RAINS and Chapter 14

ECON 4910

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.

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.

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, d j.

• 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

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)

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

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

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

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?

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

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.

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.)

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:

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.

´

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?

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.

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…

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

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.

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.

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

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 ))

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))

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.

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

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?

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?

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