Estimation of Optimal Storage Level in Korea Estimation of Optimal Storage Level in Korea Rice Industry Rice Industry : : Application of Dynamic Application of Dynamic

Stochastic Optimization ModelStochastic Optimization Model

2004. 7. 232004. 7. 23

Department of Agricultural Economics Department of Agricultural Economics Gyeongsang National University Gyeongsang National University

Jeong-Bin, ImJeong-Bin, Im

< 발 표 목 차 >

1. 1. Necessity of Grain StorageNecessity of Grain Storage

2. Review of the Previous Studies2. Review of the Previous Studies

3. Analytical Approach in This Study3. Analytical Approach in This Study

4. Model Specification and Analytical Result4. Model Specification and Analytical Result

5. Summary and Conclusion5. Summary and Conclusion

1. Necessity of Grain 1. Necessity of Grain

StorageStorage

○ ○ Preparation for uncertainty in world grain supply and demand Preparation for uncertainty in world grain supply and demand

- in order to stabilize domestic market supply : Food security/availa- in order to stabilize domestic market supply : Food security/availability bility

- 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 haveGovernments 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?

2. Review of the Previous Studies2. 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

3. Analytical Approach in This 3. Analytical Approach in This StudyStudy

○ ○ Political Preference Function(PPF) approachPolitical 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 functi- Optimal storage level in Korean rice industry with policy objective function. on.

- 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 mconventional utilitarian social welfare model( or competitive market model) odel)

4. Model Specification and Analytical 4. Model Specification and Analytical Results Results

    A. Dynamic optimization model in PPF A. Dynamic optimization model in PPF approachapproach

○ ○ Maximize the following policy objective function to derive the optimal storage levelMaximize the following policy objective function to derive the optimal storage level

(4-1) (4-1)

subject to Ssubject to Stt≥0 ≥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, res- CS, PS and GS represent the consumer surplus, producer surplus and taxpayer surplus, respectively. pectively.

- λ- λii(i =P, C, G) is the welfare weight assigned to each interest group.(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[λc CSt + λp PSt + λG GSt]St

Max

Σt =0

∞

δ t

(4-2) V(4-2) Vtt(H(Htt, S, St-1t-1) = [SWG) = [SWGtt(H(Htt, S, St-1t-1, S, Stt) + ] ) + ]

subject to Asubject to At+1t+1 = H = Ht+1 t+1 + S+ Stt

○ ○ state variables: current harvest level (Hstate variables: current harvest level (Htt) and previous carry-over storage level( ) and previous carry-over storage level( SSt-1 t-1 ).).

- Action(control) variable: optimal current storage level(S- Action(control) variable: optimal current storage level(St t ). ).

※ ※ If interest groups`s political weight is equal, then the following arbitrage conditiIf interest groups`s political weight is equal, then the following arbitrage condition holds: on holds:

⇒ ⇒ P(AP(Att-S-Stt) + k =δE[P(A) + k =δE[P(At+1t+1-S-St+1t+1)]. )].

※ ※ This is the equilibrium condition of determining optimum storage level in tradiThis is the equilibrium condition of determining optimum storage level in traditional social welfare maximization model and determining optimum storage level at tional social welfare maximization model and determining optimum storage level at competitive market storage model (Miranda,1998, Williams and Wright, 1991). competitive market storage model (Miranda,1998, Williams and Wright, 1991).

