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Screening Workers with Affirmative Action

Charles Po-Cheng Huang

Abstract

This paper examines the optimal contracts in a two-dimensional screening model where one dimension(group identity) is verifiable by agents but not falsifiable. A principal offers contracts to agents who differ in cost types and group membership. Motivated by the United States Federal policy, Work Opportunity Tax Credit, the principal receives tax benefits for hiring agents from protected groups. Under the assumption that the protected agents tend to have higher cost types, the optimal contract induces full separation across both dimensions: agents reveal the cost type and the group identity through contract choice. Furthermore, the principal is willing to hire the trait agents with a higher cost threshold than the non-trait agents, and this threshold increases with the tax credit. Conversely, when the protected agents tend to have lower cost types, the optimal design without tax credits pools groups while separating by cost type. These results demonstrate that both affirmative action and non-discrimination can be optimal depending on the cost distribution ordering across groups.

Screening Workers with Affirmative Action

Abstract

This paper examines the optimal contracts in a two-dimensional screening model where one dimension(group identity) is verifiable by agents but not falsifiable. A principal offers contracts to agents who differ in cost types and group membership. Motivated by the United States Federal policy, Work Opportunity Tax Credit, the principal receives tax benefits for hiring agents from protected groups. Under the assumption that the protected agents tend to have higher cost types, the optimal contract induces full separation across both dimensions: agents reveal the cost type and the group identity through contract choice. Furthermore, the principal is willing to hire the trait agents with a higher cost threshold than the non-trait agents, and this threshold increases with the tax credit. Conversely, when the protected agents tend to have lower cost types, the optimal design without tax credits pools groups while separating by cost type. These results demonstrate that both affirmative action and non-discrimination can be optimal depending on the cost distribution ordering across groups.

Paper Structure

This paper contains 15 sections, 11 theorems, 65 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Two-Dimensional Screening Model
  3. Timeline
  4. Agent's Problem
  5. Principal's Objective
  6. Optimal Contracts
  7. The Agent's Problem
  8. The Principal's Problem
  9. Optimal Contract under the Quadratic Cost
  10. Under MLRP
  11. Under Reverse MLRP
  12. Conclusion
  13. Omitted Proofs
  14. Proofs of Section \ref{['sec:optimal']}
  15. Standard Method for Results under MLRP

Key Result

Lemma 1

A set of contracts $(w^j, q^j)$ is within-group incentive compatible if and only if where $j = \{N,T\}.$$\blacktriangleleft$$\blacktriangleleft$

Figures (5)

  • Figure 1: Timeline of the Model
  • Figure 2: Optimal quantities under different tax credit levels
  • Figure 3: Hiring probabilities under different tax credit levels
  • Figure 4: IC comparison from full separation to pooling the group.
  • Figure 5: Optimal quantities under different tax credit levels

Theorems & Definitions (27)

  • Definition 1: Within-Group Incentive Compatibility
  • Definition 2: Across-Group Incentive Compatibility
  • Definition 3: Individual Rationality
  • Lemma 1: Within-Group IC
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Proposition 1: No Distortion at the Top
  • Theorem 1
  • Corollary 1
  • ...and 17 more