Smart Contracts Address Coordination in Fragmented Markets

This lecture explores how smart contracts can address coordination problems, particularly in fragmented markets with privately issued securities. The core idea is to leverage distributed ledgers not just for information, but for contracting, especially concerning time, risk, and location-specific commodities.

Theoretical Framework: Time, Risk, and Pareto Efficiency

The theoretical foundation extends previous discussions to explicitly incorporate time and risk. Commodities are indexed by time and the history of states of nature (e.g., rainfall). Agent utility is defined as discounted expected utility, summing utilities over time and taking expectations over states of nature.

The objective is to maximize a lambda-weighted sum of agent utilities subject to resource constraints. This is formulated as a Lagrangian problem, where first-order conditions equate the lambda-weighted discounted marginal utility of consumption across all households for every date and state. This implies that consumption allocation for an agent type can be captured by a household-specific function that depends only on aggregate income.

This "mutual insurance society" concept suggests that individual consumption should depend on aggregate income, not individual shocks, as individual contributions are pooled and redistributed. Another implication is the co-movement of consumption: while consumption levels may differ, their trends should move together, never crossing. These are testable hypotheses.

Policy Guidance from Data: Village Studies

The theory is applied to real-world data from villages in India and Thailand to assess how well people are doing and identify areas for intervention.

Village India (ICRISAT Data)

• Data Source: 10 years of data from Indian villages, tracking household income and consumption.
• Income Volatility: Income profiles are highly erratic, resembling "Rocky Mountains," indicating significant individual shocks.
• Consumption Smoothing: Grain consumption, a dominant dietary item, appears remarkably flat, like "Kansas," despite income fluctuations.
• Quantitative Findings: For every dollar increase in income, there's only a $0.07 increase in consumption, meaning only about 7% of income fluctuations translate to consumption changes. This varies by sector (e.g., trade and handicraft profits show higher transmission).
• Implications: This surprising degree of consumption smoothing in poor Indian villages, despite traditional social structures, suggests effective internal mechanisms like grain storage, gifts, and transfers. However, some groups still suffer more risk.

Thai Villages (Production and Risk Premium)

• Extension to Production: The theory is extended to include production, where households invest capital to produce output, then decide how much to consume and save.
• Risk Diversification: The focus is on how much risk a producer bears. While aggregate risk must be borne by someone, idiosyncratic risk (affecting one person's land but not another's) is potentially smoothable through a mutual fund.
• Risk Premium: The rate of return on projects (like equity) should be higher if producers bear risk.
• Empirical Findings: Investment and rate of return data suggest that, on average, 90% of idiosyncratic risk is diversified away, implying effective pooling.
• Cross-Village Smoothing: While individual villages pool risk, the aggregate risk for each village is not common. A larger platform could smooth risk across villages.
• Mismeasurement: An outlier case (Buriram, with over 100% diversified idiosyncratic risk) was attributed to data mismeasurement due to instability and transitions in the region.

Broader Applications of Risk Sharing

The concept of risk sharing and consumption co-movement is not limited to developing countries. * US Data: Worker betas (finance terminology for co-movements) can distinguish various groups. * EU Monetary Union: Countries in the Eurozone, lacking a fiscal union, show limited co-movement in consumption, suggesting potential gains from a cross-country unemployment scheme.

Policy Guidance from Theory: High-Velocity Private Debt

The lecture then shifts to the theoretical implications for high-velocity private debt, or privately issued monies, and the coordination problems they present.

Historical Context: English Inland Bills of Exchange

• Industrial Revolution: During the 18th and 19th centuries in Northern England, inland bills of exchange circulated as a medium of exchange, demonstrating that privately issued notes can function as money.
• Monetary Theory Definition: Money is defined as an object (in this case, a security) that appears frequently in exchange, making privately issued securities candidates for money based on their velocity.

The First Welfare Theorem and Fragmented Markets

• Review: The First Welfare Theorem states that under certain conditions, a Walrasian equilibrium is Pareto-optimal.
• Fragmented Markets: The model retains fragmented markets where traders meet in subgroups, extending this to dynamics with explicit time and self-interested, utility-maximizing agents.
• Economic Focus: The focus is on asset issuance and ownership changes, particularly circulating private IOUs.

