Agriculture as a Managed Ecosystem:

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Agriculture as a Managed Ecosystem Implications
for Econometric Analysis of Production
Risk   John M. Antle Susan M. Capalbo Department
of Agricultural Econ Econ Montana State
University March 2001
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• Understanding and predicting the behavior of
  agroecosystems is important for a number of
  leading public policy issues, including
• sustaining and enhancing the productivity of
  agricultural production systems
• environmental and human health consequences of
  agricultural technology
• impacts of climate change on the global food
  supply

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The question we address is whether risk concepts
can help us understand and predict the behavior
of agroecosystems.
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We premise our analysis on the commonsense view
that farmers use a variety of strategies to
manage the risks associated with the spatial and
temporal variability in agroecosystems. This
variability is driven by both bio-physical and
economic processes.
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We argue that the prevailing analytical and
empirical paradigm used by the agricultural
economics profession, which largely abstracts
from the spatial and temporal aspects of these
complex systems, suffers from a number of
significant limitations.
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These limitations explain why this paradigm has
not been successful in improving the predictive
power of economic models, and why models used in
policy analysis do not typically incorporate risk
features. How then can we develop a more useful
quantitative approach to understand the role of
risk in agricultural production systems?
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The Paradigm of Agriculture as a Managed Ecosystem
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Implications for Specification of Decision Making
Processes Temporal Variability Intra-seasonal
and Inter-seasonal Dynamics
A general representation of a discrete, time
dependent production process can be written
as q0 q0x0, ,0,   (1) qt qtx1, qt-1,
,1, 0 lt t lt tH,   qH qHxH, qt, ,H If
time intervals are endogenous, this model is not
well-defined
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To obtain a model with well-defined production
stages, let the ith production activity occur at
time ti ti!1 i q0 q0x0, ,0,
(2) q1 q1x1, qi-t, ti-1, ?i, ,i, i 1,
, N, qH qHxH, qN, tN, ?H, ,H.
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Recursively substituting the stage functions qi
into qH in (2) gives the composite production
function qH qHxH, qNqN!1..., tN!1, N,
,N, tN, N, ,H / qcHx, Nt, N,
H,, where Hx (x0,...,xH) etc.

• In conventional econometric analysis,
  intermediate products are not observed by the
  econometrician, hence the composite function qc
  typically is estimated in econometric models.

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In the production function we can substitute out
qs for s i1,,N,H, to obtain the conditional
composite production function for stage i, qH
qcixi, qi-1, ti-1, ?i, ,i , where ,i (,i,,
,N, ,H). Define ?i as the moments of the error
,i in the conditional composite production
function for stage i.
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The values of xi and ?i that maximize expected
returns or expected utility of returns,
conditional on information available at the time
ti-1, are generally of the form x0 x0?0,
w0, ?0 (4) xi xi?i-1, wi, qi-1, ti-1,
?i, i 1,,N, H ?i ?i?i-1, wi, qi-1,
ti-1, ?i, where we use the notation wi (wi,,
wN, wH).
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We hypothesize that the moments of the
distribution of output at time ti in the growing
season take the structural form ?0 ?0(x0)
(7) ?i ?i(xi, qi-1, ti-1, ?i,), i 1,,N,
H or using (4), the moments take the reduced
form ?0 ?0r(?0, w0) (8) ?i ?ir(?i-1,
wi, i-1x, i-1t, i-1?, ?i, i-1,), i 1,,N, H.
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Spatial Variability Site-Specific Production
Decisions Site-specific models have a structural
form with discrete land use decisions and
continuous input decisions see Antle and
Capalbo (2001).
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• Implications for Econometric Analysis of
  Production Risk
• Input Endogeneity and Production Risk Measurement
• period 0 structural and reduced form moments can
  be estimated consistently using Just-Pope or
  Antle methods
• period 1,,N, H moments depend on endogenous
  inputs and cannot be estimated consistently using
  conventional methods

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• Estimation Strategies
• Account for input endogeneity in estimation of
  sequential moment functions
• What are properties of residual-based moment
  estimators?
• Note intraseasonal variation in input prices may
  make estimation of sequential moments difficult
• 2. Use two-stage model with predetermined inputs
  and intermediate inputs
• ? ?(?0, w0, x0)
• where w0 is a vector of intermediate input
  prices.

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• Econometric Analysis of Discrete Land-Use
  Decisions
• Econometric specification and estimation of
  disaggregate, site-specific production models may
  need to account for
• the discrete structure of land use decisions
• the dynamics of crop rotations
• the spatial variation in physical conditions
• statistical properties of the spatial data
• other features of the farmers management
  behavior such as risk aversion.

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• Recent econometric approaches to modeling land
  use decisions use risk-neutral share-equation
  models or discrete choice models with data
  aggregated to county or larger spatial units.
• Disaggregate, site-specific data are unbalanced
  and do not provide observations for all decisions
  on all land units (implies censoring problem)
• Reduced forms do not represent output explicitly
• Estimation and simulation of high-dimensional
  discrete choice models is problematic

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• Spatial and Temporal Aggregation
• Spatial and temporal aggregation of output and
  input data are likely to significantly reduce the
  information content of the data and bias
  inferences based on them
• particularly for risk models based on residuals
• Similar problems caused by failure to account for
  aggregation of outputs and iputs of differing
  qualties
• Grain quality
• Pesticides
• Machinery

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• Does Incorporating Risk Improve the Predictive
  Power of Economic Models?
• A strong test of the importance of risk is to ask
  if it can significantly improve the ability of a
  model to predict either within-sample or
  out-of-sample behavior.
• We conduct this test using the econometric-process
  model of Antle and Capalbo (2001)
• This model is designed to predict site-specific
  land use based on simulation of distributions of
  expected returns

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Figure 4. Structure of an Econometric-Process
Simulation Model and Linkages to Biophysical
Simulation Models in a Closely-Coupled Model of
an Agroecosystem (Antle and Capalbo, 2001).
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Variance Functions for MT Dryland Grain Production
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Figure 3. Observed vs. Simulated Mean Land Use
in Montana Dryland Grain Production, Risk Neutral
and Risk Averse Models.
Variance Functions for MT Dryland Grain Production
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A New Approach to the Analysis of Production
Risk Does the static risk aversion model capture
the ways that spatial and temporal variability in
the crop growth process interact with farmers
land use and management decisions? We propose a
new approach that exploits the agroecosystem
paradigm.
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• Examples
• Input Endogeneity in the Intraseasonal Decision
  Model
• Endogeneity caused by lack of observations on
  crop growth (intermediate outputs in the dynamic
  production function model).
• Discrete Choice in the Spatial Model
• Discrete choice caused by site-specific decision
  making

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• Coupling an economic decision model to a
  biophysical crop growth model, the production
  system can be estimated and simulated taking into
  account intra-seasonal and spatial variation
• Econometric problems of input endogeneity,
  discrete choice can be finessed.
• Our hypothesis is that this type of model will
  show strong interactions between spatial and
  temporal variability and farm decisions.
• For an illustration, see the dynamic factor
  demand equations in Antle, Capalbo and Crissman
  (1994) and (1998).

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This paper and presentation are available at
www.climate.montana.edu