1. Estimation of Optimal Storage Level in Korea Rice Industry : Application of Dynamic Stochastic Optimization Model 2004. 7. 23 Department of Agricultural Economics Gyeongsang National University Jeong-Bin, Im

2. 1. Necessity of Grain Storage 2. Review of the Previous Studies 2. Review of the Previous Studies 3. Analytical Approach in This Study 3. Analytical Approach in This Study 4. Model Specification and Analytical Result 4. Model Specification and Analytical Result 5. Summary and Conclusion 5. Summary and Conclusion

3. 1. Necessity of Grain Storage ○ Preparation for uncertainty in world grain supply and demand - in order to stabilize domestic market supply : Food security/availability - in order to stabilize domestic market supply : Food security/availability - in order to stabilize domestic price and income : Market stability - in order to stabilize domestic price and income : Market stability ⇒ Governments in both developing and developed countries have ⇒ Governments in both developing and developed countries have intervened in the grain market by means of stockpiling schemes. intervened in the grain market by means of stockpiling schemes. ○ ○ Research Motivation (1) Why is many governments’ grain storage level higher than that in efficiency criterion? (2) Why is the current storage decision sensitive to current harvest level rather than carry-overed stocks level? (3) What is the optimal grain storage rule if policymaker put the different welfare weight toward interest groups?

4. 2. Review of the Previous Studies ○ Two types of the previous study on optimal storage level. (1) Optimal inventory problem: Social planner ’ s dynamic optimization model (1) Optimal inventory problem: Social planner ’ s dynamic optimization model - stockpiling requires back quantities from current consumption such that - stockpiling requires back quantities from current consumption such that the expected social welfare, as measured by an objective function, is maximized the expected social welfare, as measured by an objective function, is maximized given the current state of the world. given the current state of the world. (Gustafson (1958),Gardner (1979), Burt, Koo and Dudly (1980)). (Gustafson (1958),Gardner (1979), Burt, Koo and Dudly (1980)). (2) Competitive private storage : private rational expectation (2) Competitive private storage : private rational expectation - Competitive private industry could carry socially optimum stocks. - Competitive private industry could carry socially optimum stocks. (Wright and Williams (1982,1984,1991), Miranda and Glauber (1993) etc.). (Wright and Williams (1982,1984,1991), Miranda and Glauber (1993) etc.). ○ Limit of existing research - Only focus on stabilizing domestic market - Only focus on stabilizing domestic market - Can not explain high grain storage level in many countries - Can not explain high grain storage level in many countries - Limitation on explaining many government ’ s storage behavior - Limitation on explaining many government ’ s storage behavior

5. 3. Analytical Approach in This Study ○ Political Preference Function(PPF) approach - Different welfare weights(or political weights) toward interest groups. - Different welfare weights(or political weights) toward interest groups. - Optimal storage level in Korean rice industry with policy objective function. - Optimal storage level in Korean rice industry with policy objective function. - Comparison with the optimal storage rules derived from PPF Model and - Comparison with the optimal storage rules derived from PPF Model and conventional utilitarian social welfare model( or competitive market model) conventional utilitarian social welfare model( or competitive market model)

6. 4. Model Specification and Analytical Results A. Dynamic optimization model in PPF approach A. Dynamic optimization model in PPF approach ○ Maximize the following policy objective function to derive the optimal storage level ○ Maximize the following policy objective function to derive the optimal storage level (4-1) (4-1) subject to S t ≥0 subject to S t ≥0 - δ is discount factor defined by δ=, - δ is discount factor defined by δ=, - r denotes the social discount rate - r denotes the social discount rate - t denotes the time - t denotes the time - CS, PS and GS represent the consumer surplus, producer surplus and taxpayer surplus, respectively. - CS, PS and GS represent the consumer surplus, producer surplus and taxpayer surplus, respectively. - λ i (i =P, C, G) is the welfare weight assigned to each interest group. - λ i (i =P, C, G) is the welfare weight assigned to each interest group. - E[.] denotes the expectation operator - E[.] denotes the expectation operator ○ Numerically using dynamic programming technique to solve the above problem. ○ Numerically using dynamic programming technique to solve the above problem. 1+ r 1 < 1 E[λ c CS t + λ p PS t + λ G GS t ] StSt Ma x Σ t =0 ∞ δ t

7. (4-2) V t (H t, S t-1 ) = [SWG t (H t, S t-1, S t ) + ] subject to A t+1 = H t+1 + S t subject to A t+1 = H t+1 + S t ○ state variables: current harvest level (H t ) and previous carry-over storage level( S t-1 ). ○ state variables: current harvest level (H t ) and previous carry-over storage level( S t-1 ). - Action(control) variable: optimal current storage level(S t ). - Action(control) variable: optimal current storage level(S t ). ※ If interest groups`s political weight is equal, then the following arbitrage condition holds: ※ If interest groups`s political weight is equal, then the following arbitrage condition holds: ⇒ P(A t -S t ) + k =δE[P(A t+1 -S t+1 )]. ⇒ P(A t -S t ) + k =δE[P(A t+1 -S t+1 )]. ※ This is the equilibrium condition of determining optimum storage level in traditional social welfare maximization model and determining optimum storage level at competitive market storage model (Miranda,1998, Williams and Wright, 1991). ※ This is the equilibrium condition of determining optimum storage level in traditional social welfare maximization model and determining optimum storage level at competitive market storage model (Miranda,1998, Williams and Wright, 1991). E t [ V t+1 (A t+1 )] 0≤ S t ≤ A t Max ○ Equation (4-1) is generally transferred to Equation (4-2) called Bellman`s equation ○ Equation (4-1) is generally transferred to Equation (4-2) called Bellman`s equation

