We study the distribution of envy in random matching markets under the Deferred Acceptance (DA) algorithm. Using tools from applied probability, we compute the expected number of proposing agents whom nobody envies and those who envy nobody. We obtain an exact finite-market expression for the former, based on a connection with the coupon collector problem, and asymptotic bounds for the latter. To put these quantities into perspective, we compare them to their counterparts under Random Serial Dictatorship (RSD): while RSD assigns a constant fraction of agents to their top choice, both DA and RSD leave exactly $H_n$ proposing agents unenvied in expectation. Our results show that these clearly unimprovable proposing agents constitute a vanishing fraction of the market.

This survey (re)introduces reinforcement learning methods to economists. The curse of dimensionality limits how far exact dynamic programming can be effectively applied, forcing us to rely on suitably "small" problems or our ability to convert "big" problems into smaller ones. While this reduction has been sufficient for many classical applications, a growing class of economic models resists such reduction. Reinforcement learning algorithms offer a natural, sample-based extension of dynamic programming, extending tractability to problems with high-dimensional states, continuous actions, and strategic interactions. I review the theory connecting classical planning to modern learning algorithms and demonstrate their mechanics through simulated examples in pricing, inventory control, strategic games, and preference elicitation. I also examine the practical vulnerabilities of these algorithms, noting their brittleness, sample inefficiency, sensitivity to hyperparameters, and the absence of global convergence guarantees outside of tabular settings. The successes of reinforcement learning remain strictly bounded by these constraints, as well as a reliance on accurate simulators. When guided by economic structure, reinforcement learning provides a remarkably flexible framework. It stands as an imperfect, but promising, addition to the computational economist's toolkit. A companion survey (Rust and Rawat, 2026b) covers the inverse problem of inferring preferences from observed behavior. All simulation code is publicly available.

The foundation model industry exhibits unprecedented concentration in critical inputs: semiconductors, energy infrastructure, elite talent, capital, and training data. Despite extensive sectoral analyses, no comprehensive framework exists for assessing overall industrial vulnerability. We develop the Artificial Intelligence Industrial Vulnerability Index (AIIVI) grounded in O-Ring production theory, recognizing that foundation model production requires simultaneous availability of non-substitutable inputs. Given extreme data opacity and rapid technological evolution, we implement a validated human-in-the-loop methodology using large language models to systematically extract indicators from dispersed grey literature, with complete human verification of all outputs. Applied to six state-of-the-art foundation model developers, AIIVI equals 0.82, indicating extreme vulnerability driven by compute infrastructure (0.85) and energy systems (0.90). While industrial policy currently emphasizes semiconductor capacity, energy infrastructure represents the emerging binding constraint. This methodology proves applicable to other fast-evolving, opaque industries where traditional data sources are inadequate.

We provide the first asymptotic analysis of the Boston Mechanism under equilibrium play in random markets. We provide two results. First, while 63\% of students receive their first preference under truthful reporting-outperforming any other known mechanism in the literature-this rate converges to zero in any Nash equilibrium of the corresponding preference revelation game as the market size grows. Second, we show there exists a Nash equilibrium where the average student receives a dramatically inferior assignment: in markets with 1,000 students, the average placement shifts from the 7th choice (under truthfulness) to the 145th choice, representing a change from logarithmic to nearly linear average rank.

As the development and use of artificial intelligence (AI) continues to grow, policymakers are increasingly grappling with the question of how to regulate this technology. The most far-reaching international initiative is the European Union (EU) AI Act, which aims to establish the first comprehensive, binding framework for regulating AI. In this article, we offer the first systematic analysis of non-state actor preferences toward international regulation of AI, focusing on the case of the EU AI Act. Theoretically, we develop an argument about the regulatory preferences of business actors and other non-state actors under varying conditions of AI sector competitiveness. Empirically, we test these expectations using data from public consultations on European AI regulation. Our findings are threefold. First, all types of non-state actors express concerns about AI and support regulation in some form. Second, there are nonetheless significant differences across actor types, with business actors being less concerned about the downsides of AI and more in favor of lax regulation than other non-state actors. Third, these differences are more pronounced in countries with stronger commercial AI sectors. Our findings shed new light on non-state actor preferences toward AI regulation and point to challenges for policymakers balancing competing interests in society.

