WORKING PAPER NO. 4 OPTIMAL STOCK FOR THE PUBLIC FOODGRAIN DISTRIBUTION SYSTEM IN BANGLADESH FRANCESCO GOLETTI RAISUDDIN AHMED NUIMUDDIN CHOWDHURY INTERNATIONAL FOOD POLICY RESEARCH INsrlTUTE Working papers of thelntematlonal food Policy Research In.titute encompall a wide range of .ubl.cts drawn from ih research program• . Th. papers-primarily data anaIYM., hl.torlcal description., or caM.tudle.-contaln Information that IFPRI ben.v" may be of Interest to o'hers. Working popers undergo Informat review but do no' neceaorlty present final r...arch reautts. OPTIMAL STOCK FOR THE PUBLIC FOODGRAIN DISTRIBUTION SYSTEM IN BANGLADESH Francesco Goletti Raisuddin Ahmed Nuimuddin Chowdhury Working Papers on Food Policy in Bangladesh, No.4 International Food Policy Research Institute Washington, D.C. December 1991 CONTENTS Foreword viii l. Summary 1 2. Introduction 4 3. Choice of Approach to the Optimal Stock Problem 9 4. Components of Food Stock Policy. 12 5. A Model of the Public Foodgrain Distribution System in Bangladesh . . . . . . . . . . . . . . 29 6. Policy Constraints and Policy Objectives 36 7. Open Market Operations 39 8. Specification of Policy Options 43 9. Evaluation of Counterfactual Simulations 47 10. Conclusions . . . . . . . 77 Appendix 1: Procurement Supply 81 Appendix 2: Has Procurement Been Effective at Supporting Prices? . . . . . . 84 Appendix 3: Derivation of Storage Equation 87 Appendix 4: Nature and Sources of the Data 89 Appendix 5: Food Budget 91 Appendix 6: The Model for the Benchmark Policy 94 Appendix 7: Approximation Policies 96 Glossary 97 Bibliography 98 - iii - TABLES . . .5 1. Nominal rice and wheat prices, 1972/73-1989/90 2. Rice and wheat prices deflated by index of manufactured goods, 1972/73-1989/90 . . 6 3. Total foodgrain stocks, 1972/73-1989/90 7 4. Rice and wheat stocks, 1972/73-1989/90 8 5. Components of public distribution of foodgrains, 1972/73-1989/90 . . . . . . . . . . . . . . . 6. Sources of public distribution of foodgrains, 1972/73-1989/90 . . . . . . . . . . . . . 13 7. Total production of rice, 1972/73-1989/90 . 14 8. Growth of foodgrain production per capita, 1972/73-1989/90 . . . . . . . . . . . . . . 15 9. Growth of foodgrain production, 1972/73-1989/90 15 10. Production trends of rice and wheat, 1972/73-1989/90 . . . . . . . . . . . . . 17 11. Correlation matrix of crop residuals from trend regression . . . . . . . . . . 18 12. Yearly procurement of rice and wheat, 1973/74-1989/90 18 13. Mean divergence with respect to market prices of rice and wheat, 1972-89 . . . . . . . . . . . . . 19 14. Yearly offtakes of rice and wheat, 1972/73-1989/90 21 15. Estimated equations for imports of rice and wheat, 1975/76-1989/90 . . . . . . . . . . . . . . . . 24 16. Coefficients of variation of world and domestic prices of rice and wheat, 1973/74-1989/90 . . . . . . 25 - iv - . . 12 17. Correlation matrix of world and domestic price levels for rice and wheat. . . . . . . . . . . . . . 26 18. Correlation matrix of world and domestic price differences for rice and wheat . . 26 19. Yearly imports of rice and wheat, 1972/73-1989/90 28 20. Estimated equations of the foodgrain system, 1975/76-1989/90 . . . . . . . . . . . . . . . . . 33 21. Three-stage least squares estimation of price equations of foodgrain system, constrained, 1975/76-1989/90 35 22. Variables in the baseline, 1985-88 48 23. Costs in the baseline, 1985-88 49 24. Historical values of prices used in the baseline, 1985-88 . . . . . . . . . . . . . . . . . . . . . 50 25. Historical values of quantities in the baseline, 1985-88 . . . . . . . . . . . . . . . . . . 51 26. Variables in the price band policy, 1985-88 61 27. Costs in the price band policy, 1985-88 . . 62 28. Variables in the optimal price stabilization policy, 1985-88 . . . . . . . . . . . . . . . . . . . . . 63 29. Costs in the optimal price stabilization policy, 1985-88 . . . . . . . . . . . . . . . . 64 30. Variables in the import policy, 1985-88 65 31. Costs in the import policy, 1985-88 . . 66 32. Variables in the cost minimization policy, 1985-88 67 33. Costs in the cost minimization policy, 1985-88 68 34. Variables in the benchmark policy: price stabilization cum cost minimization, 1985-88. 35. Costs in the benchmark pol icy: pri ce stabil i zat ion cum cost minimization, 1985-88. . ..... . - v - . . .... 69 70 Variables in the benchmark policy with 30 percent increase in world prices, 1985-88 . . . . . . 71 37. Costs in the benchmark policy with 30 percent increase in world prices, 1985-88 . . . . . . 72 38. Variables in the benchmark policy when monetary off takes are eliminated, 1985-88 . . . . . 73 39. Costs in the benchmark policy when monetary off takes are eliminated, 1985-88 . . . . . 74 40. Variables in the approximation policy, 1985-88 75 41. Costs in the approximation policy, 1985-88 76 42. Summary of various policies . . . . . . 79 43. Average stock and total cost of various policies 80 44. Ordinary least squares estimation of rice and wheat procurement supply . . . . . . . . . . . . . . . 83 45. Three-stage least squares estimation of foodgrain system with public food distribution 85 46. Foodgrain nominal costs, 1976-89 92 47. Foodgrain deflated costs, 1976-89 93 36. - vi - FIGURES l. Total rice production, by harvest season, 1972-89 15 2. Rice production per capita, by harvest season, 1972-89 . . . . . . . . ...... . 16 3. Total rice production per capita, 1972-89 16 4. Divergence between procurement and market prices of rice, 1972-89 . . . . . . . . . . . . . . . . 20 5. Divergence between procurement and market prices ..... . of wheat, 1975-89 . . . . 20 6. Divergence between ration and market prices . ..... . of rice, 1972-89 . . . . 22 7. Divergence between ration and market prices of wheat, 1973-89 . . 22 8. Rice prices, 1972-89 27 9. Wheat prices, 1973-89 27 10. Actual and simulated values of the foodgrain system with public distribution, 1975-89 . . . . . . . . . 41 11. Policy options considered in the simulation exercises 44 12. Pri ce band pol icy . 52 13. Price stabilization policy 53 14. Import pol icy. . 54 15. Cost minimization policy 56 16. Benchmark policy: cost minimization 17. Approximate versus optimal open market operations price stabilization cum - vi i - 57 60 FOREWORD In early 1989, the International Food Policy Research Institute entered into a contract with the U.S. Agency for International Development (USAID), Dhaka (under Contract No. 388-0027-C-00-9026-00), to conduct research on food policies and to extend technical assistance to the Ministry of Food, Government of Bangladesh. The Bangladesh Food Policy Project is the basis for a tripartite collaboration between IFPRI, the Government of Bangladesh, and USAID, Dhaka. This project consists of four subprojects and a large number of well-defined research topi cs. The subprojects together const i tute a comprehens i ve approach for addressing the food policy problems of Bangladesh. The subprojects include- the following studies: a price stabilization framework encompassing public and private marketing, evaluation of the effects of targeted distribution of foodgrains on consumption and nutrition, diversification of agriculture as a source of sustained growth of production, and capacity-building in food policy analysis. This paper on determination of optimal publ ic stocks of foodgrains for the purpose of price stabilization and targeted distribution is an important study under the first subproject. The level of stock is a significant determinant of the level of cost of the public distribution system. It is hoped that this study on optimal stock will enable a greater degree of efficiency in the use of stock in the public distribution system than has been possible in the past. Raisuddin Ahmed Series Editor and Project Director Bangladesh Food Policy Project - vi i i - 1. SUMMARY The search for an estimate of the optimal stock of publ ic foodgra in has been a constant and intense demand from donors and pol icymakers in Bangladesh. The meaning of optimal ity has, however, remained different to different persons. A general perception in these debates is that there may be a preci se figure that represents the optimal level of·public stock. Optimality implies minimization of cost or maximization of net gains in achieving an objective. In the context of the present exercise (that is, estimation of an optimal foodgrain stock for the government), the optimal level of public foodgrain stock is defined as the level of stock that ensures a number of objectives such as a certain degree of price stabilization and a certain amount of foodgrain supply through the rationing system and for the food-for-work operations, vulnerable group development, and other relief programs at minimum cost. The definition of optimality is somewhat limited in the sense that the benefits from these public interventions are not questioned and incorporated into the analysis. However, sensitivity to changes in various types of interventions and their implications for the estimates of optimal stock are shown in this paper. As a result, it is possible to point out the optimal level of public stock for the present degree of public interventions and the stock levels for reduced degrees of public interventions or changes in policies. This procedure gives a range of estimates of optimal stocks and the corresponding types and degrees of public interventions, providing a space for gradual reform in policies and management of interventions. The estimation of the optimal public stock obviously requires a comprehens i ve model that integrates a dynami c foodgra in sector with chosen pol icy regimes and well-defined objective and cost functions. Further, the mechanisms of simulation and sensitivity analysis are requi red for exami nat i on of results with varyi ng assumptions. These analytical elements are developed in the paper. The dynamic foodgrain sector model captures the inherent seasonality of foodgrain prices, the effects of private storage decisions, and government activities involving procurement and off takes from public godowns. In defining the objective function of the government the main concerns of price stabil ity, minimal fiscal costs, and food security through targeted distribution (rations, food-for-work, vulnerable group development, and relief programs) were taken into consideration. Because results of the analysis vary with the types of policies, it is necessary to understand the pol i ci es well before readi ng the estimates of stocks. Estimates of optimal stock relate to six types of policies specified in this paper. These are price band policy, optimal pri ce stabil i zat i on pol icy, import po 1icy approach to pri ce - 2 - stabilization, cost minimization policy, price stabilization cum cost minimization (also called the benchmark policy in this paper), and approximation to optimal price stabilization. An estimate with a norationing policy is also added at the end. The specific contents of each of these policies can be gauged from the presentations in the main text. A baseline picture is developed in order to show how each policy simulation compares with the baseline. The estimated stock requirements and costs for the specified policies are shown in the following table. Pol icy Baseline Price band Optimal price stabilization Import policy Cost minimization Benchmark: price stabilization cum cost minimization Approximation to optimal price stabil i zat ion No ration distribution Average Total Foodgrain Stock Tota 1 Cost (1,000 metric tons) (Tkmillion) 1,075 1,452 1,128 847 686 17, 045 19,632 8,392 14,716 6,046 724 5,137 876 690 8,473 2,741 The baseline in the table is obtained by simulating the foodgrain model for the period July 1985-June 1988. The price band is defined by a plus or minus 4 percent margin around the target price. The optimal price stabilization policy uses open market operations to minimize the variance of rice prices around the target. The import pol icy uses imports to minimize variance of rice prices around the target. The cost minimization policy uses open market operations to minimize the total cost of food operations. The benchmark refers to cost minimization cum price stabilization, which uses open market operations and imports to minimize the total cost of food operations subject to price stabilization and foreign reserves constraints. The approximation to optimal price stabilization was computed through stochastic simulations of production shocks and ordinary least squares over rice production, wheat production, and a lagged term. No ration distribution refers to the benchmark when monetary off takes are eliminated. Total cost equals procurement cost plus import cost minus ration sales minus open market sal es. - 3 - The estimates in the table show that the optimal stock varies from the level of 686,000 metric tons for the cost minimization policy to 1,452,000 tons for the effective price band policy. Cost minimization implies allowing prices to go up in the peak price season in order to make a profit by publ ic sale or to go down sharply in order to buy grains at cheap prices. Price stabilization is of no concern. Such a strategy forsakes the prime objective (that is, price stabilization) of the public system. Therefore, it may not be acceptable to policymakers. The policy of price stabilization cum cost minimization appears to be one of the best options and can be further improved by elimination of rationing if evaluation of the rationing scheme justifies such el imination. One interesting piece of evidence that emerges from this exercise is that the cost and level of stock are higher for the price band policy than for other policies. This result originates from the maintained rigidity of a price band policy. When this assumption of a rigid price band is abandoned; the policy becomes similar to the approximation to optimal price stabilization, in which case both the stock level and cost are substantially reduced. For the sake of simplicity, the policies are specified discretely and with somewhat narrower domain than would be dictated by the exigencies of actual application. In actual application, some of these policies would be combined to achieve multiple goals. But discrete analysis provides a sense of direction of change in levels of stock and costs due to these combinations. For example, some flexible price band, import, open market operations, and cost minimization goals would be implicit in an ideal price stabilization mechanism. In the present context it is important that these policies, if applied in a balanced and effect i ve manner, woul d not requi re a stock 1eve 1 above about 750,000 tons and would also cost much less than historically experienced. For low-cost operation of price stabilization, the analysis indicates that use of three policy instruments, that is, import policy, open market purchase, and open market sal e (purchase and sale are defined as open market operations) have to be very judicious. In the past, import of foodgrain has not been based on rational analysis. Open market operations have also remained very timid. Moreover, management of these operations (not specifically analyzed here) is known to have caused inefficiency and high cost. The analysis here shows that private trade is very sensitive in price speculation and stocking behaviors to the public stock situation and operation. Therefore, erratic behavior in the public sector will compound the adverse effects throughout the foodgrain market. . This paper assumes that the public sector will continue in the Bangl adesh foodgra in market and analyzes how the objectives of thi s sector can best be achieved with optimal stock and lower cost. There is of course a larger issue, which the paper does not address: Is the public sector necessary at all? Inefficiency in the public sector may generate the momentum for a comprehensive look at this larger issue. 2. INTRODUCTION The foodgrain sector in Bangladesh is characterized by the active presence of the government sector, which is involved in various operations related to domestic procurement, public distribution, imports, and open market sales. Central to this involvement is the management of public foodgrain The main issue related to public stocks is the need to stocks. understand the policy principles informing the stock policy. The broad concern of foodgrain stock pol icy is to guarantee food security at minimum cost. Ways of mitigating this concern are examined in this study. Until as recently as 1988, the general guidelines of stock policy in Bangladesh followed the recommendations of the World Bank expressed in an influential report (World Bank 1979). That report suggested that the total foodgrain stock be 1.5 million metric tons as of July 1 of every year and 1.2 million tons as of November 1.1 As pointed out by Chowdhury (1990), the World Bank's recommendation of a fixed stock on July 1 of every year misses the point that the multiple crop pattern of Bangladesh rice cultivation allows production downfalls that occur in one crop season to be compensated for within the same year. The recommendations of the World Bank in 1979 appear to be overly cautious, understandably so in light of the severe drought experienced in Bangladesh in that year. Nevertheless, in the years following 1981, government stocks have rarely exceeded the level of 1.2 million tons. Taking into account the population growth, the per capita figures of stock 1eve 1s have been much sma 11 er than those the Worl d Bank recommended in 1979. Thi s situat i on has not prevented both nomi na 1 prices of rice and wheat and nominal prices deflated by the index of manufactured goods to become more stable from the 1970s to the 1980s. Tables 1 and 2 indicate both lower coefficients of variation of price and small er yearly spreads between hi gh and low pri ces for ri ce and wheat. The variability of total stocks decreased during 1972/73-1989/90 (Tables 3 and 4), even though Bangladesh experienced two of the worst production calamities of its history in 1987/88 and 1988/89. The foregoing observations suggest that stock policy guidelines have to be revised substantially. During 1981-91 the foodgrain sector of Bangladesh has witnessed a few remarkable changes: a changed pattern of seasonality of production and prices (Ahmed and Bernard 1989; Chowdhury 1987); a reduced role for subsidized distribution (Chowdhury 1990); increasing experience with open market sales (Chowdhury 1990); 1 All tons referred to in this report are metric tons. - 5 - Tabl e I--Nominal rice and wheat prices, 1972/73-1989/90 Rice Price yearl Average c.v. b (Tk/maund) 1972/73 1973/74 1974/75 1975/76 1976/77 1977 /78 1978/79 1979/80 1980/81 1981/82 1982/83 1983/84 1984/85 1985/86 1986/87 1987/88 1988/89 1989/90 75 100 210 124 113 138 152 201 168 220 240 262 294 280 341 352 362 355 Wheat Price Spreadc (percent) 14 21 17 24 11 6 18 8 6 17 6 7 6 7 9 5 5 5 Average (Tk/maund) 50 64 89 94 42 20 68 31 22 69 21 23 23 22 34 17 18 20 n.a. 62 141 77 79 91 91 124 111 135 162 167 170 181 209 215 224 233 c.v. b Spreadc (percent) n.a. 35 22 34 12 9 10 15 3 15 9 9 8 7 5 