Introduction

Examines when purpose-driven stakeholders exit or engage firms to reduce social harm. Develops a general equilibrium, multi-sided matching model incorporating heterogeneous stakeholders (e.g. workers, banks) differing in productivity and purpose. Key determinant is whether firm-level harm scales with productivity, addressing gaps in existing literature based on Hirschman’s framework.

Model

Firms match with multiple stakeholder types, generating output and social harm. Purpose-driven stakeholders experience disutility from harm, incentivising mitigation. Mitigation reduces harm at a cost. Equilibrium outcomes depend on stakeholder composition, productivity, and matching, with surplus maximised through transferable utility and optimal mitigation choices.

Independence benchmark

When harm is unrelated to productivity, stakeholders sort purely by productivity. Increased purpose-driven stakeholders leads only to engagement, with firms adjusting compensation (compensating differentials) to fund mitigation. There are no spillovers across stakeholder groups, and firm-level and aggregate outcomes align, explaining prior empirical approaches.

General characterisation

When harm scales with productivity, sorting depends jointly on productivity and purpose. High-productivity firms prefer profit-driven stakeholders to avoid mitigation costs, while purpose-driven stakeholders cluster in “clean” firms. Equilibrium features segmentation at the top and mixing at lower productivity levels, with complex multi-stakeholder interactions requiring a sequential matching framework.

Rents

Scarce profit-driven stakeholders earn rents beyond compensating differentials, particularly at high productivity levels where firms compete to avoid mitigation. This creates a wedge in compensation and limits the feasibility of engagement for highly productive stakeholders, reinforcing exit behaviour.

Exit vs ngagement in general equilibrium

An increase in purpose-driven stakeholders generates both engagement and exit. Lower-productivity stakeholders engage, remaining with existing firms and sharing mitigation costs. Higher-productivity stakeholders exit to smaller, purpose-aligned firms, as engagement becomes too costly. A productivity threshold determines behaviour, contrasting with the engagement-only outcome under independence.

Impact trickles down

xit generates indirect effects through reallocation. High-productivity stakeholders displace lower-productivity purpose-driven stakeholders, who then move to smaller firms and induce mitigation. This “trickle-down” mechanism concentrates aggregate harm reduction in mid-tier firms, exceeding the direct impact of treated stakeholders and highlighting limitations of firm-level analysis.

Spillover effects on payoffs

Preference shocks create cross-stakeholder spillovers. Purpose-driven stakeholders at the top may experience lower payoffs due to increased competition, while profit-driven stakeholders benefit from scarcity rents. Other stakeholder groups are affected through changes in matching and productivity, unlike the independence case with no spillovers.

Discussions

Applied to bank decarbonisation post-Paris Agreement. Empirical patterns include: large banks exiting rather than engaging; limited firm-level environmental impact due to substitution by smaller lenders; and underestimated aggregate effects. Calibration shows green bank share rising from 7% to 15%, with impact concentrated in mid-tier firms via spillovers rather than direct firm-level changes.

Calibration

Uses two stakeholder types (banks and workers). Parameters include 33% purpose-driven workers and 7% banks, emissions scaling with productivity (σ≈5,000), and mitigation cost calibrated to carbon capture data. Results illustrate engagement at the bottom, exit at the top, and amplified aggregate effects through displacement dynamics.

Conclusion

Finds that when harm scales with productivity, exit and engagement coexist, with exit generating broader market effects through reallocation. Firm-level studies underestimate impact by ignoring spillovers. Implication: policy and empirical analysis should account for general equilibrium effects when evaluating stakeholder-driven environmental actions.