Paper: arXiv 2601.07626

Authors: Kim Weston

Abstract

Universal basic income (UBI) is a tax scheme that uniformly redistributes aggregate income amongst the entire population of an economy. We prove the existence of an equilibrium in a model that implements universal basic income. The economic agents choose the proportion of their time to work and earn wages that can be used towards consumption and investment in a financial market with a traded stock and annuity. A proportion of the earned wages is uniformly distributed amongst all agents, leading to interconnectedness of the agents’ decision problems, which are already dependent on one another through the financial market. The decision problems are further entangled by Nash perceptions of labor; the agents respond to the labor choices of others and act upon their perceived income in their decision problems. The equilibrium is constructed and proven to exist using a backward stochastic differential equation (BSDE) approach for a BSDE system with a quadratic structure that decouples. We analyze the effects of a universal basic income policy on labor market participation, the stock market, and welfare. While universal basic income policies affect labor market participation and welfare monotonically, its effects on the stock market are nontrivial and nonmonotone.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a highly rigorous theoretical analysis using BSDE systems to prove the existence of a financial equilibrium under UBI, showcasing sophisticated mathematical modeling. However, it lacks empirical backtesting, real-world data application, or calibration, relying entirely on continuous-time mathematical proofs.

Research Flowchart

  flowchart TD
    A[Research Goal: Prove Equilibrium & Effects of Universal Basic Income] --> B[Model Inputs: Financial Market, Labor Choices, Tax Scheme]
    B --> C[Formulate Entangled Agent Decision Problems via Nash Perceptions]
    C --> D[Methodology: Construct Coupled System of Quadratic BSDEs]
    D --> E[Decouple & Solve BSDE System to Prove Equilibrium Existence]
    E --> F[Findings: Monotonic Effects on Labor & Welfare; Non-monotone Stock Market Effects]

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