The Problem of Late Payments

Tomaž Fleischman from Informal Systems presented on Multilateral Trade Credit Set-off (MTCS), an algorithm designed to address the systemic problem of late payments in business. The presentation covered the nature of late payments, how they can be observed in obligation networks, the formalization of MTCS, its empirical application, and future possibilities like liquidity injection.

The Problem of Late Payments

Late payment occurs when a business provides goods or services on credit, expecting payment within a set period (e.g., 30 days), but payment is delayed. This issue has significant negative consequences:

• Increased Costs: Businesses incur financing costs for unpaid invoices and deplete cash reserves, particularly affecting small, vulnerable companies.
• Administrative Burden: Managing late payments requires additional administrative effort.
• Reduced Productivity: It drains labor productivity and creates distractions.
• Systemic Impact: Late payments can lead to substantial losses, poorly managed working capital, unemployment, and are a leading cause of bankruptcies, even for otherwise profitable businesses. This creates high barriers for small firms to enter markets.

Data from Intrum Justitia for the UK in 2020 showed that actual payment terms consistently exceed agreed terms. Larger companies often demand extended payment terms from suppliers. The COVID-19 pandemic significantly worsened the sentiment regarding late payments. Across Europe, average payment times are around 60 days, well above agreed terms, and this issue spans all sectors.

Reasons for late payments are complex, ranging from tactical delays (e.g., to improve cash flow), genuine inability to pay (default), administrative issues, or even deliberate bad faith. This complexity makes managing late payments a significant challenge for individual firms.

Slovenia, Fleischman's home country, implemented a system for reporting and clearing late payments. During periods of economic crisis (early 1990s war economy, 2008 financial crisis, COVID-19), reported late payments and the amounts cleared through the mechanism significantly increased, highlighting the mechanism's utility during liquidity shortages.

Observing Late Payments through Obligation Networks

To understand and manage late payments, it's useful to visualize them as an obligation network.

Example: Alice, Bob, and Charlie Consider a simple scenario: * Alice owes 2 to Bob. * Bob owes 2 to Charlie. * Charlie owes 1 to Alice.

This forms a cycle. The smallest amount in this cycle is 1. Multilateral set-off allows clearing this cycle of 1 without external money. After clearing, Alice would owe 1 to Bob, and Bob would owe 1 to Charlie.

The challenge is that individual parties lack a full view of the network. Alice doesn't know Bob's obligations to Charlie. Detecting cycles in large networks is also computationally intensive.

Formalizing MTCS as an Algorithm

The MTCS algorithm reformulates the problem from cycle detection to balancing the network.

1. Calculate Balances: For each entity, determine its net balance (total owed minus total received).

   • Alice: owes 2, is owed 1 => balance -1
   • Bob: owes 2, is owed 2 => balance 0
   • Charlie: owes 1, is owed 2 => balance +1

2. Introduce Source and Sink: To balance the network, an imaginary "source" of funds and a "sink" for funds are introduced.

   • Entities with negative balances (like Alice) receive funds from the source.
   • Entities with positive balances (like Charlie) send excess funds to the sink.
   • The capacity of these new edges equals the absolute value of the balance.

3. Find a Saturating Flow: A minimum cost, maximum flow algorithm is applied from the source to the sink. This pushes liquidity through the network in the most efficient way possible. In the example, a flow of 1 goes from source to Alice, Alice to Bob, Bob to Charlie, and Charlie to sink.

4. Remove the Saturating Flow: Subtracting this saturating flow from the original obligations reveals the cleared cycle. This method works regardless of network size.

Mathematical Formalization: * A network G0 with nodes and edges is defined. * Balance for each node is outflows - inflows. * A balanced network G is created by adding a source and sink. Edges are added from the source to nodes with negative balances and from nodes with positive balances to the sink. Edge capacities are set to the balance (or minus balance for source edges). * All edges are assigned a cost (typically 1 for the basic case). Different costs can be used for optimization based on factors like risk or social benefit. * The minimum cost, maximum flow algorithm identifies the saturating s-t flow. * Subtracting this flow from the original network results in a new network where all nodes are balanced, and no flows remain from the source or to the sink, effectively identifying and removing cycles.

Algorithm Steps (Pseudocode): 1. Balance Network: * Create new nodes: source, sink. * For each node in the original graph: * Calculate net position. * If net position < 0, add edge from source to node with capacity = abs(net_position). * If net position > 0, add edge from node to sink with capacity = net_position. 2. Find Saturated S-T Flow: * If source is in the network (meaning it wasn't already balanced), apply a minimum cost, maximum flow algorithm. 3. Subtract Flow: * Initialize an empty result network. * For each original edge, subtract the flow amount returned by the algorithm.

