This paper examines the effects of the 2019 universalization of Mexico's Social Pension Program (PAM), one of the country's most expansive and politically salient social programs. The reform simultaneously increased the cash transfer and extended eligibility to all individuals aged 65 and over, regardless of income or contributory pension status. Using nationally representative data from the ENIGH and a triple-differences (DDD) identification strategy, we estimate the causal effect of the universalization on poverty and labor market outcomes. Our empirical approach exploits variation across time (pre- and post-reform), age (eligible vs. ineligible), and pension scheme status (non-contributory vs. contributory), allowing us to separate the effects of expanded eligibility from those of increased benefit levels. We find strong increases in take-up rates and no significant change in overall poverty rates, suggesting that many new beneficiaries were not economically vulnerable. However, we document a surprising increase in extreme poverty, concentrated among low-income elderly who responded to the reform by exiting the labor force. This reduction in labor supply, driven by a significant drop in employment among individuals in the bottom income quartile, suggests that the pension acted as a substitute for labor income rather than a supplement. Taken together, the results highlight the trade-offs inherent in universal pension programs: while broader access reduces administrative exclusion, extending transfers to economically secure individuals may dilute redistributive impacts and generate behavioral responses that offset potential welfare gains.

Industrial symbiosis fosters circularity by enabling firms to repurpose residual resources, yet its emergence is constrained by socio-spatial frictions that shape costs, matching opportunities, and market efficiency. Existing models often overlook the interaction between spatial structure, market design, and adaptive firm behavior, limiting our understanding of where and how symbiosis arises. We develop an agent-based model where heterogeneous firms trade byproducts through a spatially embedded double-auction market, with prices and quantities emerging endogenously from local interactions. Leveraging reinforcement learning, firms adapt their bidding strategies to maximize profit while accounting for transport costs, disposal penalties, and resource scarcity. Simulation experiments reveal the economic and spatial conditions under which decentralized exchanges converge toward stable and efficient outcomes. Counterfactual regret analysis shows that sellers' strategies approach a near Nash equilibrium, while sensitivity analysis highlights how spatial structures and market parameters jointly govern circularity. Our model provides a basis for exploring policy interventions that seek to align firm incentives with sustainability goals, and more broadly demonstrates how decentralized coordination can emerge from adaptive agents in spatially constrained markets.

Current macroeconomic models with agent heterogeneity can be broadly divided into two main groups. Heterogeneous-agent general equilibrium (GE) models, such as those based on Heterogeneous Agent New Keynesian (HANK) or Krusell-Smith (KS) approaches, rely on GE and 'rational expectations', somewhat unrealistic assumptions that make the models very computationally cumbersome, which in turn limits the amount of heterogeneity that can be modelled. In contrast, agent-based models (ABMs) can flexibly encompass a large number of arbitrarily heterogeneous agents, but typically require the specification of explicit behavioural rules, which can lead to a lengthy trial-and-error model-development process. To address these limitations, we introduce MARL-BC, a framework that integrates deep multi-agent reinforcement learning (MARL) with real business cycle (RBC) models. We demonstrate that MARL-BC can: (1) recover textbook RBC results when using a single agent; (2) recover the results of the mean-field KS model using a large number of identical agents; and (3) effectively simulate rich heterogeneity among agents, a hard task for traditional GE approaches. Our framework can be thought of as an ABM if used with a variety of heterogeneous interacting agents, and can reproduce GE results in limit cases. As such, it is a step towards a synthesis of these often opposed modelling paradigms.

We study fairness-accuracy tradeoffs when a single predictive model must serve multiple demographic groups. A useful tool for understanding this tradeoff is the fairness-accuracy (FA) Pareto frontier, which characterizes the set of models that cannot be improved in either fairness or accuracy without worsening the other. While characterizing the FA frontier requires full knowledge of the data distribution, we focus on the finite-sample regime, quantifying how well a designer can approximate any point on the frontier from limited data and bounding the worst-case gap. In particular, we derive worst-case-optimal estimators that depend on the designer's knowledge of the covariate distribution. For each estimator, we characterize how finite-sample effects asymmetrically impact each group's welfare and identify optimal sample allocation strategies. Finally, we provide uniform finite-sample bounds for the entire FA frontier, yielding confidence bands that quantify the reliability of welfare comparisons across alternative fairness-accuracy tradeoffs.

