Sunspot Equilibrium. Karl Shell Cornell University Benhabib-Farmer NBER Conference Federal Reserve Bank of San Francisco

Transcription

1 Sunspot Equilibrium Karl Shell Cornell University Benhabib-Farmer NBER Conference Federal Reserve Bank of San Francisco Thursday Evening, May 14, 2015

2 Early History of Sunspots at Penn Dave Cass Karl Shell Costas Azariadis Roger Farmer Yves Balasko

3 Mea Culpa Totally unfair spoof of Jevons (1884)

4 Mea Culpa Totally unfair spoof of Jevons (1884) Granger, Schuster

5 Mea Culpa Totally unfair spoof of Jevons (1884) Granger, Schuster Cass-Shell Sunspots Extrinsic Randomizing Device

6 Mea Culpa Totally unfair spoof of Jevons (1884) Granger, Schuster Cass-Shell Sunspots Extrinsic Randomizing Device Unfair to extrinsic uncertainty: too cute for central banks Stanley Fischer

7 Mea Culpa Totally unfair spoof of Jevons (1884) Granger, Schuster Cass-Shell Sunspots Extrinsic Randomizing Device Unfair to extrinsic uncertainty: too cute for central banks Stanley Fischer Excess Volatility (Shiller)

8 Fundamentals Economy Outcomes Gain = Volatility of Outcome Volatility of Fundamentals = + 0 in SSE

9 How was SSE received by the profession? Saltwater was non-positive : too much math.

10 How was SSE received by the profession? Saltwater was non-positive : too much math. Freshwater was non-positive : SSE might call for active government policies. Quantity Theory. REH.

11 How was SSE received by the profession? Saltwater was non-positive : too much math. Freshwater was non-positive : SSE might call for active government policies. Quantity Theory. REH. Game theorists : SSE treatment of expectations is natural.

12 How was SSE received by the profession? Saltwater was non-positive : too much math. Freshwater was non-positive : SSE might call for active government policies. Quantity Theory. REH. Game theorists : SSE treatment of expectations is natural. Some fellow travelers. Used other names such as self-fulfilling prophesies, animal spirits, multiple equilibria, sentiments,....

13 How was SSE received by the profession? Saltwater was non-positive : too much math. Freshwater was non-positive : SSE might call for active government policies. Quantity Theory. REH. Game theorists : SSE treatment of expectations is natural. Some fellow travelers. Used other names such as self-fulfilling prophesies, animal spirits, multiple equilibria, sentiments,.... SSE combines ideas from micro, macro, and game theory

14 What are SSE? Expectations can be individually rational while not necessarily socially rational

15 What are SSE? Expectations can be individually rational while not necessarily socially rational Beliefs about the beliefs of others,.... Best to model others.

16 What are SSE? Expectations can be individually rational while not necessarily socially rational Beliefs about the beliefs of others,.... Best to model others. Not necessarily public randomizing device

17 What are SSE? Expectations can be individually rational while not necessarily socially rational Beliefs about the beliefs of others,.... Best to model others. Not necessarily public randomizing device Rational expectations, but not necessarily co-ordinated on solution to planning problem

18 What are SSE? Expectations can be individually rational while not necessarily socially rational Beliefs about the beliefs of others,.... Best to model others. Not necessarily public randomizing device Rational expectations, but not necessarily co-ordinated on solution to planning problem Not merely randomizations over certainty equilibria (more later)

19 Economies that generate SSE Overlapping Generations

20 Economies that generate SSE Overlapping Generations Double infinity and bubbles

21 Economies that generate SSE Overlapping Generations Double infinity and bubbles Restricted participation

22 Economies that generate SSE Overlapping Generations Double infinity and bubbles Restricted participation Incomplete Financial markets

23 Economies that generate SSE Overlapping Generations Double infinity and bubbles Restricted participation Incomplete Financial markets Imperfect competition

