This paper derives necessary and sufficient conditions under which the firstorder characterization of Holmström (1979) robustly produces affine solutions: a risk-neutral principal, an agent with logarithmic utility, and output whose distribution depends on effort through a one-parameter exponential family with a linear sufficient statistic. For this primitive structure, I establish existence of an optimal contract and validity of the first-order approach in two cases: first,...

We characterize the conditions under which a socially responsible (SR) fund induces firms to reduce externalities, even when profit-seeking capital is in perfectly elastic supply. Such impact requires that the SR fund's mandate permits the fund to trade off financial performance against reductions in social costs---relative to the counterfactual in which the fund does not invest in a given firm. Based on such an impact...

We study bank capital requirements as a tool to address climate-related financial risks and evaluate whether a prudential mandate for bank regulators remains appropriate in the presence of carbon externalities. We show that a prudential mandate maximizes welfare if carbon taxes are set optimally and fully characterize optimal capital requirements under such a mandate. Optimal transition-risk adjustments can crowd out clean lending. When carbon pricing...