Integrated Assessment of Sustainability

1. Integrated Assessment of Sustainability = Economic analysis + Non-market analysis

2. 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

3. Graphical Analysis Trade Leakage

4. Multi-region analysis Only shown on board Slides will be added later

5. 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)

6. 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

7. Linear Programming, 1 Max c1 * X1 +…+ cN *XN = z s.t. a11 * X1 +…+ a1N*XN b1 … aM1 *X1 +…+ aMN*XN bM X1 , XN  0

8. Linear Programming, 2 Max c1 *X1 +…+cn *Xn = z s.t. a11*X1 +…+a1n*Xn  b1 … am1*X1 +…+amn*Xn  bm X1 , X2  0 Max c1 *X1 +…+cn *Xn+0*S1 +…+0*Sm= z s.t. a11*X1 +…+a1n*Xn+1*S1 +…+0*Sm = b1 … am1*X1 +…+amn*Xn+0*S1 +…+1*Sm =bm X1 , X2 , S1 , Sm  0

9. 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

10. 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)

11. Non-Linear Programming • More structural flexibility • Computationally more difficult • Less specialization effects • Multiple local optima possible Max z = f(X1, … , XN) s.t. g(X1, … , XN)  0

12. Econometric Models, 1 Ykit = fk(X1it, … , XNit) i .. Economic agents t .. time periods X .. n independent variables Y .. k dependent variables

13. Econometric Models, 2 • 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,

14. 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

15. 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

16. Econometric Example Estimating a timber yield function

18. 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.

20. 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.

22. 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

23. 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

24. 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

25. 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)

26. 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

27. 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

28. Neuronal Networks • Modeling technique from computer science • Find nonlinear relationships without explicitly specifying • Beginning to be used for agricultural-environmental relationships (Ex: relationship between climate, soil, and crop yields)

29. 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

30. Spatial Scope of Agricultural Models • Field point (Crop simulation models) • Field • Farm level • Agricultural region • Agricultural sector • Multi-sector • All sectors (CGE models)

31. Temporal Scope of Agricultural Models • Hours (Crop growth models) • Days (Farm level models) • Month (Soil models) • Years (Agricultural sector models) • Decades (Forest models)

32. 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

33. 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