Model Environment: Two Locations, Circulating Debt

• Setup: Two locations, agents meet pairwise. Some agents stay put, others move between locations.
• Debt Chains: Debts can be familiar (borrower and lender agree, repaid later) or circulating (a security issued by one party is traded through multiple intermediaries before redemption by the original issuer).
• No Reneging: For simplicity, it's assumed debts are always repaid, abstracting from default risk to highlight coordination problems.
• Two-Date Problem: If the economy only has two dates, circulating debt cannot be redeemed, leading to autarky (a horrible outcome). This highlights the potential damage of restricted trading and limited securities.
• Multilateral Agreements: A complete market solution would allow for multilateral agreements, but the current model restricts this to sequential, pairwise interactions.

Payment Matrices and Velocity

• Payment Matrices: A conceptual matrix where rows and columns represent consumption goods (indexed by dates and locations) and different types of debt (non-circulating and circulating). Circulating debt fills more "boxes" as it's traded more frequently.
• Velocity: Defined as the amount traded in a given date divided by the stock outstanding, averaged over the security's existence.
  • Consumption Goods: Velocity is less than 1 (only a fraction of endowment is traded).
  • Non-Circulating Debt: Velocity is 2/3 (traded at issuance and redemption, but not in between).
  • Circulating Debt: Velocity is 1 (traded every date).
• Conclusion: Circulating debts act as monies, appearing frequently in exchange and having high velocity.

Achieving Complete Markets Equilibrium with Debt

• Notation: A more general notation is introduced for locations, dates, persons, and securities (units of consumption promised by one person, issued at one date, due at another).
• Security Markets Rules: Rules govern security issuance, redemption (issuer must demand back what they issued), and the requirement to acquire an asset before selling it.
• Budget Constraint: A person's budget constraint equates their excess supply/demand of goods with their net security trades.
• Debt Equilibrium: Specifies consumption and debt demands and prices such that utility is maximized, and markets clear for both goods and securities.
• Target: The goal is to achieve the complete markets equilibrium (Walrasian allocation) using these debt instruments.
• Debt Prices: Debt prices are conjectured to be ratios of complete market prices, reflecting the value of consumption at redemption relative to issuance.
• Coordination Problem: While the underlying allocations are unique, there are infinite ways to achieve them through debt. Agents need to coordinate on which debts to issue and in what quantities. This is akin to Ostroy-Starr's need for information or agreement on what constitutes money.

Market Crises and Coordination Failure

• The Problem: If agents in different locations incorrectly assume they are the sole issuer of circulating money, they will violate the necessary coordination equation.
• Consequences: The price of circulating debt will plummet, leading to a "slow-moving crisis." While some adjustments occur, they are insufficient. Agents holding circulating debt suffer significant consumption losses.
• Heterogeneous Impact: The impact of such crises is heterogeneous across agents due to varying economic roles.
• The Fix: Coordination on debt issuance is crucial. This requires a mechanism (like a distributed ledger) to track and restrict security issues.

Applications and Relevance

• Digital Assets and Tokenization: The coordination problem discussed is relevant to the emerging digital asset space, where tokenization and dynamic ledgers are prevalent. The lecture argues that this specific risk has not been adequately articulated by policymakers.
• Bagehot's London Money Markets: The historical crisis of inland bills of exchange in London is a real-world example of the coordination problem. Bagehot's work on central banking emerged from this context, debating "real bills" (debt backed by real economic activity) versus the "quantity theory" (controlling the money supply).
• Low- and Middle-Income Countries: Similar issues arise with the dual use of electronic accounts and currency, though the connection to this specific coordination problem is often missed.
• DeFi Fragmentation: The lecture suggests a connection to the fragmentation of liquidity in decentralized finance (DeFi).

Smart Contracts on a Blockchain: Ethereum

The lecture concludes with a brief review of smart contracts, particularly on Ethereum.

• Blockchain as Distributed Ledger: A blockchain is a distributed ledger recording transactions in blocks, with a consensus algorithm for validation. Bitcoin primarily handles cryptocurrency movement.
• Ethereum's Generalization: Ethereum generalizes the notion of blockchain state. It provides a complete language for coding arbitrary functionality, moving beyond simple balance transfers.
• Two Account Types:
  1. Bitcoin-type accounts: For balances and transfers.
  2. Contract accounts: Contain code and data storage, receive messages (transactions), update state, and send out transactions as part of contract execution.
• Generalized State: Ethereum's state is generalized to accommodate contracts, not just balances.
• Functionality: Contract accounts are valid nodes with different functionality compared to agents performing simple transactions.
• Relevance: Smart contracts on Ethereum provide the infrastructure for building the kind of coordinated mechanisms discussed in the lecture, enabling the tracking and restriction of security issues to prevent market crises.