Estimating a dual value function as a meta-model of a detailed dynamic mathematical programming model

Mathematical programming (MP) is a widespread approach to depict production and investment decisions of agents in agent-based models (ABM) related to agriculture. However, introducing dynamics and indivisibilities in MP models renders their solution computing time intensive. We present a meta-modeling approach as an alternative to directly integrating MP in an ABM. Specifically, we estimate a dual symmetric normalized quadratic (SNQ) value function from a set of MP solutions. The approach allows us to depict relationships between key attributes, like the farm endowment with (quasi-) fixed factors and discounted farm household incomes, without modeling the technology in detail. The estimated functions are integrated in the ABM to derive agents' decisions. The meta-modeling approach relaxes computational restrictions such that spatial interactions in large regions can be simulated improving our understanding of structural change in agriculture. It can also be used to extrapolate to farming populations where data availability might be restricted.