Discussion of

Learning and Price Volatility in Duopoly Models of Resource Depletion by Martin Ellison and Andrew Scott Ulf S¨oderstr¨om IGIER, Bocconi University and CEPR

April 2008

Outline

1. Summary 2. Comments

This paper

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Oligopoly market with depletable resources

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Producers decide on supply given a known demand function

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Imperfect control of own supply

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Competitor’s supply unobservable

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Producers observe price, learn about competitor’s supply and decide on own supply

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Producer’s supply depends on beliefs of competitor’s supply ⇒ self-confirming equilibrium

Results

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SCE depends on level of resource scarcity: I I

No scarcity: SCE = noncooperative eqm Scarcity: SCE = cooperative eqm

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Perturbations (supply shocks) ⇒ escape dynamics towards cooperative eqm

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More scarcity ⇒ escapes more likely and longer

Implications

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Prices and quantities occasionally move away from “fundamentals”

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Periods of non-cooperation mixed with periods of apparent cooperation

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Learning acts as coordination device

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Similar to Sargent (1999): game between central bank and private agents

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Here: game between two producers

Comments

1. SCE and escape dynamics in Sargent (1999) 2. SCE and escape dynamics here 3. Practical relevance 4. Welfare consequences and the role of policy 5. Other comments

Sargent (1999)

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“The Conquest of American Inflation” (Summary in Sargent and S¨oderstr¨om, 2000)

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Central bank sets inflation to minimize loss function

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Classical model (Lucas, Kydland-Prescott, Barro-Gordon) CB learns the slope of the Phillips curve

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Misspecified model: Disregards expectations Discounts past observations: Suspects structural breaks

Private agents knows CB’s rule, form expectations

Sargent (1999) I

Circularity: CB policy depends on its beliefs, given observed outcomes, which depend on policy

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Self-confirming equilibrium: Outcomes confirm beliefs, even if beliefs initially incorrect

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SCE: Nash eqm with inflation bias, inefficient

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Learning with discounting ⇒ recurrent escapes from SCE to Ramsey eqm with zero inflation, efficient

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Escapes: Series of shocks make CB believe PC is steeper ⇒ sets inflation lower ⇒ reinforces beliefs ⇒ Ramsey eqm

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CB learns the natural rate hypothesis

Crucial ingredients in Sargent (1999)

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Misspecified model

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Learning with discounting

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Disturbances to Phillips curve

Self-confirming equilibria in Ellison and Scott

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SCE = cooperative or non-cooperative equilibria

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But any equilibrium can be sustained with suitable strategies

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Why focus only on these equilibria? Only these are SCE?

Escape dynamics in Ellison and Scott

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Misspecification? I

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Producers believe competitor’s supply invariant in past?

Discounting? ε → 0 in analysis? (ε = 0.95 in Ellison and Scott, 2006) Escapes still possible?

Disturbances I I I

Necessary to generate escapes Imperfect control of supply realistic? Interpret as demand shocks?

SCE shifts and Escape dynamics

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Scarcity or shocks ⇒ Both producers reduce supply

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Each producer believes own contraction has a large effect on price, concludes that demand is inelastic, and contracts more

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Introspection would lead producer to realize that the other producer is doing the same thing

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Cf. Sargent (1999): central bank and private sector face different problems

More on learning and discounting

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Inconsistency: I I I

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Producers update while discounting past observations. . . . . . but assume that competitor’s past supply was constant . . . and that the future will be constant

Kreps (1998): inconsistency learning–unchanged demand leads to small errors. Also with discounting?

Practical relevance

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Do these mechanisms help to explain market movements in practice? Evidence?

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Oil price “shocks”: supply contraction (cooperation) in 1970s, demand expansion in 2000s. Consistent with escape dynamics?

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Analysis rules out exploration and discovery of new supplies. Important in practice, even more here than in standard model, as price is even higher.

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Ellison and Scott (2006)

Welfare consequences and the role of policy

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Non-cooperation is better than cooperation for welfare Resource depletion ⇒ double welfare effects: I I

Non-cooperative eqm worse Move towards cooperative eqm

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Escapes welfare-reducing

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Cf. Sargent (1999): Escapes welfare-improving

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Role for policy here?

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Stricter regulation when resources more scarce?

Final words

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Nice application of learning in a theoretical setup

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Technical but intuitive

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Explain better importance of misspecification and discounting

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Empirical application would be nice (Ellison and Scott, 2006)

Additional comments for Martin

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Escape dynamics = “most likely series of belief perturbations”. But how likely are they? How often do they happen? And how long are they?

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Time intervals in Figs 1–3?

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Fig 4?

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Fig 3: Earlier escape from noncooperative eqm with high scarcity. But the SCE is the cooperative eqm. . . ?

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Fig 3: How is scarcity parameterized?