RAINS and Chapter 14

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RAINS and Chapter 14

• ECON 4910

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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.

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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.

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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 Siaij ei bj
• bj is exogenous depositions from sources not
  covered in the model. Mainly United States

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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)

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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

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The model

• Minimise ?ci j1,2 , 38
• subject to ci ?iei Bi
• dj Siaij 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

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Feasibility

• Turns out 5 critical loads are not feasible.
  (Cant be done)
• Question is How to modify the model? Let us try
  Gap Closure for the non-feasible constraints.
• dj s(dj(historical) Dj) Dj.
• Here s is the percentage of closure
• Alternative Area exceedance closure

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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?

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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

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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.

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Total Factor Productivity Growth

• Consider the macro production function
  YAf(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.)

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Some manipulations to decompose productivity
growth

• Differentiate to get
• ?Y ?Af(L,K) AFL?L AFK?K
• Divide by Y to get
• ?Y/Y
• ?A/A (LAFL/AY)(?L/L) (KAFK/AY)(?K/L)
• Use that pL pYAFLand pK pYAFK. and zero
  profits in macro equilibrium to get

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Finally

• Á/A Ý/Y sLL/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.

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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?

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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.

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Example - China

• Example - China
• GDP per capita in 2004 US 5600
• US GDP per capita in 2004 US40100
• 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

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But something is a amiss

• Each year 400000 Chinese die from airpollution
• 70 of Chinas freshwater is polluted to the
  point of being undrinkable
• These things are not measured

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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.

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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.

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Deriving GDP measure from a Optimally Managed
Economy

• Consider the following economy
• Utility W?tU(ct)ßt with Kt1 Kt F(Kt,Rt)
  dKt ct and Et1 Et f(Et) Rt
• Lagrangian for this problem is
• ? ?t(U(ct)ßt ?(Kt1 Kt (F(Kt,Rt) dKt)
  ct) µ (Et1 Et (f(Et) Rt))
• R is a natural resource

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Deriving GDP measure from a Optimally Managed
Economy

• Let us look at the first term in the Lagrangian
• (U(c0)ß0 ?(K01 K0 (F(K0,R0) dK0) ct)
  µ (E0 1 E0 (f(E0 ) R0 ))
• Does it look familiar?
• How about now?
• (U()c0ß0 ?(K01 K0 (F(K0,R0) dK0) ct)
  µ (E0 1 E0 (f(E0 ) R0 ))

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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()c0ß0 ?(K01 K0 (F(K0,R0) dK0) ct)
  µ (E0 1 E0 (f(E0 ) R0 ))
• (pc0 pK(Capital investment) pE(Change in
  resource stock))

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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.

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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

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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?

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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?

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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