G31.3001-02, Fall 1997 Yaw Nyarko

Wednesdays, 12:05-2:05 269 Mercer St. Rm 711B

269 Mercer St Rm 715 998-9828 yaw.nyarko@nyu.edu

The Economics of Speculation

The goal of the class will be to study a number of theoretical models and to see how each one analyzes the issue of speculation in economic markets. The models will involve the interplay of imperfect information on the one hand (common knowledge, agreeing-to-disagree and Bayesian learning models); and dynamics on the other (the infinitely-lived and overlapping generations models). Below is a somewhat long course outline. The particular topics we will study will be determined by the interests of the students.

Course Outline

Part A: The Basic Theory

I. Single Agent Bayesian (or Statistical) Decision Theory.

0. Digression on Probability Theory and Dynamic Programming.

1. Priors, Likelihoods and Updating:

Non-Informative Priors.

Updating:

i. The Discrete Model; The Brams-Kilgour Letter Changing Example.

The Prisoners Problem.

The Paper of Gilboa "Hempel, Good and Bayes."

ii. The Continuous Model. Conjugate Families. Linear-Normal,

Dirichlet-Multinomial and Gamma distributions.

2. Optimal Stopping and Search Theory.

3. The Two Armed Bandit Problem.

4. The Monopolist Problem.

5. The Comparison of Experiments. The Value of Information.

The Convexity of the Value Function. The GKM paper.

II. Single Agent Bayesian Learning:

0. Some More Probability Theory. Weak and Strong Topology.

1. On the Question of Complete Learning:

a. The Stong Law of Large Numbers.

b. Beliefs Converge on each sample path to some limit.

c. Optimality of Bayesian Learning: If there exists a consistent estimator then Bayesian Posterior Converges.

d. Method of Counting Equations and Unknowns.

e. Under monotonicity the limiting observation distribution is identified.

f. Model of Blume and Easley.

2. Mis-Specified Models.

3. On the Question of Learning in the Limit:

3.1. Job Search (Only finitely many observations made).

3.2. The Two Armed Bandit Problem.

3.2. Game Version of Two armed Bandit Problem.

3.3. The Monopolist Problem. (Failure of the Identification condition).

4. Exponential Convergence of Bayesian Learning.

5. The Zellner/Blume-Easley work on perturbed Bayes' rule.

III. The Common Knowledge and Rational Expectations Literature

i. The Agreeing-to-disagree Results: The Aumann result. The Geanakoplos-Polemarcharkis result. The extension to priors which are not common. McKelvey-Page et. al. results.

ii. The No-Trade and "prices are revealing" Theorems: Milgrom, P. and N. Stokey; Grossman, S.; Tirole; The Dutch Book.

iii. Dynamic Speculation: Harrison and Kreps; Tirole's dynamic model.

Aumann, R. (1976):"Agreeing to Disagree," Annals of Statistics, 4, 1236-39.

Geanakoplos, J. and H. Polemarchakis (1982): "We Can't Disagree Forever," Journal of Economic Theory, 28, 192-200.

Grossman, S. (1977):"The Existence of Futures Markets, Noisy Rational Expectations, and Informational Externalities," Review of Economic Studies, 44, 431-449.

Grossman, S. and J. Stiglitz (1980): "On the Impossibility of Informationally Efficient Markets," American Economic Review, 70, 393-408.

Harrison, J.M. and David Kreps (1978):"Speculative Investor Behavior in a Stock Market with Heterogeneous Expectations," Quarterly Journal of Economics, XCII(2), 323-336.

McKelvey, R. and T. Page (1986):"Common Knowledge, Consensus and Aggregate Information," Econometrica, 109-127.

(1982):"Information, Trade and Common Knowledge," Journal of Economic Theory, 26, 17-27.

Nielson, L., A. Brandenberger, J. Geanakoplos, R. McKelvey and T. Page (1990):"Common Knowledge of an Aggregate of Expectations," Econometrica, 58, 1235-1239.

Tirole, J (1982):"On the Possibility of Speculation Under Rational Expectations," Econometrica, 50(5), 1163-1182.

Radner, R.(1972):"Existence of Equilibrium Plans, Prices, and Price Expectations in a Sequence of Markets," Econometrica, XL(2), 289-303.

IV. Bubbles in the Overlapping Generations and Optimal Growth Models.

The basic mathematics. Euler and Transversality conditions.

Diba, B. and H. Grossman (19??):"Explosive Rational Bubbles," American Economic Review,78(3), pp. 520-530.

(1978):"On the Inception of Rational Bubbles," Quarterly Journal of Economics, 697-700.

(1988):"Rational Inflationary Bubbles," Journal of Monetary Economics, 21, 35-46.

O'Connell, S. and S. Zeldes (1988):"Rational Ponzi Games," International Economic Review, 29(2).

Tirole, J. (1985):"Asset Bubbles and Overlapping Generations: A synthesis," Econometrica, 53, 1071-1100.

(1982):"On the possibility of speculation under Rational Expectations," Econometrica, 50, 1163-1100.

Weil, P. (1987):"Confidence and the Real Value of Money in an Overlapping Generations Economy," CII(1), 1-22.

Part B: Some Applications

1. Historical Episodes of Speculative Frenzies

Carswell, J (1960): "The South Sea," Stanford University Press.

Galbraith, J.K. (1988):"The Great Crash of 1929," Houghton Mifflin Co., Boston.

Garber, P. (1990):"Famous First Bubbles," Journal of Economic Perspectives, 4(2), 35-54.

(1990):"Who Put the Mania in Tulipmania?" in "Crashes and Panics," ed. Eugene N. White.

Kindleberger, C.P. (1989)"Manias, Panics and Crashes," Basic Books Inc., New York.

Mackay, C. (1932):"Extraordinary Popular Delusions and the Madness of Crowds," L.C. Page and Co. Boston.

Neal, L. (1990):"How the South Sea Bubble was Blown up and Burst: A new look at old data."

Russel, F. (19??):"Bubble, Bubble, no toil, no trouble," a magazine article on Charles Ponzi.

White, E. (1990):"The Great Crashes of 1929 and 1987," in "Crashes and Panics," ed. E. N. White.(** This contains a very good account of the 1929 Crash.)

2. The Speculative Attacks on Currencies and Bank Runs

The Mathematics of the he gambler's Ruin problem and the basic inventory control model.

Diamond, D. and P. Dybvig (1983):"Bank Runs, Deposit Insurance, and Liquidity," Journal of Political economy," 91(3), 401-419.

Obstfeld, M. (1993):"The Logic of Currency Crises," Manuscript, U.C. Berkeley.

Krugman, P. (1992): Currencies and Crises, MIT Press, Cambridge, Mass. (chpts. 4,5,6).

3. Finance Theory and the Market Micro-Structure Literature.

Topics from the Maureen O'Hara Book "Market Micro-Structure" book.

4. Social Learning Models and Learning in Repeated Games

Papers by Jordan, Kalai and Lehrer, Nyarko, Nachbar and Blume and Easley.