Distributed Ledger Fix for Fragmented Market Efficiency

The lecture begins by emphasizing efficiency as a core objective for both public policy and private sector innovations, particularly in the context of distributed ledgers. It highlights that central banks often propose use cases for new technologies without clearly articulating the underlying economic need or motivation, focusing instead on what the technology can do rather than what problem it solves. To address this, the lecture delves into the economic concept of efficiency, specifically Pareto efficient allocations, using the planner's problem and competitive markets as frameworks.

Pareto Efficient Allocations and Competitive Markets

The discussion revisits concepts from general equilibrium theory, illustrating them with a pure exchange economy involving two goods and two households.

• Pareto Efficiency: An allocation is Pareto efficient if it's impossible to make one party better off without making another worse off. This is visually represented by the tangency of indifference curves in an Edgeworth box, where the marginal rates of substitution are equated.
• Programming Problem: Efficient allocations can also be found by maximizing a weighted sum of agents' utilities subject to resource constraints. Varying the weights traces out the entire Pareto frontier.
• Competitive Equilibrium: In a private ownership economy with endowments and prices, a competitive equilibrium is a particular Pareto optimal allocation where agents trade at common prices.

The lecture then generalizes these concepts:

• Commodities: Goods can be indexed by time or states of the world to incorporate intertemporal allocations and uncertainty.
• Economy Components: An economy consists of:
  • L commodities.
  • I households with consumption sets and utility functions.
  • J firms with production sets.
  • Aggregate resources (endowments).
• Feasibility: Consumption and production allocations must be feasible, meaning consumption cannot exceed available resources (aggregate endowment plus production).
• Utility Possibility Frontier: This represents the outer boundary of all feasible utility combinations for an economy, where no point northeast of it exists.
• Formal Pareto Optimality: An allocation is Pareto optimal if it's feasible and no other feasible allocation can make any household better off without making another worse off.
• Competitive Markets: To implement an efficient allocation, markets are assumed to exist for all goods. Ownership is specified by individual endowments and shares in firm profits (theta IJ).
• Walrasian Equilibrium: This is a state where:
  • Firms maximize profits.
  • Households maximize utility subject to budget constraints (expenditures not exceeding endowment valuation plus distributed profits).
  • Allocations are feasible (aggregate consumption equals aggregate resources).
• Excess Demand: The difference between a household's consumption and its endowment. In a competitive equilibrium, the value of excess demand for each household is zero, and the sum of all excess demands is zero.
• Fundamental Theorems of Welfare Economics:
  1. Any Walrasian equilibrium is Pareto optimal.
  2. Any Pareto optimal allocation can be supported as a competitive equilibrium if wealth can be redistributed lump sum.

Problems from Fragmented Markets

The lecture then introduces two problems arising from fragmented markets: the challenge of ensuring common prices and the information problem of decentralized exchange.

Common Prices in Fragmented Markets

The ideal of a competitive market involves all traders exchanging at a common price. However, real-world markets, especially financial ones, are often fragmented.

• US National Market System (NMS): The US has multiple equity markets. The SEC's NMS (2005) aims to ensure retail orders are executed at the exchange with the most favorable pricing. This means exchanges must match the best quotes from other exchanges, fostering competition for orders.
• Regulatory Challenges: Recent amendments to NMS regulations include smaller minimum pricing increments, addressing access fees, and increasing order transparency.
• Inconsistency in Regulation: A puzzling contrast is drawn with an antitrust suit against Amazon, which was accused of anti-competitive practices despite its actions (matching competitor discounts, featuring deals, efficient delivery) appearing to benefit consumers. This highlights a potential inconsistency in regulatory standards between financial markets and other sectors. The question is posed whether financial markets inherently require different or more difficult regulation.

The Information Problem of Decentralized Exchange (Ostroy-Starr Theorem)

This section focuses on a seminal paper by Ostroy and Starr (1974) that explores the information requirements for achieving a Walrasian equilibrium in a fragmented market.

• Setup:
  • A finite number of goods (commodities or assets).
  • Traders own endowments and have utility functions.
  • The goal is to achieve the Walrasian equilibrium allocation.
  • Traders are matched pairwise in a sequence of markets; a fully centralized market is not assumed.
  • Common prices are imposed to simplify the problem, focusing solely on fragmentation.
  • Bilateral exchanges satisfy a "quid pro quo" condition: the value of goods received equals the value of goods sold.
  • Traders are modeled as algorithms aiming to achieve the Walrasian allocation. The core question is what information each trader (node) needs.
• Information Requirements:
  • D1 (Minimal): When traders I and J meet, their actions depend only on their initial excess demands and, if not the first pairing, the sum of their previous actions (current balances). This implies anonymity, as traders don't know each other's names.
  • D2 (With Names): Same as D1 but traders know each other's identities (names).
  • D3 (Full History): Same as D2 but traders know the entire history of trades for both I and J.
  • C (Centralized): Same as D3 but traders have access to the entire history of trades for all traders in the system.
• Theorems:
  • Possibility Theorem: There exists a trading rule using information C (centralized) that satisfies action restrictions and completes trading in a single round for any Walrasian environment.
  • Impossibility Theorem: There is no trading rule using D3 (decentralized, even with full individual history) that satisfies action restrictions and completes trading in a single round for any Walrasian environment. This means for any D3 rule, a counterexample environment can be found where it fails.

