Stochastic equilibrium modeling: The impact of uncertainty on the - - PowerPoint PPT Presentation

Stiftelsen Frischsenteret for samfunnsøkonomisk forskning Ragnar Frisch Centre for Economic Research www.frisch.uio.no

• Oslo Centre of Research on Environmentally friendly Energy

Stochastic equilibrium modeling: The impact of uncertainty on the European energy market

Rolf Golombek EcoMod2016 Lisbon July 6-8, 2016

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Uncertainty, several decision makers and market equilibrium

• Several studies on uncertainty:

– Informal policy exercise: scenario analysis – Formal analysis: one decision maker and/or stochastic price path independent of decisions

• Basic economics: prices and quantities are interrelated

– If demand for one good increases, the price of this good will be affect, and also all other prices will be affected

• With no uncertainty: standard general equilibrium theory
• With uncertainty: What to do when there are many

agents and markets?

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Contribution

• Guide to transform a deterministic model with several

agents and markets to a stochastic model

• No programming of a stochastic solution algorithm is

necessary

• Case: Large equilibrium model for the European energy

markets (LIBEMOD)

• Framework for stochastic equilibrium modeling. Should

not be mixed with scenario analysis; informal policy exercise where no agents make decisions under uncertainty

• Why not use Monte Carlo simulations?

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Monte Carlo Simulations

• Draw a value from a distribution
• Put it into the deterministic model. Get an output
• Repeat and find the average values
• Each time agents falsely assume they know the future for

sure

– Investment will differ across scenarios !

• In economics: theory under certainty versus theory under
• uncertainty. Two different behvior of agents

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Modeling uncertainty

• Future states – scenarios s
• Each scenario is assigned a probability q
• Some decisions are taken under uncertainty (investment), others are

not: Like a two-period model

• Seemingly complicated way of modeling uncertainty, but effecient in

transforming a deterministic model to a truly stochastic model.

• Our method to model uncertainty: Make one choice (investment) for

each scenario s (Monte Carlo). But: Because you do not know which scenario that will materialize, you have to make the same decision for all scenarios (!)

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Simple model of uncertainty – 2 periods

• Each possible future state has an assigned probability
• Period 1: Each producer has to determine investment in

energy capacity K before the uncertainty is resolved

– There is a cost of investment, but no cost of production

• Period 2: First, the uncertainty is resolved. Next, producer

determines how much to produce, given the capacity and the price facing the producer (Standard deterministic decision problem)

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Investment decision problem of the producer (Period 1)

• foc:
• Define:
• Rewrite foc:
• Can show:
• Number of equations: s+1 (Deterministic model: 1

equation)

• In period 2 there are s standard equilibrim equations; one

for each scenario s (Deterministic model: 1 equilibrium equation)

• Transformation guide

 

max s.t. for all .

s s s s s S s

q p K cK K K s S



  



s s s s

q p q c   

s s

q s 

  ~

for all

s s

p c s S     

.

~   E

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Numerical deterministic model of the Western European Energy Market - LIBEMOD

• 16 countries
• 7 energy goods
• 4 types of energy users (in each country; demand 7 energy goods)
• 18 electricity technologies
• Investment, extraction/production, trade and consumption
• Investment (if profitable)

– Capacity of new power plants – Capacity of international electricity lines – Capacity of international natural gas pipes

• Determines all prices, quantities and CO2 emissions
• Transform deterministic LIBEMOD model to stochastic LIBEMOD

model using the developed guide

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Uncertainty in LIBEMOD – Scenarios for 2030

• Scenarios: Uncertain economic development

– growth rates, future oil and coal prices; 10 scenarios for 2030

• Investors know today (2000) the probability of each 2030 scenario

and the corresponding equilibrium prices (rational expectations)

• Investors decide investment today (2000) under uncerainty. Build

capacities (electricity plants and international transmission capacity) for 2030.

• Uncertainty is revealed in 2030. Then standard general equilibrium

determination of prices and quantities

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Investment (GW or mtoe) under economic uncertainty 10 scenarios in 2030

Gas transmissio n Electricity transmissio n Total power capacity Coal power capacity Wind power capacity Expected values 157 5 365 304 9 Stochastic 154 16 358 250 31 Monte Carlo

• w. average

minimum maximum 157 130 173 19 3 146 354 238 432 250 54 367 28 89

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Main contribution and findings

• Simple way to transform a deterministic model to a

stochastic model

• Stochastic model vs. using expected values: rather large

differences

• Stochastic model vs. Monte Carlo average: small

differences for most aggregate variables, but large differences for some disaggregate variables

• Extensions

– Multi-period models; learing by partitioning the set of scenarios – Irreversibilities – Risk-aversion (decisions may be taken by risk-averse managers)