Artificial intelligence (AI) changes social learning when aggregated outputs become training data for future predictions. To study this, we extend the DeGroot model by introducing an AI aggregator that trains on population beliefs and feeds synthesized signals back to agents. We define the learning gap as the deviation of long-run beliefs from the efficient benchmark, allowing us to capture how AI aggregation affects learning. Our main result identifies a threshold in the speed of updating: when the aggregator updates too quickly, there is no positive-measure set of training weights that robustly improves learning across a broad class of environments, whereas such weights exist when updating is sufficiently slow. We then compare global and local architectures. Local aggregators trained on proximate or topic-specific data robustly improve learning in all environments. Consequently, replacing specialized local aggregators with a single global aggregator worsens learning in at least one dimension of the state.

In the contest design problem, there are $n$ strategic contestants, each of whom decides an effort level. A contest designer with a fixed budget must then design a mechanism that allocates a prize $p_i$ to the $i$-th rank based on the outcome, to incentivize contestants to exert higher costly efforts and induce high-quality outcomes. In this paper, we significantly deepen our understanding of optimal mechanisms under general settings by considering nonconvex objectives in contestants' qualities. Notably, our results accommodate the following objectives: (i) any convex combination of user welfare (motivated by recommender systems) and the average quality of contestants, and (ii) arbitrary posynomials over quality, both of which may neither be convex nor concave. In particular, these subsume classic measures such as social welfare, order statistics, and (inverse) S-shaped functions, which have received little or no attention in the contest literature to the best of our knowledge. Surprisingly, across all these regimes, we show that the optimal mechanism is highly structured: it allocates potentially higher prize to the first-ranked contestant, zero to the last-ranked one, and equal prizes to the all intermediate contestants, i.e., $p_1 \ge p_2 = \ldots = p_{n-1} \ge p_n = 0$. Thanks to the structural characterization, we obtain a fully polynomial-time approximation scheme given a value oracle. Our technical results rely on Schur-convexity of Bernstein basis polynomial-weighted functions, total positivity and variation diminishing property. En route to our results, we obtain a surprising reduction from a structured high-dimensional nonconvex optimization to a single-dimensional optimization by connecting the shape of the gradient sequences of the objective function to the number of transition points in optimum, which might be of independent interest.

The European colonization of sub-Saharan Africa drove a massive shift from indigenous religions to Christianity, yet the channels through which this transformation occurred remain poorly understood. Using a geographic regression discontinuity design at colonial borders in sub-Saharan Africa, I find that Christian adherence is substantially higher under French and Portuguese direct rule than under British indirect rule -- a gap that implies a correspondingly greater persistence of traditional religions where indirect rule prevailed. Neither mission presence nor pre-colonial political centralization can account for the discontinuity. Instead, the evidence points to the disruption of the inherited social order as the key channel: where direct rule eroded rigid traditional social structures, Christianity -- which bypassed hereditary boundaries -- expanded to fill the void; where indirect rule preserved them, indigenous religions endured. These findings shed light on the dynamics of religious identity change and how it was shaped by colonialism.

We develop a dynamic factor stochastic volatility-in-mean (SVM) specification for vector autoregressions (VARs) that embeds an SVM component within a dynamic factor stochastic volatility structure. A small number of latent volatility factors capture common movements in conditional variances, while volatility enters the conditional mean of the VAR. This specification allows time-varying uncertainty to influence macroeconomic dynamics through both second moments and expected outcomes while preserving tractability in large panels. We construct an efficient Markov chain Monte Carlo algorithm for estimation in this high-dimensional, non-Gaussian setting. Using quarterly data on twenty variables from the FRED-QD database, we compare predictive performance with the benchmark stochastic volatility VAR model. The dynamic factor SVM specification delivers superior forecasts for more variables during major macroeconomic disruptions such as the 2008 global financial crisis. The results indicate that allowing volatility to enter the mean captures an important transmission channel in macroeconomic dynamics.

We propose a unified mixture sampler (UMS) that provides a universal estimation framework for nonlinear state-space models with "exp-exp" likelihood kernels. Unlike existing methods that require deriving new mixture approximations for each specific distribution, our approach dynamically adapts the standard ten-component mixture from Omori et al. (2007) through a deterministic re-centering and rescaling algorithm. Applying this to the stochastic conditional duration (SCD) model, we demonstrate that the proposed sampler can efficiently handle unknown shape parameters - such as those in Weibull or Gamma distributions - by updating mixture components near-instantaneously during MCMC iterations. The UMS not only simplifies implementation but also ensures exact inference via a lightweight Metropolis-Hastings step. Numerical examples show that our method substantially outperforms the conventional slice sampling approach, significantly reducing autocorrelation in MCMC samples while maintaining high computational efficiency. This unified framework encompasses a wide range of applications, including logit, Poisson, and various SCD model specifications, providing a highly efficient alternative to model-specific samplers.

