Management 8 Food Security and Supply Stability 9 Price Stabilization ...... iI ••••••• :. _ 0 •• 10 Fanners' and Consumers I Goals ••••••••• 11 A Reserve as an Investment •••••••••••• 12 II. ANALYSES OF GRAIN RESERVES 14 Previous Research ......................... 14 Statistical Analyses •••••••••••••••••• 14 Welfare Theory •....................... 14 Multimarket Simulation •••••••••••••••• 15 Grain Reserve Simulations ••••••••••••• 16 Dynamic Programming Models •••••••••••• 18 Evaluation of Previous Research •••••••••••• 18 Statistical Analyses •••••••••••••••••• 19 Welfare Economics Theory .....•••.••..• 19 S:i1nula tions .......................... 20 Dynamic Programming ...........••••.•.• 20 A Research Agenda ••••••••••••••••••••••••.• 21 III. POTENTIAL TRANSFERABILITY OF WATER RESOURCES THEORY TO GRAIN RESERVES ANALYSIS 28 Characterization of Time Series 28 Reservoir Design •••..••••.••....••.••••••.• 30 Sizing Techniques ........ :'t •• Ii-' •••••• " •• 31 Operating Rules •••••.•••••..•••••••••. 34 How to Assess the Reliability of Results 35 IV. SYNTHESIS OF GRAIN PRODUCTION SERIES 41 Time Series Behavior .•...•••••.•.••...•...• 41 Expected Volume •••••.••.••..••.••. ~ ••• 41 Variance .. 0 ••••••••••••••••••••••••••• 43 Lagged Effects ................. ,~ ..... 43 Deviations of Residuals ••••••••••• , ••• 45 Proof of Unbiasedness of Equation (4-16) 49 Proof of Constant Variance ••••••••••••• 50 Shortfall Patterns ........................ 51 ii V. BUFFER STOCK SIZING METHODS .......... ~ ....... 54 Formulating a lwo-Objective Method •••• < •••• 54 The Constraint Method of Solution Generation 57 A Demand/Price Function ••••.•••• ft ••••••••••• 58 A Price Funct'ion ...•................... 58 An Illustrative Demand Function ••••••• 60 Efficiency ................................ " 61 Benefits •••.••.•.•.•••...••.•.••••.••• 61 Costs of the Reserve 62 Grain Production Costs 65 Net Economic Efficiency Benefits 66 Profitability of the Reserve ••••••••••••••• 67 Price Stability Objectives ••••••••••••••••• 68 Farmers' Obj ectives ...•... "... 'J ........... .. 70 Consumers' Objectives ~ ••••.•••.....•.•....• 72 Computational and Display Issues ••••••••••• 7l. Equilibrium Reserve Sizing ••••••••••••••••• 77 Grain Supply •....•....• c •••••••••••••• 79 Demand for Grains •••••• "••.•••.•.••••• 81 The Equilibrium Cobweb •••••••••••••••• 82 VI. RELIABILITY ANALYSIS 85 Background •••••••.••.••.••.....•••.••.•.••• 86 Derivation of a Cumulative Distribution Function .••............•...•..... 88 Methodology Development ••••••••••••••• 90 Application of the Order Statistics Method •• 92 Use in Policy Analysis ••••••••••••••••••••• 97 VII. OPERATING RULES 99 Selection of C.<I.ndidate Rules 101 Evaluating Rule Effectiveness 103 VIII. AN EMPIRICAL EXAMPLE 105 A Grain Production Generating Function 105 Expected Volume and Variance •••••••••• 106 Lagged Covariance Structure ••••••••••• 109 Grain Production Generation ••••••••••• III The Reserve Sizing Procedure ••••••••••••••• ll2 Buffer Stocks Analysis Results ••••••••••••• ll6 Reserve Size Versus Food Security ll8 Size Versus Reliability Versus Food Security .....................•••. 119 Multidimensional Display of Tradeoffs 121 Comparisons of Results with Joseph's Results 122 iii SUMMARY The author deveJops techniques (1) to size =~d operate grain reserves to achieve multiple public objectives, (2) to assess buffer stock requirements that would stabilize supplies, and (3) to evaluate buffer stock reliability. The techniques are used to find a lower bound on the size of a world buffer stock that would stabilize grain supplies from 1975 to 2000. Grain supplies in a lean year during 1975-2000 could fall as much as 5.5 percent below the historical trend if future production patterns mimic recent behavior and if no grain reserve exists. There is a tradeoff between the size of a reserve and its ability to provide grain during sequential lean years -- the more stability desired, the more grain needed in the buffer stock. There is no "optimal" grain reserve size. Rather, the size of global reserves will reflect judgments based on the importance of competing public objectives. Following a background discussion that focuses upon the intended contributions of the research, the author presents and evaluates several historical analyses of grain reserves. He identifies issues underlying the grain reserve problem, including grain demand, the grain produc­ tion process, and the international trade context of a buffer stock. After presenting mathematical methods an analyst can use in designing buffer stocks, the author generates synthetic grain production futures; formulates reserve sizing models that can incorporate objectives of supply stability, price stability, farmer goals, consumer interests, and net economic benefits; assesses reliability of a buffer stock; and develops ways to ascertain operating rules. iv A Systems Analysis of Grain Reserves David J. Eaton * I. -- INTRODUCTION One of the first acts of any permanent human settlement is likely to be the creation of a grain reserve. Early humans, as hunters and gatherers, moved with the seasons and their prey. Agriculture, and the implicit security of a renewable source of food, led people to settle in one place. The discovery of the buffer stock idea encouraged permanent human settlement. Throughout record:~d human history, a community's grain reserve has served as a source of social, economic, and political power. The role of a reserve in mediating supply and price fluctuation will remain as long as weather can influence the security of food production. Because grain stocks represent a political issue, researchers should explore the impacts of grain reserve policies. Specifically, the objectives are to: Examine multiple objectives which reflect economic and political goals, Design a reserve to stabilize supplies through a series of back-to-back lean years as well as isolated shortfall years, Characterize how grain production fluctuates over time, Include supply and demand interactions through a market, and Develop nonparametric procedures to assess result reliability. *The author is an assistant professor of public affairs with the Lyndon B. Johnson School of Public Affairs at the University of Texas at Austin. 1 EARLY GRAIN RESERVES Both Joseph (the Biblical figure) and Li K'o (who lived in China in the 12th Century B.C.) needed to stabilize supplies of grain through good and lean years. Each devised a management strategy and each observed how grain supply and price fluctuations with a "no reserve" policy could cause. social disruption. Joseph and the Pharaoh's Dreams The most famous grain reserve