6 5 3 n.a. 143 120 157 44 40 40 64 11 48 36 25 29 26 20 22 12 13 Source: Based on data from Bangladesh Bureau of Statistics. Monthly Statistical Bulletin. various dates. Note: I b C n.a. means not available. The fiscal year starts in July. C,v. ;s the coefficient of variation, computed with monthly prices. Spread is the percentage difference between the highest and the lowest price of the year. reduced gaps between market pri ces, ration pri ces, and procurement prices (Abdullah 1989b); and reduced subsidies on agricultural inputs such as fertilizers and irrigation equipment (Abdullah 1989a). At the same time, the need for a new framework to analyze the foodgrain stock problem has arisen. The initial attempts by Abbott (1988) for the FAD, Ahmed and Bernard (1989) at IFPRI, and Chowdhury (1987, 1988, 1990) and Shahabuddin (1990) for IFPRI form part of the growing literature. The general direction of these studies is away from a passive endorsement of quantity targets toward a more complete analysis of the food system of Bangladesh that tries to capfure the complex interrelation between the free market and government operations. Moreover, a new concern related to the optimal stock problem has been emerging, where the word "optimal" refers to some prespecified policy or welfare concept. In particular, there is a growing awareness of the financial cost impl ications of different stock levels. - 6 - Table 2-Rice and wheat prices deflated by index of manufactured goods, 1972/73-1989/90 Year- Average Rice Price c.v. b (percent) (Tk/maund) 0.3.1 0.30 0.41 0.29 0.26 0.30 0.33 0.35 0.26 0.31 0.31 0.35 0.37 0.33 0.38 0.38 0.37 0.33 1972/73 1973/74 1974/75 1975/76 1976/77 1977/78 1978/79 1979/80 1980/81 1981/82 1982/83 1983/84 1984/85 1985/86 1986/87 1987/88 19B8/89 19B9/90 Spread c Jl 17 16 30 9 14 12 II 4 15 6 Jl 7 5 9 6 4 5 Average Wheat Price c,v. b (Tk/maund) 42 58 73 126 37 57 48 42 16 60 22 42 30 17 34 19 16 19 n.a. 0.18 0.28 0.18 0.18 0.20 0.20 0.22 0.17 0.19 0.21 0.22 0.21 0.21 0.23 0.23 0.23 0.22 Spreadc (percent) n.a, n.a. 31 22 40 9 20 10 18 5 12 9 109 124 189 38 87 33 80 15 36 40 37 35 26 25 25 20 13 Jl 10 8 6 7 6 3 Source: Based on data from Bangladesh Bureau of Statistics, Monthly Statistical Bulletin, various dates. Note: a b C n.a. means not available. The fiscal year starts in July. C.v. is the coefficient of variation, computed with monthly prices. Spread is the percentage difference between the highest and the lowest price of the year. To give a very rough dimension of this financial cost, one may think of the cost of 100,000 tons of foodgrains (35 percent of which consists of rice and the rest of wheat) evaluated at average 1988/89 world prices. This cost, equal to US$20.8 million, or 671.2 million taka (Tk), represents approximately 5.8 percent of the agricultural Annual Development Programme (ADP) budget and 1.4 percent of the total ADP budget. The main purpose of this study is to present a general framework for designing a cost-effective stock policy that addresses the government's concerns related to ensuring price stability and the food security of the vulnerable groups. The design of an optimal foodgrain stock policy entails the construction of a dynamic model of the foodgrain sector of Bangladesh and the use of programming techniques to fac il itate the anal ys is of di fferent pol icy i ntervent ions (for a simil ar approach applied to foodgrains in India, see Krishna and Chhibber 1983; for other commodities, see Ghosh, Gilbert, and Hughes Hallett 1987). - 7 - Table 3-Total foodgrain stocks, 1972/73-1989/90 year8 Average Total Stocks C.V. of Total Stocks b (1,000 metric tons) 1972/73 1973/74 1974/75 1975/76 1976/77 1977 /78 1978/79 1979/80 1980/81 1981/82 1982/83 1983/84 1984/85 1985/86 1986/87 1987/88 1988/89 1989/90 326 239 262 852 583 608 637 666 1,230 1.029 687 637 817 882 736 1,053 1.208 1,181 Spread of Total StocksC (percent) 39 29 41 16 29 17 26 28 15 27 17 20 21 17 36 15 18 20 Average Total Stocks per Capita Security Daysd (kilograms/person) 268 169 351 60 142 83 180 331 80 139 70 80 105 67 206 66 73 73 4.44 3.18 3.39 10.76 7.20 7.30 7.48 7.62 13.79 11.34 7.39 6.70 8.38 8.86 7.23 10.09 11.33 10.82 9 7 7 22 15 15 15 16 28 23 15 14 17 18 15 21 23 22 Source: Bangladesh Bureau of Statistics, Monthly Statistical Bulletin, various dates . • The fiscal year starts in July. b C.v. is the coefficient of variation, computed with monthly stocks. C Spread is the percentage difference between the highest and the lowest stock of the year. d Security days express the number of days that public stocks would guarantee to the population of Bangladesh for that year a diet of 15.5 ounces of foodgrains. In Chapter 3 the general approach to the design of stock policy is explained and formal ized. In Chapter 4 the components of stock pol icy are put in their historical context. Chapter 5 presents a model of the foodgrain sector, incorporating decisions related to consumption and private storage. In Chapter 6 the pol icy constraints and pol icy objectives are spelled out. Various policy options are specified in Chapter 7, and the rol e of open market operations is di scussed in Chapter 8. In Chapter 9 the evaluation of policy simulations is presented. Conclusions are given in Chapter 10. A series of appendixes deal with the technical aspects of the paper. - 8 - Table 4-Rice and wheat stocks, 1972/73-1989/90 Rice Stocks Year- Average cov,s (1,000 metric tons) 1972/73 1973/74 1974/75 1975/76 1976/77 1977 /78 1978/79 1979/80 1980/81 1981/82 1982/83 1983/84 1984/85 1985/86 1986/87 1987/88 1988/89 1989/90 44 38 63 382 311 234 200 294 453 481 312 213 268 400 215 350 540 619 (percent) 44 48 102 43 28 64 30 35 38 26 12 30 43 14 36 21 26 25 Wheat Stocks Spreadc Average c.v,s (1,000 metric tons) 271 689 4619 182 161 530 182 533 187 158 46 239 388 57 197 89 152 154 Source: Based on data from Bang ladesh Bureau of Stat i st; cs dates . 282 201 200 470 272 373 437 372 777 548 375 424 549 482 520 703 668 562 I Spread' (percent) 45 39 45 17 33 35 39 34 25 32 27 29 21 26 41 14 21 44 433 260 312 80 157 200 250 312 116 148 143 172 113 163 355 68 116 368 Month ly Stat; st; ca 1 Bu 11et in. var iaus • The fiscal year starts in July. b C.v. is the coefficient of variation, computed with monthly stocks. c Spread 1s the percentage difference between the highest and the lowest stock of the year. 3. CHOICE OF APPROACH TO THE OPTIMAL STOCK PROBLEM The search for an estimate of the optimal level of publ ic foodgrain stock has been constantly demanded by donors and some policymakers in Bangladesh. Optimality has, however, been understood differently by different persons. In these debates the general perception is that there may be a precise figure that represents the Optimality implies both minimization of cost and optimal level. maximization of gains in achieving an objective. In the context of the present study, the optimal level of public foodgrain stock is defined as the level of stock that helps attain certain objectives such as price stabilization within given bands and a sufficient supply of foodgrains through the public distribution system at a minimum cost. This definition is somewhat limited, since the benefits of these publ ic interventions are not questioned and incorporated into the analysis. 2 However, various levels of these interventions and their implications for the estimates of optimal stocks are covered in this paper. This enables the study to recommend the optimal level of public stock under the present degree of public interventions and under reduced degrees of such interventions. This procedure gives a range of estimates of optimal stocks and the corresponding degrees of publ ic interventions, providing room for gradual reform in public stock management and interventions. The estimation of the optimal public stock obviously requires a comprehens i ve model that integrates a dynami c foodgra in sector wi th chosen policy regimes and well-defined objectives and cost functions. The techniques for simulation and sensitivity analysis are also required for examination of results with varying assumptions. Three stages are involved in the design of the optimal stock The first stage consists of the specification, policy problem. identification, and estimation of a dynamic model of the foodgrain sector. The second stage comprises the specification and solution of an opt imi zat i on exerci se based on the dynami c model constructed in the first stage. The third stage is the evaluation of the optimal stock policy determined in the second stage. 2 The main reasons for not adopting a standard economic surplus approach are that. first, theoretical difficulties related to the use of consumers' surplus as an appropriate indicator of welfare still remain unanswered (Scandizzo and Bruce 1980; Scandizzo and Knudsen 1981; Cochrane 1980; ladd 1987). Second, measures of consumers' surplus are of very limited value given the absence of reliable information about foodgrain consumption on a monthly or even a quarterly basis. Third, the object ives of food security and price stab;' izat ion are seen as the most re levant concerns for po 1icy intervention, and their efficient implementation may be regarded as "optimal" policy, - 10 - The optimal stock problem may some object i ve funct i on defi ni ng subject to the constraints imposed market. Formally, the optimization follows: be formulated as the optimization of the pri orit i es of the government, by the feasible performance of the problem [P] can be expressed as ,=T-l [P]: ~ J t , T = min(x) (ZTPZT + L W,), T=t subject to 1, where W, . z, + B, • xr and = A, ZHI ~ ZI z, ~ , a, (1) (2) u" • z". + x' , . R, • x, (3) and the time index 1 = t, ... ,T. In this notation z, is a vector of state variables, x is the vector of control variables, with respect to which the government is optimizing. T is the time horizon of the optimization exercise, and the length of the optimization period is T - t + 1. P, A, and a are matrices conformable with the vector Z; Band R 'are mathces conformabl e with x . '" The current' period objective of the government is W" which is assumed to be a quadratic form in the state and control variables; the final period objective is Z/TPZT. The state variables evolve according to the law of motion specified in equation (1) and are subject to inequality constraints as in equation (2). 1 is the lower bound and u is the upper bound for the state variable z,.' ' * The optimal policy is a sequence of T-t+l functions x satisfying , the problem [p].3 3 Because of the recursive structure of the problem. the optimal policy functions can be found by applying Bellman's equation recursively: Jt,T(Zt) = minx, Et [Wt(Xt,Zt) + Jt+"T(Zt+,)] I subject to Zt-t1 = AtZ t 't : ; + StXt Zt+1 S and ut ' In the numerical solution of the optimal policy options considered in the text, the GAMS software has been used to find an open loop solution (Brooke, Kendrick, and Meeraus 1988). - 11 - Note that by specifying different government objectives and instruments, the general model can be used to deal with many different policy issues (see Chapter 7). The system in equation (1) represents the structural model of the foodgrain private sector, which the government is influencing by intervening through holding and distribution of stock. During the design of stock policy, the government takes into account the reaction of the private sector implied by a dynamic model of market behavior. At the same time, a set of other inequality constraints is imposed as specified in equation (2). Examples of these inequality constraints are capacity constraints, minimum stock requirements for food security, foreign reserves ceilings on food imports, and so on. 4. COMPONENTS OF FOOD STOCK POLICY One way to gauge the extent of government operations in the foodgrain sector is to consider the ratio of total offtakes to total availability, the latter being defined as net domestic production (gross production less 10 percent for wastage and feed) plus imports plus opening stocks, for any particular year. The dimension of government intervention in foodgrain distribution has been substantial, ranging from 8 percent to 21 percent, with an average value of 13 percent for the ratio of total off takes to total availability (Table 5). Table 5-Components of public distribution of foodgrains, 1972/73-1989/90 Net Year- Production Production b Offtake Procurement Initial Stocks Ava 11Imports (1,000 metric tons) 1972/73 1973/74 1974/75 1975/76 1976/77 1977/78 1978/79 1979/80 1980/81 1981/82 1982/83 1983/84 1984/85 1985/86 1986/87 1987/88 1988/89 1989/90 10,023 11,832 11,226 12,780 11,825 13,120 13,140 13,362 14,975 14,598 15,312 15,719 16,086 16,083 16,498 16,462 16,382 18,656 9,021 10,649 10,103 11,502 10,643 11, 808 11, 826 12,026 13,478 13,138 13,781 14,147 14,477 14,475 14,848 14,816 14,744 16,790 2,657 1,756 1,785 1,679 1,374 1,863 1,762 2,203 1,686 1,840 1,893 1,896 2,426 1,419 1,820 2,016 2,685 1,981 0 72 129 503 320 559 358 354 1,034 303 192 272 340 361 188 374 408 962 Off take/ abi 1itye Availability (percent) 303 269 215 761 836 422 601 210 794 1,208 615 611 800 1,008 976 751 1,498 905 2,871 1,719 2,401 1,488 825 1,665 1,165 2,809 1,089 1,234 1,840 2,069 2,580 1,198 1,767 2,911 2,138 1,534 12,195 12,709 12,848 14,254 12,624 14,453 13,949 15,399 16,394 15,883 16,428 17,099 18,197 17,042 17,779 18,852 18,788 20,191 21.8 13.8 13.9 11.8 10.9 12.9 12.6 14.3 10.3 11.6 11.5 11.1 13.3 8.3 10.2 10.7 14.3 9.8 Source: Based on data from Bangladesh Bureau of Statistics, Statistical Yearbook 1989, (Ohaka: BBS, 1990) . • The fiscal year starts in July. b Net production is 90 percent of production. C Availability = initial stock + net production + imports + procurement - off takes. - 13 - There are three sources of public supply:4 domestic procurement, imports, and go,vernment stocks, The relative importance of each of these factors is illustrated in Table 6, which shows that the role of domestic procurement was greater during the second half of the 1970s than in the 1980s, The role of imports has always been crucial in government, with an average ratio of total imports to off takes of foodgrains equal to 90 percent over the period from 1972/73 to 1989/90, Table 6-Sources of public distribution of foodgrains. 1972/73-1989/90 Year- Procurement Procurement Ratlo b (1,000 (percent) (1,000 (percent) 0 4 7 30 23 30 20 16 61 16 10 14 14 25 10 19 15 49 0 72 129 503 320 559 358 354 1,034 303 192 272 340 361 188 374 408 962 Stocks Change (1,000 Stocks Change Ratio (percent) 2,871 1,719 2,401 1,488 825 1,665 1,165 2,809 1,089 1,234 1,840 2,069 2,580 1,198 1,767 2,911 2,138 1.534 108 98 134 89 60 89 66 128 65 67 97 109 106 84 97 144 80 77 0 -34 -54 546 75 -415 179 -390 583 415 -593 -4 189 208 -32 -225 747 -593 1 3 -31 -4 30 -10 22 -26 -25 32 0 -10 -9 2 12 -37 22 0 Source: Based on data from Bangladesh Bureau of Statistics, Statistical Yearbook 1989, 1990) . Offtake (1,000 metric tons) metric tons) metric tons) metric tons) 1972/73 1973/74 1974/75 1975/76 1976/77 1977/78 1978/79 1979/80 1980/81 1981/82 1982/83 1983/84 1984/85 1985/86 1986/87 1987/88 1988/89 1989/90 Imports Imports Ratio 2,657 1,756 1,785 1.679 1.374 1,863 1,762 2,203 1.686 1.840 1,893 1,896 2,426 1.419 1.820 2,016 2,685 1,981 (Ohaka: 88S, • The fiscal year starts in July. b The ratios are taken with respect to off takes. 4 From the balance equation for stocks, stock~ = oj • stock i".1 + m~ + qp~ - oftakes~ i - oms T• it ;s pas,sible to. see that ,the sources of off takes and open mar:ket sales are given by changes in stocks (8' • stOCk~'1 - stock~). imports (m~) and procurement (qp~). Divergences from the share of the imputed sources and the actual figures come fram unreported losses and from omissions. I - 14 - THE CONTEXT OF PRODUCTION Rice is produced seasonally in Bangladesh. Within a year, three main crops denoted aman (harvested from November to January), boro (harvested from April to June), and aus (harvested from July to September) are grown. Traditionally, aman has been the largest crop. In the 1ast few years, however, boro production has been increasing rapidly, taking its share from 21 percent of total production in 1973 to 35 percent in 1989, largely due to the diffusion of high-yielding varieties (HYVs) and the extension of irrigation facilities. Aus and aman shares have declined commensurately (Table 7). Therefore, production is now more evenly distributed over the year. Consequently, arrivals in the market occur more smoothly, implying less need for storage than in the past to mitigate seasonal shortfalls. The annual growth of total ri ce product i on between 1972/73 and 1989/90 was 2.62 percent, with 3.08 percent in the 1970s and 2.57 percent in the 1980s (Tables 8 and 9; Figures 1 and 2). Moreover, total product i on per capita does not exhi bit any trend. It has osci 11 ated around its mean of 148 kilograms in a random fashion (Figure 3). Table 7-Total production of rice, 1972/73-1989/90 Year~ Bora Aman Aus Share of Total Rice Production Boro Aus Aman (1.000 metric tons) 1972/73 1973/74 1974/75 1975/76 1976/77 1977 /78 1978/79 1979/80 1980/81 1981/82 1982/83 1983/84 1984/85 1985/86 1986/87 1987/88 1988/89 1989/90 5.587 6.699 6.000 7.045 6.906 7,422 7,429 7,303 7,964 7,209 7,604 7,936 7,930 8,542 8,267 7,690 6,857 9,202 2.071 2.220 2.250 2.286 1.650 2,239 1.929 2,427 2,630 3,152 3,546 3,350 3,909 3,671 4,010 4,731 5,831 6,166 (percent) 2.274 2.802 2.859 3.230 3,010 3,104 3,288 2,809 3,289 3,270 3,067 3,222 2,783 2,828 3,130 2,993 2,856 2,488 56 57 54 56 60 58 59 58 57 53 53 55 54 57 54 50 44 52 21 19 20 18 14 18 15 19 19 23 25 23 27 24 26 31 38 35 23 24 26 26 26 24 26 22 24 24 22 22 19 19 20 19 18 14 Source: Based on data from Bangladesh Bureau of Statistics, Statistical Yearbook 1989, (Dhaka: BSS, 1990) . a The fiscal year starts in July. - 15 - Table 8-Growth of foodgrain production per capita. 1972/73-1989/90 Rice Bora Aman Period Aus Wheat Total Rice 15.68 37.97 -3.51 2.62 3.08 2.57 (percent) I. 72 3.66 1.08 1972/73-1989/90 1972/73-1980/81 1981/82-1989/90 6.83 1.50 8.49 0.09 2.91 -2.20 Source: Based on data from Bangladesh Bureau of Statistics, Statistical Yearbook 1989. (Dhaka: BSS, 1990). Note: Growth rates are derived from regression of logarithms of production on time and constant. Table 9-Growth of foodgrain production. 1972/73-1989/90 Rice Bora Aman Period Aus Wheat Total Rice 13.05 34.71 -5.70 0.29 0.64 0.24 (percent) -0.58 I. 21 -1.21 1972/73-1989/90 1972/73-1980/81 1981/82-1989/90 4.41 -0.90 6.03 -2.18 0.48 -4.42 Source: Based on data from Bangladesh Bureau of Statistics, Statistical Yearbook 1989. (Dhaka: BSS, 1990) . Note: Growth rates are derived from regression of logarithms of production on time and constant. Figure I--Total rice production. by harvest season. 1972-89 6 " 4 2 n ~ ~ ~ 77 ~ ~ = 6' YEAR Source: Based on data from Bangladesh Bureau of Statistics, Statistical Yearbook (Dhaka: various years). BSS, - 16 - Figure 2-Rice production per capita, by harvest season, 1972-89 Kg/CAPITA ,o~=- eo - -BORO - -..: 40 20 ~ :,.."::""" .• -:;;,..., '."-:' " -- ."