Future directions in modeling

Report
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?
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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

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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.

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