This paper proposes a nonparametric test of pairwise independence of one random variable from a large pool of other random variables. The test statistic is the maximum of several Chatterjee's rank correlations and critical values are computed via a block multiplier bootstrap. We show in simulations that other popular tests based on distance covariances do not necessarily control size under this null. Our test, on the other hand, is shown to asymptotically control size uniformly over a large class of data-generating processes, even when the number of variables is much larger than sample size. The test is consistent against any fixed alternative. It can be combined with a stepwise procedure for selecting those variables from the pool that violate independence, while controlling the family-wise error rate. All formal results leave the dependence among variables in the pool completely unrestricted. In simulations, we find that our test is typically more powerful than competing methods (in settings where they are valid), particularly in high-dimensional scenarios or when there is dependence among variables in the pool.

Improving social welfare is a complex challenge requiring policymakers to optimize objectives across multiple time horizons. Evaluating the impact of such policies presents a fundamental challenge, as those that appear suboptimal in the short run may yield significant long-term benefits. We tackle this challenge by analyzing the long-term dynamics of two prominent policy frameworks: Rawlsian policies, which prioritize those with the greatest need, and utilitarian policies, which maximize immediate welfare gains. Conventional wisdom suggests these policies are at odds, as Rawlsian policies are assumed to come at the cost of reducing the average social welfare, which their utilitarian counterparts directly optimize. We challenge this assumption by analyzing these policies in a sequential decision-making framework where individuals' welfare levels stochastically decay over time, and policymakers can intervene to prevent this decay. Under reasonable assumptions, we prove that interventions following Rawlsian policies can outperform utilitarian policies in the long run, even when the latter dominate in the short run. We characterize the exact conditions under which Rawlsian policies can outperform utilitarian policies. We further illustrate our theoretical findings using simulations, which highlight the risks of evaluating policies based solely on their short-term effects. Our results underscore the necessity of considering long-term horizons in designing and evaluating welfare policies; the true efficacy of even well-established policies may only emerge over time.

Revised proofs of Kenneth Arrow's impossibility theorem have been presented in prose form, incorporating novel ideas such as decisive sets and pivotal voters. This study develops another approach to proving the theorem. Using a proof calculus in formal logic, we construct a proof with a full mathematical representation. While previous proofs emphasize intuitive accessibility, this one focuses on meticulous derivation and reveals the global structure of the social welfare function central to the theorem.

Sensitivity analysis is widely used to assess the robustness of causal conclusions in observational studies, yet its interaction with the structure of measured covariates is often overlooked. When latent confounders cannot be directly adjusted for and are instead controlled using proxy variables, strong associations between exposure and measured proxies can amplify sensitivity to residual confounding. We formalize this phenomenon in linear regression settings by showing that a simple ratio involving the exposure model coefficient and residual exposure variance provides an observable measure of this increased sensitivity. Applying our framework to smoking and lung cancer, we document how growing socioeconomic stratification in smoking behavior over time leads to heightened sensitivity to unmeasured confounding in more recent data. These results highlight the importance of multicollinearity when interpreting sensitivity analyses based on proxy adjustment.

We develop a decision-theoretic model of human-AI interaction to study when AI assistance improves or impairs human decision-making. A human decision-maker observes private information and receives a recommendation from an AI system, but may combine these signals imperfectly. We show that the effect of AI assistance decomposes into two main forces: the marginal informational value of the AI beyond what the human already knows, and a behavioral distortion arising from how the human uses the AI's recommendation. Central to our analysis is a micro-founded measure of informational overlap between human and AI knowledge. We study an empirically relevant form of imperfect decision-making -- correlation neglect -- whereby humans treat AI recommendations as independent of their own information despite shared evidence. Under this model, we characterize how overlap and AI capabilities shape the Human-AI interaction regime between augmentation, impairment, complementarity, and automation, and draw key insights.

