Multi-market modeling of agricultural supply when area allocation is endogenous

1. Multi-market modeling of agricultural supply when area allocation is endogenous Roehlano M. Briones Research Fellow, PIDS Brown Bag Seminar 08 November 2012

2. Motivation: Prelude to lunch • Discussions of long term adequacy of food supply – balance between food requirements of a growing population as opposed to scarcity of productive factors, especially land • The issue has been pointed out since Malthus • “Checks” avoided due to growth in yields owing to modern technologies • Malthusian anxiety has reappeared in an era of global price volatility, climate change, and a population seven billion-strong

3. Yield-area dichotomy • Contrast between yield (growing) and area (fixed, more or less) – useful distinction • Both are integral to agricultural supply • Allocation of resources across crops reduces to a land use problem • Compared to modeling yield, relatively little has been done in modeling the area side • Land  area; a quasi-fixed factor

4. Aims and scope • Presents: tractable model of agricultural supply within area x yield framework • Area allocation problem rooted in optimization (not ad hoc) • Calibrated with minimal priors • Useful for multi-market modeling, e.g. AMPLE

5. Related literature • Shumway, Pope, and Nash (1984): first to model area allocation with aggregate land constraint • Bewley, Young, and Colman (1987): directly model area shares in multinomial logit framework • Chambers and Just (CJ, 1989): area allocation as two-stage optimization problem

6. Related literature • Coyle (1993): econometric model for estimating area allocation under CJ but omits yield determination • Arnade and Kelch (2007): yield and area allocation model, with land a quasi-fixed factor whether at the level of the farmer or of the industry. Pointed to the importance of shadow prices in the land allocation problem

7. Related literature • Numerical partial and general equilibrium models: • Area x yield; area allocation modeled, but no aggregate area constraint: e.g. AGLINK of FAO, IMPACT of IFPRI, CAPSIM of China • Direct modeling of agricultural supply (by-passing area x yield formulation): e.g. GTAP • APSIM of the Philippines: area share allocation but aggregate constraint imposed ad hoc

8. Related literature • Modeling strategy sketched in Alba and Briones (2010): fairly general approach, based on Slutsky matrix of output supply and input demand functions • The strategy outlined here is even more austere, but requires much more structure, reminiscent of Bouis (1996) on the demand side

9. The model • Two-stage problem • Constant returns to scale in all inputs: express output on area x yield formulation • First we model yield: per ha production function • Impose:

10. The model • We infer: • Optimal net revenue is given by: • Own-price elasticity is positive:

11. The model: area allocation • Aggregate area constraint (at baseline): • Substitution across land use is subject to a constant elasticity of transformation

12. The model: area allocation • The second stage problem is: • Form the Lagrangian:

13. The model: area allocation • Expression for area allocation: • Calibrates for shadow price: • Elasticity of area with respect to profit (relative):

14. Application

15. Application

16. Extensions • The first stage can accommodate more flexible functional forms, conditional on an explicit dual net revenue function. • Second stage can be enriched by partitioning the set of crop categories into related crop types and nesting the transformation functions. For instance crops can be partitioned into temporary and perennial