A model-free measure of Granger causality in expectiles is proposed, generalizing the traditional mean-based measure to arbitrary positions of the conditional distribution. Expectiles are the only law-invariant risk measures that are both coherent and elicitable, making them particularly well-suited for studying distributional Granger causality where risk quantification and forecast evaluation are both relevant. Based on this measure, a test is developed using M-vine copula models that accounts for multivariate Granger causality with $d+1$ series under non-linear and non-Gaussian dependence, without imposing parametric assumptions on the joint distribution. Strong consistency of the test statistic is established under some regularity conditions. In finite samples, simulations show accurate size control and power increasing with sample size. A key advantage is the joint testing capability: causal relationships invisible to pairwise tests can be detected, as demonstrated both theoretically and empirically. Two applications to international stock market indices at the global and Asian regional level illustrate the practical relevance of the proposed framework.

We study how a first heart-failure hospitalization, an adverse health shock, changes patients' care, and whether a nurse-led chronic-care program sustains those post-shock investments. Using linked population-wide administrative records from Italy's Romagna Local Health Authority (2017-2023), we anchor event time at each patient's first CHF admission and exploit staggered timing to estimate dynamic effects. The shock triggers a sharp post-discharge surge: beta-blocker adherence, cardiology follow-up, and echocardiography rise immediately, while emergency-room use spikes just before admission and then stabilizes. We then estimate the incremental impact of enrollment in the Nurse-led Program for Chronic Patients (NPCP) using the interaction-weighted event-study estimator for staggered adoption. Under conventional difference-in-differences inference, NPCP strengthens long-run preventive engagement, with little detectable change in emergency-room use. HonestDiD sensitivity analysis indicates these gains are economically meaningful but not statistically definitive under modest departures from parallel trends.

Single-index models or time-to-event models are frequently applied in empirical research. These models are non-identifiable in presence of unknown (dependent) censoring or competing risks and do not give informative results in empirical analysis unless rather strong, non-testable restrictions hold. Little is known, whether the known robustness properties of the single-index model carry over to models with dependent censoring or competing risks. This paper shows that the ratio of partial covariate effects on the margins is identifiable in nonparametric models with unknown dependent censoring or nonparametric competing risks models with nonparametric dependence structure, provided an exclusion restriction holds. Commonly used (semi)parametric models for the margin and independent censoring, such as Cox proportional hazards, accelerated failure time or proportional odds models, can be used to obtain relative covariate effects despite their misspecified censoring mechanism. Several nonparametric estimators for the general model are introduced and their numerical properties are studied.

This paper examines how regulatory interventions in high-frequency financial markets affect price discovery. We focus on Breaking news, where dynamic circuit breakers trigger trading halts immediately after the release of macroeconomic fundamentals. Within a high-frequency signal-in-noise model, we show that triggering rules complicate statistical inference for the price impact of news, rendering conventional non-parametric jump estimators inconsistent. Building on this insight, we develop a regression-based test for fundamental pricing that accounts for non-vanishing transition times. The test compares transition price changes to efficient jumps implied by observable factors. Our empirical analysis of CME E-mini S\&P 500 futures shows that Breaking news are associated with systematic deviations from fundamental pricing, predominantly in the form of overshooting. Our findings highlight a regulatory trade-off: the appeal of simple and transparent circuit breaker rules must be weighed against their cost of preventing fundamentals from being priced contemporaneously, thereby creating adverse incentives and introducing distortions.

We study Cressie Read power divergence (CRPD) estimation for moment based models, focusing on finite sample behavior. While generalized empirical likelihood estimators, dual to CRPD, are known to outperform generalized method of moments estimators in small to moderate samples, the power parameter is typically chosen arbitrarily by the researcher, serving mainly as an index. We interpret it as a hyperparameter that determines the loss function and governs the learning procedure, shaping the curvature of the objective and influencing finite sample performance. Using second order asymptotics, we show that it affects both the structural estimator and the associated Lagrange multipliers, governing robustness, bias, and sensitivity to sampling variation. Monte Carlo simulations illustrate how estimator performance varies with the choice of the power parameter and underlying distributional features, with implications for second order bias and coverage distortion. An empirical illustration based on Owen (2001)s classical example highlights the practical relevance of tuning the power parameter.

The rapid expansion of Artificial Intelligence is hindered by a fundamental friction in data markets: the value-privacy dilemma, where buyers cannot verify a dataset's utility without inspection, yet inspection may expose the data (Arrow's Information Paradox). We resolve this challenge by introducing the Trustworthy Influence Protocol (TIP), a privacy-preserving framework that enables prospective buyers to quantify the utility of external data without ever decrypting the raw assets. By integrating Homomorphic Encryption with gradient-based influence functions, our approach allows for the precise, blinded scoring of data points against a buyer's specific AI model. To ensure scalability for Large Language Models (LLMs), we employ low-rank gradient projections that reduce computational overhead while maintaining near-perfect fidelity to plaintext baselines, as demonstrated across BERT and GPT-2 architectures. Empirical simulations in healthcare and generative AI domains validate the framework's economic potential: we show that encrypted valuation signals achieve a high correlation with realized clinical utility and reveal a heavy-tailed distribution of data value in pre-training corpora where a minority of texts drive capability while the majority degrades it. These findings challenge prevailing flat-rate compensation models and offer a scalable technical foundation for a meritocratic, secure data economy.

