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 c 1 * X 1 +…+ c N *X N = z s.t. a 11 * X 1 +…+ a 1N *X N  b 1 … a M1 *X 1 +…+ a MN *X N  b M X 1, X N  0

8. Linear Programming, 2 Max c 1 *X 1 +…+c n *X n +0*S 1 +…+0*S m = z s.t. a 11 *X 1 +…+a 1n *X n +1*S 1 +…+0*S m = b 1 … a m1 *X 1 +…+a mn *X n +0*S 1 +…+1*S m = b m X 1, X 2, S 1, S m  0 Max c 1 *X 1 +…+c n *X n = z s.t. a 11 *X 1 +…+a 1n *X n  b 1 … a m1 *X 1 +…+a mn *X n  b m X 1, X 2  0

9. Linear Programming, 3 N + M + 1 Variables – 1 objective function variable (z) – N choice variables (X 1.. X N ) – M slack variables (S 1.. S M ) 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/db m ) * S m = 0 … at optimum (dz/dX n ) * X n = 0 … at optimum Number of nonzero X n  M (specialization)

11. Non-Linear Programming More structural flexibility Computationally more difficult Less specialization effects Multiple local optima possible Max z = f(X 1, …, X N ) s.t. g(X 1, …, X N )  0

12. Econometric Models, 1 Y kit = f k (X 1it, …, X Nit ) 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 ModelTimber = 25.3 * Age Adjusted R Square0.91 Standard Error0.23 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