Et [ Vt+1 (A t+1)] 0≤ St ≤ At

Max

○ ○ Equation (4-1) is generally transferred to Equation (4-2) called Equation (4-1) is generally transferred to Equation (4-2) called Bellman`s equationBellman`s equation

B. Derive optimum storage level with PPF model 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- Price elasticity of demand: - 0.117(Doo Bong, Han 2003) : - 0.117(Doo Bong, Han 2003)

- 8years(1995- 8years(1995 ～～ 2002) average price and consumption data 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 : λλpp = 1.15, λ = 1.15, λcc = 0.88, λ = 0.88, λGG = 0.96(Jeong-Bin, Im 2003) = 0.96(Jeong-Bin, Im 2003)

■ ■ Optimal Storage RuleOptimal Storage Rule

<Figure 4-1> Optimal storage rule : Equilibrium storage <Figure 4-1> Optimal storage rule : Equilibrium storage and supply and supply

Note: SWG0 : λNote: SWG0 : λpp = 1.15, λ = 1.15, λGG = 0.96, λ = 0.96, λcc = 0.88, = 0.88,

SWG1 : λSWG1 : λpp = λ = λGG = 1.12 > λ = 1.12 > λcc = 0.76 = 0.76

SWF : λSWF : λpp = λ = λGG = λ = λcc = 1, and CMS: Competitive Market Storage. = 1, and CMS: Competitive Market Storage.

<Table 4-1> Optimal Carryover Levels for alternative policy <Table 4-1> Optimal Carryover Levels for alternative policy objective function in Korea Rice Industry objective function in Korea Rice Industry

(Use average harvest and carried stock data during 1995 ~ 2002)

Total Market SupplyTotal Market Supply

=6000 meter ton=6000 meter ton

Optimal Storage LevelOptimal Storage Level

(meter ton)(meter ton)

HarvestHarvest Carried StockCarried Stock SWG0SWG0 SWG1SWG1 SWF or CMSSWF or CMS

52005200 800800 1,0051,005 1,0311,031 580580

Note: SWG0: λNote: SWG0: λpp = 1.15, λ = 1.15, λGG = 0.96, λ = 0.96, λcc = 0.88, = 0.88,

SWG1: λSWG1: λpp = λ = λGG = 1.12 > λ = 1.12 > λcc = 0.76 = 0.76

SWF : λSWF : λpp = λ = λGG = λ = λcc = 1, and CMS: = 1, and CMS: Competitive Market Storage. Competitive Market Storage.

<figure 4-2> Optimal Storage Rule in 3-D : λ<figure 4-2> Optimal Storage Rule in 3-D : λpp = 1.15, λ = 1.15, λGG = 0.96, λ = 0.96, λcc = 0.8 = 0.88 8

<Figure 4-3> Optimal Storage Rule in 3-D : λ<Figure 4-3> Optimal Storage Rule in 3-D : λpp = λ = λGG = λ = λcc = 1, or CMS = 1, or CMS

5. Summary and 5. Summary and ConclusionConclusion(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.

        

(4) Optimal storage level in this research is similar to FAO level (4) Optimal storage level in this research is similar to FAO level

    - optimal rice storage level is 19% level of average consumption - optimal rice storage level is 19% level of average consumption during 1995 ~ 2002 year during 1995 ~ 2002 year

- storage for market stabilization: 11%, reserved stock for food - storage for market stabilization: 11%, reserved stock for food security: 8% security: 8%

  

※ ※ Optimal rice storage level in the previous Optimal rice storage level in the previous research research

(1) (1) Rice consumption`s 11% ~ 13% is optimal storage level: Rice consumption`s 11% ~ 13% is optimal storage level: KREI(2003) KREI(2003)

        (2) (2) Rice consumption`s 11% ~ 15% is optimal storage level: Rice consumption`s 11% ~ 15% is optimal storage level: KREI(2003) KREI(2003)

if considered the import trouble from international marketif 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- Distribution Stock 12%, Reserved stock 7 ～～ 8% 8%

  

■ ■ Policy Implication for decreasing rice Policy Implication for decreasing rice stocksstocks

    ○ ○ Efforts for expanding rice consumption : Efforts for expanding rice consumption : - more elastic demand reduces the incentive for holding stocks

○ ○ Efforts for reducing production uncertaintyEfforts for reducing production uncertainty

    - less production uncertainty reduces the incentive for holding stocks