This paper investigates the impact of Reconstruction-era amnesty policy on the officeholding and wealth of elites in the postbellum South. Amnesty policy restricted the political and economic rights of Southern elites for nearly three years during Reconstruction. I estimate the effect of being excluded from amnesty on elites' future wealth and political power using a regression discontinuity design that compares individuals just above and below a wealth threshold that determined exclusion from amnesty. Results on a sample of Reconstruction convention delegates show that exclusion from amnesty significantly decreased the likelihood of ex-post officeholding. I find no evidence that exclusion impacted later census wealth for Reconstruction delegates or for a larger sample of known slaveholders who lived in the South in 1860. These findings are in line with previous studies evidencing both changes to the identity of the political elite, and the continuity of economic mobility among the planter elite across the Civil War and Reconstruction.

We establish general "collapse to the mean" principles that provide conditions under which a law-invariant functional reduces to an expectation. In the convex setting, we retrieve and sharpen known results from the literature. However, our results also apply beyond the convex setting. We illustrate this by providing a complete account of the "collapse to the mean" for quasiconvex functionals. In the special cases of consistent risk measures and Choquet integrals, we can even dispense with quasiconvexity. In addition, we relate the "collapse to the mean" to the study of solutions of a broad class of optimisation problems with law-invariant objectives that appear in mathematical finance, insurance, and economics. We show that the corresponding quantile formulations studied in the literature are sometimes illegitimate and require further analysis.

This paper is concerned with the analysis of blow-ups for two McKean-Vlasov equations involving hitting times. Let $(B(t); \, t \ge 0)$ be standard Brownian motion, and $\tau:= \inf\{t \ge 0: X(t) \le 0\}$ be the hitting time to zero of a given process $X$. The first equation is $X(t) = X(0) + B(t) - \alpha \mathbb{P}(\tau \le t)$. We provide a simple condition on $\alpha$ and the distribution of $X(0)$ such that the corresponding Fokker-Planck equation has no blow-up, and thus the McKean-Vlasov dynamics is well-defined for all time $t \ge 0$. Our approach relies on a connection between the McKean-Vlasov equation and the supercooled Stefan problem, as well as several comparison principles. The second equation is $X(t) = X(0) + \beta t + B(t) + \alpha \log \mathbb{P}(\tau > t)$, whose Fokker-Planck equation is non-local. We prove that for $\beta > 0$ sufficiently large and $\alpha$ no greater than a sufficiently small positive constant, there is no blow-up and the McKean-Vlasov dynamics is well-defined for all time $t \ge 0$. The argument is based on a new transform, which removes the non-local term, followed by a relative entropy analysis.

This study proposes a method to identify treatment effects without exclusion restrictions in randomized experiments with noncompliance. Exploiting a baseline survey commonly available in randomized experiments, I decompose the intention-to-treat effects conditional on the endogenous treatment status. I then identify these parameters to understand the effects of the assignment and treatment. The key assumption is that a baseline variable maintains rank orders similar to the control outcome. I also reveal that the change-in-changes strategy may work without repeated outcomes. Finally, I propose a new estimator that flexibly incorporates covariates and demonstrate its properties using two experimental studies.

We study the principal component analysis based approach introduced by Reisinger & Wittum (2007) and the comonotonic approach considered by Hanbali & Linders (2019) for the approximation of American basket option values via multidimensional partial differential complementarity problems (PDCPs). Both approximation approaches require the solution of just a limited number of low-dimensional PDCPs. It is demonstrated by ample numerical experiments that they define approximations that lie close to each other. Next, an efficient discretisation of the pertinent PDCPs is presented that leads to a favourable convergence behaviour.

As machine learning algorithms start to get integrated into the decision-making process of companies and organizations, insurance products will be developed to protect their owners from risk. We introduce the concept of algorithmic insurance and present a quantitative framework to enable the pricing of the derived insurance contracts. We propose an optimization formulation to estimate the risk exposure and price for a binary classification model. Our approach outlines how properties of the model, such as accuracy, interpretability and generalizability, can influence the insurance contract evaluation. To showcase a practical implementation of the proposed framework, we present a case study of medical malpractice in the context of breast cancer detection. Our analysis focuses on measuring the effect of the model parameters on the expected financial loss and identifying the aspects of algorithmic performance that predominantly affect the price of the contract.

We propose a method of retrospective counterfactual imputation in panel data settings with later-treated and always-treated units, but no never-treated units. We use the observed outcomes to impute the counterfactual outcomes of the later-treated using a matrix completion estimator. We propose a novel propensity-score and elapsed-time weighting of the estimator's objective function to correct for differences in the observed covariate and unobserved fixed effects distributions, and elapsed time since treatment between groups. Our methodology is motivated by studying the effect of two milestones of European integration -- the Free Movement of persons and the Schengen Agreement -- on the share of cross-border workers in sending border regions. We apply the proposed method to the European Labour Force Survey (ELFS) data and provide evidence that opening the border almost doubled the probability of working beyond the border in Eastern European regions.

Yield farming has been an immensely popular activity for cryptocurrency holders since the explosion of Decentralized Finance (DeFi) in the summer of 2020. In this Systematization of Knowledge (SoK), we study a general framework for yield farming strategies with empirical analysis. First, we summarize the fundamentals of yield farming by focusing on the protocols and tokens used by aggregators. We then examine the sources of yield and translate those into three example yield farming strategies, followed by the simulations of yield farming performance, based on these strategies. We further compare four major yield aggregrators -- Idle, Pickle, Harvest and Yearn -- in the ecosystem, along with brief introductions of others. We systematize their strategies and revenue models, and conduct an empirical analysis with on-chain data from example vaults, to find a plausible connection between data anomalies and historical events. Finally, we discuss the benefits and risks of yield aggregators.