Copyright law focuses on whether a new work is "substantially similar" to an existing one, but generative AI can closely imitate style without copying content, a capability now central to ongoing litigation. We argue that existing definitions of infringement are ill-suited to this setting and propose a new criterion: a generative AI output infringes on an existing work if it could not have been generated without that work in its training corpus. To operationalize this definition, we model generative systems as closure operators mapping a corpus of existing works to an output of new works. AI generated outputs are \emph{permissible} if they do not infringe on any existing work according to our criterion. Our results characterize structural properties of permissible generation and reveal a sharp asymptotic dichotomy: when the process of organic creations is light-tailed, dependence on individual works eventually vanishes, so that regulation imposes no limits on AI generation; with heavy-tailed creations, regulation can be persistently constraining.

Obtaining reliable inferences with traditional difference-in-differences (DiD) methods can be difficult. Problems can arise when both outcomes and errors are serially correlated, when there are few clusters or few treated clusters, when cluster sizes vary greatly, and in various other cases. In recent years, recognition of the ``staggered adoption'' problem has shifted the focus away from inference towards consistent estimation of treatment effects. One of the most popular new estimators is the CSDID procedure of Callaway and Sant'Anna (2021). We find that the issues of over-rejection with few clusters and/or few treated clusters are at least as severe for CSDID as for traditional DiD methods. We also propose using a cluster jackknife for inference with CSDID, which simulations suggest greatly improves inference. We provide software packages in Stata csdidjack and R didjack to calculate cluster-jackknife standard errors easily.

We analyze strategic communication when advice is generated by a reinforcement-learning algorithm rather than by a fully rational sender. Building on the cheap-talk framework of Crawford and Sobel (1982), an advisor adapts its messages based on payoff feedback, while a decision maker best-responds. We provide a theoretical analysis of the long-run communication outcomes induced by such reward-driven adaptation. With aligned preferences, we establish that learning robustly leads to informative communication even from uninformative initial policies. With misaligned preferences, no stable outcome exists; instead, learning generates cycles that sustain highly informative communication and payoffs exceeding those of any static equilibrium.

Assessing an individual's contribution within a team remains a fundamental challenge across many domains, particularly when recognition for collective achievements is limited to only a few members. This issue is especially important in professional road cycling, where personal success depends on both individual talent and group effort. Existing points-based ranking systems tend to disproportionately reward high-scoring team leaders while undervaluing domestiques - riders who sacrifice personal success to support group performance. To better capture a rider's impact on the team, we propose a weighted measure of cycling productivity that factors in race points, a redistribution metric, and an adapted version of the CoScore formula. This formula assesses an individual's productivity relative to their teammates' performance. Using data from the 2023 season, we show that our approach offers a comprehensive evaluation of professional cyclists, addressing key limitations of existing ranking systems.

Optimal transport is the problem of designing a joint distribution for two random variables with fixed marginals. In virtually the entire literature on this topic, the objective is to minimize expected cost. This paper is the first to study a variant in which the goal is to minimize a quantile of the cost, rather than the mean. For the semidiscrete setting, where one distribution is continuous and the other is discrete, we derive a complete characterization of the optimal transport plan and develop simulation-based methods to efficiently compute it. One particularly novel aspect of our approach is the efficient computation of a tie-breaking rule that preserves marginal distributions. In the context of geographical partitioning problems, the optimal plan is shown to produce a novel geometric structure.

Televised debates between presidential candidates are often regarded as the exemplar of persuasive communication. Yet, recent evidence from Le Pennec and Pons (2023) indicates that they may not sway voters as strongly as popular belief suggests. We revisit their findings through the lens of the persuasion rate and introduce a robust framework that does not require exogenous treatment, parallel trends, or credible instruments. Instead, we leverage plausible monotonicity assumptions to partially identify the persuasion rate and related parameters. Our results reaffirm that the sharp upper bounds on the persuasive effects of TV debates remain modest.

We consider estimation of large approximate factor models in high-dimensional panels of stationary time series using Principal Component Analysis (PCA). We review the key results establishing the necessary and sufficient conditions for consistency and asymptotic normality of the estimators. We compare two equivalent approaches to PCA and present the asymptotic properties associated with each formulation. Special emphasis is placed on identification, where we discuss the restrictions required to uniquely determine factors and loadings and examine their consequences for statistical inference.

We present a collaboration ring model -- a network of players playing the prisoner's dilemma game and collaborating among the nearest neighbours by forming coalitions. The microscopic stochastic updating of the players' strategies are driven by their innate nature of seeking selfish gains and shared intentionality. Cooperation emerges in such a structured population through non-equilibrium phase transitions driven by propensity of the players to collaborate and by the benefit that a cooperator generates. The robust results are qualitatively independent of number of neighbours and collaborators.

Combining forecasts from multiple experts often yields more accurate results than relying on a single expert. In this paper, we introduce a novel regularized ensemble method that extends the traditional linear opinion pool by leveraging both current forecasts and historical performances to set the weights. Unlike existing approaches that rely only on either the current forecasts or past accuracy, our method accounts for both sources simultaneously. It learns weights by minimizing the variance of the combined forecast (or its transformed version) while incorporating a regularization term informed by historical performances. We also show that this approach has a Bayesian interpretation. Different distributional assumptions within this Bayesian framework yield different functional forms for the variance component and the regularization term, adapting the method to various scenarios. In empirical studies on Walmart sales and macroeconomic forecasting, our ensemble outperforms leading benchmark models both when experts' full forecasting histories are available and when experts enter and exit over time, resulting in incomplete historical records. Throughout, we provide illustrative examples that show how the optimal weights are determined and, based on the empirical results, we discuss where the framework's strengths lie and when experts' past versus current forecasts are more informative.

