The RAINS Model: Bridging Theory and Reality in Environmental Economics

1. RAINS and Chapter 14 ECON 4910

2. The Rains Model • An example of applied environmental economics. • Illustrates how economic theory is translated into a real world model. • The lack of data makes compromises necessary. • This implies a few warts.

3. What is captured by the RAINS model? • Several versions of the model, some with sulphur, NOx, ammonia etc. • Here we focus on the sulphur model.

4. Components of the Rains model • 38 regions (For the most part countries). These are the sources of pollution, ei. • 700 grid squares covering Europe, each 150 km ×150 km. These are receptors of pollution, dj. • A meteorolocial model, a matrix where the coefficent aij is the fraction of pollution from i that ends up in j. dj = Σiaij ei + bj bj is exogenous depositions from sources not covered in the model. Mainly United States

5. More components of the Rains model • Ecological consequences – A function that maps depositions into ecological consequences – fraction of ecosystems in a grid square that is severly damaged. • These functions are called critical loads. The 5% critical load implies that 5% of ecosystems will be destroyed or damaged. • Stepwise function (Draw figure on Board)

6. The cost module • For each source there is a purification cost curve ci(ei). • Purification is the cost of reducing emissions keeping output constant • Marginal cost curves in steps. • Represented by ci = iei + Bi

7. The model • Minimise ∑ci j=1,2 … , 38 • subject to ci ≥iei + Bi dj = Σiaij ei + bj ≤ Di i = 1,2,…,700 Di are usually n% critical loads. That is we allow 5% of the ecosystems in each grid to be destroyed or severly damaged

8. Feasibility • Turns out 5% critical loads are not feasible. (Can’t be done) • Question is: How to modify the model? Let us try Gap Closure for the non-feasible constraints. • dj≤ σ(dj(historical) – Dj) + Dj. • Here σ is the ”percentage of closure” • Alternative: Area exceedance closure

9. Now Questions • What compromises have been made? • Exogenous output • No valuation of damages. Arbitrary protection at 5% of ecosystems. • Gap Closure not even related to ecosystem protection • So, is this a good model?

10. Economy-Wide effects • Into macro-economics and the effect of environemental regulation on total productivity. • Issue # 1. How does environmental protection affect productivity. • Issue # 2. How does environmental protection affect our measures of productivity

11. Productivity growth • Production grows for three reasons: • Increased use of inputs (such as labor and capital) • Increased efficiency • Technological progress • Problem right here. Production must be measured properly, i.e. include environmental services. However, all three may lead to less production of environmental services.

12. Total Factor Productivity Growth • Consider the macro production function Y=Af(L,K). • Here A is a technology variable assumed to capture the effect of progress. (Einsteins theory of relativity, The Slutsky Equation and the invention of Tofu.)

13. Some manipulations to decompose productivity growth • Differentiate to get ΔY = ΔAf(L,K) + AF’LΔL + AF’KΔK Divide by Y to get: ΔY/Y = ΔA/A + (LAF’L/AY)(ΔL/L) + (KAF’K/AY)(ΔK/L) Use that pL = pYAF’Land pK = pYAF’K. and zero profits in macro equilibrium to get:

14. Finally… ´ • Á/A = Ý/Y – sLĹ/L – sKK/K Here sL = pLL/(pLL + PKK) and sK = pKK/(pLL + PKK) sK and sL are cost shares. Technological growth Á/A is the increase in production not attributed to increased input use.

15. The effect on prouctivity when we look at a bad measure • Productivity growth is often reported only as Labour productivity growth. • What is the effect of environmental regulations that raises the price of capital?

16. Green National Accounting • Why national accounting? • Indispensable tool for planning purposes. Macroeconomic policy without national accounting does not make much sense. • Important metric for people with a size fetish. My GDP is bigger than your GDP. • For both purposes it is important to get things right.

17. Example - China • Example - China • • GDP per capita in 2004: US$ 5600 • • US GDP per capita in 2004: US$40100 • • So USA is more than 7 times as rich as • China • • China GDP per capita grew at 9.1% in 2004 • • USA grew at 4.4% • • If this continues…

19. But something is a amiss • Each year 400000 Chinese die from airpollution • 70% of China’s freshwater is polluted to the point of being undrinkable • These things are not measured

20. What can go wrong with national accounting • Some things are not measured correctly or at all • Goods not produced for sale in a market e.g. raising kids, house cleaning, pollution induced health problems. • Goods that are produced by government e.g. the value of education • Prices do not reflect social cost • Some things are categorized wrong. • Extraction of natural resources such as fish and oil represents (possibly) depletion of wealth rather than production of income.

21. National Accounting • Y = C + G + I + A – B. • GDP equals Consumption + Real Investment + Financial Investment through trade surplus. All measured at market prices. • Here we only consider a closed economy without a government.

22. Deriving GDP measure from a Optimally Managed Economy • Consider the following economy: • Utility W=∑tU(ct)βt with Kt+1 – Kt = F(Kt,Rt) – δKt – ct and Et+1 – Et = f(Et) – Rt • Lagrangian for this problem is • Λ= ∑t(U(ct)βt – λ(Kt+1 – Kt – (F(Kt,Rt) – δKt) – ct) – μ (Et+1 – Et – (f(Et) – Rt)) • R is a natural resource

23. Deriving GDP measure from a Optimally Managed Economy • Let us look at the first term in the Lagrangian: (U(c0)β0 – λ(K0+1 – K0 – (F(K0,R0) – δK0) – ct) – μ (E0+1 – E0– (f(E0 ) – R0 )) Does it look familiar? • How about now? (U’()c0β0 – λ(K0+1 – K0 – (F(K0,R0) – δK0) – ct) – μ (E0+1 – E0– (f(E0 ) – R0 ))

24. The point: • If the market prices are equal to the shadow prices and to marginal utility, GDP for period t is equal to the corresponing term in the Lagrangian! This can be shown formally but is a bit tricky. • (U’()c0β0 – λ(K0+1 – K0 – (F(K0,R0) – δK0) – ct) – μ (E0+1 – E0– (f(E0 ) – R0 )) = • (pc0 – pK(Capital investment) – pE(Change in resource stock))

25. A wrongly calculated GDP • (pc0 – pK(Capital investment) + pE(Resource extraction)) • Two errors are made. Resource extraction counts as positive when it should be negative (and vice versa) • Note: In a steady state economy this does not matter.

26. The relationship between wealth and GDP • It can be proven that if NNP is measured correctly then: • Wealth = NNP/Discount rate • An increase in NNP implies higher utility

27. Issues not touched upon: • Adjusting GDP for risk? Catastrophic risk. The easy way is NNP + Pr(catastrophe in a year)×Cost of catastrophe • – Risk distributed across population. Very contested topic • – Income distribution?

28. Income distribution • Although China is growing rapidly, a largepart of the population is left behind. • Imposes political risk on future NNP development. • Is a dollar to Farmer Poor Joe the same as a dollar toBill Gates? • Is distributionally skewed NNP growth sustainable?

29. Income distribution - USA • From 1985 to 2003, the richest 1% saw an increase in income equal to 60% (adjusted for inflation) • From 1985 to 2003, the richest 1% saw an increase in income equal to 2% (adjusted for inflation) • Based on tax returns. The truth is even worse. • Recipe for revolution