In many consumer electronics and appliance markets, manufacturers sell products through competing retailers while simultaneously relying on take-back programs to recover used items for remanufacturing. Designing such programs is challenging when firms compete on prices and consumers differ in their willingness to return products. Motivated by these settings, this paper develops a game theoretic framework to analyze pricing and take-back decisions in a dual-channel closed loop supply chain (CLSC) with two competing manufacturers and two competing retailers. Manufacturers act as Stackelberg leaders, simultaneously determining wholesale prices and consumer take-back bonuses, while retailers engage in Nash competition over retail prices. The model integrates three key elements: (i) segmented linear demand with cross-price effects, (ii) deterministic product returns, and (iii) an inertia responsiveness allocation mechanism governing the distribution of returned products between manufacturers. Closed form Nash equilibria are derived for the retailer subgame, along with symmetric Stackelberg equilibria for manufacturers. We derive a feasibility threshold for take-back incentives, identifying conditions under which firms optimally offer positive bonuses to consumers. The results further demonstrate that higher remanufacturing value or return rates lead the manufacturers to lower wholesale prices in order to expand sales and capture additional return volumes, while high consumer inertia weakens incentives for active collection. Numerical experiments illustrate and reinforce the analytical results, highlighting how consumer behavior, market structure and product substitutability influence prices, bonuses, and return volumes. Overall, the study provides managerial insights for designing effective take-back programs and coordinating pricing decisions in competitive circular supply chains.

Among two-candidate elections that treat the candidates symmetrically and never result in a tie, which voting rules are fair? A natural requirement is that each voter exerts an equal influence over the outcome, i.e., is equally likely to swing the election one way or the other. A voter's influence has been formalized in two canonical ways: the Shapley-Shubik (1954) index and the Banzhaf (1964) index. We consider both indices, and ask: Which electorate sizes admit a fair voting rule (under the respective index)? For an odd number $n$ of voters, simple majority rule is an example of a fair voting rule. However, when $n$ is even, fair voting rules can be challenging to identify, and a diverse literature has studied this problem under different notions of fairness. Our main results completely characterize which values of $n$ admit fair voting rules under the two canonical indices we consider. For the Shapley-Shubik index, a fair voting rule exists for $n>1$ if and only if $n$ is not a power of $2$. For the Banzhaf index, a fair voting rule exists for all $n$ except $2$, $4$, and $8$. Along the way, we show how the Shapley-Shubik and Banzhaf indices relate to the winning coalitions of the voting rule, and compare these indices to previously considered notions of fairness.

Appropriate decisions depend on information gathered beforehand, yet such information is often obtained through intermediaries with biased preferences. Motivated by settings such as testing and recertification in organ transplantation, we study the problem faced by a decision-maker who can only access costly information through an agent with misaligned preferences. In a dynamic framework with exogenous decision timing, we ask how requests for verifiable information (evidence) should be scheduled and their implications for the quality of attained choices. When the agent's incentives are ignored, evidence requests do not condition on previously reported information. However, such policies may be susceptible to strategic manipulation by the agent. We show that, in these cases, optimal requests should be biased: additional evidence is more likely to be sought when previous reports favor the agent's preferred outcome.

Forecasting presents a complex estimation challenge, as it involves balancing multiple, often conflicting, priorities and objectives. Conventional forecast optimization methods typically emphasize a single metric--such as minimizing the mean squared error (MSE)--which may neglect other crucial aspects of predictive performance. To address this limitation, the recently developed Smooth Sign Accuracy (SSA) framework extends the traditional MSE approach by simultaneously accounting for sign accuracy, MSE, and the frequency of sign changes in the predictor. This addresses a fundamental trade-off--the so-called accuracy-smoothness (AS) dilemma--in prediction. We extend this approach to the multivariate M-SSA, leveraging the original criterion to incorporate cross-sectional information across multiple time series. As a result, the M-SSA criterion enables the integration of various design objectives related to AS forecasting performance, effectively generalizing conventional MSE-based metrics. To demonstrate its practical applicability and versatility, we explore the application of the M-SSA in three primary domains: forecasting, real-time signal extraction (nowcasting), and smoothing. These case studies illustrate the framework's capacity to adapt to different contexts while effectively managing inherent trade-offs in predictive modelling.