Empirical Setting and Results

The MTCS algorithm was tested on a real-world network from Infocert, an Italian tax compliance company. This dataset contained high-quality invoice data among Italian companies.

• Network Size: The network comprised 45,000 firms (nodes) and approximately 2 million edges (obligations).
• Firm Distribution: The majority of firms were micro-companies, but large firms acted as major hubs.
• Clearing Results: Monthly clearing over two years (2019-2020, including the COVID-19 crisis) showed that the algorithm cleared, on average, 11% of the initial debt. The network structure remained stable even during the pandemic.
• Beneficiaries: Larger firms (small, medium, and especially large) benefited most from the clearing. Net creditors also benefited more, indicating the mechanism acts like an accounts receivable collection service.
• Significance: While 11% might seem small, it's a significant amount for businesses.

Network Topology Challenges: The limited clearing percentage (10-12%) is attributed to the network's scale-free topology: * Power Law Distribution of Amounts: Invoice amounts follow a power law, meaning most transactions are small. These small amounts act as a bottleneck for clearing larger cycles. * Power Law Distribution of Connections: The number of business partners per firm also follows a power law. Many firms have few connections, limiting the flow through their nodes and thus restricting the overall clearing potential.

Liquidity Injection

To overcome topological limitations, "engineered obligations" or liquidity injection can be used.

Concept: * An "engineered node" (e.g., a bank, mutual credit system, cryptocurrency) is introduced. * This node represents a source of accepted liquidity. * The MTCS algorithm is applied to this enhanced network.

Example with Alice, Bob, Charlie, and Engineered Node: If Alice has access to 1 unit of engineered liquidity, and Charlie is willing to accept it, the clearing process can be enhanced. The algorithm identifies how this engineered liquidity can facilitate more extensive clearing.

Experimental Setup: Experiments were conducted by varying the amount of engineered liquidity (gamma, from 0 to 1, representing 0% to 100% of indebtedness).

Results: * Multiplier Effect: Even a small amount of engineered liquidity (e.g., 20%) can significantly increase the cleared debt (close to 50%), demonstrating a strong network multiplier effect. * Stability: The relationship between engineered liquidity and cleared debt is stable across different months, indicating the robustness of the real-life network structure. * Firm Size Impact: Micro-firms are highly dependent on engineered liquidity, while larger firms benefit even more. * Late Payment Reduction: As engineered liquidity increases, the problem of late payments significantly decreases. * Value Added: The mechanism provides the biggest effect during crises or in liquidity-constrained regions, acting as a tool to kickstart economic activity.

Combining Liquidity Sources: The system can incorporate multiple types of engineered liquidity (e.g., bank deposits, mutual credit, cryptocurrency, vouchers). A key finding is that due to the flow conservation principle, there is no flow between different liquidity sources. This means different types of liquidity can coexist and contribute to clearing without needing to be exchanged.

Future Directions: Blockchain Implementation

Informal Systems is developing "Cycles Protocol," a blockchain-based solution for MTCS: * Single Source of Truth: Blockchain serves as a transparent and immutable record for obligations. * Privacy-Preserving: Firms' "intents" (obligations) are encrypted on-chain. A "solver" decrypts, applies the MTCS algorithm, re-encrypts, and writes results back on-chain. * Zero-Knowledge Proofs: Attestations and zero-knowledge proofs verify that the MTCS process was correctly executed without revealing sensitive data. * Collaboration in Competition: This design enables collaboration to resolve indebtedness while preserving privacy in a competitive environment.

Historical Context and Comparison to Netting

The concept of multilateral clearing is ancient, dating back to medieval merchant fairs where traders would settle debts collaboratively without cash. English banking clearing clubs are a more recent example.

MTCS vs. Netting: * Netting: Involves creating new obligations (novation) after offsetting. This assumes all parties know and trust each other equally and can introduce new risks. It works best in tight, closed groups. * MTCS (Set-off): Only reduces original debts. It does not redistribute risk or create new obligations. It is a pure risk reduction technique, making it suitable for larger, less trusting networks like trade credit.

Practical Considerations

• Incentives for Adoption: The primary incentive for firms is reduced costs in managing working capital and accounts receivable. Additional incentives can include premiums for providing liquidity or discounts for receiving it, creating a market for liquidity.
• Integration: A major challenge is integrating the system with existing ERP and accounting systems, though accounting standards are generally uniform.
• Timing: The frequency of running the algorithm (e.g., monthly, daily, every 15 seconds like CHAPS) depends on the specific network's dynamics and engineering requirements.
• Liquidity Solicitation: The system can solicit liquidity from net debtor nodes, allowing them to contribute a fraction of their debt in advance to facilitate clearing, leading to significant multiplier effects.