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How Fast do Rational Agents Learn?

Review of Economic Studies 1993 60(2), 329
A simple dynamic model of rational learning through market interaction by asymmetrically informed risk-neutral agents, uncertain about a valuation parameter but whose pooled information reveals it, is presented. The model is a variation of the classical partial equilibrium model of learning in rational expectations in which the market price is informative about the unknown parameter only through the actions of agents. It is found that learning from market prices and convergence to the rational expectations equilibrium is slow, at the rate 1/√n1/3 (where n is the number periods of market interaction), whenever the average precision of private information in the market is finite. Convergence obtains at the standard rate 1/√n if there is a positive mass of perfectly informed agents. Comparative static results on more refined measures of the speed of convergence with respect to basic technological and informational parameters are also provided.

Small Income Effects: A Marshallian Theory of Consumer Surplus and Downward Sloping Demand

Review of Economic Studies 1987 54(1), 87
We formalize the Marshallian idea that when the proportion of income spent on any commodity is small then the income effects are small. If n is the number of goods, we show, under certain assumptions on preferences and prices, that the order of magnitude of the norm of the income derivative of demand is 1/√n. As a corollary we get that for the case of a single price change the percentage error in approximating the Hicksian Deadweight Loss by its Marshallian counterpart goes to zero at least at the rate 1/√n and that demand is downward sloping for n large enough.

Strategic Complementarity, Fragility, and Regulation

Review of Financial Studies 2014 27(12), 3547-3592
Fragility is affected by how the balance sheet composition of financial intermediaries, the precision of information signals, and market stress parameters all influence the extent of strategic complementarity among investors' strategies. A solvency and a liquidity ratio are required to control the likelihood of insolvency and illiquidity. The solvency requirement must be strengthened in the face of increased competition, whereas the liquidity requirement must be strengthened under more conservative fund managers and higher penalties for fire sales. Greater disclosure may aggravate fragility and require an increase in the liquidity ratio, so regulators should establish prudential and disclosure policies in tandem.

Short-Term Investment and the Informational Efficiency of the Market

Review of Financial Studies 1995 8(1), 125-160
A dynamic finite-horizon market for a risky asset with a continuum of risk-averse heterogeneously informed investors and a risk-neutral competitive market-making sector is examined. The article analyzes the effect of investors' horizons on the information content of prices. It is shown that short horizons enhance or reduce accumulated price informativeness depending on the temporal pattern of private information arrival. With concentrated arrival of information, short horizons, reduce final price informativeness; with diffuse arrival of information, short horizons enhance it. In the process a closed-form solution to the dynamic equilibrium with long-term investors is derived.

Competition for Deposits, Fragility, and Insurance

Journal of Financial Intermediation 1996 5(2), 184-216
In the presence of economies of scale, depositors' expectations are shown to give rise to vertical differentiation and to yield multiple market equilibria, some of which exhibit institutional or systemic collapse. This fragility is due to a coordination problem among depositors and not to bank competition. Nevertheless, failure perceptions do influence rivalry which in turn affects the failure probability in particular equilibria. Deposit insurance improves welfare by preventing collapse, extending the market, and minimizing frictions. However, deposit insurance also may induce fiercer competition for deposits and increase the deadweight losses associated with failing institutions. The welfare impact of deposit insurance is shown to depend on market structure, and is thus ambiguous even in a world of full liability and no moral hazard in bank investments.Journal of Economic LiteratureClassification Numbers: G21, G28.

Aggregation of Information in Large Cournot Markets

Econometrica 1988 56(4), 851
Consider a homogeneous product market where firms have private information about an uncertain demand parameter and compete in quan tities. The author examines the convergence properties of Bayesian-Co urnot equilibria as the economy is replicated and concludes that larg e Cournot (or almost competitive) markets do not aggregate informatio n efficiently except possibly when the production technology exhibits constant returns to scale. A competitive market is nevertheless cons trained efficient when taking as given the decentralized private info rmation structure of the economy. The results are shown to be robust to the consideration of endogenous information acquisition and to the addition of extra rounds of competition.

Regulating Insider Trading When Investment Matters

Review of Finance 2004 8(2), 199-277
We provide a general framework for analyzing the effects of insider trading on real investment and welfare as well as the consequences of different regulatory policies in a model where all traders are rational expected-utility maximizers and aware of their position in the market. We find that: with costly information acquisition, an “abstain-or-disclose” rule tends to be optimal; with free information acquisition, laissez-faire is better. This suggests enforcing an abstain-or-disclose rule with a high standard of proof for inside information. Our approach also uncovers the pitfalls of welfare analysis in the noise-trader model.

Implementation in Economies with a Continuum of Agents

Review of Economic Studies 1993 60(3), 613
We study a general implementation problem for exchange economies with a continuum of players and private information, and test the robustness of the results for sequences of approximating finite economies. Assuming that the designer knows the distribution of the characteristics in the economy we consider continuous and unique implementation in both its equilibrium and dominant strategies versions and obtain results for general self-selective (first- and second-best) allocations. An upper hemicontinuity property of Bayesian equilibria of approximating economies for continuous mechanisms is demonstrated. Using this, we can, for example, conclude that if a given continuous mechanism implements uniquely a Walrasian allocation in the continuum economy then all Bayesian equilibria of large approximation economies will (with probability close to one) yield an allocation which is almost ex-post Pareto optimal.

Market Opacity and Fragility: Why Liquidity Evaporates When It Is Most Needed

American Economic Review 2026 116(7), 2454-2503
Lack of market transparency can impair the liquidity provision of nonstandard liquidity suppliers and make liquidity demand increasing in illiquidity. This can yield strategic complementarities and induce multiple equilibria. Then an initial dearth of liquidity may degenerate into a liquidity rout (as in a “flash crash”), and traders faced with the largest cost of trading are those trading more intensely at equilibrium. An increase in order flow transparency and/or in the mass of dealers who are in the market at all times has a positive impact on total welfare.

Bank Runs as an Equilibrium Phenomenon

Journal of Political Economy 1987 95(3), 485-491
A standard demand-deposit contract in which individuals are entitled to their full deposit at any time provided the bank is solvent is analyzed in a context in which there are no exogenous events on which agents condition their behavior and a unique equilibrium involving a bank run with positive probability is shown to exist.