Every year, over one million EU students choose a secondary school track based on teacher recommendations, yet little evidence shows this yields optimal assignments. Using Dutch data, we examine whether access to standardized test scores improves recommendation quality. We develop a Principal-Stratification metric in a quasi-randomized setting, conduct a welfare analysis that flexibly weights short- and long-term losses, and assess principal fairness by examining whether test-score access affects equity across protected attributes. Results are robust to replacing the Exclusion Restriction assumption underlying our main identification strategy with alternative assumptions. Allowing recommendation upgrades when test scores exceed expectations increases successful placement in more demanding tracks by at least 6%, while misplacing 7% of weaker students. Only unrealistically high weights on short-term losses would justify banning such upgrades. Test-score access also yields fairer recommendations for immigrant and low-SES students. Our methodology and findings contribute to the literature on algorithm-assisted human decisions.

The external validity of regression discontinuity designs is crucial for informing policy but is rarely examined in applied work. To advance empirical practice, we propose a joint inference procedure for the treatment effect and its local external validity, captured by the treatment effect derivative (TED), within a robust bias correction framework. We further introduce a locally linear treatment effects assumption, which extends the scope of the TED and enables identification and the construction of a uniform confidence band for extrapolated effects. These methods apply to most empirical studies. Empirical illustrations demonstrate their practical usefulness.

We study instrumental variable regression (IVaR) under differential privacy constraints. Classical IVaR methods (like two-stage least squares regression) rely on solving moment equations that directly use sensitive covariates and instruments, creating significant risks of privacy leakage and posing challenges in designing algorithms that are both statistically efficient and differentially private. We propose a noisy two-stage gradient descent algorithm that ensures $ρ$-zero-concentrated differential privacy by injecting carefully calibrated noise into the gradient updates. Our analysis establishes finite-sample convergence rates for the proposed method, showing that the algorithm achieves consistency while preserving privacy. In particular, we derive precise bounds quantifying the trade-off among optimization, privacy, and sampling error. To the best of our knowledge, this is the first work to provide both privacy guarantees and provable convergence rates for instrumental variable regression in linear models. We further validate our theoretical findings with experiments on both synthetic and real datasets, demonstrating that our method offers practical accuracy-privacy trade-offs.

Teamwork is vital in many settings, and it is socially beneficial for teams to cooperate in some situations (``good games'') and not in others (``bad games;'' e.g., those that allow for corruption). A team's cooperation in any given game depends on expectations of cooperation in future iterations of both good and bad games. We identify when sustaining cooperation on good games necessitates cooperation on bad games. We then characterize how a designer should optimally assign workers to teams and teams to tasks that involve varying arrival rates of good and bad games. Our results show how organizational design can be used to promote cooperation while minimizing corruption.

We show that, in large population games, decentralized information aggregation generically corrects for individual-level biases. This establishes a new testable aggregate efficiency benchmark where the behavior of boundedly rational agents mimics that of fully rational agents. However, we find that structural economic forces such as strategic network formation and profit-maximizing platforms can systematically select pathological environments to exploit individuals' biases, thereby causing aggregate inefficiencies. We characterize these inefficiencies in monopoly and labor markets. Our findings therefore suggest that policy should shift focus from correcting individuals' behavior to monitoring and regulating information structures.