8. B. Derive optimum storage level with PPF model ○ Used parameter for solving the dynamic optimum model ○ Used parameter for solving the dynamic optimum model - Price elasticity of demand: - 0.117(Doo Bong, Han 2003) - Price elasticity of demand: - 0.117(Doo Bong, Han 2003) - 8years(1995 ～ 2002) average price and consumption data - 8years(1995 ～ 2002) average price and consumption data - Harvest distribution : average 5,195 ton, standard - Harvest distribution : average 5,195 ton, standard deviation =257 ton deviation =257 ton - Welfare weight toward interest groups : - Welfare weight toward interest groups : λ p = 1.15, λ c = 0.88, λ G = 0.96(Jeong-Bin, Im 2003) λ p = 1.15, λ c = 0.88, λ G = 0.96(Jeong-Bin, Im 2003)

9. ■ Optimal Storage Rule Optimal storage rule : Equilibrium storage and supply Optimal storage rule : Equilibrium storage and supply Note: SWG0 : λ p = 1.15, λ G = 0.96, λ c = 0.88, Note: SWG0 : λ p = 1.15, λ G = 0.96, λ c = 0.88, SWG1 : λ p = λ G = 1.12 > λ c = 0.76 SWG1 : λ p = λ G = 1.12 > λ c = 0.76 SWF : λ p = λ G = λ c = 1, and CMS: Competitive Market Storage. SWF : λ p = λ G = λ c = 1, and CMS: Competitive Market Storage.

10. Optimal Carryover Levels for alternative policy objective function in Korea Rice Industry Optimal Carryover Levels for alternative policy objective function in Korea Rice Industry (Use average harvest and carried stock data during 1995 ~ 2002) Total Market Supply =6000 meter ton Optimal Storage Level (meter ton) Harvest Carried Stock SWG0SWG1 SWF or CMS 52008001,0051,031580 Note: SWG0: λ p = 1.15, λ G = 0.96, λ c = 0.88, Note: SWG0: λ p = 1.15, λ G = 0.96, λ c = 0.88, SWG1: λ p = λ G = 1.12 > λ c = 0.76 SWG1: λ p = λ G = 1.12 > λ c = 0.76 SWF : λ p = λ G = λ c = 1, and CMS: Competitive Market Storage. SWF : λ p = λ G = λ c = 1, and CMS: Competitive Market Storage.

11. Optimal Storage Rule in 3-D : λ p = 1.15, λ G = 0.96, λ c = 0.88 Optimal Storage Rule in 3-D : λ p = 1.15, λ G = 0.96, λ c = 0.88

12. Optimal Storage Rule in 3-D : λ p = λ G = λ c = 1, or CMS Optimal Storage Rule in 3-D : λ p = λ G = λ c = 1, or CMS

13. 5. Summary and Conclusion (1) (1)Optimal grain storage level : - depend on the relative magnitude of welfare weights toward interest groups - depend on the difference in marginal propensities of current harvest and carryover stocks (2) In PPF approach, we can explain many governments’ public storage behavior with high concerns for grain producer (3) Estimated optimal rice storage level derived by PPF approach is larger than derived by traditional utilitarian social welfare maximization problem or competitive storage market model.

14. (4) Optimal storage level in this research is similar to FAO level - optimal rice storage level is 19% level of average consumption during 1995 ~ 2002 year - optimal rice storage level is 19% level of average consumption during 1995 ~ 2002 year - storage for market stabilization: 11%, reserved stock for food security: 8% - storage for market stabilization: 11%, reserved stock for food security: 8% ※ Optimal rice storage level in the previous research (1) Rice consumption`s 11% ~ 13% is optimal storage level: KREI(2003) (1) Rice consumption`s 11% ~ 13% is optimal storage level: KREI(2003) (2) Rice consumption`s 11% ~ 15% is optimal storage level: KREI(2003) (2) Rice consumption`s 11% ~ 15% is optimal storage level: KREI(2003) if considered the import trouble from international market if considered the import trouble from international market (3) Storage Level recommended by FAO (3) Storage Level recommended by FAO - Consumption`s 17% ~ 19% level before 1997 - Consumption`s 17% ~ 19% level before 1997 - Consumption`s 19% ~ 20% level at 1997 - Consumption`s 19% ~ 20% level at 1997 - Distribution Stock 12%, Reserved stock 7 ～ 8% - Distribution Stock 12%, Reserved stock 7 ～ 8%

15. ■ Policy Implication for decreasing rice stocks ○ Efforts for expanding rice consumption : ○ Efforts for expanding rice consumption : - more elastic demand reduces the incentive for holding stocks ○ Efforts for reducing production uncertainty ○ Efforts for reducing production uncertainty - less production uncertainty reduces the incentive for holding stocks