Transcript Integrated Assessment of Sustainability

Integrated Assessment of
Sustainability
=
Economic analysis
+
Non-market analysis
Analytical Tools
• Qualitative Analysis
– graphical tools, derivative analysis
• Optimization
– maximize/minimize constrained objective
• Statistics
– find functional relationships (curve fitting)
• Life-cycle assessment
– Cross-sector impact accounting
• Simulation
– solve complex systems of (differential)
equations with random variables
Graphical Analysis
Trade
Leakage
Multi-region analysis
Only shown on board
Slides will be added later
Optimization Models, 1
• simulate decision-making of rational
agents (primal approach)
• suitable for new technologies / policies
• may be solved explicitly (analytically or
numerically)
• may not be solved explicitly
(comparative statics, comparative
dynamics)
Optimization Models, 2
• used at firm level to determine optimal
input and output quantities
• used at sector level to determine
optimal technologies and aggregate
production levels
• for real world problems often
numerically solved
– linear programming
– nonlinear programming
Linear Programming, 1
Max c1 * X1 +…+ cN *XN = z
s.t. a11 * X1 +…+ a1N*XN  b1
…
aM1 *X1 +…+ aMN*XN  bM
X1 ,
XN  0
Linear Programming, 2
Max c1 *X1 +…+cn *Xn
s.t. a11*X1 +…+a1n*Xn
…
am1*X1 +…+amn*Xn
X1 ,
X2
= z
 b1
Max c1 *X1 +…+cn *Xn
s.t. a11*X1 +…+a1n*Xn
…
am1*X1 +…+amn*Xn
X1 ,
X2
+0*S1 +…+0*Sm = z
+1*S1 +…+0*Sm = b1
 bm
 0
+0*S1 +…+1*Sm = bm
, S1 ,
Sm  0
Linear Programming, 3
• N + M + 1 Variables
– 1 objective function variable (z)
– N choice variables (X1 .. XN)
– M slack variables (S1 .. SM) to convert
inequalities into equalities
• M + 1 Equations
– 1 objective function
– M constraints
Linear Programming, 4
• Solution at extreme point of convex
feasibility region
• Complementary slackness:
(dz/dbm) * Sm = 0
… at optimum
(dz/dXn) * Xn = 0
… at optimum
• Number of nonzero Xn  M
(specialization)
Non-Linear Programming
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More structural flexibility
Computationally more difficult
Less specialization effects
Multiple local optima possible
Max
s.t.
z = f(X1, … , XN)
g(X1, … , XN)  0
Econometric Models, 1
Ykit = fk(X1it, … , XNit)
i .. Economic agents
t .. time periods
X .. n independent variables
Y .. k dependent variables
Econometric Models, 2
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Based on theory, functional form(s)
are chosen and constraints imposed
Functional form tested and modified
Functional parameters and
statistical properties are estimated
prediction and extrapolation using
specific combinations of X variables
and estimated parameters,
Econometric Models, 3
• Based on observed behavior and data
(dual approach)
• Uncertainty statement through
confidence and prediction intervals
• Useful especially in context of
agricultural heterogeneity
• Useful for quantifying impacts of
various (unobservable) human or
natural attributes
Econometric Models, 4
• Maximize functional fit, minimize sum
of squared errors between observed
and predicted data
• Explain variance in dependent variables
through functional relationship with
independent variables
• Knowledge about structure sometimes
more important than mathematical
skills
Econometric Example
Estimating a timber yield
function
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Forest growth
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Linear Model Results
Model
Timber = 25.3 * Age
Adjusted R Square
0.91
Standard Error
0.23
P-value
0.00000…
Thus, it seems to be a good fit.
However, the forest scientist is not
pleased with a linear yield function.
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Environment
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Cubic Model Results
Timber = 4.14 Age + 0.56 Age^2
– 0.0037 Age^3 + 0.38 Environment
Adjusted R Square: 0.99
P-values very low
This is not only a better fitting model, it
also conforms to forest science.
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Corrected Growth
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Multicollinearity
• Potential problem in econometric models
• Right hand side variables are correlated
(Ex: Land quality and profits)
• Involved coefficient estimates wrong
• Prediction can be ok
• Fix: take out correlation through
regression and transformation of right
hand side variables
Demand or Supply?
• q = f(p)
• Price and quantity data are not
sufficient to estimate demand or supply
curves
• need supply shifting variable for supply
curve and demand shifting variable for
demand curve
Environmental Models, 1
Often simulation models because
• Many environmental processes don't
involve choices.
• Random events frequent in
environmental sciences (Randomness
indicates a combination of complex
processes and limited knowledge)
• Observational limits
Environmental Models, 2
• Combine physics, chemistry, biology,
geology, atmospheric science,
oceanography, and others
• Differential equations to model
flows (dx/dt) of energy, nutrients,
pollutants, water
• Time integral of flow yields stock
effect (concentration, volume,
deposit)
Earth System Models, 1
• Recent trend in environmental science
• Earth is modeled as complete system
consisting of several regionalized
compartments
• Mathematical equations define flows
and transformations between/within
compartments
Earth System Models, 2
• Useful for modeling complex, global
processes (climate, fate of pollutants)
• High computer effort
• Substantial data needs
• Partial vs. general equilibrium data
problem
• Current reliability limited
Neuronal Networks
• Modeling technique from computer
science
• Find nonlinear relationships without
explicitly specifying
• Beginning to be used for agriculturalenvironmental relationships (Ex:
relationship between climate, soil, and
crop yields)
Linking economic and
environmental models, 1
• High in demand
• Basis for integrated assessments
• However, linked models often very
different
– spatial scope
– time scale
– management details
Spatial Scope of
Agricultural Models
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Field point (Crop simulation models)
Field
Farm level
Agricultural region
Agricultural sector
Multi-sector
All sectors (CGE models)
Temporal Scope of
Agricultural Models
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Hours (Crop growth models)
Days (Farm level models)
Month (Soil models)
Years (Agricultural sector models)
Decades (Forest models)
Linking economic and
environmental models, 2
• Three types of linkages
– One directional (easiest)
– iterative
– integrative (most difficult)
• Appropriate type depends on
– research question to be addressed
– available resources (human, computers)
– costs and benefits
Linking economic and
environmental models, 3
• account for heterogeneous
environmental conditions
• cover large region to obtain
macroeconomic impacts
• results in large data requirements and
big models and large model outputs
• critics: GIGO models, black boxes,
(no) validation