- -. '. _ ~ ~ _ ~ _ _ ~ e, _ _ _ _ _ ~ _ _ YEAR Source: Based on data from Bangladesh Bureau of Statistics, Statistical Yearbook (Dhaka: BSS, various years). Figure 3-total rice production per capita, 1972-89 YEAR Source: Based on data from Bangladesh Bureau of Statistics, Statistical Yearbook (Dhaka: various years). BSS, - 17 - These facts are also borne out by a trend analysis over the period 1972-90 (Table 10). Except for boro production, the growth rates are decelerating, as indicated by the negative sign of the quadratic trend terms. In the past, publ ic stocks have often shown a tendency to be overreplenished in expectation of a big shortfall in one crop. This tendency may be interpreted as a failure to understand the negative correlation among foodgrain crops. As the negative correlation between aman and boro and between aus and wheat shows (see Table 11), large shortfalls in one crop are associated with opposite movements in another crop, making the overall yearly production less variable than the seasonal production. These negative correlations are the reflections of adjustment mechanisms that are operative after a natural calamity. When a crop failure occurs due to drought or flood, farmers tend to make an above-normal effort to raise the subsequent crop in order to compensate for the loss. Moreover, a flood that causes loss to the aman or aus crop increases the supply of water for irrigation or in retained soil moisture that enhances the yields of boro and wheat crops in the subsequent dry season. PROCUREMENT Rice procurement was higher during the 1970s than during the 1980s (Table 12). However, procurement was abnormally high in 1980/81 and 1989/90 foll owi ng major product ion shortfalls. Thus, procurement in these years may be seen as an excessive reaction of the government, more for the purpose of replenishing public stocks than to support a floor price. Table lO-Production trends of rice and wheat, 1972/73-1989/90 Aman Variable Constant Trend Trend 2 R' SER Mean of dependent variable 5.698.12 287.61 -8.61 0.64 549.90 7,421.78 Rice Boro 2.343.41 -147.34 19.48 0.95 310.70 3,226.00 Aus 2,412.92 161.39 -8.41 0.55 199.58 2,961.22 Wheat -400.75 217.15 -7.97 0.84 189.51 728.72 Source: Based on data from Bangladesh Bureau of Statistics, Statistical Yearbook 1989, (Dhaka: BBS, 1990) . Notes: The coefficients of the regression are all significant at least at 5 percent, except the quadratic term for aman, whose t-statistic ;s -1.59. The regression was done taking production levels over a constant. a linear trend term, and a quadratiC trend term. Production levels are measured in 1,000 metric tons. SER;s standard error of regression. - 18 - Table ll-Correlation matrix of crop residuals from trend regression Aman Rice Bora Aus Wheat 1.00 -0.02 -0.27 -0.07 -0.27 -0.03 1.00 0.14 -0.02 1.00 -0.03 -0.42 -0.07 -0.42 0.14 1.00 Crop Rice Aman Bora Aus Wheat Source: Based on data from Bangladesh Bureau of Statistics, Statistical Yearbook 1989, (Dhaka: BSS. 1990) . Notes: The residuals are obtained from a quadratic trend regression as computed from the results in Table 10. Table 12-Yearly procurement of rice and wheat, 1973/74-1989/90 Rice of Production Rice per capita (1,000 (percent) (grams) Rice Procurement as Share Year- metric tons) 1973/74 1974/75 1975/76 1976/77 1977 /78 1978/79 1979/80 1980/81 1981/82 1982/83 1983/84 1984/85 1985/86 1986/87 1987/88 1988/89 1989/90 72 129 503 317 548 306 228 855 290 168 154 130 231 136 288 364 919 0.6 1.2 4.0 2.7 4.3 2.4 1.8 6.2 2.1 1.2 1.1 0.9 1.5 0.9 1.9 2.3 5.1 957 1. 669 6,356 3,898 6,576 3,596 2,600 9,596 3,201 1,800 1.623 1,328 2,322 1,325 2,747 3,411 8,403 Wheat Procurement as Share Wheat per Wheat of Production capita (1,000 metric tons) (percent) (grams) n.a. n.a. n.a. n.a. 1.2 3.1 10.5 15.3 16.4 1.3 2.2 9.7 14.3 12.5 4.8 8.2 5.3 5.4 n.a. n.a. n.a. 11 52 126 179 13 24 118 210 130 52 86 44 43 n.a. n.a. n.a. 37 133 604 1,432 1,998 147 256 1,231 2,143 1 .. 297 506 819 409 391 Source: Based on data from Bangladesh Bureau of Statistics, Statistical Yearbook 1989, (Dhaka: BBS, 1990) . n.a. means not available. Note: • The fiscal year starts in July. - 19 - Wheat is much more dominant in public procurement than rice. As a percentage of production, procurement of rice averaged 3 percent in the 1970s and 2 percent in the 1980s, whereas wheat averaged 5 percent in the 1970s and 7 percent in the 1980s. Moreover, in per capita terms, ri ce procurement has been decl i ni ng, whereas wheat procurement has exhibited an upward trend. Wheat is procured only in the three to four months following the March-April harvest. Rice is procured throughout the year, reaching its peak in December-January, during the aman harvest, and in June-July, following the boro harvest. In the past few years, because of the growi ng importance of the boro season, ri ce procured duri ng May-Jul y has been greater than the procurement made during the aman season. The following general observations in terms of procurement prices can be made. It seems that wheat procurement prices have been closer to market prices than rice procurement prices (Table 13; Figures 4 and 5). Moreover, both ri ce and wheat procurement pri ces foll owed a cl ear pattern during the second part of the 1980s, consisting of a smoothening of the devi at ions from market pri ces. In the case of wheat, the smoothening was associated with a general movement toward relatively higher procurement prices. Nevertheless, as shown in the analysis of procurement supply in Append i xl, procurement pri ces have not been effective in stimulating procurement supply. Table 13-Mean divergence with respect to market prices of rice and wheat, 1972-89 Fiscal Procurement Ration Years Price Price World Price Sales Price8 Open Market (percent) Rice price divergences 1972-89 1970s 1980s 1980-84 1985-89 -14.4 -18.3 -11.3 -11.4 -11.3 -27.7 -45.1 -13.7 -18.2 -9.1 10.2 17.2 4.7 17 .5 -8.2 1.9 -2.5 2.3 4.4 0.3 Wheat price divergences b 1972-89 1970s 1980s 1980-84 1985-89 -8.3 -5.2 -9.8 -10.8 -8.8 -16.0 -28.7 -7.0 -9.7 -4.4 -5.4 -9.5 -2.4 0.0 -4.9 3.8 0.3 4.1 4.3 4.0 Source: Based on data from Bangladesh Bureau of Statistics. Monthly Statistical Bulletin, various dates. Notes: The divergences are computed with respect to domestic market prices. The 1970s are from July 1972 to June 1980; the 1980s are from July 1980 to June 1990; 1980-84 is from July 1980 to June 1985; and 1985-89 is from July 1985 to June 1990 . • Data for open market sales mean divergences calculations are available fram July 1979 onward for both rice and wheat. b For wheat, data for ration price and world price mean divergences calculations are available from July 1973 onward and for procurement from July 1975 onward. - 20 - Figure 4-Divergence between procurement and market prices of rice, 1972-89 PERCENT ·20 ·40 -80L~ 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 FISCAL YEAR Source: Based on data from Bangladesh Bureau of Statistics, Monthly Statistical Bulletin. various dates. Figure 5-Divergence between procurement and market prices of wheat, 1975-89 PERCENT FISCAL YEAR Source: Based on data from Bangladesh Bureau of Statistics, Monthly Statistical Bulletjn, various dates. - 21 - OFFTAKES The purported objective of a dual market system is to make foodgrains available to those sections of the population that are most sensitive to food prices and who, even in normal circumstances, experience malnutrition and hunger, Unfortunately, in the past, most of the public supply in Bangladesh has been geared to the needs of the urban population and government employees, with a strong bias against rural areas, where the food problems are often more severe, This longterm bias has been partly corrected in recent years through changes in the rationing system (Chowdhury 1988; World Bank 1990; Goletti and Ahmed 1991), Wheat offtakes have been growing both in absolute levels and in per capita terms, Rice has exhibited an opposite trend, to the extent that wheat off takes in the most recent years have been about three times as much as rice offtakes (Table 14), The seasonal pattern of rice off takes and wheat off takes is quite similar, with a peak before the aman harvest (October-November) and before the boro season (March-May), In terms of ration prices, the subsidies on both rice and wheat have been gradually reduced (Table 13; Figures 6 and 7), and wheat ration prices are exhibiting less divergence from market prices than rice, Table 14-Yearly offtakes of rice and wheat, 1972/73-1989/90 Year 8 1972/73 1973/74 1974/75 1975/76 1976/77 1977/78 1978/79 1979/80 1980/81 1981/82 1982/83 1983/84 1984/85 1985/86 1986/87 1987/88 1988/89 1989/90 Rice Rice per Capita Wheat Wheat per Capita (1,000 metric tons) (grams) (1,000 metric tons) (grams) 425 125 182 502 717 600 569 695 450 589 533 426 360 309 339 340 522 655 5,794 1.660 2,356 6,339 8,830 7,218 6,683 7,962 5,049 6,479 5,743 4,478 3,710 3,106 3,322 3,271 4,890 5,990 2,232 1.630 1.603 1.177 656 1,263 1,193 1.508 1.236 1,251 1.360 1,470 2,066 1,110 1,481 1.676 2,163 1.326 30,348 21,639 20,768 14,902 8,086 15,195 13,978 17,290 13,867 13,752 14,623 15,431 21. 248 11,139 14,515 16,088 20,258 12,149 Source: Based on data from Bangladesh Bureau of Statistics. Statistical Yearbook 1989. (Ohaka: BSS, 1990) . • The fiscal year starts in July. - 22 - Figure 6-Divergence between ration and market prices of rice, 1972-89 PERCENT ·20 ·40 ·60 --- ·10L-~ 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 FISCAL YEAR Source: Based on data from Bangladesh Bureau of Statistics, Monthly Statistical Bulletin, various dates. Figure 7-Divergence between ration and market prices of wheat, 1973-89 PERCENT 20 ·20 ·40 ·60 ·80 ·10~ 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 FISCAL YEAR Source: Based on data from Bangladesh Bureau of Statistics, Monthly Statistical Bulletin, various dates. - 23 - The analysis of the demand for ration distribution in Appendix 2 shows that ration prices of rice have had a significant impact on ration distribution, whereas for wheat ration prices this is not the case. IMPORTS AND WORLD PRICES Traditionally, imports of foodgrains in Bangladesh have been the domain of public monopoly. Only recently, under pressure from donors, some private imports have been allowed, but their importance is still negl igible (USAID 1988, 1989). The most powerful factor affecting imports has been food aid, which in turn has been responsive to both public stocks and expected production shortfalls. From the analysis of a simple model of import demand where imports are related to world prices, public stocks, domestic production, and lagged imports, it seems that imports have not been influenced by world prices, as indicated by the low significance of the coefficients of world prices (Table 15). The gap between worl d and doinest i c pri ces of ri ce has been fl uctuat i ng considerably, with domestic prices losing competitiveness with international prices in the last half of the 19805 (Tables 16-18; Figures 8 and 9). Per capita imports of both rice and wheat have not exhibited any definite trend. Most of the large arrivals occur in JulySeptember (Table 19). - 24 - Table 15-Estimated equations for imports of rice and wheat, 1975/761989/90 Coeff i c; eot Variable t-statistic Rice imports equation 1.365 1.369 -0.297 -0.017 -0.002 0.237 Constant R WOPt stOCk~.1 StOCk~1 q,R R ID t _, 1.80 0.62 -3.59 -0.23 -0.31 1.92 59 0.27 0.96 N R' SEE Wheat imports equation Constant wop,":, 5.207 11.381 -0.497 -0.534 0.030 0.005 stOCk~.1 StOCk~1 q,R m~1 2.10 0.90 -2.07 -2.19 2.15 0.03 59 0.28 2.67 N R' SEE Source: Est imated by the authors based on data from Bang ladesh Bureau of Stat; 5t i cs r Month' y Statistical Bulletin. various dates. I Definitions of terms: wop~, wop~ stOCk~.1' m~1' q~ StOCk~1 = world prices of rice and wheat in period t; '" opening public stocks of rice and wheat; '" domestic rice production in period t; m~1 = lagged imports of rice and wheat; SEE = standard error of estimation. - 25 - Table 16-Coefficients of variation of world and domestic prices of rice and wheat, 1973/74-1989/90 Average Average Difference Difference of World/ of World/ World World Domestic Domestic Rice Wheat Domestic Price c.v. Price c,v. Price c.v. Price c.v. Rice Rice Wheat Domestic Wheat Prices Domestic c.v.! Domestic c.v.! World c,v. of Rice World c.v. of -8.38 -42.21 -20.63 -0.62 5.94 26.96 16.74 43.72 11. 25 0.79 -9.64 5.64 124.56 -19.01 9.49 36.08 10.12 17.87 -12.18 1.13 10.28 4.78 5.88 -11.37 34.25 30.67 -9.29 2.45 1. 01 1.02 1. 79 1.88 0.32 2.36 0.93 0.49 1.11 1. 21 1. 23 0.93 1.19 2.90 0.43 0.84 0.80 2.65 1.61 6.25 1.12 1.00 1.02 1.90 0.38 4.59 1.52 3.94 1.09 1.00 0.92 0.42 1.99 0.86 -2.84 -7.42 -23.27 5.68 11.53 14.20 30.17 12.98 2.14 14.52 1.20 1.43 1.02 1.14 1.24 1.90 2.91 1.08 2.43 1.05 Prices Wheat (percent) 1973/74 1974/75 1975/76 1976/77 1977/78 1978/79 1979/80 1980/81 1981/82 1982/83 1983/84 1984/85 1985/86 1986/87 1987/88 1988/89 1989/90 20.44 16.64 13.51 6.12 17.80 7.49 8.94 12.66 15.44 4.84 6.06 5.95 5.60 3.12 12.07 6.01 6.71 13.33 13.62 5.42 10.70 9.47 9.80 7.90 8.47 3.19 5.61 2.25 7.74 7.43 5.56 14.00 2.40 3.49 20.66 17.02 24.17 11.49 5.74 17.65 8.34 6.16 17.15 5.86 7.45 5.55 6.68 9.06 5.25 5.05 5.36 -32.70 50.75 -23.64 -24.09 -24.71 35.28 21.88 33.84 12.01 9.47 10.03 15.02 3.24 14.66 8.51 8.87 8.48 7.43 5.09 5.85 4.76 3.02 -17.79 Means 1973-89 1973-76 1977-80 1981-85 1986-89 9.96 14.18 11. 72 7.58 6.98 7.67 10.76 8.91 5.24 6.38 10.51 18.34 9.47 8.54 6.18 12.20 25.76 9.44 9.59 4.68 Source: Based on data from Bangladesh Bureau of Statistics, Monthly Statistical Bulletin. various dates; and World Bank, Conmodity Trade and Price Trends (Washington, D.C.: World Bank. various years). Notes: World price of rice: 5 percent broken, white, milled, government st~ndar, f.o.h. Bangkok export price. World price of wheat: from July 1973 to September 1973. no.1 Canadian Western Red Spring; from October 1973 to March 1985. na.1 Canadian Western Red Spring. 13.5 percent prate;n; from April 1985 to June 1990. St. Lawrence export. C.v. ;s the coefficient of variation of monthly prices . • The fiscal year starts in July. - 26 - Table 17-Correlation matrix of world and domestic price levels for rice and wheat War ld Price of Rice Item 1.00 World price of rice World price of wheat World Price of Wheat Domestic Price of Rice Domestic Price of Wheat 0.85 0.75 0.78 I. 00 0.87 0.86 1.00 0.96 Domestic price of rice Domestic price of wheat I. 00 Source: Based on data from Bangladesh Bureau of Statistics, Monthly Statistical Bulletin, various dates; and World Bank, Commodity Trade and Price Trends (Washington, D.C.: World Bank. various years). Notes: World price of rice: export price. 5 percent broken. white, milled. government standard, f.o.h. Bangkok World price of wheat: from July 1973 to September 1973, no.1 Canadian Western Red Spring; from October 1973 to March 1985, no.1 Canadian Western Red Spring, 13.5 percent protein; from April 1985 to June 1990, St. Lawrence export. C.v. is the coefficient of variation of monthly prices. Table 18-Correlation matrix of world and domestic price differences for rice and wheat Wor ld Price of Rice Item World price of rice World price of wheat Domestic price of rice Domestic price of wheat 1.00 World Price of Wheat Domestic Price of Rice Domestic Price of Wheat 0.18 -0.04 -0.01 1. 00 -0.04 -0.05 1.00 0.52 1.00 Source: Based on data from Bangladesh Bureau of Statistics, Monthly Statistical Bulletin, various dates; and World Bank. CormlOdity Trade and Price Trends (Washington, D.C.: World Bank. various years). Notes: World price of rice: 5 percent broken, white, milled, government standard, f.o.b. Bangkok export price. World price of wheat: from July 1973 to September 1973, no.l Canadian Western Red Spring; from October 1973 to March 1985, no.l Canadian Western Red Spring, 13.5 percent protein; from April 1985 to June 1990, St. Lawrence export. C.v. is the coefficient of variation of monthly prices. - 27 - Figure 8-Rice prices, 1972-89 TAKA/MAUND n n n n n ~ 00 ~ 81 M ~ M ~ M ~ U 00 FISCAL YEAR Source: Based on data from Bangladesh Bureau of Statistics. Monthly Statistical Bulletin, various dates; and World Bank commodity prices. Figure 9-Wheat prices, 1973-89 TAKA/MAUND 150 n ~ n n n N 00 81 82 M M ~ 00 ~ U 00 FISCAL YEAR Source: Based on data from Bangladesh Bureau of Statistics, Monthly Statistical Bulletin, various dates; and World Bank commodity prices. - 28 - Table 19-Yearly imports of rice and wheat, 1972/73-1989/90 Year- Rice Rice per capita Wheat Wheat per capita (1,000 metric tons) (grams) (1,000 metric tons) (grams) 396 83 270 394 195 304 57 723 85 148 316 185 695 35 260 583 75 300 1972/73 1973/74 1974/75 1975/76 1976/77 1977 /77 1978/79 1979/80 1980/81 1981/82 1982/83 1983/84 1984/85 1985/86 1986/87 1987/88 1988/89 1989/90 5,417 1,115 3,480 4,990 2,402 3,676 664 8,322 957 1,620 3,411 1,938 7,159 352 2,539 5,606 705 2,767 2,475 1,635 2,130 1.094 630 1,361 1,108 2,086 1,004 1,085 1.524 1,884 1,885 1.163 1,507 2,328 2,063 1,234 33,643 21,690 27,542 13,848 7,743 16,410 13,045 23,924 11,302 11,941 16,416 19,781 19,391 11,663 14,767 22,359 19,305 11,335 Source: Based on data from Bangladesh Bureau of Statistics, Statistical Yearbook 1989. (Dhaka: BBS, 1990) . • The fiscal year starts in July. 5. A MODEL OF THE PUBLIC FOODGRAIN DISTRIBUTION SYSTEM IN BANGLADESH INTRODUCTION Foodgrain prices are determined by the interrelationship between private sector decisions concerning production, consumption, storage, and marketing, and government sector decisions related to public distribution, procurement of domestic production, imports, and stock management. Whereas, in describing the behavior of the private sector, prices may be assumed as given, for the public sector this is not the case, since a 1arge number of options for affecting pri ces are avail abl e to the government. Therefore, in modeling the interaction between the government and private sectors, there is an asymmetry of behavior in relation to prices. The design of stock policy should take into account this kind of asymmetry. The foodgrain sector in Bangladesh is represented mainly by rice and wheat. Whereas rice is predominant in production, contributing more than 95 percent of total foodgrains, wheat is predominant in publ ic distribution, mainly because of the quantities made available by food aid. Given the substitutabil ity of rice and wheat (the cross price elasticity of demand for rice with respect to wheat is 0.13 according to Bouis 1989), the demand for these grains has to be determined simultaneously. Government operations, in both distribution and procurement activities, affect prices of rice and wheat. Both commodities are storable and, especially for rice, there is a very active network of intermediaries between farmers and consumers (Crow and Murshid 1989). One fundamental aspect of this network is the presence of storage along with a demand for storage generated by profit motives. THE MODEL In equil ibrium, demand for foodgrains is equal to marketable supply, (4) where dl is the demand for grain i at time 1, and ms; is the marketable supply bf grain i at time 1. Marketable