24 Economies that generate SSE Overlapping Generations Double infinity and bubbles Restricted participation Incomplete Financial markets Imperfect competition Information frictions, asymmetric information

25 Economies that generate SSE Overlapping Generations Double infinity and bubbles Restricted participation Incomplete Financial markets Imperfect competition Information frictions, asymmetric information Non-convex economies

26 Economies that generate SSE Overlapping Generations Double infinity and bubbles Restricted participation Incomplete Financial markets Imperfect competition Information frictions, asymmetric information Non-convex economies Bank runs, panics, financial fragility

27 Economies that generate SSE Overlapping Generations Double infinity and bubbles Restricted participation Incomplete Financial markets Imperfect competition Information frictions, asymmetric information Non-convex economies Bank runs, panics, financial fragility Political Economy

28 Economies that generate SSE Overlapping Generations Double infinity and bubbles Restricted participation Incomplete Financial markets Imperfect competition Information frictions, asymmetric information Non-convex economies Bank runs, panics, financial fragility Political Economy Winners & Losers from volatility

29 Economies that generate SSE Overlapping Generations Double infinity and bubbles Restricted participation Incomplete Financial markets Imperfect competition Information frictions, asymmetric information Non-convex economies Bank runs, panics, financial fragility Political Economy Winners & Losers from volatility Choice between money taxation and commodity taxation

30 Money Taxation : Example of Source of SSE 1 commodity, l = 1, chocolates 3 guys, h = 1, 2, 3 money taxes τ = (τ 1, τ 2, τ 3 ), dollars τ 1 + τ 2 + τ 3 = 0, dollars endowments ω = (ω 1, ω 2, ω 3 ) > 0, chocolates allocations x = (x 1, x 2, x 3 ) > 0, chocolates

31 Certainty Economy max u h (x h ) s.t. x h = ω h P m τ h = ω h where P m is the chocolate price of money x 1 + x 2 + x 3 = ω 1 + ω 2 + ω 3, or x 1 + x 2 + x 3 = ω 1 + ω 2 + ω 3 0 P m < P m

32 Certainty Economy: Example ω = (20, 10, 5) τ = (5, 0, 5) 0 P m < 4 = P m Equilibrium: {x = (x 1, x 2, x 3 ) R 3 ++ x 1 = 20 5P m, x 2 = 10, x 3 = 5 + 5P m, P m 0}

33 Sunspots Economy Extrinsic random variable: s {α, β}, π(α) + π(β) = 1 Information: τ h (α) = τ h (β) = τ h, incomplete instruments ω h (α) = ω h (β) = ω h, extrinsic uncertainty

34 Sunspots Economy: Example ω = (20, 10, 5) τ = (5, 0, 5) u h = log π(α) = 3/4, π(β) = 1/4 P m (α) = 1, P m (β) = 2 α is inflationary state, β is deflationary Mr 1 is taxed. He fears deflation. Mr 3 fears inflation. Mr 2 is a banker. He can only gain from volatility.

35 Sunspots Economy: Example ( ω 1 (α), ω 1 (β)) = (15, 10) ( ω 2 (α), ω 2 (β)) = (10, 10) ( ω 3 (α), ω 3 (β)) = (10, 15) x 3 (α) = ω 3 (α) = 10 x 3 (β) = ω 3 (β) = 15 Therefore, x 1 (α) + x 2 (α) = = 25 x 1 (β) + x 2 (β) = = 20 TA-EB is a proper rectangle,

36 Tax-Adjusted Edgeworth Box β 20 Slope = p( α ) 12 = p( β ) 5 Contract Curve Slope = 4/5 Mr SSE Allocation Endowment Mr The Tax-Adjusted Edgeworth Box α

37 Not mere randomization over CE x 2 (α) = > 10 x 2 (β) = = 81 2 < 10 Mr 2 ( banker ) gains from volatility Mr 3 ( passive ) loses from volatility Mr 1 and Mr 2 in aggregate lose Hence Mr 1 is a loser