It is well established that the US prewar output was more volatile and less shock persistent than the postwar output. This is often attributed to the data interpolation employed to construct the prewar series. Our analytical results, however, indicate that commonly used linear interpolation has the opposite effect on shock persistence and volatility of a series - it increases shock persistence and reduces volatility. The surprising implication of this finding is that the actual differences between the volatility and shock persistence of the prewar and postwar output series are likely greater than the existing literature recognizes, and interpolation has dampened rather than magnified this difference. Consequently, the view that postwar output was more stable than prewar output because of the effectiveness of the postwar stabilization policies and institutional changes has considerable merit. Our results hold for parsimonious stationary and nonstationary time series commonly used to model macroeconomic time series

Japan's population is shrinking, the share of working-age people is falling, and the number of elderly is growing fast. These trends squeeze public finances from both sides--fewer people paying taxes and more people drawing on pensions and healthcare. Policy discussions often focus on one fix at a time, such as raising taxes, reforming pensions, or boosting productivity. However, these levers interact with each other through feedback loops and time delays that are not yet well understood. This study builds and calibrates an integrated system dynamics model that connects demographics, labor supply, economic output, and public finance to explore two questions: (RQ1) What feedback structure links demographic change to fiscal outcomes, and how do different policy levers work through that structure? (RQ2) Which combinations of policies can stabilize key fiscal indicators within a meaningful timeframe? The model, grounded in official statistics, tracks historical trends reasonably well. Policy experiments show that productivity improvements and controlling per-person costs offer the most effective near-term relief, because they act quickly through revenue and spending channels. In contrast, raising fertility actually worsens the fiscal picture in the medium term, since it takes decades for newborns to grow up and join the workforce. A combined scenario pairing moderate productivity gains with moderate cost control nearly eliminates the deficit by 2050. These findings underscore the importance of timing when evaluating demographic policy. Stabilizing finances within a practical timeframe requires levers that improve the budget directly, rather than those that work through slow demographic channels. The model serves as a transparent testing ground for designing time-aware fiscal policy packages in aging, high-debt economies.

Standard models of bounded rationality typically assume agents either possess accurate knowledge of the population's reasoning abilities (Cognitive Hierarchy) or hold dogmatic, degenerate beliefs (Level-$k$). We introduce the ``Connected Minds'' model, which unifies these frameworks by integrating iterative reasoning with a parameterized network bias. We posit that agents do not observe the global population; rather, they observe a sample biased by their network position, governed by a locality parameter $p$ representing algorithmic ranking, social homophily, or information disclosure. We show that this parameter acts as a continuous bridge: the model collapses to the myopic Level-$k$ recursion as networks become opaque ($p \to 0$) and recovers the standard Cognitive Hierarchy model under full transparency ($p=1$). Theoretically, we establish that network opacity induces a \emph{Sophisticated Bias}, causing agents to systematically overestimate the cognitive depth of their opponents while preserving the log-concavity of belief distributions. This makes $p$ an actionable lever: a planner or platform can tune transparency, globally or by segment (a personalized $p_k$), to shape equilibrium behavior. From a mechanism design perspective, we derive the \emph{Escalation Principle}: in games of strategic complements, restricting information can maximize aggregate effort by trapping agents in echo chambers where they compete against hallucinated, high-sophistication peers. Conversely, we identify a \emph{Transparency Reversal} for coordination games, where maximizing network visibility is required to minimize variance and stabilize outcomes. Our results suggest that network topology functions as a cognitive zoom lens, determining whether agents behave as local imitators or global optimizers.

We develop an empirical Bayes (EB) G-modeling framework for short-panel linear models with nonparametric prior for the random intercepts, slopes, dynamics, and non-spherical error variances. We establish identification and consistency of the nonparametric maximum likelihood estimator (NPMLE) under general conditions, and provide low-level sufficient conditions for several models of empirical interest. Conditions for regret consistency of the EB estimators are also established. The NPMLE is computed using a Wasserstein-Fisher-Rao gradient flow algorithm adapted to panel regressions. Using data from the Panel Study of Income Dynamics, we find that the slope coefficient for potential experience is substantially heterogeneous and negatively correlated with the random intercept, and that error variances and autoregressive coefficients vary significantly across individuals. The EB estimates reduce mean squared prediction errors relative to individual maximum likelihood estimates.

Many studies exploit variation in the timing of policy adoption across units as an instrument for treatment. This paper formalizes the underlying identification strategy as an instrumented difference-in-differences (DID-IV). In this design, a Wald-DID estimand, which scales the DID estimand of the outcome by the DID estimand of the treatment, captures the local average treatment effect on the treated (LATET). We extend the canonical DID-IV design to multiple period settings with the staggered adoption of the instrument across units. Moreover, we propose a credible estimation method in this design that is robust to treatment effect heterogeneity. We illustrate the empirical relevance of our findings, estimating returns to schooling in the United Kingdom. In this application, the two-way fixed effects instrumental variable regression, the conventional approach to implement DID-IV designs, yields a negative estimate. By contrast, our estimation method indicates a substantial gain from schooling.

A goodness-of-fit index measures the consistency of consumption data with a given model of utility-maximization. We show that for the class of well-behaved (i.e., continuous and increasing) utility functions there is no goodness-of-fit index that is continuous and accurate, where the latter means that a perfect score is obtained if and only if a dataset can be rationalized by a well-behaved utility function. While many standard goodness-of-fit indices are inaccurate we show that these indices are (in a sense we make precise) essentially accurate. Goodness-of-fit indices are typically generated by loss functions and we find that standard loss functions usually do not yield a best-fitting utility function when they are minimized. Nonetheless, welfare comparisons can be made by working out a robust preference relation from the data.