supply is given by production plus the net distribution from the government, since exports of foodgrains are either not allowed or are not yet feasible, and imports are monopolized by government. The distribution by the government consists of monetized distribution - 30 - through rationing and open market sales, and in nonmonetized distribution such as food-for-work, gratuitous relief, and vulnerable group feeding. To obtain the net distribution from public stock, procurement has to be subtracted from total offtakes. Therefore, msi7 = qiT + mofTi + nmof1i + omsir _ qpi7' (5) where q; production of grain i at time T, mof1i monetary off takes of grain i at time T, nmof; nonmonetary offtakes of grain i at time T, oms 1i open market sales of grain i at time T, and qp; procurement of grain i at time T. Note that this equation allows computation of the demand for foodgrains, which consists of both demand for consumption and demand for storage. This can also be expressed by saying that the marketable supply of foodgrains is either consumed or stored; that is, (6) where ms; the marketable supply of grain i as of time T, c; consumption of grain i as of time T, and variation of private stocks of grain as of As it is, data on either consumption or private stock are not ava il ab 1e on an aggregate bas is. Therefore, both consumption and private stock changes have to be expressed in terms of underlying variables such as prices and income. In part i cul ar, consumpt i on of grai n i wi 11 be expressed as a, function of its own price, p', the price of the substitute grain, p; (where i+j), and income, Y1: 1 (7) - 31 - Private storage will depend on the difference between expected prices for the next period and current prices, so the change in private storage can be expressed, as follows: ( 8) where A is the difference operator, and pi+ is the price of grain i expected to prevail at time T+l, based on t~ information available at time 1The expression for the change in private stocks can be derived from an underlying model of private storage that is reported in Appendix 3. As a result of this analysis, the behavior of the private sector can be described by the following set of equations: (9) (10) where the are error terms. The set u,i of instrumental variables is ~/s (11 ) where stock i is ending period public stocks of grain i at time T, mi denotes imports of grain i at time T, and lose~ denotes rice losses at time 1A three-stage least squares estimation of the system is implemented to take into account the simultaneity of the price of rice and wheat. The complete specification of the foodgrain dynamic system is given below: r -r (12) + a3m, + a4losses, + asy" PHI al + a2stock~_1 -w bl + b2stock~_1 PHI pr, r ci + C2P,_1 + C3P~+1 pW, stockr " dl + d2P~_1 = (13) (14) + d5ms~ + d6y" + mr + qpr _ mof r _ nmof r - oms r + d3P~+1 ljrstock r + b3mW, + b4losses, + bsy" W r + c4P, + csms, + c6Y" 1-1" + d4p~ 7" 1 7" ,,' (15) (16) - 32 - W + mW + qpW _ mofw stockrW= aWstock.,.-1 r r ,. _ w nmofTw - oms 1"' (17) ms rr = qrr + mofrr + nmof1r + oms ,.r _ qprl' and (18) msW,. = qW1 + mof",. + nmof,.w + oms ,.w _ qpW1· (19) Equations (12) and (13) try to forecast the next period price by using opening publ ic stocks, imports, forecast of rice losses, and income. Equations (14) and (15) relate the current prices of both rice and wheat to the lagged price, the forecast of future price, the marketable surplus defined in equations (18) and (19), and income. Note that income and current pri ce of the a lternat i ve foodgra income from the demand for consumption, whereas the lagged and expected future prices come from the demand for private stocks. Equations (16) and (17) give the law of motion for public stocks. ESTIMATION OF THE MODEL The system specified above has been estimated by three-stage least squares using seasonal observations from 1975/76 to 1989/90. Each year contains 4 seasons, and 59 seasons have been used in the estimation. Prices are deflated by the index of manufactured goods and quantities are in per capita terms. For a description of the data see Appendix 4. The first two equations reported i.n Table 20 give the instrumental variable estimation of future price, p~+. All the variables have the expected sign and most of them are significant. In particular, opening stocks have an important negat i ve effect on future pri ces. Si nce imports add to the available supply, their coefficients are expected to be negative; nevertheless, the coefficients are not statistically significant. Losses in rice production that originate from cyclone, drought, and flood affect future prices because of an expected shortfall over the upcoming period. For rice, the effect of losses on prices is significant, whereas the opposite is true for wheat, mainly because the behavi or of expected wheat pri ces is not so heavily i nfl uenced by the production of rice, given the predominant role of wheat imports in the public distribution. Income positively affects future prices by increasing current consumption and lowering the supply available during the coming period. In terms of goodness of fit, the price equations explain a good deal of the total variation of prices. For rice, the speculative effect of future prices on current price is particularly important, as demonstrated by the coefficient of P~+l in Table 20. In fact, the coefficient of future price is of the same order of magnitude as the coefficient of lagged prices, indicating a support for the hypothesis of profit maximizing demand for storage (Goletti 1990). Both wheat prices - 33 - Table 2O-Estimated equations of the foodgrain system, 1975/76-1989/90 Variable Coefficient t-Value Equation for lead price of rice Constant stock~ mRt losses t Yt Valid cases R' SEE -0.0777 -0.0090 -0.0043 0.0031 0.0648 -1.1509 -3.9992 -1.1459 3.4254 6.5778 59 0.60 0.0314 Equation for lead price of wheat Constant stock":, mw t losses t Yt Valid Gases R' SEE -0.0520 -0.0040 -0.0011 0.0004 0.0413 -1.2435 -3.3182 -1.3023 0.7166 6.4386 59 0.46 0.02 Rice price equation Constant R Pt-, _R Pt+1 p';' ms~ Yt Va 1 id cases R' SEE 0.0133 0.3577 0.3767 0.8059 -0.0007 -0.0094 0.3500 6.2749 4.4274 5.1137 -8.6816 -1.1840 59 0.88 0.17 Wheat price equation Constant w Pt-1 P";'+1 p~ ms~ Yt Valid cases R' SEE -0.0174 0.2218 -0.4951 1.8096 -0.0673 0.3014 -0.0013 0.0145 -0.3135 2.2013 -1.3566 I. 8839 59 0.65 0.16 (continued) - 34 - Table 2O-Continued Source: Estimated by the authors, with seasonal data. Definitions of terms: stock~ 1>~+ stock of grain; at time t; n\ imports of grain i at time t; losses t losses of rice during time t; Y. p~ income at time t; price of grain; at time t; 1 ms~ instrumental variable estimation of price of grain i at time t+l; marketable supply of grain; time t; t refers to season (season 1, Ju lY-October; season 2 SEE season 3. March-April; season 4, May-June); and standard error of estimation. I November-February; and marketable supply have the expected signs. Wheat prices have a positive effect on rice price due to the substitutability of rice and wheat in consumption. Income does not have a s i gni fi cant effect on current pri ces, rna i nly because its i nfl uence is captured by future pri ces P~t' For wheat, it is noteworthy that the speculative effect is not sign,Ticant, as pointed out by the coefficient of future price pW+l (Table 20). This suggests a reestimation of the model with the 'constraint of zero coefficient of future wheat prices. The reduced form of this estimation is the one that is used in the simulations. The coefficients of the estimation are reported in Table 21. The model tracks the price of rice and wheat quite well. For rice and wheat, the root mean square error for the overall period is 11 and 12 percent, respectively. For more recent samples, the performance improves. For example, for the period 1985/86-1989/90 it is 4 and 5 percent, respectively. Within this model, the tracking of stock variables depends on the accuracy of the data on both procurement and off takes. The balance equations for stock (given by equations [16] and [17]) are the basis for the tracking of stock variables. The less than perfect match between predi cted values and actual values is due to unreported storage losses. By applying a storage decaying factor of 6 percent it is poss i bl e to improve the dynami c s imul at i on of stocks considerably. - 35 - Table 21-ihree-stage least squares estimation of price equations of foodgrain system, constrained, 1975/76-1989/90 Variable Coefficient t-Statistic 0.0130 0.3648 0.3789 0.7784 -0.0007 -0.0090 0.3436 6.4014 4.4535 4.9369 -8.7219 -1.1298 Rice price equation Constant R p., P:+1 p,w ms~ y, 59 0.8834 0.0170 N R' SEE Wheat price equation -0.0171 0.2385 0.2777 -0.0012 0.0129 Constant w Pt.' p~ ms~ y, -0.4868 -2.4379 3.4312 -1.9158 1.9261 59 0.6546 0.0164 N R' SEE Source: Est imated by the authors. Note: The coefficient of future prices in the wheat price equation has been set equal to zero. Definitions of terms: income at time t; price of grain i at time t; instrumental variable estimation of price of grain; at time t+l; ; ms, marketable supply of grain i time t; t refers to season (season 1. Ju ly-October; season 2, November-February: season 3, March-April; season 4, May-June); and SEE standard error of estimation. 6. POLICY CONSTRAINTS AND POLICY OBJECTIVES With reference to the general approach of Chapter 3, so far only equation (1) has been made explicit by introducing the response of the private foodgrain sector in Chapter 5. The specification of the policy constraints, as in equation (2), and the objective function, as in equation (3) of problem (P), remains to be done. This task is taken up in this chapter. THE POLICY CONSTRAINTS The endogenous variables in the general framework introduced above are constrained as in equation (2). Some of these constraints simply state the non neg at i v.ity of some endogenous vari abl es, namely, pri ces and stocks. Some other constraints are capacity constraints, imposed upon stock variables to take into account the physical storage facilities constraints. The capacity constraints are expressed as follows: 1 stockTi < Gmax' - (20) where i stands for either ri ce or wheat, 'f = t, ... , T, and G~ax is the maximum stock of grain i (assumed independent of time). A third set of constraints on stock variables takes into account mlnlmum stock requirements that may be related both to deadstocks (the amount of stock needed for the system to be operat i ona 1) and to the mi nimum stock 1eve 1s needed for food securi ty consi derat ions. An example of the latter is that the public food distribution system must hold sufficient stocks to meet three months of offtake requests (505,000 tons), allowing the time frame necessary for importing foodgrains to replenish the stock facilities. These minimum stock requirements can be expressed as follows: 5 i stock.,.i > - G min' (21) 5 Note that both minimum and maximum stock requirements imply constraints for, decision then variables. For example, assuming that the decision variables are open market sales (oms~). ;s equivalent to - 37 - A fourth set of constrai nts is related to maximum domest i c procurement and can be expressed as follows: (22) where qpi is procurement of grain i at time 1, and qi is production of grain i 1t time 1, that is, maximum procurement is just a fraction, r, of total production. Finally, a fifth set of constraints that are considered in the following policy exercises is related to foreign reserves. This type of constraint can be expressed as follows: wapi • mi . < Fi 'T 'T - l' (23) where wapi1 is the world price of grain i at time 1, and ~i is the maximum amount of foreign exchange allocated to food imports m;; THE OBJECTIVE FUNCTION The objective function specification depends on the type of policy pursued. In the following pol icy exercises, two main objectives are considered: price stabilization and cost minimization. 6 The objective of price stabil ization is to be understood as minimization of the variance of prices around a target price. In order for such an objective to be made precise, a target price 8 has to be specified for the period of the policy exercise going from ~=t to 1=T. The objective can then be expressed as follows: T L(p~ -8 1 )2/(T -t+l) (24) 1=1; The difficulty 1 ies with an appropriate specification of the target price. Several elements will be taken into account in the specification of the target price. First, a long-term trend of domestic prices; second, a concern for seasonality fluctuations; third, the behavior of 6 Note that a third important objective of food stock policy ;s poverty reduction. This objective can be expressed by means of one commonly used poverty measure, such as that proposed by Foster, Greer, and Thornbecke (1984). In order to do that, a value for the parameter a of the severity of poverty has to be chosen. Moreover, some parameters relative to rice and wheat consumption of subgroups of the population have to be provided to make operational the computation of the poverty index. In this context, note also that the objective of food security has already been incorporated in the policy constraints, related to minimum stock requirements. - 38 - world prices. The target becomes a weighted average of these elements, where the weights reflect the relative importance attributed to them by the government. 7 The objective of cost minimization can be readily specified, once an expression for the cost is provided. The relevant cost expression here is the operating balance of the food accounts. Basically this cost refers to the difference between expenditures and revenues, as these items have been defined in Appendix 5. For the time period of the policy exercise, the expression of the cost is given by T :E :E T=t p'-t[wop;m; + pp;qp; - p;oms; - pr;mof;l. (25) i :::r,W Expenditures are here simply given. by .the value, at international prices, of food imports (the term ~op; •.m;) and by the cash outlays for domestic procurement (the term pp' • qp'). Revenues are given ~y the monetary off takes evaluated at ration p?ices (the term pr; • mof;) and br the value of open market sales, evaluated at market prices (the term P, • oms;). Note that p is the parameter used to discount the future. 7 The expression for the weighted average is 1n(9,) = A, • 1n(p;) + A, • 1n(p:) + A, • 1n(wop~. where p~ denotes the long-term domestic price of rice, p~ ;s the seasonal factor, and wop~ is the world price of rice. Note that the target price considered here is the target for rice prices. 7. OPEN MARKET OPERATIONS In most of the policy exercises presented in the text, the policy instruments controlled by the government are open market operations (omo'). Open market operations are conducted at market prices. It is posslble to express open market operations in terms of both open market sales (oms;) and open market purchases (omp;) as follows: (26) Both open market sal es and open market operations are pos it i ve, but their difference can be any sign. From this observation, it follows the convention that positive open market operations have to be interpreted as open market sales, and negative open market operations have to be interpreted as domestic procurement. The way the government has impl emented open market sal es and domestic procurement so far can be schematically represented as follows: sell oms; at price poms;; buy qp; at price pp;. The prices poms i are called "oms prices," and the prices ppi are called prices "procurement prlces." Note that both oms prices and procu~ment are preannounced. At this point there are some conceptual and practical problems. What follows refers to procurement, but similar observations apply to open market sales. The,basic conceptual problem is, How can government ensure that an amount qp' is procured at price pp'? Procurement depends on the capacity and willihgness of the farmers anB traders to sell. Unless some forced arrangement is put into effect, procurement is constrained by the supply decisions of traders and farmers. These supply decisions depend, among other things, on the differential between procurement prices and open market prices. Following the model of Appendix 1, one can postulate a relation of the type (27) - 40 - The basic, point,to be made here is that the government can decide upon either p~ or, qp~. Wi,thin this contractual arrangement, it cannot decide upon both pp' and qp'. The procurement policy of the government then is reduced mainly to the setting of procurement prices, while taking into account both the effect of procurement prices on quantities actually procured (see equation (27)) and the effect of procurement quantities on market prices have to be (see equations [5] and [10]). In fact, both these ef~ts considered simultaneously, as is done in Appendix 2. The results given in Table 45 in Appendix 2 show, among other things, that procurement prices have not been a significant determinant of procurement. Now a practical problem emerges. Even though the fit of price equations is reasonably high (Figures lOa and lOb), in any estimation of procurement supply and monetary off takes as in equation (27), the goodness of fit is very low (Table 45, Appendix 2; Figures 10c-lOf). This implies that use of such equations for planning purposes and for the eval uation of different pol icies is bound to be very uncertain, resulting in a large margin of error. Moreover, because of the linear specification of equation (27) that is often used in many other studies, there is no reason for the predicted value of this equation to be positive. It may perfectly be the case that the predicted val ue of procurement is negative, an outcome that does not make sense. Supposedly, the intention of the government in setting procurement prices is to support domestic prices, especially in periods immediately after harvest. By announcing procurement prices in advance of harvest time, the government cannot really know the level of market prices. However, based on some predictions, it may still establish a reasonable 1eve 1 of procurement pri ces. Yet, as observed above, there is no reliable way of estimating how much grain could be procured. This would make any estimate of its impact on market prices even more unreliable. Moreover, one should keep in mind that the way procurement activities are actually implemented, mainly through a system of licensed dealers, always generates rent-seeking activities that produce waste and make any evaluation of the effects of procurement prices again very unreliable. Because of all these observations, it seems appropriate to consider open market purchases as an instrument to repl ace domest;ic procurement (that is, in terms of the notation introduced above, qp' = ompi). This would achieve the same purported effect of procuem~nt activities as they are currently conducted, namely to support prices, and their effect on prices could be calculated with a relatively higher degree of reliability. Finally, this would reduce the opportunities for rent-seeking activities, since the purchases will be conducted at market prices. In view of these considerations, by reca,ll ing that marketable plus off takes (both supply, ms!, is equal to domestic production, q~, monetary and nonmonetary) plus open market sales minus domestic procurement, the following equation is developed: (28) Figure lO-Actual and simulated values of the foodgrain system with public distribution, 1975-89 lOa-Rice price n Kg./CAPITA TAKA/MAUND TAKNMAUND n IOc-Rice procurement IOb-Wheat price n ~ 00 M ro ~ ~ ~ M ~ M M ~ n n ~ 00 m ro ~ M 00 ffi ~ 00 IOe-Rice monetized off takes IOd-Wheat procurement ~ M M & M ~ ffi M ~ 00 ~ ~ ..... IOf-Wheat monetized offtakes Kg./CAPITA Kg./CAPITA n n n $ Kg./CAPITA '" u n n n 00 M ~ & ~ ~ ~ ~ • ~ M n ~ N 00 M ~ ~ ~ ~ ~ u ~ ~ n n n N 00 M ~ ~ M ~ ~ ~ • N - 42 - Since open market operations affect the domestic supply of foodgrains, they directly affect prices, as can be seen from the price equation (10) derived in Chapter 4. It is reproduced here for convenience: Therefore, it is expected that open market operations (oms i - omp~) have a negative effect on prices insofar as they contribute to' augmentation of the domestic supply. 