Analyzing Wage Theft in Day Labor Markets via Principal Agent Models

TL;DR

Wage theft in day-labor markets is studied through a principal-agent lens with external enforcement. The authors show penalty-based approaches require unrealistically large fines to eliminate theft, and that theft persists under typical inspection regimes; however, introducing worker awareness in a dynamic, information-sharing setting can fully deter theft when employers adopt optimal fixed wages. The work combines theoretical reductions to a one-dimensional search, explicit wage- and theft-structure results, and numerical experiments to illustrate policy levers. The findings highlight practical implications: stronger inspections alone are insufficient, but transparency about wage-theft histories and worker education can substantially reduce exploitation with meaningful real-world impact.

Abstract

In day labor markets, workers are particularly vulnerable to wage theft. This paper introduces a principal-agent model to analyze the conditions required to mitigate wage theft through fines and establishes the necessary and sufficient conditions to reduce theft. We find that the fines necessary to eliminate theft are significantly larger than those imposed by current labor laws, making wage theft likely to persist under penalty-based methods alone. Through numerical analysis, we show how wage theft disproportionately affects workers with lower reservation utilities and observe that workers with similar reservation utilities experience comparable impacts, regardless of their skill levels. To address the limitations of penalty-based approaches, we extend the model to a dynamic game incorporating worker awareness. We prove that wage theft can be fully eliminated if workers accurately predict theft using historical data and employers follow optimal fixed wage strategy. Additionally, sharing wage theft information becomes an effective long-term solution when employers use any given fixed wage strategies, emphasizing the importance of raising worker awareness through various channels.

Figures (7)

• Figure 1: Optimal values for $w_H$ and $w_L$ as functions of effort $a$ (Proposition \ref{['prop:Wages']}) for cost function $C(a)=a/(1-a)$ and outside option $u=1$.
• Figure 2: Optimal wage theft amounts $b_H$ and $b_L$ as functions of effort $a$ and ideal theft $\beta$ for cost function $C(a)=a/(1-a)$ and outside option $u=1$. The ideal wage theft amount $\beta$ increases from (a) to (c), implying that the wage theft becomes more costly for the employer. The vertical lines indicate places where the first derivative is discontinuous.
• Figure 3: Impact of $\sigma$ for different inspection rates ($P=10$, $y_H=50$, $y_L=30$, $u=200$, $k=0.1$, $q=3$, $p=1.1$).
• Figure 4: Impact of $\gamma$ for different penalty coefficients. ($P=10$, $y_H=50$, $y_L=30$, $u=200$, $k=0.1$, $q=3$, $p=1.5$)
• Figure 5: Impact of $u$ for different inspection rates ($P=10$, $y_H=50$, $y_L=30$, $\sigma=1$, $k=0.1$, $q=1$, $p=1.5$).

Theorems & Definitions (20)

• Definition 1: Principal's ideal wage theft
• Proposition 1: Optimal Theft
• Theorem 1
• Proposition 2: Optimal Wages
• Proposition 3
• Proposition 4
• Corollary 1
• Theorem 2
• Theorem 3
• Proposition 4: Optimal Theft