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Integrated Assessment Models of Economics of Climate Change. Economics 331b Spring 2009. Slightly Simplified Equations of DICE-2007 Model: Revised. Note: For complete listing, see Question of Balance, pp. 205-209. How do we solve IA models numerically?.

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Integrated assessment models of economics of climate change

Integrated Assessment Modelsof Economics of Climate Change

Economics 331b

Spring 2009


Slightly Simplified Equations of DICE-2007 Model: Revised

Note: For complete listing, see Question of Balance, pp. 205-209.


How do we solve ia models numerically
How do we solve IA models numerically?

We take discrete version of model, simplified as follows.

We solve using various mathematical optimization techniques.

  • GAMS solver (proprietary). This takes the problem and solves it using linear programming (LP) through successive steps. It is extremely reliable.

  • Use EXCEL solver. This is available with standard EXCEL and uses various numerical techniques. It is not 100% reliable for difficult or complex problems.

  • MATHLAB. Useful if you know it.

  • Genetic algorithms. Some like these.


Example minimize cost of emissions to limit the sum of emissions over time
Example: Minimize cost of emissions to limit the sum of emissions over time


Setup
Setup

Start with an initial feasible solution, which is equal reductions in all periods.


Number crunch
Number crunch….

Then maximize PV output

Subject to the constraint that:

the sum of emissions

< target sum of emissions


This is the solver dialogue box
This is the solver dialogue box

Objective function

Control variables

Constraints


If you have set it up right and have a good optimization program then voil
If you have set it up right and have a good optimization program, then voilà !!!

Note that the emissions controls are generally “backloaded” because of the positive discounting (productivity of capital) and because damages are in future.


Can also calculate the shadow prices here the efficient carbon taxes
Can also calculate the “shadow prices,” here the efficient carbon taxes

Remember that in a constrained optimization (Lagrangean), the multipliers have the interpretation of d[Objective Function]/dX.

So, in this problem, interpretation is MC of emissions reduction.

Optimization programs (particularly LP) will generate the shadow prices of carbon emissions in the optimal path.

For example, in the problem we just did, we have the following shadow prices:

With a little work, you can show that the rate of growth of prices = interest rate for this case.


Applications of ia models
Applications of IA Models

Major applications of IA Models:

  • Project the impact of current trends and of policies on important variables.

  • Assess the costs and benefits of alternative policies

  • Determine efficient levels of policy variables (carbon taxes, emissions control rates, emissions, …)

    For these, I will illustrate using the DICE-2007 model:

  • Full analysis Question of Balance (see reading list).

  • There is a “beta” version using an Excel spreadsheet at http://www.econ.yale.edu/~nordhaus/homepage/DICE2007.htm (both an *.xls and *.xlsx version)


1. No controls ("baseline"). No emissions controls.

2. Optimal policy. Emissions and carbon prices set for economic optimum.

3. Climatic constraints with CO2 concentration constraints. Concentrations limited to 550 ppm

4. Climatic constraints with temperature constraints. Temperature limited to 2½ °C

5. Kyoto Protocol. Kyoto Protocol without the U.S.

6. Strengthened Kyoto Protocol. Roughly, the Obama/EU policy proposals.

7. Geoengineering. Implements a geoengineering option that offsets radiative forcing at low cost.

Illustrative Policies for DICE-2007


Snapshot of dice excel model
Snapshot of DICE-Excel model

http://www.econ.yale.edu/~nordhaus/homepage/DICE2007.htm




Ipcc ar4 model results history and projections
IPCC AR4 Model Results: History and Projections

DICE-2007

model

2-sigma range

DICE model





Policy outcomes variables
Policy outcomes variables

Overall evaluation

Two major policy variables are

- emissions control rate

- carbon tax


Economic evaluation
Economic evaluation

We want to examine the economic efficiency of each of the scenarios.

Some techniques:

- PV of abatement, damages, and total

- PV as percent of PV of total consumption

- Consumption annuity equivalent:









What do carbon prices mean in practice

Carbon tax,

2010

Increase, price of energy, US

All energy

[$/tC]

Gasoline

expenditures

Kyoto: global average

$2

0.2%

0.3%

"Optimal"

35

3.3%

5.4%

Climate constrained

50

4.8%

7.7%

"Ambitious"

200

19.0%

30.7%

What do carbon prices mean in practice?



Policy question
Policy question

The impact of efficient/climate target carbon taxes is relatively modest:

  • abatement/output circa 0.1 – 0.6 % of output

  • net impact -0.1 to +0.2 % of output

    Why is the debate so strident? Why are some people so opposed?


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