8. SPECIFICATION OF POLICY OPTIONS In the simulations of policy options for the foodgrain sector of Bangl adesh, two types of exerci ses can be done. In the fi rst type, counterfactual simulations of various policy options can be examined, based on the historical values of exogenous variables. In the second type, ex ante simulations can be performed, using stochastic simulation for the exogenous vari abl es. In thi s paper, only the fi rst type of simulation is reported. Several elements have to be clarified at the outset of the exercises. Among these elements are the time period of the simulations, the initial conditions, the exogenous variables, the endogenous variables, the control variables, and the objective of the policy. In each policy, a baseline is computed in order to compare the effect of different policies. Six pol icies are evaluated: price band; optimal price stabilization; import approach to price stabilization; cost minimization; price stabilization cum cost minimization (this is is called the benchmark policy in this paper); and approximation to optimal price stabilization. A summary of these options is gi ven in Figure 11. A detail ed description of each policy follows. PRICE BAND POLICY Establishing a price band mechanism implies setting a target price, a price band, and a rule of intervention. The target price is denoted by 8 , where the time index T varies over the period of the pol icy exercise. Generally, the target price chosen is a weighted average that takes into account the long-term trend of domestic prices, seasonality, and the long-term trend of world prices (Ahmed 1990). It is constructed in the same way as the target price described in the definition of the price stabilization objective (see Chapter 6). The price band is defined with reference to the target price and the specification of an upper and a lower intervention price that should trigger open market operations. Usually, the upper ands lower trigger prices are symmetrical in relation to the target price. a Denoting these trigger prices by phigh and plow, they are related to the target price, 6T • as follows: phigh, = (1 + p) • plow, = (1 + p) • e,. e,. and - 44 - Figure Il-Policy options considered in the simulation exercises Baseline Simulation of the foodgrain model for the period July 1985-June 1988. All exogenous and control variables are taken at their historical value. Price Band Uses open market operations to maintain a real price band of plus or minus 4 percent around the target. Optimal Price Stabilization Uses open market operations to minimize variance of prices around the target. Import Uses imports to minimize the variance of rice prices around target. Cost Minimization Uses open market operations to minimize the total cost of food operations. Benchmark Uses open market operations and imports to minimize the total cost of food operations subject to price stabilization and foreign reserves constraints. Approximation Approximates the optimal price stabilization. It is obtained by stochastic simulation of production shocks, and by expressing open market operations as a function of ri ce and wheat production and of their own past. Under the rule of intervention, open market sales are undertaken by the government until either prices drop to the ceiling of the band or public stocks reach the minimum operational level. The minimum stock requirement is the same as the one mentioned in Chapter 6 that would guarantee food security, and translates into equation (21). Similarly, when prices in the absence of intervention tend to go below the lower price of the band, open market purchases are undertaken by the government until either the maximum stock capacity is reached or The maximum stock pri ces ri se to the lower 1eve 1 of the band. requirement translates into equation (22). Finally, when prices are within the band, no open market operations are undertaken unless stock constraints are binding. When this is the case, open market operations are undertaken in order to satisfy the constraints. - 45 - The main advantage of a price band rule seems to be that the rule can be simply stated, is relatively easy to implement, and is readily understandable. Therefore, it has desirable features from an operational point of view. Nevertheless, the outcome is not optimal, because it does not use all the available information. A price band rule is a fixed rule, clearly suboptimal with respect to the rule that can be computed as a solution of an optimization problem (Buiter 1981). OPTIMAL PRICE STABILIZATION POLICY The objective of this policy is to minimize the variance of rice prices around a target price path as it was defined in Chapter 6. As in the case of price band policy, the underlying motivation is to stabilize prices. But, unlike price band policy, the objective of price stabilization is stated explicitly, and the policy is the outcome of an optimization exercise. The instruments available to the government are open market operations. Following the general approach of Chapter 3, the constraints are given by the foodgrain model of Chapter 5, and the constraints on open market operations that are implicit in equations (21) and (22). IMPORT POll CY In this context, stabil ization pol icy, variance of rice prices is in the instruments imports of foodgrains. trade policy is similar to the optimal price insofar as the objective is to minimize the around a target price path. The only difference used. The control variables are now given by It is assumed that no exports take place. COST MINIMIZATION POLICY In this case the explicit objective of the policy is to minimize the present value of cost, as given in equation (25). The basic policy issue here is to see how the public food distribution. assumed in the baseline can be carried out at minimum cost. The instruments chosen are again given by open market operations. BENCHMARK: PRICE STABILIZATION CUM COST MINIMIZATION POLICY In this policy option all the previous considerations regarding cost efficiency, price stability, and food security are included. The objective is again to minimize the cost of operations, but new policy instruments and constraints are now added. - 46 - The policy instruments are given by both open market operations and imports. Besides the reaction of the private sector, given by the system of equations in Chapter 5, constraints on minimum and maximum stock requirements are specified. In addition to these constraints, two more constraints related to price variabil ity and foreign exchange reserves are considered. The constraint on price variability requires that prices move in a plus or minus 4 percent band around the target price. The foreign exchange constraint imposes a ceil ing on foreign exchange that can be spent on imports. The ceil i ng is gi ven by the foreign exchange equivalent of foodgrain imports in the baseline. The formal expression of this policy is reported in Appendix 6. APPROXIMATION POLICY In general, the optimal paths of the policy instruments used for the previous policies are not easily related to the underlying variables of the system. It would be interesting to approximate the optimal policies, with "simpler" policies, easily understood and implementable (Pinckney 1988, 1989).9 Examples of these approximation policies are linear feedback rules, expressed in terms of the current state of the system. One specific way to get such an approximation is described in Appendix 7. 9 To make this intuition clear, one should introduce a norm in some metric space of functions. 9. EVALUATION OF COUNTERFACTUAL SIMULATIONS In this case, the model of the foodgrain sector is used ex post to do counterfactual simulations. The three-year period 1985/86-1987/88 is considered in this exercise, for a total of 12 seasons, characterized by the first two years as just above average in terms of production, and the third as a "bad" production year (see rice production in Figure 3). The baseline for these simulations is constructed by taking exogenous values and predetermined variables at their historical values (Tables 22-25) and running the reduced form of the model in order to get the endogenous variables (prices and stocks). In the pol icy options presented below, open market operations and imports are policy instruments that, as such, are choice variables in the optimization problems considered. Their counterparts in the baseline are open market sa 1es, procurement quant i ties, and imports actually performed by the government during the period 1985/86-1987/88. The total cost for the pipeline is more than Tk 17 billion, and the average foodgrain stock level is nearly 1.1 million tons. The insight gained from this type of exercise facilitates comparison of different policy options with the one that is already in place from the perspective of the government's objectives of ensuing price stability, cost efficiency, and food security. The detailed results for each policy are given in Tables 26-39 at the end of this chapter. The summary statistics of the various policy options appear in Chapter 10. PRICE BAND POLICY This policy is very effective at stabilizing prices (the coefficient of variation goes from 6.0 percent in the baseline to 4.4 percent), yet it is not cost-effective (Tables 26 and 27; Figure 12). The total cost of operations is Tk 19.6 billion, which represents an increase of 15 percent in relation to the baseline cost, mainly due to the increased rol e of procurement (that is, open market purchases). Note that by intervening to buy when prices are lower than the target, the overall price path is altered, causing an accumulation of stocks that puts a downward pressure on prices. The average foodgrain stock for this policy is nearly 1.5 million tons. Therefore, the attempt to stabilize prices above the floor of the band is frustrated by the rule of operations of the policy. Clearly, this outcome could be avoided if the government were allowing stocks to accumulate indefinitely, but this is not possible given that public storage facilities have a limited capacity (2 million tons is the level used in the simulations). - 48 - Table 22-Variables in the baseline, 1985-88 Price b Year/ Season- Rice Stock Wheat Rice Wheat Winter Bora 1986/87 Aus Aman Winter Bora Im[!orts Rice Wheat (kilograms/capita) (Tk/maund) 1985/86 Aus Aman agen Market Ogerations C Rice Wheat 33.7 30.7 35.0 36.0 20.9 20.5 20.7 . 22.2 3.67 3.98 3.64 3.32 6.66 3.22 4.39 6.12 0.07 0.01 0.06 0.04 0.35 0.14 0.00 0.00 0.12 0.09 0.14 0.00 4.42 1. 39 2.78 3.08 37.5 35.6 38.4 38.3 23.0 22.3 22.0 23.2 2.17 2.17 1.92 3.29 7.72 3.59 3.38 5.63 0.50 0.03 0.48 0.30 0.64 0.40 0.04 0.03 0.23 0.55 0.79 0.97 5.19 2.10 3.21 4.27 37.9 36.2 37.5 36.3 23.1 22.4 22.0 22.7 4.87 5.55 5.04 7.24 7.84 10.14 10.27 10.68 0.88 0.19 0.10 0.04 0.68 0.12 0.03 0.00 2.90 1.61 0.32 0.77 8.43 9.23 2.36 2.34 36.1 22.1 3.90 6.64 0.22 0.20 0.71 4.07 2.2 0.9 1.56 2.74 0.27 0.25 0.83 2.47 1987/88 Aus Aman Winter Bora Mean Standard deviation Source: Estimated by the authors. Note: The baseline is obtained by simulating the foodgrain madel for the period July 1985-June 1988 . • The seasons are defined as follows: aus, July-October; aman, November-February; winter, March- April; and boro, May-June. b Prices are deflated by the index of manufactured goods. C Positive open market operations have to be interpreted as open market sales: negative open market operations have to be interpreted as domestic procurement. Some of these undesirable outcomes may be avoided by planning a more adequate price band width and a different target price. All that is pointed out here is a caveat against an enthusiastic support of fixed rul es of ope rat ions that do not a11 ow for a necessary degree of flexibil ity in reacting to new information in an efficient way. The substance that emerges from this analysis is that price bands are a very complex policy to plan. One main criticism of price bands that should be kept in mind is that, unless the band itself is changed periodically, the buffer stock either tends to depl ete to a very low 1evel or to accumulate, at times, to an unmanageably high level. In the simulation presented here, for example, the capacity constraints are binding, since the maximum stock level of almost 2 million tons is reached. - 49 - Table 23--tosts in the baseline, 1985-88 Year/ Procurement Cost Season- Imports Ration Sales Open Market Sales Totalb Cost (Tk million) 1985/86 Aus Foreign Exchange (US$ Cash OutflowC million) (Tk million) 514 888 492 303 1,308 862 1,682 1,673 1,619 1,366 518 515 111 70 50 35 1,001 313 1,607 1,426 77 28 56 55 -1,087 -461 90 -98 47 169 107 1,021 2,353 1,237 1,913 2,464 1,515 1.790 984 804 813 244 472 313 72 -628 564 2,367 78 40 62 80 -1.918 . -1.550 -865 516 Aus 292 404 273 1,860 5,720 5,765 1,452 2,120 2,346 2,296 803 479 1,242 249 112 37 2,424 3,624 810 3,463 185 186 46 67 -684 212 -67 2,286 Total 6,380 29,548 15,035 3,848 17,045 959 -3,623 489 1,535 642 351 1. 274 50 1,047 Aman Winter Bora 1986/87 Aus Aman Winter Bora 1987/88 Aman Winter Bora Standard deviation Source: Estimated Note: The baseline is obtained by simulating the foodgrain model for the period July 1985-June 1988 . by the authors. • The seasons are defined as follows: aus, July-October; aman, November-February; winter, MarchApr;l; boro, May-June. b Total cost = procurement cost + import cost - ration sales - open market sales. C Cash outflow = total cost - foreign exchange. OPTIMAL PRICE STABILIZATION POLICY In this case the objective is to mlnlmlze the variance of prices around the target price; the policy instruments are open market operations (Figures 13a, 13b, and 13c). Stabil ization is perfect (Figure 13a) and is achieved at approximately half the cost of the baseline, that is, about Tk 8.4 billion (Tables 28 and 29). This remarkable result was mainly due to an intensive use of open market sales and domestic procurement. The variability of total cost is very high across seasons in the simulation period. The standard deviation of total cost is almost three times the level in the baseline. Note that in thi s case both imports and monetary offtakes are kept at thei r historical levels. If imports were eliminated it would not be possible to sustain the level of off takes specified in the simulation. This is because domestic procurement of wheat is insufficient to meet the demand of wheat through both monetized and nonmonetized channels of the public . food distribution system. It will also be seen in the following policy exercises that if both open market operations and imports are rationally used as policy instruments, wheat imports can be reduced substantially. - 50 - Table 24-Historical values of prices used in the baseline, 1985-88 Year/ Season- Rice Wheat Price Price Rice Wheat Rice Procurement Procurement Ration Price Price Price Wheat Ration Rice World Wheat World Price Price b Price b (Tk/maund) 1985/86 Aus Aman Winter Bora 278 259 303 317 173 173 178 196 263 255 255 260 162 162 175 180 262 268 269 273 173 179 181 187 235 255 238 228 191 216 214 201 336 318 340 362 207 199 194 219 265 274 284 300 180 180 190 200 283 283 283 283 192 192 192 192 235 230 244 246 157 156 157 154 346 334 351 347 211 207 206 218 300 308 308 308 198 200 200 200 288 301 313 315 196 201 204 208 279 331 357 351 149 166 170 206 1986/87 Au, Aman Winter Bora 1987/88 Aus Aman Winter Bora Source: Based on data from Bangladesh Bureau of Statistics, Monthly Statistical Bulletin, various dates . • The seasons are defined as follows: aus, July-October; aman, November-February; winter, MarchApril; bora, May-June. b World prices are converted from U.S. dollars. The result obtained from this policy analysis is that a flexible policy approach to price stabilization, where open market operations are used more intensively than in the case of price bands, brings about sUbstantial improvements. The average foodgrain stock level is about 1.1 million tons. IMPORT POLICY Here imports are used to stabilize prices. Open market sales are kept at their historical levels so that the effect of imports is felt through future prices. Since imports negatively affect the expectations of future prices, they also moderate current prices. The reduction of price level and price variability is remarkable (Tables 30 and 31; Figure 14). Compared with the case where open market operations were the only policy instrument (that is, in the optimal price slabilization option), the total cost associated with the import policy is now higher (Tk 14.7 billion versus Tk 8.4 billion). Table 25-Historical values of quantities in the baseline, 1985-88 Year/ Season a Product ion Rice Wheat ImI10rts Rice Wheat Procurement Rice Wheat Monetary Offtake Rice Wheat Open Market Stock Sa les Rice Wheat Rice Wheat (1,000 metric tons) 1985/86 Aus Aman Winter Bora 3,084 8,286 367 3,304 0 0 1,042 0 12 9 14 0 437 138 278 310 70 130 9 22 7 0 92 31 99 61 27 27 199 193 67 63 7 1 6 4 35 13 0 0 378 413 344 351 620 275 401 619 3,378 8,019 401 3,609 0 0 1,091 0 23 56 81 100 525 214 329 439 6 23 0 107 1 0 21 30 68 62 35 24 194 256 139 121 50 3 49 31 65 41 4 3 178 175 119 241 728 274 268 506 3,224 7,459 473 4,258 0 0 1,048 0 300 168 34 81 872 962 248 246 35 49 0 204 2 0 51 33 54 96 43 17 367 284 81 60 91 20 10 4 70 12 3· 0 329 415 277 640 633 825 654 849 1986/87 Aus Aman Winter Bora 1987/88 Aus Aman Winter Bora Source: Based on data from Bangladesh Bureau of Statistics, Monthly Statistical Bulletin, various dates. I The seasons are defined as follows: aus, July-October; aman, November-February; winter, March-April; boro, May-June. 01 ...... - 52 - Figure 12-Price band policy 12a-Prices of rice AMAN YEAR/SEASON 12b-Open market operations of rice Kg./Caplta 4 2 -2 -4 AMAN BORO " AMAN BORO YEAR/SEASON '" AMAN BORO AMAN BORO 12c-Open market operations of wheat Kg,/Capita -2 AMAN BORO " AMAN YEAR/SEASON BORO ", - 53 - Figure 13-Price stabilization policy 13a-Prices of rice AMAN BORO II AMAN BOAO YEAR/SEASON "' AMAN BORO 13b-Open market operations of rice Kg./Capita 8r:~mD] -BASELINE 8 2 o t't"........