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

PixelClassification

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 ??

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

Calibrated output level = 865 tons Note difference in curvature

Example of PMP v RTS

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