This implies that decentralized information, even with full individual trade histories, is insufficient to guarantee achieving a Walrasian equilibrium in a single round of trading.

Institutional Workarounds for Fragmented Markets

The lecture then explores three institutional workarounds that address the information problem identified by Ostroy-Starr.

1. Money as a Medium of Exchange

• Mechanism: One commodity (money) is designated such that every trader has enough of it to purchase their required target goods, regardless of the order or timing of meetings. This provides "ample ex-ante liquidity."
• Theorem 4: A trading rule using D1 (minimal information, no names) can complete trade in a single round if there exists a "money" commodity m whose valuation for each trader I is not less than the value of their positive excess demands for all other commodities.
• Intuition: Money allows traders to buy before selling, bridging temporary liquidity gaps. The "quid pro quo" condition is still maintained, but money facilitates the necessary exchanges.
• Contemporary Relevance: This relates to large-value payment systems operated by central banks (e.g., Fedwire, TARGET2). These systems, like real-time gross settlement (RTGS), aim for instantaneous settlement but require significant liquidity. Liquidity-saving mechanisms (LSMs) are designed to reduce the required liquidity by queuing payments and offsetting them where possible, as exemplified by the Bank of England's system.

2. One Large Trader or Broker-Dealer

• Mechanism: A single designated intermediary (broker-dealer) holds sufficiently large inventories of all securities to honor any demand placed upon it by any customer. All trade effectively happens through this central dealer.
• Condition: The broker-dealer I must have endowments of each commodity C such that they can cover the sum of all other traders' positive excess demands.
• Information: This workaround requires more than D1; it needs names (D2 or D3) to implement the algorithm.
• Problem: This creates market power. The central dealer could act as a monopolist, potentially distorting prices.
• Contemporary Relevance:
  • Core Banking Services: In the US, a few aggregators (Fiserv, Jack Henry, FIS) dominate the market for processing bank clearings, with Fiserv holding a significant share. This raises questions about market concentration.
  • Foreign Exchange Markets: A few large broker-dealers (e.g., Citibank, Deutsche Bank, UBS) dominate FX trading, especially for major currencies. This concentration means smaller currencies often need to be converted to a major currency (like USD) before trading, increasing costs and risks. The question is posed whether distributed ledgers could mitigate this concentration by enabling more direct trading of diverse currencies.

3. Overdraft Credit Facility

• Mechanism: Traders are given initial overdraft facilities (credit) that they can use for trading. The requirement is that they repay the overdraft by the end of the trading period.
• Comparison to Money: Similar to money, but the "money" here is an abstract credit rather than a specific commodity. This credit can be created in arbitrary amounts, as long as repayment is guaranteed. The amount of credit would be agent-specific, tailored to their individual excess demands.
• Medieval Trade Fairs: This concept is illustrated with medieval trade fairs, where bankers provided credit (IOUs) to traders to minimize the need for physical coin. Trades occurred in sequence, with final settlement at the end. Overdrafts that couldn't be repaid led to the issuance of promissory notes ("lettres de foire"), which could circulate and sometimes lead to financial crises.
• Problem: The possibility of default.
• Contemporary Relevance: The US repo market, used by the Federal Reserve for monetary policy, experienced issues with intraday credit provided by clearing banks exceeding the US monetary stock. Reforms focused on altering timing to ensure broker-dealers had more balance sheet capacity.

Distributed Ledgers as a Solution

The lecture concludes by bringing the discussion back to distributed ledgers and blockchain technology as a potential solution to the information problem.

• Blockchain and the Impossibility Theorem: The impossibility theorem states that decentralized information (D3) is insufficient; centralized information (C) is needed. Distributed ledgers, by recording all trades on a shared, immutable ledger accessible to everyone, effectively provide this "C" level of information.
• Mechanism: Even if traders meet pairwise, their trades are reported to the ledger. If their value is sequestered in escrow on the ledger, this shared history allows for coordination to achieve the socially desirable Walrasian outcome.
• Real-World Examples:
  • Tracking Goods: Walmart Canada uses distributed ledgers to track goods, mitigating discrepancies in invoices, payments, and theft in the transportation industry.
  • Diamond Provenance: De Beers uses a distributed ledger to track the origin of diamonds, enhancing transparency.
  • Trade Finance: Ghana, in collaboration with Singapore, is prototyping a distributed ledger solution for trade finance. This allows small merchants to ensure payment in foreign currency and track goods, with money held in escrow via smart contracts (to be discussed in future lectures).

The lecture highlights that while the Ostroy-Starr counterexample is complex, its core idea is that in a fragmented market, traders, even with their individual histories, lack sufficient global information to make optimal trading decisions to reach a Walrasian equilibrium. A distributed ledger, by providing a shared, transparent record of all transactions, effectively solves this information asymmetry.