- ___-7"" -4 -6 -8 -1 0 P---""-'--'4-'----'---"--t-""-'-'----+---'----'---'t--'--'-----' I AMAN BORa II AMAN BOAO III AMAN BORO YEAR/SEASON 13c-Open market operations of wheat Kg ./Caplta 15 r-''------='''"'= 1or====-:' -5 AMAN BORO II AMAN BORO YEAR/SEASON 111 AMAN BORO - 54 - Figure 14-1mport policy 14a-Prices of rice Taka/Maund AMAN BORO II AM AN BORO YEAR/SEASON "' AMAN BORO "' AMAN BORO 14b-Imports of rice -1 -2 AMAN BORO II AM AN BORO YEAR/SEASON 14c-Imports of wheat 2 -1 AMAN BOAO II AMAN YEAR/SEASON BORO "' AMAN BORO - 55 - Nevertheless, the total cost of this policy option still represents a 14 percent saving in relation to the baseline. The main reason for this relatively high cost is that stocks are not used efficiently. In other words, an import policy divorced from a stock policy is not an effective tool. This suggests that in order to look for a real improvement in both cost and stabilization, both trade and stock policy have to be used judiciously. The average foodgrain stock level for this policy is 847,000 tons. COST MINIMIZATION POLICY In this case the only objective of the policy is to minimize total cost to carry out publ ic distribution. The outcome is a pol icy path that results in a total cost equal to just 35 percent of the original baseline cost, that is, Tk 6 billion (Tables 32 and 33; Figure 15). The main instrument to be used intensively to get this result is open market sales. Under this scenario, the government allows the prices to move up to a relatively high level so as to make profits by selling part of the imported grains in the open market. Note also that in this case open market purchases (that is, domest i c procurement) are very small in comparison with all previous cases. The average foodgrain stock level in this case is only 686,000 tons. The effect of cost minimization is to reduce the amount of public stock considerably. BENCHMARK: PRICE STABILIZATION CUM COST MINIMIZATION POLICY With a total cost equal only to 30 percent of the baseline (that is, Tk 5.1 billion), it is possible to achieve perfect stabilization around the target price (Tables 34 and 35; Figure 16). The flexibility of this policy allows use of both imports and open market operations to take advantage of both the domestic and the international grain markets. This implies a more effective import policy and more active open market operations. The average foodgrain stock is 724,000 tons. As in previous pol icy options, the capacity to implement the benchmark policy depends on being able to predict the exogenous variables of the policy exercise accurately enough. For this reason, sensitivity analysis with respect to production and world prices deserves some attention. Given the extreme variability of world prices, it is important to see how this policy is affected by different levels of world prices. In particular, it is interesting to perform a simple exercise to compute the benchmark pol icy when world prices are 30 percent higher. The results are reported in Tables 36 and 37. The total cost of the policy rises from Tk 5.1 bill ion to Tk 12.9 bill ion. Therefore, when world prices rise by 30 percent across the period of the simulation, total costs rise by 251 percent. This is mainly the result of lower revenues from open market sales. - 56 - Figure 15-Cost minimization policy 15a-Prices of rice 42 r=-",.~ Taka/Maund AMAN BORO " 111 AMAN BORO BORO III AMAN BORO BORO III AMAN BORO BORO AMAN YEAR/SEASON 15b-Open market operations of rice 4 2 AMAN BORO II AMAN YEAR/SEASON 15c-Open market operations of wheat Kg./Capita AMAN BORO " AMAN YEAR/SEASON - 57 - Figure 16-8enchmark policy: price stabilization cum cost minimization 16a-Prices of rice Taka/Maund AMAN BORO " AMAN III AMAN BOAO BOAO III AMAN BORO BORO 111 AMAN BORO BORO YEAR/SEASON 16b-Open market operations of rice AMAN BORO " AMAN YEAR/SEASON 16c-Open market operations of wheat Kg./Caplta -1 -2 -3 -4 AMAN BORO " AMAN YEAR/SEASON - 58 - Figure 16-Continued 16d-Imports of rice 6 \ - -_ _ _,-1, 4 AMAN BORO II AMAN BORO 111 AMAN BORO BORO III AMAN BORO YEAR/SEASON 16e-Imports of wheat -2~4+ I AMAN BORO II AMAN YEAR/SEASON Another interesting sensitivity analysis of the benchmark case is done by considering the situation where no ration distribution takes place (Tables 38 and 39). The saving in total cost is noteworthy, about 50 percent of the benchmark case (the total cost is Tk 2.7 billion). Yet the saving is not comparable to the loss of ration sales, which was much higher (Tk 15 billion, as seen in Table 37). What is the explanation for this overcompensation of the revenue loss from ration sales? Clearly, procurement activities are lower than in the benchmark case, because a lesser amount of public stock is needed for distribution - 59 - (only 690,000 tons). The import cost is almost the same, since the same ceiling on foreign reserves is binding. The big difference lies in the open market sales, since part of the stock that was previously distributed at ration shops can now be sold in the open market. APPROXIMATION POLICY In the attempt to find an approximation to the optimal policies, the methodology described in Appendix 7 has been applied to approximate the optimal stabilization policy, pursued only with open market operations. It is remarkable that the approximate pol icy tracks the optimal solution quite well (Figure 17) and also that the total cost of almost Tk 8.5 billion is extremely close to the level obtained in the optimal policy (Tables 40 and 41). The average foodgrain stock level is 876,000 tons. This amount is less than in the optimal stabilization policy, mainly because on average the open market sales are higher in the approximation policy than in the optimal policy. The result is very promising insofar as only a very limited number of variables have been included as independent variables in approximation. In fact, the feedback expression of the approximation policy is the truncated (see Appendix 7) version of oms ".i = f i (qrT' qWT' omo 7"-1 i ). (29) Therefore, only production and past open market operations are in the feedback expression. If imports also are a policy instrument, then one should include world prices as independent variables in equation (29). - 60 - Figure 17-Approximate versus optimal open market operations 17a-Rice Kg./CAPITA 8~-' 6 4 2 -2 -4 -6 -8 -10~=4" I AMAN BORO II AMAN BORO III AMAN BORO BORO III AMAN BORO YEAR 17b-Wheat Kg./CAPITA 15r7~C=- 10 5 -5 AMAN BORO II AMAN YEAR - 61 - Table 26--Variables in the price band policy, 1985-88 Price b Year/ Season- Rice Open Market Stock Wheat Rice Wheat (Tk/maund) e OQerat; cns Rice Wheat ImQorts Rice Wheat (kilograms/capita) 1985/86 Aus Aman Winter Boro 33.7 31.3 34.0 34.3 20.9 20.7 20.3 21.6 3.03 6.77 6.23 5.57 6.94 3.63 3.85 5.31 0.00 -4.68 0.00 0.00 0.00 0.00 0.00 0.00 0.12 0.09 0.14 0.00 4.42 1.39 2.78 3.08 35.7 33.6 36.9 35.4 22.5 21.7 22.0 22.4 4.73 4.87 6.90 7.23 7.60 3.87 8.80 10.46 0.00 -0.5 -1.96 0.00 0.00 0.00 -5.32 0.00 0.23 0.55 0.79 0.97 5.19 2.10 3.21 4.27 34.4 32.8 34.7 33.3 21. 7 20.9 20.8 21.5 7.65 7.65 7.65 7.65 11. 09 11. 09 11. 09 11.09 1.47 0.24 -0.54 0.15 1.95 2.22 -0.38 0.05 2.90 1.61 0.32 0.77 8.43 9.23 2.36 2.34 34.2 21.4 6.33 7.9 -0.49 -0.12 0.71 4.07 1.5 0.7 1.49 3.12 1.53 1.83 0.83 2.47 1986/87 Aus Aman Winter Bora 1987/88 Aus Aman Winter Bora Mean Standard deviation Source: Estimated by the authors. Note: The price band 1s defined by a plus or minus 4 percent margin around the target price. a The seasons are defined as follows: aus, July-October; aman. November-February; winter. March- April; bora, May-June. b Prices are deflated by the index of manufactured goods. o Positive open market operations have to be interpreted as open market sales; negative open market operations have to be interpreted as domestic procurement. - 62 - Table 27-Costs in the price band policy, 1985-88 Procurement Cost Year/ Season- Ration Imports Sales Open Market Sales Total Cost b (Tk mill ion) 1985/86 o Aus 3,304 Aman o o Winter Bora 1986/87 o Aus Aman Winter 407 4,607 o Bora 1987/88 o o Foreign Exchange Cash OutflowO (US$ million) (Tk million) 2,308 862 1,682 1. 673 1,619 1,366 518 515 o o 2,353 1. 237 1,913 2,464 1,515 1,790 984 804 o 2,346 2,296 803 479 2,352 1.391 689 2,799 1,164 1,158 77 28 56 55 -1,400 2,025 -352 -366 838 -146 5,536 1,660 78 40 62 80 -1,152 -1,068 4,107 -191 159 1,022 2,078 1,352 1,482 185 186 46 67 -2,086 -1,334 475 305 o o o o o Bora o 5,720 5,765 1,452 2,120 Total 9,020 29,548 15,035 3,902 19,632 959 -1,036 Standard deviat ion 1,473 1,535 642 720 1,366 50 1,634 Aus Aman 703 Winter o Source: Est imated by the authors. Note: The price band is defined by a plus or minus 4 percent margin around the target price . • The seasons are defined as follows: aus, July-Octoher; aman, November-February; winter, MarchApril; bora, May-June. b Total cost = procurement cost + import cost - ration sales - open market sales. o Cash outflow = total cost - foreign exchange. - 63 - Table 28-Variables in the optimal price stabil i zat ion policy. 1985-88 Priceb Year/ Season- Rice Open Market O[!erat ions e Stock Wheat Rice Wheat (Tk/maund) Rice Wheat ImQorts Rice Wheat (kilograms/capita) 1985/86 Aus Aman Winter Bora 33.5 32.2 34.2 33.6 20.9 20.9 21.0 21.6 1. 47 8.83 8.07 6.08 6.61 3.32 8.76 9.93 1.56 -8.21 0.09 1. 23 0.33 0.00 -5.20 0.00 0.12 0.09 0.14 0.00 4.42 1. 39 2.78 3.08 34.8 34.6 38.5 35.7 22.2 21.9 22.5 21.3 1. 47 2.53 4.70 2.58 11.94 7.95 12.63 3.32 3.73 -1.22 -1.96 2.58 0.00 0.00 -5.32 10.75 0.23 0.55 0.79 0.97 5.19 2.10 3.21 4.27 36.2 35.7 36.5 33.9 21.9 21.7 21.5 21.8 3.47 6.93 7.42 1. 47 3.32 3.32 3.32 3.32 1. 29 -2.98 -0.99 6.12 3.01 2.68 0.08 0.52 2.90 1.61 0.32 0.77 8.43 9.23 2.36 2.34 35.0 21.6 4.58 6.48 0.10 0.57 0.71 4.07 1.7 0.5 2.77 3.65 3.64 4.09 0.83 2.47 1986/87 Aus Aman Winter Bora 1987/88 Aus Aman Winter Bora Mean Standard deviation Source: Estimated by the authors. Note: The optimal price stabilization policy uses open market operations to minimize the variance of rice prices around the target . • The seaso'ns are def; ned as fa 1lows : aus, Ju ly-October; aman, November-February; wi nter. March- April; bora, May-June. Prices are deflated by the index of manufactured goods. Positive open market operations have to be interpreted as open market sales; negative open market operations have to be interpreted as domestic procurement. b C - 64 - Table 29-Costs in the optimal price stabilization policy. 1985-88 Procurement Cost Year/ Season 8 Imports Ration Sales Open Market Sales Total Cost b (Tk million) 1985/86 Aus Aman Winter Bora 5,955 2,549 1986/87 Aus Aman Winter Bora 1,026 4,742 o 1,619 1,366 518 515 1,288 2,353 1,237 1. 913 2,464 1,515 1,790 984 804 3,151 0 5,720 2,737 951 0 5,765 1,452 2,120 17,961 1,979 o o -599 5,450 3,641 175 77 28 56 55 -2,688 4,677 2,125 -1,349 o o 8,368 -2,314 473 5,671 -6,707 78 40 62 80 -4,304 -449 4,242 -8,558 2,346 2,296 803 479 2,843 1.497 46 5,834 531 4,710 1,554 -4,193 185 186 46 67 -2,577 1,298 677 -5,370 29,548 15,035 24,083 8,392 959 -12,276 1,535 642 2,560 3,682 50 3,769 1987/88 Aus Aman Winter Bora Total Standard deviation Cash OutflowC (US$ million) (Tk m1111on) 2,308 862 1.682 1.673 o Foreign Exchange o 72 983 Source: Est lmated by the authors. Note: The optimal price stabilization policy uses open market operations to minimize the variance of rice price around the target. The seasons are defined as follows: aus, July-October; aman, November-February; winter, MarchApril; bora, May-June. b Total cost = procurement cost + import cost - ration sales - open market sales. C Cash outflow = total cost - foreign exchange. a - 65 - Table 3O-Variables in the import policy, 1985-88 Priceb Year/ Season- Rice Open Market Ogerat ions e Stock Wheat Rice Wheat (Tk/maund) Rice Wheat Imgorts Rice Wheat (kilograms/capita) 1985/86 Aus Aman Winter Bora 33.6 30.8 34.7 34.6 20.9 20.5 20.5 21.7 2.84 2.71 6.31 5.61 3.32 3.32 3.32 3.32 0.07 0.01 0.06 0.04 0.35 0.14 0.00 0.00 0.00 0.90 4.10 0.00 1.16 4.62 2.53 1.60 35.8 33.9 37.2 36.6 22.4 21.7 21. 4 22.6 4.04 3.15 2.05 6.65 3.32 3.32 3.32 3.32 0.50 0.03 0.48 0.30 0.64 0.40 0.04 0.03 0.00 0.00 0.00 5.25 3.43 5.97 3.61 2.31 36.0 35.5 36.7 33.8 22.4 22.1 21.6 21.9 4.80 3.40 9.50 8.73 3.32 3.32 3.32 3.32 0.88 0.19 0.10 0.04 0.68 0.12 0.03 0.00 0.00 0.00 6.81 0.00 6.09 6.66 2.31 1.82 34.9 21.6 4.98 3.32 0.22 0.20 1. 42 3.51 1.8 0.7 2.42 0.00 0.27 0.25 2.47 1.90 1986/87 Aus Aman Winter Bora 1987/88 Aus Aman Winter Bora Mean Standard deviation Source: Estimated by the authors. Note: The imports pol icy uses open market operations to minimize the variance of prices around the target . • The seasons are defined as follows: aus, July-October; aman, November-February; winter, March- April; bora. May-June. Prices are deflated by the index of manufactured goods. Positive open market operations have to be interpreted as open market sales; negative open market operations have to be interpreted as domestic procurement. b C - 66 - Table 31-Costs in the import policy, 1985-88 Procurement Year/ Season 8 Cost Imports Ration Open Market Sales Sales Total Cost b (Tk million) 1985/86 Forelgn Exchange Cash OutflowO (US$ m; 11 ion) (Tk m; 11 ion) o o o o 584 3,277 4,077 866 1,619 1,366 518 515 210 70 50 33 -1,245 1,840 3,510 318 19 107 135 29 -1,777 -1,035 270 -471 o o o o 1,459 2,536 1,555 4,530 1,515 1,790 984 804 783 237 457 300 -840 509 114 3,426 48 82 50 146 -2,115 -1,708 -1,245 1,102 Aus o Aman Winter Bora o o 2,512 3,092 7,924 1,058 2,346 2,296 803 479 1,189 245 110 35 -1,023 552 7,012 544 81 100 252 34 -2,744 -1,565 4,047 -181 o 33,469 15,035 3,719 14,716 1.083 -7,421 o 1,966 642 336 2,288 63 1,744 Aus Aman Winter Bora 1986/87 Aus Aman Winter Bora 1987/88 o Total Standard deviation Source: Est imated by the authors. Note: The imports policy uses open market operations to minimize the variance of rice prices around the target . • The seasons are defined as follows: aus, July-October; aman, November-February; winter, March- April; boro, May-June. b Total cost = procurement cost + import cost - ration sales - open market sales. C Cash outflow = total cost - foreign exchange, - 67 - Table 32-Variables in the cost minimization policy. 1985-88 Yearl Price Seas anti Rice b Open Market Stock Wheat Rice O[!erat ions Wheat (Tk/maund) Rice e Wheat Im[!orts Rice Wheat (kilograms/capita) 1985/86 Aus Aman Winter Bora 33.5 31.6 35.9 37.4 20.9 20.8 21.0 22.7 1.47 2.80 1.47 1.47 6.68 3.39 4.30 5.B2 1.56 -2.18 1.03 -0.37 0.33 0.00 0.24 0.12 0.12 0.09 0.14 0.00 4.42 1.39 2.78 3.08 39.2 36.9 39.5 38.8 23.7 22.9 22.4 23.2 1.47 1. 47 1.47 1.47 8.18 4.42 4.56 4.77 -0.60 -0.16 0.28 0.65 0.00 0.00 -0.36 1.99 0.23 0.55 0.79 0.97 5.19 2.10 3.21 4.27 38.5 37.6 39.9 38.8 23.0 22.5 22.7 23.5 1.47 1.47 1.47 1.47 4.71 4.62 5.03 5.24 2.24 0.61 -0.17 0.52 3.01 2.68 0.08 0.52 2.90 1. 61 0.32 0.77 8.43 9.23 2.36 2.34 37.3 22.4 1.58 5.15 0.28 0.72 0.71 4.07 2.5 1.0 0.39 1. 26 1.13 1.15 0.83 2.47 1986/87 Aus Aman Winter Bora 1987/88 Aus Aman Winter Bora Mean Standard deviation Source: Estimated by the authors. Note: The cost minimization policy uses open market operations to minimize the total cost of food operations. a The seasons are defined as follows: aus, July-October; aman, November-February; winter, MarchApril; boro, May-June. b Prices are deflated by the index of manufactured goods. C Positive open market operations have to be interpreted as open market sales; negative open market operations have to be interpreted as domestic procurement. - 68 - Table 33-Costs in the cost minimization policy. 1985-88 Ration Procurement Year/ Season' Cost Sales Imports Open Market Sales Total Cost b (Tk mi 1110n) Foreign Exchange Cash OutflowO (US$ million) (Tk mi 1110n) 1985/86 Aus Aman Winter Bora 0 1,558 0 327 2,308 862 1.682 1.673 1,619 1,366 518 515 1,289 0 980 65 -599 1.053 184 1.420 77 28 56 55 -2,688 279 -1,332 -104 571 141 195 0 2,353 1.237 1.913 2,464 1,515 1,790 984 804 0 0 265 1,863 1.409 -412 859 -203 78 40 62 80 -581 -1,334 -569 -2,054 0 0 179 0 5,720 5,765 1.452 2,120 2,346 2,296 803 479 3,931 2,138 49 860 -557 1.332 779 781 185 186 46 67 -3,664 -2,080 -98 -396 2,971 29,548 15,035 11,438 6,046 959 -14,622 430 1.535 642 1,156 748 50 1,149 1986/87 Aus Aman Winter Bora 1987/88 Aus Aman Winter Bora Total Standard deviation Source: Estimated by the authors. Note: The cost minimization policy uses open market operations to minimize the total cost of food operat 10ns . • The seasons are defined as follows: aus, July-October; aman, November-February; winter, March- April; boro, May-June. b C Total cost = procurement cost + import cost - ration sales - open market sales. Cash outflow = total cost - foreign exchange. - 69 - Table 34-Variables in the benchmark policy: cost minimization, 1985-88 Price b Year/ Season8 Rice Open Market Dgerat ionse Stock Wheat Rice price stabilization cum Wheat (Tk/maund) Rice Wheat ImQorts Rice Wheat (kilograms/capita) 1985/86 Aus Aman Winter Bora 33.6 32.0 34.9 35.0 20.9 20.9 21.1 22.0 1.47 6.37 3.69 1.47 3.32 3.32 5.02 3.32 1.44 -5.84 2.03 4.75 0.00 0.00 -4.23 0.00 0.00 0.00 0.00 3.03 0.80 4.48 0.00 0.00 36.0 35.4 38.7 37.2 22.6 22.2 22.4 23.0 1.47 2.38 1.47 3.69 3.32 3.32 3.32 3.32 6.30 -1.61 0.34 4.22 0.00 0.00 -3.57 0.00 7.13 0.00 0.00 6.76 2.79 5.57 0.00 2.28 37.7 37.2 37.7 35.2 22.8 22.6 22.5 22.5 3.98 7.43 6.86 1.47 3.32 3.32 5.26 3.32 -1.09 -4.60 -0.28 4.81 2.17 0.00 -4.22 0.00 0.00 0.00 0.00 0.00 7.58 6.54 0.00 0.00 35.9 22.1 3.48 3.62 0.87 -0.82 1.41 2.50 1.9 0.7 2.28 0.71 3.81 2.02 2.73 2.86 1986/87 Aus Aman Winter Bora 1987/88 Aus Aman Winter Bora Mean Standard deviation Source: Estimated by the authors. Note: The benchmark policy uses open market operations and imports to minimize the total cost of food operations subject to price stabilization and foreign reserves constraints . • The seasons are defined as follows: aus, July-October; aman, November-February; winter. March- April; bora. May-June. Prices are deflated by the index of manufactured goods. Positive open market operations have to be interpreted as open market sales; negative open market operations have to be interpreted as domestic procurement. b C - 70 - Table 35--Costs in the benchmark policy: minimization, 1985-88 Procurement Cost Year/ Season' Imports Ration Sales price stabilization cum cost Open Market Sales Total Cost b (Tk million) Foreign Exchange Cash OutflowC (US$ mi 11 ion) (Tk mi 11 ion) 1985/86 Aus Aman Winter Bora 0 4,220 2,080 0 406 2,588 0 1,864 1,619 1,366 518 515 1.054 0 1.649 3,942 -2,267 5,442 -86 -2,592 14 84 0 62 -2,636 3,084 -86 -3,953 1986/87 Aus Aman Winter Bora 0 1,390 1,946 0 5,728 2,366 0 5,541 1. 515 1,790 984 804 5,491 0 319 4,087 -1. 278 1,965 643 650 189 77 0 179 -4,195 -103 643 -2,087 1987/88 Aus Aman Winter Bora 1,035 4,400 2,768 0 3,127 3,034 0 0 2,346 2,296 803 479 1,249 0 0 4,530 567 5,138 1,965 -5,009 101 98 0 0 -1,575 3,060 1,965 -5,009 17,839 24,654 15,035 22,321 5,137 803 -10,893 1,566 1,995 642 1.977 2,905 65 2,667 Total Standard deviation Source: Estimated by the authors. Note: The benchmark policy uses open market operations and imports to minimize the total cost of food operations subject to price stabilization and foreign reserves constraints . • The seasons are defined as follows: aus, July-October; aman, November-February; winter, MarchApril; bora, May-June. b Total cost = procurement cost + import cost - ration sales - open market sales. C Cash outflow = total cost - foreign exchange. - 71 - Table 36-Variables in the benchmark policy with 30 percent increase in world prices. 