Economic models often rely on assumptions that are simplifying statements about the counterfactual world and cannot be verified given observable data. At the same time, algorithmic predictions are increasingly used to guide policy decisions. This dissertation focuses on understanding how unverifiable assumptions shape the causal conclusions we draw and on developing statistical inference methods to inform policy design in the context of algorithmic fairness. The first chapter proposes a new framework for identifying causal effects in panel data settings, nesting popular empirical strategies as special cases while remaining robust to violations of their identifying assumptions. The second chapter (joint with Francesca Molinari) develops rigorous statistical methods for understanding the trade-offs between fairness and accuracy in predictive algorithms, leveraging a convex representation of the set of risk allocations between legally protected groups induced by a given class of algorithms. The third chapter (joint with Francesca Molinari and Amilcar Velez) builds on and extends the second chapter. It allows different loss functions for measuring fairness and for evaluating accuracy, examines algorithms trained on selectively observed labels, addresses the identification challenges thereof, and proposes inference methods for counterfactual fairness-accuracy trade-off analyses. Together, these three chapters provide new identification and inference tools for policy evaluation in causal and algorithmic decision-making settings.