This study clarifies the relationship between Riesz regression [Chernozhukov et al., 2021] and density ratio estimation (DRE) in causal inference problems, such as average treatment effect estimation. We first show that the Riesz representer can be written as a signed density ratio and then demonstrate that the Riesz regression objective coincides with the least-squares importance fitting criterion [Kanamori et al., 2009]. Although Riesz regression applies to a broad class of representer estimation problems, this equivalence with DRE allows us to transfer existing DRE results, including convergence rate analyses, generalizations based on Bregman divergence minimization, and regularization techniques for flexible models such as neural networks.

An agent is a misspecified Bayesian if she updates her belief using Bayes' rule given a subjective, possibly misspecified model of her signals. This paper shows that a belief sequence is consistent with misspecified Bayesian updating if and only if the set of posteriors admits a countable partition such that the prior contains a grain of the conditional average posterior on each cell. The condition imposes essentially no restrictions on posteriors given a full-support prior over a finite state space and reduces to a support inclusion condition on compact state spaces under mild regularity assumptions. However, it rules out posterior beliefs with heavier tails than the prior on unbounded state spaces. In Gaussian environments, it implies that posterior uncertainty cannot exceed prior uncertainty. The results delineate the boundary between updating rules that are observationally equivalent to Bayesian updating under misspecification and genuinely non-Bayesian rules. As an application, the paper shows that diagnostic expectations are consistent with misspecified Bayesianism, whereas some parameterizations of smooth diagnostic expectations are not.

Empirical instrumental variables (IV) studies often report separate results based on low-dimensional instruments and many base instruments. This paper proposes a combination test that integrates these commonly reported statistics. The test linearly combines a cluster-robust Wald statistic based on low-dimensional IVs with leave-one-cluster-out Lagrangian Multiplier (LM) and Anderson-Rubin (AR) statistics constructed from many IVs. We establish joint asymptotic normality and asymptotic optimality of the proposed test. The procedure yields costless efficiency improvements, automatically adapts to weak identification of many instruments, and is accompanied by a practical rule of thumb for assessing efficiency gains.

Generative AI (GenAI) is rapidly transforming knowledge work, yet its implications for organizational hierarchies remain poorly understood. Unlike earlier automation technologies, GenAI can both perform tasks autonomously and assist human workers, while its intrinsic fallibility, the tendency to produce confident but incorrect outputs, demands continuous human oversight. We develop a theoretical model to study how GenAI reshapes workforce composition and organizational structure in knowledge-based hierarchies. Our analysis highlights two deployment dimensions, namely mode (automation vs.\ augmentation) and location (worker vs.\ expert layer), which generate a 2X2 design space whose organizational implications are not predicted by traditional technology adoption theories. We obtain three main findings. First, GenAI's effect on entry-level skill requirements is critically mode-dependent. Worker-level automation leads firms to hire fewer but more skilled workers who validate AI outputs and limit costly escalation to experts. Worker-level augmentation, by contrast, expands workers' effective capability, allowing firms to relax entry-level knowledge requirements while sustaining performance. The decline in junior employment documented in recent studies therefore reflects deployment choices favoring automation over augmentation, not an inevitable consequence of GenAI itself. Second, expert-level deployment uniformly lowers entry-level skill requirements, regardless of whether GenAI automates or augments. By expanding experts' capacity to support downstream workers, it enables organizations to employ a broader base of less specialized workers, thereby broadening entry-level access to knowledge work. Third, organizational structure evolves non-monotonically as GenAI improves: across all four deployment architectures, the span of control initially contracts before eventually expanding.

We show that the higher-order terms and interactions of the common sparse linear factors are significantly priced in the cross-section of equity returns. A higher-order model with only a small number of selected higher-order terms from six widely used factors outperforms traditional benchmarks both in-sample and out-of-sample. It also substantially reduces the alphas of the extensive factor zoo, suggesting that the pricing power of many zoo factors is attributable to their exposure to higher-order terms of common linear factors. We identify and rank the most relevant higher-order terms by developing a forward selection Fama-MacBeth procedure.