1985-88 Year/ Season/! Price Rice b Open Market Stock Wheat Rice OI;!erat; on SO Wheat (Tk/maund) Rice Wheat Imgorts Rice Wheat (kilograms/capita) 1985/86 Aus Aman Winter Boro 33.6 32.1 34.6 35.0 20.9 20.9 21.1 22.0 1.47 7.33 5.69 4.95 3.32 3.32 5.02 3.32 1.44 -6.80 0.93 O.l! 0.00 0.00 -4.23 0.00 0.00 0.00 0.00 0.00 0.8 4.48 0.00 0.00 36.0 35.3 38.8 37.2 22.6 22.2 22.4 23.0 1.47 2.25 1.47 3.52 3.32 3.32 3.32 3.32 3.27 -1.48 0.22 4.45 0.00 0.00 -3.57 0.00 0.82 0.00 0.00 6.82 2.79 5.57 0.00 2.28 37.7 37.2 37.7 35.2 22.7 22.6 22.5 22.5 3.94 7.42 6.85 1.47 3.32 3.32 5.26 3.32 -1.21 -4.63 -0.28 4.81 2.91 0.00 -4.22 0.00 0.00 0.00 0.00 0.00 8.32 6.54 0.00 0.00 35.9 22.1 3.99 3.62 0.07 -0.76 0.64 2.57 1.9 0.7 2.41 0.71 3.41 2.13 1.96 2.98 1986/87 Aus Aman Winter Bora 1987/88 Aus Aman Winter Bora Mean Standard deviation Source: Estimated by the authors. II The seasons are defined as follows: aus, July-October; aman, November-February; winter, March- April; boro, May-June. b Prices are deflated by the index of manufactured goods. Positive open market operations have to be interpreted as open market sales; negative open market operations have to be interpreted as domestic procurement. C - 72 - Table 37-Costs in the benchmark policy with 30 percent increase in world prices, 1985-88 Year/ Season- Procurement Cost Imports Ration Open Market Sales Sales Total Cost b (Tk million) Foreign Exchange Cash OutflowO (US$ million) (Tk million) 1985/86 Au. Aman Winter Bora 0 4,923 2,073 0 527 3,364 0 0 1,619 1,366 518 515 1,054 0 749 92 -2,145 6,921 807 -607 18 110 0 0 -2,636 3,787 807 -607 0 1,276 1,947 0 2,222 3,075 0 7,257 1,515 1,790 984 804 2,851 0 203 4,309 -2,144 2,561 760 2,144 73 100 0 234 -3,910 -216 760 -2,286 1.148 4,430 2,769 0 4,462 3,944 0 0 2,346 2,296 803 479 1.669 0 0 4,527 1,596 6,078 1,967 -5,006 144 127 0 0 -I. 785 3,090 1,967 -5,006 18,567 24,852 15,035 15,453 12,931 806 -6,035 1,679 2,285 642 1,628 3,219 74 2,615 1986/87 Au. Aman Winter Bora 1987/88 Au. Aman Winter Bora Total Standard deviation Source: Estimated by the authors. • The seasons are defined as follows: aus, July-October; aman, November-February; winter. MarchApril; bora, May-June. b Total cost = procurement cost + import cost - ration sales - open market sales. C Cash outflow = total cost - foreign exchange. - 73 - Table 38-Variables in the benchmark policy when monetary offtakes are eliminated, 1985-88 ~riceb Year/ Season' Rice Open Market Stock Wheat Rice Ol2erationsCl Wheat (Tk/maund) Rice Wheat Imgorts Rice Wheat (kilograms/capita) 1985/86 Aus Aman Winter Bora 33.8 32.3 35.6 35.0 21.2 21.2 21.3 22.1 1.47 4.87 1.47 1.47 4.53 3.32 4.35 3.32 2.44 -3.73 3.10 8.53 0.00 0.00 -2.89 0.00 0.00 0.00 0.00 8.62 0.00 1.40 0.00 0.00 36.0 35.6 39.0 37.2 22.9 22.6 22.6 23.1 1.47 1.47 1.47 3.75 3.32 3.32 3.32 3.32 7.84 -0.10 1.12 5.38 0.00 0.00 -2.21 0.47 8.00 0.00 1. 29 7.75 0.87 3.06 0.00 1.57 37.7 37.2 37.8 35.2 22.7 22.9 22.5 22.6 4.55 7.24 7.12 1.47 3.32 3.32 4.65 3.32 -1.07 -2.96 -0.31 5.22 6.11 0.00 -2.84 0.00 0.00 0.00 0.00 0.00 7.98 3.82 0.00 0.00 36.0 22.3 3.15 3.62 2.12 -0.11 2.14 1.56 1.9 0.7 2.29 0.54 4.01 2.31 3.63 2.41 1986/87 Aus Aman Winter Bora 1987/88 Aus Aman Winter Boro Mean Standard deviation Source: Estimated by the authors. • The seasons are defined as follows: aus, July-October; aman, November-February; winter, March- April; bora. May-June. b Prices are deflated by the index of manufactured goods. o Positive open market operations have to be interpreted as open market sales; negative open market operations have to be interpreted as domestic procurement. - 74 - Table 39-Costs in the· benchmark pol icy when monetary off takes are eliminated, 1985-88 Year/ Season- Procurement Cost Imports Ration Sales Open Market Sales Tota'b Cost (Tk million) 1985/86 Aus Aman Winter Bora 1986/87 Aus Aman Winter Bora 1987/88 Aus Aman Winter Bora Tota' Standard deviation Foreign Exchange Cash OutflowO (US$ million) (Tk mi llion) 0 2,716 1,437 0 0 809 0 5,303 0 0 0 0 1,800 0 2,576 7,077 -1,800 3,525 -1,138 -1,774 0 26 0 175 -1,800 2,788 -1,138 -5,645 0 83 1,216 0 5,466 1,299 861 5,914 0 0 0 0 6,836 0 1.060 5,489 -1,370 1,382 1,017 425 180 42 28 191 -3,803 247 661 -2,329 1,016 2,835 1,987 0 3,291 1,773 0 0 0 0 0 0 3,516 0 0 4,913 791 4,608 1,987 -4,913 106 57 0 0 -1,464 3,394 1,987 -4,913 11,291 24,717 0 33,267 2,741 806 -12,016 1.054 2,220 0 2,61B 2,490 73 2,B03 Source: Estimated by the authors. • The seasons are defined as follows: aus, July-October; aman, November-February; winter. MarchApril; boro, May-June. b Total cost = procurement cost + import cost - ration sales - open market sales. C Cash outflow = total cost - foreign exchange. - 75 - Table 4O-Variables in the approximation policy. 1985-88 Open Market ~r;ceb Year! Season ll Rice Stock Wheat Rice OQerat ions Wheat (Tk/maund) Rice e Wheat ImQorts Rice Wheat (kilograms/capita) 1985/86 Aus Aman Winter Bora 33.3 31.9 34.9 34.6 20.6 20.7 20.8 21.6 1.15 6.06 5.73 2.93 5.20 1.35 3.88 3.73 2.58 -4.43 -0.08 2.39 1.81 0.64 -1.25 1. 92 0.12 0.09 0.14 0.00 4.42 1.39 2.78 3.08 36.7 36.1 37.9 36.5 22.6 22.3 22.0 22.5 0.45 4.31 4.82 4.14 4.57 0.27 1.65 2.14 1.86 -3.73 -0.41 2.18 1.55 0.75 -1.35 1.89 0.23 0.55 0.79 0.97 5.19 2.10 3.21 4.27 36.3 35.7 36.2 34.1 22.3 22.0 21.6 21.8 4.38 8.17 7.81 8.42 3.65 5.43 7.03 5.86 2.18 -2.89 -0.21 1.46 1.60 0.88 -1.16 1.77 2.90 1. 61 0.32 0.77 8.43 9.23 2.36 2.34 35.3 21.7 4.86 3.73 0.08 0.75 0.71 4.07 1.7 0.7 2.57 2.04 2.52 1. 29 0.83 2.47 1986/87 Aus Aman Winter Bora 1987/88 Aus Aman Winter Bora Mean Standard deviation Source: Estimated by the authors. Note: The approximating policy was computed by dOing stochastic simulat10ns of production shocks and ordinary least squares over rice production, wheat production, and a lagged term. The seasons are defined as follows: aus, July-October; aman, November-February; winter. MarchApril; bora, May-June. b Prices are deflated by the index of manufactured goods. C Positive open market operations have to be interpreted as open market sales; negative open market operations have to be interpreted as domestic procurement. II - 76 - Tabl e 41-Costs in the approximation policy, 1985-88 Procurement Cost Year/ Season- Imports Ration Sales Open Market Sales Total Cost b (Tk million) 1985/86 Aus Aman Winter Bora Foreign Exchange Cash OutflowQ (US$ mill ion) (Tk mi 11 ion) 0 3.187 673 0 2.308 862 1.682 1.673 1.619 1.366 518 515 2.695 298 0 2.955 -2.006 2.385 1.838 -1. 797 77 28 56 55 -4.095 1.611 321 -3.321 Bora 0 3.280 1.100 0 2.353 1.237 1.913 2.464 1.515 1.790 984 804 2.498 408 0 3.175 -1.660 2.319 2.029 -1.515 78 40 62 80 -3.651 1.396 600 -3.366 1987/88 Au' Aman Winter Bora 0 2.659 852 0 5.720 5.765 1.452 2.120 2.346 2.296 803 479 2.902 498 0 2.362 472 5.630 1.501 -722 185 186 46 67 -2.636 2.218 624 -1.899 11,751 29.548 15.035 17,791 8.473 959 -12.195 1.254 1.535 642 1.305 2.228 50 2.253 1986/87 Au, Aman Winter Total Standard deviation Source: Estimated by the authors. Note: The approximating policy was computed by dOing stochastic simulations of production shocks and ordinary least squares over rice production. wheat production, and a lagged term . • The seasons are defined as follows: aus, July-October; aman, November-February; winter, MarchApril; bora, May-June. b Total cost = procurement cost + import cost - ration sales - open market sales. C Cash outflow = total cost - foreign exchange. 10. CONCLUSIONS The paper has presented a general approach to analyzing the optimal stock problem for Bangladesh. The approach chosen is responsive to the needs of a policymaker whose broad concern is to guarantee food security and price stability at minimum cost. A dynamic model of the foodgrain sector has been constructed, taki ng into account the deci s ions of the pri vate sector regardi ng consumption and private storage. A set of policies, characterized by different objectives and constraints, have been defined and evaluated. The summary statistics of the various policy options are given in Tables 42 and 43. The main conclusions are as follows: • The higher the number of pol icy instruments available to the government, the more effective the policy becomes in achieving the objectives of price stabil ization, cost efficiency, and food security. The policy instruments that have been analyzed in the paper are open market sales, domestic procurement, and food imports. • In order to keep the foodgrain distribution system going, imports, especially of wheat, cannot be eliminated. At the same time, a policy that would rely only on imports to stabilize prices would not be as cost-effective as a policy that relied on an effective management of open market operations (that is, domestic purchase and sale). • The benchmark for optimal pol icy is given by a pol icy whose objective is to minimize cost, subject to several constraints including food security, price stabilization, and the reaction of the pri vate sector. The benchmark is characteri zed by its flexibility in adapting to changes in both the domestic economy (for example, production shocks) and in the world economy (for example, world commodity prices). Fixed rules, such as price band schemes, even if effective in reducing price variability, are not likely to be cost-effective, and, vice versa, when they are cost effective, they are not likely to stabilize prices. • Price stabilization around a target can be effectively achieved at a relatively low cost in comparison with historical performance. The main instruments to be used for this purpose are open market operat ions and imports. In part i cul ar, open market ope rat ions have to be used much more intensively than in the past. Table 42--Summary of various policies Policy Variables Rice price Wheat price Open market sales Base 1ineAvg Std 323 198 19.7 8.1 44 b Price Band Avg Std 306 192 13.4 6.3 52 Price Stabi1izat ione Std Avg 314 194 15.2 4.5 289 Approimation to Price Stab; lizationd Std Avg 316 194 15.2 6.3 216 . Cost Mini- mization Std Avg Iml20rt Pol lei:' Avg Std BenchmarkG Avg Std 334 201 313 194 322 198 22.4 9.0 135 16.1 6.3 17.0 6.3 221 44 Bencha30 Avg Std h No ration i Std Avg 322 198 323 200 17.0 6.3 154 17.0 6.3 342 Open market purchases Rice stock Wheat stock R; ce imports Wheat imports 0 398 677 72 415 159.1 279.5 84.7 251.9 114 646 806 72 415 152.0 318.2 84.7 251.9 220 467 661 72 415 282.5 372.3 84.7 251.9 132 496 380 72 415 262.1 208.1 84.7 251.9 33 161 525 72 415 39.8 128.5 84.7 251.9 0 508 339 145 358 246.8 0 251.9 193.8 216 355 369 144 255 232.6 72.4 278.5 291.7 224 407 369 65 262 245.8 72.4 199.9 304.0 137 321 369 218 159 233.6 55.1 370.3 245.8 Std Total Std Total Std Total Std (Tk million) Total 5td Total Std Std ..... Std Total std Total 8,473 2,228 6,046 748 14,716 2,288 959 50 959 50 959 17,961 1,979 11.751 1,254 2,971 -12,276 3.769 -12,195 2,253 -14,622 50 430 1,149 Total Total Costs Tota 1 cost Foreign 17,045 1,274 19,632 1,366 exchange 959 50 6,380 489 -3,623 1.047 959 50 9,020 1,473 -1.036 1.634 Procurement Cash outflow 8,392 3,682 5,137 2,905 1,083 63 803 65 0.00 0.00 17,839 1,566 -7,421 1.744 -10,893 2,667 12,931 3,219 2.741 2,490 806 74 806 73 18,567 1. 679 11,291 1. 054 -6,035 2,615 -12,016 2,803 Source: Computed by the authors. Notes: Avg = average; Std = standard deviation. Prices are in taka/maund. not deflated. Quantities are in 1,000 metric tons. Costs are in million taka . • The baseline is obtained by simulating the foodgrain model for the period July 1985-June 1988. b The price band is defined by a plus or minus 4 percent margin around the target price. ~ The optimal price stabilization policy uses open market operations to minimize the variance of rice prices around the target. d The approximation to price stabilization was computed through stochastic simulations of production shocks and ordinary least squares over rice production. wheat production. and a lagged term . • The cost minimization policy uses open market operations to minimize the total cost of food operations. f The import policy uses imports to minimize the variance of rice prices around the target. g Benchmark refers to price stabilization cum cost minimization. It uses open market operations and imports to minimize the total cost of food operations subject to price stabilization and foreign reserves constraints. h Bencha30 refers to the benchmark with a 30 percent increase in world prices. i No ration refers to the benchmark when monetary off takes are eliminated. (X) - 79 - Table 43-Average stock and total cost of various policies Po 1icy Average Total Foodgrain Stock lota 1 Costa (1,000 metric tons) (Tk million) Base 1ineb Price band c Optimal price stabilizat;on d Approximation to optimal price stabilizat;on 8 Cost min imizat ion f Import po 1icyQ Benchmark: price stabilization cum cost minim;zation h No ration distribution i 1,075 1,452 1.128 17,045 19,632 8,392 876 686 847 8,473 6,046 14,716 724 5,137 2,741 690 Source: Computed from information in Table 42. a Total cost = procurement cost + import cost - ration sales - open market sales. The baseline is obtained by simulating the foodgra;n model for the period July 1985-June 1988. C The price band ;s defined by a plus or minus 4 percent margin around the target price. d The optimal price stabilization policy uses open market operations to minimize the variance of rice prices around the target. S The approximation to price stabilization was computed through stochastic simulations of production shocks and ordinary least squares over rice production, wheat production, and a lagged term. f The cost minimization policy uses open market operations to minimize the total cost of food operations. 9 The imports policy uses imports to mi.nimize the Variance of rice prices around the target. n Benchmark refers to price stabilization cum cost minimization. It uses open market operations and imports to minimize the total cost of food operations subject to price stabilization and foreign reserves constraints. i No ration refers to the benchmark when monetary off takes are eliminated. b • The attractiveness of fixed rules as compared with more complex rules is deceiving, A price band, to be effective, may need as much careful planning as a seemingly more complex rule involving an optimization process. Nevertheless, the effort to simplify must be pursued, In particular, what is still interesting is the effort to approximate optimal poliCies with policies that are more easily implementable and are of a feedback type, that is, they can be formulated as a function of the current state of the system. An attempt in this direction has been made in this report, and the results seem promising, • The average foodgrain stock needed to support the optimal policy pursued through both open market operations and imports is equal to 724,000 tons, In the case of approximation policy, which has also been considered in the report, the level goes up to 876,000 tons as a consequence of a lesser degree of flexibility allowed to the policy instruments, APPENDIX 1: PROCUREMENT SUPPLY The quantity actually procured by the government depends on the capacity and willingness of the former to sell (Gulati and Sharma 1990). The capac i ty to sell depends on the marketable surplus, whereas the will ingness to sell depends on the differential between procurement pri ces and open market pri ces. In order to study the procurement supply, a simple model is introduced. For the sake of simplicity, superscripts denoting grains will be dropped in the following discussion. At the beginning of each time period t, farmers are endowed with an amount, qt' of foodgrains. They have to decide how much to sell to the market, ~t' at the market price, Pt' how much to sell to the government procurement station, qPt' at price PPt' and how much to store, xt+I ' The objective of farmers is to maximize expected profit, which is given for a two-period problem by (30) where o<p < 1 discount parameter, Pt+l, t c1 price at time t+l, expected to prevail as of time t, c2 cost of bringing crops to the procurement station, and cost of storing stock. The constraints faced by the farmers are that all the abovementioned quantities are non-negative and that they do not exceed the initial amount owned by the farmer: (31) It is possible to derive a closed-form solution for this problem if the cost funct ions c1 and c2 are taken to be convex in thei r respective arguments. Namely, (32) c1(qPt) = fo + f1qpt + 2- 1 • f2qp~, and 1 (33) C2(X t+l ) = go + glx t +1 + 2- • g2X~+1' - 82 - where f and g2 are both positive. It is ~ent possible to express the solution for this problem as foll ows: Xt+l = max [0, -g/g2 + (,BPt+l.t - Pt)/g2], and qPt = max [0, -f\/f2 + (pPt - pt)/f21, (34) (35) where In this formulation, procurement supply is positively related to the difference between procurement price and market price. It is conceivable that costs of adjustment must be paid in order to change the amount supplied to the procurement station from period to period, and also that the higher is the amount qt' the lower is the procurement cost. In such a case, the cost function c1 can be expressed as c1 (qPt,qPt-l'qt) = q~a • [fo + fl (qPt - 'YqPt-) + 2-1 • f 2( qp t - 'Y qp t_l)21, (36) where a and 'Yare positive constants. With this modification the procurement supply is (37) Now the amount procured is positively related to its lagged value, to the difference between procurement price and market price, and to the amount initially owned by farmers. A procurement equation derived from the previous model has been estimated in the following linear specification: (38) For both ri ce and wheat, procurement pri ces do not appear wi th a significant coefficient (Table 44). This seems a bit surprising given that the rationale for introducing procurement prices is to stimulate procurement and support farmers' prices as a result. In Appendix 2 it will be shown that, at least for rice, procurement has been effective in sustaining prices, even though the level of support has been negligible. Here the puzzle of why procurement prices did not stimulate procurement - 83 - supply, as one would expect a priori, has to be explained. A possible interpretation for the limited significance of procurement prices follows. Since procurement takes place through a system of 1icensed dealers, rent-seeking behavior may generate a process whereby the level of procurement prices does not become critically important. In any case, profits could be made by altering the qual ity of rice, the moisture content, and the quantities actually procured. However, it is clear that when market prices increase, the incentives to sell to the procurement station diminish, since the marketplace becomes more attractive. Table 44-Ordinary least squares estimation of rice and wheat procurement supply Variable Coefficient