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Future Directions for SWAP Modeling Methods
Richard Howitt and Duncan MacEwan
UC Davis and ERA Economics
California Water and Environmental Modeling ForumTechnical Workshop
Economic Modeling of Agricultural Water Use and Production
January 31, 2014
Data Requirements 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?
Remote Sensing and Agricultural Production: Land Use information 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
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 ??
A brief history of PMP
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
A brief history of calibration
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
Calibration developments
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
Current Research
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 in Calibration of RTS models
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:
PMP-RTS Model
/
1 1 2 2 ...i
i i igi gi gi gi gi gi gij gijy x x x
Model Specification
/
1 1 2 2
1 1
2 2
max 2
...
( )
( )
ii i i
i gi land i i land j jg i j land
gi gi gi gi gi gi gij gij
gigi
gigi
p y x x
subject to
y x x x
x X land
x X water
More precise supply elasticities Second order calibration for policy
response Symmetry for crop acre increase or
decrease Crop area expansion New crop introduction
Policy Value of RTS Specification
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.
Current Beta Version of SWAP-RTS