Future directions in modeling

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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

 x

 i gi 1 gi 1

  x

 i gi 2 gi 2 x

 i gij gij i

max

 g i p y i gi

   land

 

2

 x i i land

   x j j subject to y gi

   gi x

 i gi 1 gi 1

  x

 i gi 2 gi 2

 gi

 gi x

1 gi

X

1

( land ) x

2 gi

X

2

( water )

  x gij gij i 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.

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