t-Statistic 0.8416 -10.4006 8.1230 0.5385 -2.7895 1.1644 5.2532 I. 2672 Rice Constant R p, PP: R 0.0274 0.1363 q, R QPt-1 59 0.5215 0.9697 N R' SEE Wheat Constant P':' p~ w q, qp~l -0.1749 -2.7553 4.1656 -0.4626 -1.8274 0.0461 0.2478 5.2330 2.2205 59 0.4512 0.2603 N R' SEE Source: Estimated by the authors. Definitions of terms: p~ price of grain; at time t; procurement price of grain i at time t; p~ i production of grain i at time t; q, i QPt-1 SEE quantity of grain procured at time t-l; and standard error of estimation. I. 6868 APPENDIX 2: HAS PROCUREMENT BEEN EFFECTIVE AT SUPPORTING PRICES? To answer this question a simultaneous system is needed where the decisions of the private sector related to consumption and storage are combined with the response to the government activities involving procurement supply and demand for monetary offtakes. Procurement supply has been modeled in Appendix 1. To model the demand for monetary offtakes (net of open market sales), a distinction in the public distribution system has to be made between channels aimed at poverty alleviation, and those that target relatively high income groups. All of these latter channels have been lumped together in the monetary off takes category. Since individuals in this group have the option of drawing their quota at the ration price, a model of demand for rationed distribution can be postulated as follows: (39) where pr; refers to the ration price of grain i at time r. When the di fference between market pri ce and rati on pri ce decreases, monetary off takes are also expected to decrease. Putting together equation (39) with the equations for prices, procurement supply, stocks, and marketable supply, the following foodgrain system is obtained: (40) (41) (42) (43) i stock, = . i i i cS ' stock,_l + m, + qp, _ i ms, i i i - mof, - nmof, - oms" i i i q, + nmof, + oms,. and (44) (45) - 85 - The results in Table 45 show that the coefficient of rice procurement is statistically significant in the price equation. Nevertheless, as was seen in Appendix 1, procurement prices did not show any significant effect on the quant ity actually procured. For wheat procurement, as well as for wheat offtakes, it seems that their effect on price is perverse. A possible interpretation of this perverse effect is that the positive effect of procurement on prices is nullified by the contemporaneous public distribution of wheat in the same areas where most of wheat production takes place. On the other hand, rice ration prices are a significant instrument for controll ing the total amount of offtakes. In the case of wheat, monetary off takes are not affected by ration prices, but by market prices. Nevertheless, the predictive power of the off takes equation is too low to be used with any reliability in the simulation of policy exercises (see Figures lOe and lOf). Table 45-fhree-stage 1east squares estimation of foodgrain system with public food distribution Variable Coefficient t-Stat;stic Variable Rice lead price equation Constant stock~ m,I losses t y, N R' SEE -0.0593 -0.0097 -0.0047 0.0022 0.0628 -0.9303 -5.1157 -1.517 3.2626 6.7155 P:'1 ~+1P p';' ms~ mof~ qp~ y, N R' SEE Constant stock";' m,w losses t 0.3726 1. 2418 -0.0012 -0.0102 0.0178 -0.0273 59 0.7973 0.0225 -0.0542 -0.0052 -0.0016 0.0005 y, 0.0428 N 59 0.4789 0.0198 59 0.59 0.03 0.0807 0.2981 t-statistic Wheat lead price equation R' SEE -1.3078 -4.7093 -1.9719 0.9579 6.7673 Wheat price equation Rice price equation Constant Coefficient 1. 2105 4.4211 3.781 4.9768 -8.0873 -1.313 4.3942 -2.3025 Constant w Pt-1 P~+1 p~ ms";' mo{";" qp,w y, N R' SEE -0.044 -0.0152 -1.5183 -0.2636 0.4016 0.2211 0.0009 0.0108 -0.0243 0.011 3.7353 3.132 1. 6571 5.8335 -2.7853 2.1681 59 0.7259 0.0146 (continued) - 86 - Table 45-Continued Coefficient Variab 1. t-Statistic Variab 1e -0.6918 -0.8692 0.9443 6.361 1. 5733 Constant Rice procurement supply -0.9602 -3.7084 6.2543 0.0311 0.1428 Constant R Pt R PPt R qt R qPH R' SEE -0.5399 1. 5748 -11.3929 0.5798 0.2401 P~ R prt Yt mof~1 R' SEE p~ q';' qp7., R' SEE -0.2682 0.7632 -4.1771 1.5468 2.2724 59 0.4584 0.56 N P';' N Rice demand for monetary off takes Constant Constant P';' pr";' Yt mof;:, N R' SEE Definitions of terms: I q: qp~ p~ rp ~ Yt mof~ nmof~ oms~ nfs~ m~ stock~ losses t SEE 0.1383 -0.9889 0.5059 0.0475 0.2816 0.4115 -0.615 0.2445 5.8107 3.4151 59 0.4259 0.2547 Wheat demand for monetary off takes Source: Estimated by the authors. Pt t-statistic Wheat procurement supply 59 0.4732 0.9733 N Coefficient price of grain i at time t; production of grain; at time t; quantity of grain i procured at time t; procurement price of grain i at time t; ration price of grain i at time t; income at time t; monetary off takes of grain i at time t; nonmonetary off takes of grain i at time t; open market sales of grain; at time t; q~ + nmof! + oms~; import of grain; at time t; stock of grain i at beginning of time t; rice losses at time t; and standard error of estimation. 2.4591 38.0694 -1.7188 -1. 2517 0.241 59 0.3734 1. 0734 0.7412 5.564 -0.9494 -2.2331 2.6141 APPENDIX 3: DERIVATION OF STORAGE EQUATION The agents responsible for private storage are assumed to be riskneutral and profi t-maximi zi ng. That is, they sol ve the foll owi ng problem: max ~ • L fJ'-t [p,( ,=t xT +1 + x,) - c(x,+d], subject to where stock demanded by the end of period T, price of the grain, storage cost associated with stock X,+I' and expectation operator, based on information available at time t. For simplicity of notation, the superscript referring to the grain is omitted. Assumi ng the storage cost funct i on to be quadratic in the 1eve 1 of stocks, that is, (46) and assuming rational expectations (Wickens 1982; Ravallion 1985; Goletti 1990), so that where c,+1 is the expectational error and I, is the information available at time T, it follows that (47) with E[c7+11 I,] = 0, and - 88 - (48) where g is a linear function of its arguments. T~us, putting equation (48) together with the express i on for consumption contained in equation (7) and the equilibrium condition in equation (6), it is possible to derive a price equation that can be estimated in the form (49) where fl! msir the marketable supply of grain Yr the income at time 1 71 r a linear function, 1, at time 1, and the error term. Note that in th~ latter equation the error term is bound to be correlated with p~+1' . To avoid correlation between the er~o term 71; and the price p;+!, an instrumental variable estimation for pl+! has been ~sed. Therefore, denoting by the set of instrumental variables for p;+!, the following simultanous system is readily obtainable: a; (50) (51) where the 71'S denote error terms. APPENDIX 4: NATURE AND SOURCES OF THE DATA The organi zat i on of the data in thi s paper draws heavily from Shahabuddin (1990). The data related to the monthly distribution by categories under the public food distribution system were collected from the Food Planning and Monitoring Unit, Ministry of Food, for the period 1972/73-1987/88. Those data were converted into seasonal fi gures corresponding to the different seasons: Season 1, July-October; Season 2, November-February; Season 3, March-April; and Season 4, May-June. This way of defining the seasons tries to match the ideal basis for defining the seasons with the presentation of the results by fiscal year (see also Shahabuddin 1990). The procurement and ration prices for both rice and wheat, with the effective dates for the different periods, were collected from the Bangl adesh Bureau of Stat i st i cs Stat i sti ca I Yearbooks, and from Food Situation Reports published by the Food Planning and Monitoring Unit. These were distributed over the different seasons using the effective dates for each price. Data on the monthly price of rice (coarse, wholesale variety) were compiled from the Directorate of Marketing, Government of Bangladesh. All these nominal prices were deflated by the index of prices of manufactured consumer goods to convert them into real prices. Data on foodgrain production, both r.ice and wheat, as well as income (GNP at constant 1972/73 prices) were available from the Bangladesh Bureau of Statistics Statistical Yearbooks annually by fiscal year (July to June). These data were converted into seasonal figures by the following procedure. Estimates of the quantities of rice harvested each month were derived on the basis of the historical percentages of crops harvested each month in the World Bank (1979) study on food pol icy issues in Bangladesh. The following monthly percentages for the three rice crops, aus, aman, and boro, and for wheat have been used. July: August: September: October: November: December: 35 percent of aus 55 percent of aus 10 percent of aus 3 percent of aman 50 percent of aman 42 percent of aman January: February: March: April : May: June: 5 percent of aman no harvest 55 percent of wheat 45 percent of wheat and 10 percent of boro 65 percent boro 25 percent of boro - 90 - These monthly percentages were then applied to the yearly production of aus, aman, and boro rice, and to wheat as published in the Bangladesh Bureau of Statistics Statistical Yearbooks to derive estimates of the rice harvested by each month, which were then distributed over different seasons as defined earlier. These monthly percentages of crops harvested provide the following seasonal shares (as defined in this paper) for the different rice crops harvested in Bangladesh: Season 1, 100 percent of aus and 3 percent of aman; Season 2, 97 percent of aman; Season 3, 10 percent of boro and 100 percent of wheat; and Season 4, 90 percent of boro. The annual figures on GNP (at constant 1972/73 prices) collected from the Bangladesh Bureau of Stati st i cs Statist i ca I Yearbooks were distributed over different seasons by taking the average real GNP per capita for every season. APPENDIX 5: FOOD BUDGET From a broad, public finance perspective, it is important to accurately assess the aggregate cash deficit on the food account, which is simply the difference between cash revenues and cash expenditures. Cash savings can be used for financing development planning. It is only recently that the government of Bangladesh has started to rearrange the food budget in such a way that it is possible to identify the annual budgetary impact of food operations and integrate it into the consolidated public account. From an efficiency point of view, the food-security objectives of the government should be pursued, keeping in mind minimization of the total cost of food operations. To measure the total cost, cash revenues have to be subtracted from cash expenditures. For the foodgra in operations, the following definitions have been used: Cash Expenditures Procurement Cost + Value of Imports Cash Revenues Revenues from Open Market Sales and Ration Distribution Total Cost Cash Expenditures - Cash Revenues Cash Outflow Cash Expenditures - Cash Revenues - Value of Food Aid Using the notation previously introduced, Cash Expenditures(1) = Z; wop~ • m~ + p~ qp~, and Cash Revenues(1) In the definition of cost adopted here, administrative costs are not included; similarly, other type of costs, such as those related to storage, losses, and pi lferage, are not taken into account. Yet thi s first attempt at looking at the structure of the food budget is still useful to give a first rough idea of the behavior of some of the budget components (see Tables 46 and 47). - 92 - Table 46-Food9rain nominal costs, 1976-89 Open Year Procurement Import Cost' Cost b lata 1 ExpenditureC Market Sa les d Revenue' Cost" Food Aid" Outflowl 2,447 3,348 3,352 4,687 3,936 5,405 6,034 6,194 7,248 4,403 6,857 7,572 8,493 9,150 581 2,348 536 6,590 4,382 873 2,947 4,403 6,949 4,392 2,392 10,289 9,296 10,329 1,531 2,692 2,565 3,906 2,467 4,012 4,127 6,452 5,759 5,949 6,131 8,557 9,738 6,162 -950 -344 -2,029 2,684 1.915 -3,139 -1,180 -2,049 1.190 -1.558 -3,739 1. 732 -442 4,166 Total Rat 10n Sa les' Cash (Tk mill ion) 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 Sources: 1,039 1.960 1,206 1,406 4,513 1,447 1,021 1,358 1,812 2,219 1,349 2,829 3,336 8,500 1,989 3,736 2,682 9,871 3,805 4,832 7,960 9,238 12,385 6,577 7,899 15,032 14,452 10,979 3,028 5,696 3,888 11,277 8,318 6,279 8,981 10,597 14,197 8,795 9,248 17,861 17,788 19,479 0 0 0 370 0 348 719 852 1,117 391 1,763 1,652 2,135 1,320 2,447 3,348 3,352 4,317 3,936 5,057 5,314 5,342 6,131 4,012 5,094 5,920 6,357 7,831 Based on unpublished data from Bangladesh Ministry of Food; authors' calculations. • Procurement cost ;s obtained by taking procurement prices times procurement quantities. Import cost 1s computed at world prices converted 1n domestic currency. C Expenditure = procurement cost + import cost. d Open market sales (OMS) revenues are computed by taking OMS prices times OMS quant it ies . • Ration sales are computed by taking ration prices times monetary off takes. , Revenue = OMS revenue + rat ion sa les. g Cost = expenditures - revenues. h Food aid is computed from total imports. subtracting the commercial imports. I Cash outflow = cost - food aid. b - 93 - Table 47-Foodgrain deflated costs, 1976-89 Open Procurement Year Costa Import Cost b Total ExpenditureO Market Ration Sa lesd Sales' Revenue f Total CostQ Food Aidh Cash Outflow' 136 495 115 1145 680 123 382 588 876 518 266 1113 953 959 357 567 552 679 383 563 535 862 726 701 681 926 999 572 -222 -73 -436 466 297 -441 -153 -274 150 -184 -415 187 -45 387 (Tk mi 11 ion) 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 243 413 259 244 700 203 132 181 228 262 150 306 342 789 464 787 577 1715 590 679 1032 1234 1561 775 877 1626 1482 1019 707 1200 836 1960 1290 882 1164 1415 1789 1037 1027 1932 1825 1808 0 0 0 64 0 49 93 114 141 46 196 179 219 123 571 705 721 750 610 710 689 713 773 473 566 640 652 727 571 705 721 815 611 759 782 827 913 519 762 819 871 850 Sources: Based on unpublished data from Bangladesh Ministry of Note: The deflator used is the index of manufactured goods. Food; authors' calculations. • Procurement cost 1s obtained by taking procurement prices times procurement quantities. b Import cost ;s computed at world prices converted in domestic currency. o Expenditure = procurement cost + import cost. d Open market sales (OMS) revenues are computed by taking OMS prices times OMS quantities . • Ration sales are computed by taking ration prices times monetary off takes. f Revenue = OMS revenue + ration sales. g Cost = expenditures - revenues. h Food a1d is computed from total imports, subtracting the commercial imports. I Cash outflow = cost - food aid. APPENDIX 6: THE MODEL FOR THE BENCHMARK POLICY As formally expressed below, the benchmark policy, price stabilization cum cost minimization, consists of choosing a path for imports, open market sales, and open market purchases of both rice and wheat to minimize the cost of food operations: T min L L r=t .. p'-t[wo~m i 1; ; 1 1 PromPT - Proms, - pr,mof,]' + ; =r,W subject to equation (51): P~+l f~(a,TJ.) and (52) where _; ms, = i q, . stock~ + ; 6' stock,_l + ; stock~ I P~ - r,w and 1 (53) ; m; PT' T t, ... ,T. (54) G~;n' (55) ~ G~ax' (56) m;, 0T FT, ~ (57) ; 'Y ~ ~ ; - omp,), ~ Z; wop~ omp;, ; mT - offtakes, - (oms~ stock~ where ; i ; offtakes, - (oms, - omPT) , (58) qT' I ~ 0, 0.04 . 0" and (59) (60) - 95 - These choices are subject to the constraints given by the dynamic system of the foodgrain private sector (equations [51]-[54]); minimum stock requirements to guarantee the flow of stock operations (deadstocks) and food security (equation [55]); capacity constraints of maximum stocks (equation [56]); foreign exchange constraints (equation [57]); constraints on maximum domestic procurement (equation [58]); constraints on price variabil ity (equation [59]); and non-negativity constraints (equation [60]). The parameters used in the model are G~ax 7.65, corresponding to 805,000 metric tons; G~ax 11.09, corresponding to 1,168,000 metric tons; G~in = G: in 1.47, corresponding to 155,000 metric tons; 3.32, corresponding to 350,000 metric tons; 'Y 0.5; Ii 0.94; and Fr la, corresponding to US$956 million. APPENDIX 7: APPROXIMATION POLICIES If x* is the optimal solution of a policy problem such as the one described In equations (51)-(60) in Append\x 6, the problem becomes the need to fi nd a path x' that approximates x. In part i cul ar, one woul d 1ike to have a feedback pol icy, express edT as a function of the state variables, that behaves "similarly" to the optimal policy. An appealing approximation would be a linear rule, for its simplicity in calculation. This linear approximation can be expressed as a function of a subset rT of the set of state vari abl es z. The vari abl es in r shoul d be considered particularly useful to lonvey information upon which an open market operations mechanism can be based. For example, these variables could be production, losses, rainfall, imports, and lagged endogenous variables. Nevertheless, in trying to get a linear feedback rule, the possibility that some inequality constraints may be binding has to be taken into account. Therefore, a truncated version of a linear rule is more likely to be the case. Using the notation of the general approach of Chapter 3, the control variables, xT ' have to satisfy the law of motion, ZT+I = AT and the inequality constraints, IT 5 . Z1 + 81 • xr ' 5 uT' Then the approximating policy rule is given by L • rT x'T = B+T (1HI - AT B+ ( uT+I - AT ZT) ZT if 1HI < AT ZT + BT AT if 1HI > - ZT + BT LrT < uT+l' (61) (62) LrT' and (63) LrT, if UHI 5 AT ZT + BT where B+ is the generalized inverse of B. The matrix L is obtained by performing a stochastic simulation of exogenous variables in r and computing the optimal policy numerically. Then the coefficients of a regression of this numerical solution over the variable in r give the vector L. Equations (62) and (63) define a to take into account the inequality constraints. truncated linear ~ule T ZT) GLOSSARY 1 d,i ms;, ~q mof,i nmof~ oms;, omp;, omo;, qp~ C,i ; xH ! Il.X~+! P~ y, i PH!" stock~ losses, oftakes~ poms~ pr~ WOpi, denotes grain; it can be either rice (r) or wheat (w) denotes time; 1 = t, ..• , T demand for grain i at time 1 marketable supply of grain at time 1 production of grain i at time 1 monetary offtakes of grain i at time 1, net of open market sales nonmonetary offtakes of grain i at time 1 open market sales of grain i at time 1 open market purchases of grain i at time 1 open market operations of grain i at time 1 omo;, = oms,i - ompi, quantity of grain i procured at time 1 is the consumption of grain i as of time 1 ending period private stock of grain i as of time 1 refers to vari at i on, such as Il.X~ = X~+! - X~ price of grain i at time 1 income at time 1 the price of grain i expected to prevail at time 1+1, based on the information available at time 1 stock of grain i at beginning of time 1 rice losses at time 1. ration.distribution and nonmonetary off takes (that is, mof; + nmof;) of grain i at time 1 oms price of grain i at ·time 1 ration price of grain i at time 1 world price of grain i at time 1 import of grain i at time 1 BIBLIOGRAPHY Abbott, P. 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