Lecture 3: Distributed Ledger as a Solution to an Information Problem

Overview

Robert Townsend's lecture explores how distributed ledgers can solve information problems in fragmented markets, drawing on economic theory of Pareto efficiency and competitive equilibria. He analyzes the Ostroy-Starr impossibility theorem, which shows that decentralized trading with limited information cannot guarantee a Walrasian outcome. Townsend then discusses institutional workarounds like money, large broker-dealers, and overdraft facilities, highlighting their limitations and the potential for distributed ledgers to improve efficiency and mitigate market power, particularly in foreign exchange markets.

Key takeaways

The Ostroy-Starr theorem demonstrates that fully decentralized trading with limited information cannot guarantee a Walrasian equilibrium outcome.
Traditional institutional workarounds for fragmented markets (money, broker-dealers, credit) have limitations, including market power and default risk.
Distributed ledgers, by providing a shared, transparent record of all trades, can overcome the information asymmetry that plagues decentralized exchange.
The concept of 'money' as a commodity that can facilitate trade is a key workaround, requiring sufficient ex-ante liquidity for all participants.
The concentration of market power in financial intermediaries like Citibank in FX markets highlights the need for more efficient and decentralized trading mechanisms.
Distributed ledgers and smart contracts offer potential solutions for trade finance by enabling escrow, automated settlement, and transparent tracking of goods and payments.

Chapters

0:11 Introduction: Efficiency as a Policy Objective

Lecture 3 focuses on distributed ledgers as solutions to information problems in fragmented markets.
Efficiency is a key objective for public policy and private sector innovations.
Central banks' use cases should be motivated by underlying economic needs, not just technological capability.

0:59 Pareto Efficiency and Competitive Markets

Pareto efficient allocations maximize utility without making anyone worse off.
In a pure exchange economy, efficiency occurs when indifference curves are tangent and marginal rates of substitution are equal.
Competitive equilibria, under certain conditions, achieve Pareto optimal allocations.

11:45 General Equilibrium Theory Framework

Economies consist of commodities, households, firms, production sets, and aggregate resources.
The utility possibility set represents achievable utility combinations for agents.
The utility possibility frontier shows Pareto efficient allocations.

16:40 Formal Definition of Pareto Optimality

An allocation is Pareto optimal if it's feasible and no other feasible allocation can make one household better off without making another worse off.
Pareto optimality is defined by the absence of Pareto-dominating bundles.

18:21 Competitive Markets and Walrasian Equilibrium

Competitive markets aim to implement efficient allocations by having markets in all goods.
A Walrasian equilibrium involves prices and allocations where firms maximize profits and households maximize utility subject to budget constraints.
The value of endowments plus distributed profits must cover expenditures.

21:55 Excess Demand and Walras's Law

Excess demand is the difference between consumption and endowment.
The value of excess demand equals zero for each household (budget constraint).
The sum of excess demands across all traders equals zero (Walras's Law).

23:55 Fundamental Theorems of Welfare Economics

Every Walrasian equilibrium is Pareto optimal.
Any Pareto optimal allocation can be supported as a competitive equilibrium with lump-sum redistribution of wealth.

25:07 Problems from Fragmented Markets

Two main problems arise: ensuring common trading prices and the information problem of decentralized exchange.
Fragmented markets can lead to different prices on multiple exchanges.

26:53 US National Marketing System (NMS) for Equities

The NMS aims to ensure retail orders are executed at the most favorable price across exchanges.
It involves order protection to prevent trades at inferior prices.
Recent SEC amendments focus on pricing increments, access fees, and transparency.

32:06 Antitrust Suit Against Amazon and Market Standards

Amazon faced antitrust charges for innovations that benefited consumers and pushed competitors.
The spirit of the antitrust suit contrasts with the NMS standards for financial markets.
Regulation of financial markets may differ in complexity from other markets.

35:11 The Ostroy-Starr Impossibility Theorem

Regulation can sometimes be mitigated by available technology.
The Ostroy-Starr paper (1974) addresses the information problem of decentralized exchange in fragmented markets.
The goal is to achieve the Walrasian equilibrium allocation despite pairwise trading.

40:44 Information Requirements for Decentralized Trading

Traders are matched pairwise over T periods, with actions restricted to non-negative holdings.
Trades must satisfy a quid pro quo condition (value exchanged is equal).
Information types range from D1 (minimal, own endowment) to C (centralized, full system history).

55:20 Formal Statement of the Ostroy-Starr Theorem

A trading rule using centralized information (C) can complete trading in a single round for any environment.
No decentralized trading rule using D3 information can complete trading in a single round for *any* environment.
A counterexample is needed to prove the theorem's limitations.

57:30 Institutional Workarounds: Money

Workarounds address the impossibility theorem's limitations.
Money as a medium of exchange: a security that can be used in pairwise meetings to buy target goods.
Condition: The value of the money commodity must be sufficient to cover excess demands for all other commodities.

1:10:00 Institutional Workarounds: Large Broker-Dealer

Designating one trader as an intermediary broker-dealer can facilitate trade.
This dealer must have sufficiently large inventories (endowments) to honor all other traders' excess demands.
This approach requires knowledge of names (D2/D3 information) and can lead to market power issues.

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