We consider the identification of average treatment effects on the treated (ATT) in difference-in-differences (DiD) settings in the presence of endogenous sample selection. We first establish that the conventional DiD estimand generally fails to recover causally meaningful treatment effects, even if selection and treatment assignment are independent. We then partially identify the ATT for individuals whose outcomes would be observed post-treatment under either counterfactual treatment state, and derive sharp bounds on this parameter under different sets of assumptions on the relationship between sample selection and treatment assignment. These identification results are extended to allow for covariates, repeated cross-section data, and two-by-two comparisons in staggered adoption designs. Furthermore, we present identification results for the ATT of three additional empirically relevant latent groups by imposing outcome mean dominance assumptions that have intuitive appeal in applications. Finally, two empirical illustrations demonstrate the approach's usefulness by revisiting (i) the effect of a job training program on earnings and (ii) the effect of a working-from-home policy on employee performance.

Recent advancements in generative AI, such as ChatGPT, have dramatically transformed how people access information. Despite its powerful capabilities, the benefits it provides may not be equally distributed among individuals, a phenomenon referred to as the digital divide. Building upon prior literature, we propose two forms of digital divide in the generative AI adoption process: (i) the learning divide, capturing individuals' heterogeneous abilities to update their perceived utility of ChatGPT; and (ii) the utility divide, representing differences in individuals' actual utility derived from per use of ChatGPT. To evaluate these two divides, we develop a Bayesian learning model that incorporates heterogeneities in both the utility and signal functions. Leveraging a large-scale clickstream dataset, we estimate the model and find significant learning and utility divides across various social characteristics. Interestingly, individuals without any college education, non-white individuals, and those with lower English literacy derive larger utility gains from ChatGPT, yet update their beliefs about its utility at a slower rate. Furthermore, males, younger individuals, and those in occupations with greater exposure to generative AI not only obtain higher utility per use from ChatGPT but also learn about its utility more rapidly. Besides, we document a phenomenon termed the belief trap, wherein users underestimate ChatGPT's utility, opt not to use the tool, and thereby lack new experiences to update their perceptions, leading to continued underutilization. Our simulation further demonstrates that the learning divide can significantly affect the probability of falling into the belief trap, another form of the digital divide in adoption outcomes (i.e., outcome divide); however, offering training programs can alleviate the belief trap and mitigate the divide.

Predicting company growth is a critical yet challenging task because observed dynamics blend an underlying structural growth trend with volatile fluctuations. Here, we propose a Scaling-Theory-Informed Machine Learning (STIML) framework that integrates a scaling-based growth model to capture the mechanism-driven average trend, together with a data-driven forecasting model to learn the residual fluctuations. Using Compustat annual financial statement data (1950--2019) for 31,553 North American companies, we extend the growth model beyond assets to multiple financial indicators, and evaluate STIML against growth model-only and purely data-driven baselines. Across 16 target variables, we show that company growth exhibits a clear separation between trend-driven predictability and fluctuation-driven predictability, with their relative importance depending strongly on company size and volatility. Interpretability analyses further show that STIML captures multivariate dependencies beyond simple autocorrelation, and that macroeconomic variables contribute significantly less to predictive performance on average. Moreover, we find the scaling-based growth model overlooks asymmetric deviations, which instead contain the structured and learnable signals, suggesting a path to refine mechanistic models.

When multiple informative equilibria are possible in a general cheap talk game, how much information can a principal guarantee herself? To answer this question, I define the notion of worst-case implementation-implementation via the worst non-trivial equilibrium of a mechanism. Under this objective, standard full-commitment mechanisms fail, yielding the principal no more than her no-communication payoff. Partial commitment, however, can provide a strict improvement. The possibility of facing a strategic, uncommitted principal disciplines the agent's reporting incentives across all equilibria. I characterize the worst-case optimal mechanism and payoff under weak assumptions on the players' preferences. The optimal mechanism has a simple two-message structure. The agent's messages are polarizing, designed to maximize their strategic impact on the uncommitted principal's actions. If full commitment is interpreted as decision automation, these results highlight a fundamental complementarity between automated and human decision-makers: the presence of a human aligns the agent's incentives to reveal information, while the automated system leverages these informative reports to take accurate actions. This strategic interaction is often overlooked by literature that compares the two based on standalone decision accuracy. Applications of the model include bail-setting automation, fintech lending, delegation, lobbying, and audit design.

