Dynamic Games in Environmental Economics PhD minicourse Part III: - - PowerPoint PPT Presentation

Bård Harstad UiO 6 December 2017 Dynamic Games in Environmental Economics PhD minicourse Part III: Participation and Free-riding

Term Paper

 If you need credit for the course, you must either (a) pass a take-home exam, or (b) write a term paper. (a) Take-home exam: from 8am 23/1 to 8am 24/1. Exam will be posted on the course page. (b) Term paper:

• Deadline: 31st January, 2018.
• Length:

10-15 pages.

• Topic:

(a) environmental/resource economics OR (b) dynamic games/methods but not necessarily both.

• Thus:

Dynamic games/methods on other topics is also OK. I will be quite flexible on the topic.

• To pass:

It is not important to be very innovative/novel.

• Instead:

Be sufficiently precise/thourough/careful.

Relationships

Emissions Technology Duration Participation 5% 35 NA 5y (Kyoto)

Questions – and Possible Answers

• 1. Is there a trade-off between width, depth, and length?

YES: Barrett, Finus and Maus, Carraro, trade-literature

• 2. Is the equilibrium coalition necessarily small?

YES: Barrett, Carraro-Siniscalco, Hoel, Dixit-Olson

• 3. Should one attempt to contract also on R&D?

YES: Buchholtz-Konrad, Beccherle-Tirole, Harstad

• 4. Is a long-term agreement better than a short-term one?

YES: Harstad 2012-2014). NO: Karp and Zhao 2010.

The “Standard” Participation Model

 

 

 

t i N i t i t i t i t i

g C g B u n N i g y b g B

, , , 2 , ,

,..., 1 , ) ( 2





      

The linear-quadratic model (Barrett ’05 for an overview): Benefit Costs Timing: (1) Participate, (2) pollute. Internal stability: No participation should want to leave External stability: No free-rider should want to join

A Dynamic Model: Timing

Period τ ∆ gi,t gi,t+1 ri,t ri,t+1 Time

Model: Equations

 

 

 

k e k k e k e r k g C y B u r y g n N i y y b y B

t i t i N i t i t i t i t i t i t i t i ) ( 2 1 , , , , , , , 2 , ,

2 ,..., 1 , ) ( 2

   

  

      

             



A linear-quadratic model: Benefit Emission Utility Equilibria: Markov-perfect

Preliminaries  

2 1 , 1 , , 2 , , , 1 1 1 , , , , , ,

2 2 ˆ , ˆ

     

            

 

t i t j t j N j t i t i t i t t i t i t i t i t i t i

r k r d y C d b u where u v r d y g y y d   

Preferences rewritten. If: So, no past action is «payoff relevant» … except whether commitments have been made… => Simple to use Markov-perfect equilibria

Assumptions

(can be relaxed)

• 1. Countries are symmetric
• 2. Pollution is flow (stock depreciates after a period)
• 3. Technology depreciates after a period
• 4. Permits are non-tradable
• 5. Linear-quadratic utility functions

First Best

Concave&symmetric welfare f. Nonparticipants always act this way x b k r d b C n k C n y g b C n d k C n r

t i t i t i t i t i

       

, , , , ,

x b k r d b C k C y g b C d k C r

t i t i t i t i t i

       

, , , , ,

Business as Usual

If nothing is contractible

Complete Contracts

Depth: for a given m and T…

x b k r d b C m k C m y g b C m d k C m r

t i t i t i t i t i

       

, , , , ,

   

 

     m m m T m m m T if 1 if Length: Width: m* = {2,3}

Incomplete Contracts

 

k C r T, t k b g y b r

T i t i t i

    

1 , , ,

,

x b k r d b C m d k C r k C m r b C m k C m y g

t i t i t i T i t i t i

          

 , , , 1 , , ,

   

 

       m m m m T m m m m T ˆ if 1 ˆ if Larger; m*=n possible

Intuition

Participate? m = m* ⇒ T = ∞ ⇒ r = m(C/k) ≽ Deviate? m = m*-1 ⇒ T = 1 ⇒ r = C/k Proposition: m* is an equilibrium iff:            



 

 

x x m m

x I

if if 3

2 *

IFF IFF

 

n m m m

M I

, , min

* 

. 1 1 1 1 , * ˆ 1

*

         x x m where m m m m

M M

 = n →FB iff δ↑ and x moderate

13

The key variable is: x=k/b

The hold-up problem can be beneficial and a credible out-of-equilibrium threat, materialized if a participant deviates, investments are noncontractible, and T is endogenous

Bottom line

Participation: Lessons

• 1. If countries can opt out, there is a strong incentive to free-ride
• 2. In static linear-quadratic models, only 3 (!) countries want to

participate in equilibrium

• 3. This conclusion continues to hold even if we add:

a) Green technology or b) Many periods

• 4. But the coalition can be much larger if:

a) Contracts are incomplete and b) Duration is endogenous

• 5. The hold-up problem can then be beneficial: it is materialized
• nly if few countries participate, since only a large coalition

prefers to lock in the participants, and this (credible) threat can motivate many more countries to participate.

• 6. There are thus also good equilibria in Kyoto-style games

where countries negotiate emissions, but not investments.

Dynamic Games in Environmental Economics Lessons Emissions  Investments

• 1. Recent theory on repeated games, dynamic games, and

contract theory can be used to analyze environmental issues. a. In business as usual, countries may invest strategically little, to motivate others to invest more/pollute less later.

• b. In repeated games, countries may want to require over-

investments in technology to ensure compliance. c. With commitments, emission quotas should be small to motivate investments.

• d. Investments will be strategically small before bargaining
• 2. Short-term agreements can therefore be costly.
• 3. Only a large coalition prefers to lock in for the long run.
• 4. All this can motivate free-riders to participate