The Affine Wealth Model: An agent-based model of asset exchange that allows for negative-wealth agents and its empirical validation (1604.02370v2)

Abstract: We present a stochastic, agent-based, binary-transaction Asset-Exchange Model (AEM) for wealth distribution that allows for agents with negative wealth. This model retains certain features of prior AEMs such as redistribution and wealth-attained advantage, but it also allows for shifts as well as scalings of the agent density function. We derive the Fokker-Planck equation describing its time evolution and we describe its numerical solution, including a methodology for solving the inverse problem of finding the model parameters that best match empirical data. Using this methodology, we compare the steady-state solutions of the Fokker-Planck equation with data from the United States Survey of Consumer Finances over a time period of 27 years. In doing so, we demonstrate agreement with empirical data of an average error less than 0.16\% over this time period. We present the model parameters for the US wealth distribution data as a function of time under the assumption that the distribution responds to their variation adiabatically. We argue that the time series of model parameters thus obtained provides a valuable new diagnostic tool for analyzing wealth inequality.

• The paper introduces the Affine Wealth Model (AWM), which extends agent-based wealth distribution models to include negative-wealth agents using affine transformations.
• Empirical validation with U.S. wealth data showed the AWM fits distributions with an average error under 0.16% and captures wealth condensation.
• The AWM serves as a diagnostic tool connecting micro-dynamics to macro-distributions, aiding analysis and potential policy design for wealth inequality.

The Affine Wealth Model: An Analytical Framework for Negative-Wealth Agents

The paper "The Affine Wealth Model: An Agent-Based Model of Asset Exchange That Allows for Negative-Wealth Agents and Its Empirical Validation" presents an advanced interpretation of wealth distribution using agent-based models (AEMs). It extends previous AEMs by incorporating agents with negative wealth, reflecting real-world phenomena more accurately. This model, termed the Affine Wealth Model (AWM), introduces symmetry in the wealth distribution through affine transformations, enabling the inclusion of negative-wealth agents. The paper is an exploration of the model's theoretical underpinnings and its empirical validation against U.S. wealth data from the Survey of Consumer Finances.

Key Contributions and Methodology

1. Affine Transformation and Negative Wealth: The innovation of this model lies in its capacity to include negative wealth through affine transformations. Prior models, specifically the Extended Yard-Sale Model (EYSM), assumed non-negative wealth, which contradicted empirical data showing a significant percentage of the population with negative net worth. The AWM adapts the EYSM by recalibrating wealth distribution, allowing for both wealth scaling and shifts, effectively integrating negative-wealth agents.
2. Mathematical Framework: The paper derives a Fokker-Planck equation to describe the time evolution of the wealth distribution under the AWM. This equation incorporates transactional dynamics, redistribution mechanisms, and wealth-attained advantages (WAA) into a unified framework. It retains equilibrium conditions even when agents' wealth can become negative, making it robust for modeling real economies.
3. Empirical Validation and Results: The authors present a numerical solution methodology for the AWM and apply it to U.S. Survey of Consumer Finances data over a period of 27 years, achieving an average error margin of less than 0.16%. The fitting process revealed that the U.S. wealth distribution is indeed better captured by the AWM than by traditional models. The empirical analysis provides parameter values over time, offering insights into trends in wealth inequality.
4. Oligarchical Tendency: The model predicts partial wealth condensation, where a disproportionate fraction of wealth resides with a minimal segment of the population — an oligarchal distribution. This feature, supported by empirical findings, aligns often reported phenomena of wealth inequality but provides a precise, quantitative lens to examine it.

Implications and Future Research

The AWM's implications extend across both theoretical and practical domains. Theoretically, it strengthens the linkage between micro-level transactional dynamics and macro-level wealth distributions. Its capacity to handle negative wealth and predict wealth condensation brings new insights into the mechanisms driving wealth inequality. Practically, the model serves as a diagnostic tool, aiding policymakers and researchers in analyzing and potentially forecasting trends in wealth distribution, tailoring economic policies towards mitigating inequality.

Future research directions may include:

• Incorporating temporal dynamics explicitly into the model, allowing non-adiabatic parameter changes to capture rapid economic shifts.
• Extending AWM to multi-agent settings with heterogeneous strategies, providing a richer understanding of economic interactions.
• Cross-national comparisons using the AWM framework, highlighting differences in economic structures and policies on wealth distribution.

The Affine Wealth Model represents a significant stride in agent-based economic modeling, effectively bridging the gap between empirical data on wealth distribution and theoretical frameworks for understanding economic inequality. Its innovative approach to handling negative wealth and capturing oligarchical patterns offers a potent tool for both academic inquiry and practical policy design.