Significant effort with every project Land use › Recent and reliable crop data Water use › Disaggregation › Groundwater › Cost Looking forward › Remote sensing? › Actively updated central database? Land use (DWR, NAIP, NASS) Digital elevation models (USGS) Meteorological information (CIMIS) County field surveys Other survey data › Salinity With data from USDA Raster for Land Use for California http://www.nass.usda.gov/research/Cropland/cdorderform.htm Pixel Classification Error Boundary Error Initial models and LP › Overspecialization, poor policy response Positive Mathematical Programming › Howitt (1995) Central Valley Production Model (CVPM) › PMP with limited input substitution Statewide Agricultural Production Model (SWAP) › PMP with flexible CES production functions Next iteration ?? Positive Mathematical Programming › Calibration method: 3 Steps Economic first-order conditions hold exactly, elasticities are fit by OLS Curvature in objective function from PMP cost functions (quadratic – CVPM; exponential SWAP) Areas for refinement › › › › Myopic calibration First-order versus second-order calibration Consistency with economic theory Symmetry of policy response Howit (1995) › PMP first formalized Various applications › CVPM Hatchett et al (1997) › SWAP Howitt et al (2012) Heckelei (2002) › Critique of elasticity calibration, develop closed-form expression for fixed-proportions production function Merel and Bucaram (2010) › Closed form solution for implied elasticities (non-myopic) Merel, Simon, Yi (2011) › Fully calibrated (exact) decreasing returns to scale CES production function with single binding calibration constraint Howitt and Merel (2014) › Review of state-of-the-art calibration methods Garnache and Merel (2014) › Generalization of Merel, Simon, and Yi (2011) to multiple binding constraints Incorporate RTS exact calibration into SWAP Understand tradeoffs and implications Incorporating dynamic effects of crop rotations and stocks of groundwater Validate and benchmark against other models and methods LP stage I only provides consistent estimates of resource shadow values ( Lambda1) Curvature in the objective function to calibrate crop specific inputs comes from the decreasing returns to scale (Delta) Stage II– Least squares fit solves for parameters: Scale (alpha), Share(beta), RTS (delta) and Lambda2 (PMP cost) Stage III Check the VMP conditions from stage II, and solve the unconstrained RTS problem Differences › Delta is now greater than zero but less than one. › There is no non-linear PMP cost function › The PMP cost lambda2(i) is added to the cash costs Production Function: y gi gi gi1 x i gi 1 gi 2 x i gi 2 ... gij x i gij / i m ax g p i y g i la n d 2 i x i la n d jxj j la n d i su b ject to i i i y g i g i g i 1 x g i 1 g i 2 x g i 2 ... g ij x g ij x 1 gi X 1 ( la n d ) 2 gi X 2 ( w a ter ) gi x gi / i Calibrated output level = 865 tons Note difference in curvature More precise supply elasticities Second order calibration for policy response Symmetry for crop acre increase or decrease Crop area expansion New crop introduction All crop inputs and outputs calibrate exactly About half the regional crops pass the two Merel conditions. Elasticities are minimum SSE estimates. Calibration takes about half an hour, but once calibrated model solutions are fast. Bio-physical priors can be a part of calibration- a test on water use efficiency worked well. A small test version using OLS estimates over 5 years of data worked.