In an incomplete continuous-time securities market with uncertainty generated by Brownian motions, we derive closed-form solutions for the equilibrium interest rate and market price of risk processes. The economy has a finite number of heterogeneous exponential utility investors, who receive partially unspanned income and can trade continuously on a finite time-interval in a money market account and a single risky security. Besides establishing the existence of an equilibrium, our main result shows that if the investors' unspanned income has stochastic countercyclical volatility, the resulting equilibrium can display both lower interest rates and higher risk premia compared to the Pareto efficient equilibrium in an otherwise identical complete market.

Both soft, noncontractible, and hard, contractible, information are informative about managerial ability and future firm performance. If a manager's future compensation depends on expectations of ability or future performance, then the manager has implicit incentives to affect the information. We examine the real incentive effects of soft information in a dynamic agency with limited commitment. When long‐term contracts are renegotiated, the rewards for future performance inherent in long‐term contracts allow the principal partial control over the implicit incentives. This is because the soft information affects the basis for contract renegotiation. With short‐term contracts, the principal has no control over the basis for contract negotiation, and thus long‐term contracts generally dominate short‐term contracts. With long‐term contracts, the principal's control over implicit incentives is characterized in terms of effective contracting on an implicit aggregation of the soft information that arises from predicting (forming expectations of) future performance. We provide sufficient conditions for soft information to have no real incentive effects. In general, implicit incentives not controllable by the principal include fixed effects, such as career concerns driven by labor markets external to the agency. When controllable incentives span the fixed effects of career concerns, the latter have no real effects with regard to total managerial incentives—they would optimally be the same with or without career concerns. Our analysis suggests empirical tests for estimating career concerns that should explicitly incorporate noncontractible information.

We consider a dynamic trade-off model of a firm's capital structure with debt renegotiation. Debt holders only accept restructuring offers from equity holders backed by threats which are in the equity holders' own interest to execute. Our model shows that in a complete information model in which taxes and bankruptcy costs are the only frictions, violations of the absolute priority rule (APR) are typically optimal. The size of the bankruptcy costs and the equity holders' bargaining power affect the size of APR violations, but they have only a minor impact on the choice of capital structure.

We derive sufficient conditions for ranking performance evaluation systems in multi-task agency models (using both optimal and linear contracts) in terms of a second-order stochastic dominance (SSD) condition on the likelihood ratios. The SSD condition can be replaced by a variance-covariance matrix of likelihood ratios (VCM) condition when the utility function is square-root, the performance measures are normally distributed, and for LEN models. We identify existing results derived under the LEN assumptions that rely on the VCM condition and, thus, also hold for optimal contracts.

Local pollution exposures have a disproportionate impact on minority households, but the root causes remain unclear. This study conducts a correspondence experiment on a major online housing platform to test whether housing discrimination constrains minority access to housing options in markets with significant sources of airborne chemical toxics. We find that renters with African American or Hispanic/Latinx names are 41% less likely than renters with white names to receive responses for properties in low-exposure locations. We find no evidence of discriminatory constraints in high-exposure locations, indicating that discrimination increases relative access to housing choices at elevated exposure risk.