When estimating treatment effects with two-way fixed effects (2WFE) models, researchers often use matching as a pre-processing step when the parallel trends assumption is thought to hold conditionally on covariates. Specifically, in a first step, each treated unit is matched to one or more untreated units based on observed time-invariant covariates. In the second step, treatment effects are estimated with a 2WFE regression in the matched sample, reweighting the untreated units by the number of times they are matched. We formally analyze this common practice and highlight two problems. First, when different treatment cohorts enter treatment in different time periods, the post-matching 2WFE estimator that pools all treated cohorts has an asymptotic bias, even when the treatment effect is constant across units and over time. Second, failing to account for the variability introduced by the matching procedure yields invalid standard error estimators, which can be biased upwards or downwards depending on the data generating process. We propose simple post-matching difference-in-differences estimators that compare each treated cohort to the never-treated separately, instead of pooling all treated cohorts. We provide conditions under which these estimators are consistent for well-defined causal parameters, and derive valid standard errors that account for the matching step. We illustrate our results with simulations and with an empirical application.

Algorithms for computing equilibria, optima, and fixed points in nonconvex problems often depend sensitively on practitioner-chosen initial conditions. When uniqueness of a solution is of interest, a common heuristic is to run such algorithms from many randomly selected initial conditions and to interpret repeated convergence to the same output as evidence of a unique solution or a dominant basin of attraction. Despite its widespread use, this practice lacks a formal inferential foundation. We provide a simple probabilistic framework for interpreting such numerical evidence. First, we give sufficient conditions under which an algorithm's terminal output is a measurable function of its initial condition, allowing probabilistic reasoning over outcomes. Second, we provide sufficient conditions ensuring that an algorithm admits only finitely many possible terminal outcomes. While these conditions may be difficult to verify on a case-by-case basis, we give simple sufficient conditions for broad classes of problems under which almost all instances admit only finitely many outcomes (in the sense of prevalence). Standard algorithms such as gradient descent and damped fixed-point iteration applied to sufficiently smooth functions satisfy these conditions. Within this framework, repeated solver runs correspond to independent samples from the induced distribution over outcomes. We adopt a Bayesian approach to infer basin sizes and the probability of solution uniqueness from repeated identical outputs, and we establish convergence rates for the resulting posterior beliefs. Finally, we apply our framework to settings in the existing industrial organization literature, where random-restart heuristics are used. Our results formalize and qualify these arguments, clarifying when repeated convergence provides meaningful evidence for uniqueness and when it does not.

Emerging techniques in computer science make it possible to "brain scan" large language models (LLMs), identify the plain-English concepts that guide their reasoning, and steer them while holding other factors constant. We show that this approach can map LLM-generated economic forecasts to concepts such as sentiment, technical analysis, and timing, and compute their relative importance without reducing performance. We also show that models can be steered to be more or less risk-averse, optimistic, or pessimistic, which allows researchers to correct or simulate biases. The method is transparent, lightweight, and replicable for empirical research in the social sciences.

This paper describes the dependence of market-based statistical moments of returns on statistical moments and correlations of the current and past trade values. We use Markowitz's definition of value weighted return of a portfolio as the definition of market-based average return of trades during the averaging period. Then we derive the dependence of market-based volatility and higher statistical moments of returns on statistical moments, volatilities, and correlations of the current and past trade values. We derive the approximations of the characteristic function and the probability of returns by a finite number q of market-based statistical moments. To forecast market-based average and volatility of returns at horizon T, one should predict the first two statistical moments and correlation of current and past trade values at the same horizon. We discuss the economic reasons that limit the number of predicted statistical moments of returns by the first two. That limits the accuracy of the forecasts of probability of returns by the accuracy of the Gaussian approximations. To improve the reliability of large macroeconomic and market models like BlackRock's Aladdin, JP Morgan, and the U.S. Fed., the developers should use market-based statistical moments of returns.