A seller investigates a buyer before setting prices, balancing the cost of acquiring information against the gain from tailoring the contract to the buyer's private type. The optimal signal is coarse: no matter how rich the type space, the seller never needs more than three outcomes per buyer. The bound equals the number of independent post-signal decisions plus one, a quantity we call the effective policy dimension. Screening involves two decisions, whether to allocate and what to charge, giving the ternary bound. Limited liability is the source: without it, the price is pinned by the envelope, only the allocation decision remains, and signals are binary as in monitoring. The Myerson exclusion rule is an artifact of not investigating. With investigation, every marginal buyer trades with positive probability, governed by a universal function that connects information design to rational inattention. The bound holds for any strictly convex information cost.

We develop new methods for constructing confidence sets and intervals in linear instrumental variables (IV) models based on tests that remain valid under weak identification and under heteroskedastic, autocorrelated, or clustered errors. In practice, researchers typically recover such sets by grid search, a procedure that can miss parts of the confidence region, truncate unbounded sets, and deliver misleading inference. We replace grid inversion with exact and approximation-based methods that are both reliable and computationally efficient. Our approach exploits the polynomial and rational structure of the Anderson-Rubin and Lagrange multiplier statistics to obtain exact confidence sets via polynomial root finding. For the conditional quasi-likelihood ratio test, we derive an exact inversion algorithm based on the geometry of the statistic and its critical value function. For more general conditional tests, we construct polynomial approximations whose coverage error vanishes with approximation degree, allowing numerical accuracy to be made arbitrarily high. In many empirical applications with weak instruments, standard grid methods produce incorrect confidence regions, while our procedures reliably recover sets with correct nominal coverage. The framework extends beyond linear IV to models with piecewise polynomial or rational moment conditions, offering a general tool for reliable weak-identification robust inference.

We propose an overview of optimal transport theory and its applications to econometric methodology. This review is specifically designed for practitioners, be they econometric theorists or applied econometricians. The review of applications of optimal transport to econometrics is organized around the particular aspects of the mathematical theory of optimal transport they rely on.

This paper studies bargaining when buyers can continue searching for alternative sellers while negotiating, which limits their commitment to complete a transaction. Using transaction level data from a Japanese online marketplace, I document frequent post-agreement nonpurchase and show that buyers who explicitly pledge immediate payment are more likely to have their offers accepted, renege less often, and complete transactions faster. I develop and estimate a dynamic bargaining model with buyer search and limited commitment. Counterfactuals that restrict search during bargaining show that increased buyer commitment can reduce total welfare. Sellers especially those with higher valuations benefit from the elimination of delays and walkaways and respond by raising list prices. This reduces buyer welfare by lowering the option value of search and increasing expected list prices. Platform revenue also declines because buyer behavior shifts away from counteroffers and negotiated prices fall.

This paper develops an asymptotic theory for two-step debiased machine learning (DML) estimators in generalised method of moments (GMM) models with general multiway clustered dependence, without relying on cross-fitting. While cross-fitting is commonly employed, it can be statistically inefficient and computationally burdensome when first-stage learners are complex and the effective sample size is governed by the number of independent clusters. We show that valid inference can be achieved without sample splitting by combining Neyman-orthogonal moment conditions with a localisation-based empirical process approach, allowing for an arbitrary number of clustering dimensions. The resulting debiased GMM estimators are shown to be asymptotically linear and asymptotically normal under multiway clustered dependence. A central technical contribution of the paper is the derivation of novel global and local maximal inequalities for general classes of functions of sums of separately exchangeable arrays, which underpin our theoretical arguments and are of independent interest.

This study establishes a nontrivial upper bound on the out-of-sample $R^2$ ($R^2_{\text{OOS}}$) in return forecasting. In particular, we define a coin-flip oracle model that, under the same directional accuracy, theoretically outperforms practical models in terms of MSE. The $R^2_{\text{OOS}}$ of the oracle model, whose analytical expression is a quadratic function of directional accuracy, can therefore serve as a tractable upper bound on the actual $R^2_{\text{OOS}}$. Empirical analyses across multiple forecasting scenarios reveal that the $R^2_{\text{OOS}}$ values of common predictive models are fundamentally bounded by this quadratic function.

Forecasting corporate financial distress increasingly requires capturing firms' adoption of transformative technologies such as artificial intelligence, yet model performance remains vulnerable to temporal distribution shifts as these technologies diffuse. This study investigates whether firm-level artificial intelligence (AI) adoption proxies improve forecasting performance beyond standard accounting fundamentals. Using a panel of Chinese A-share non-financial firms from 2007 to 2023, we construct AI indicators from textual disclosures and patent data. We benchmark six machine learning classifiers under a strictly chronological design that fixes the final test year and progressively prunes the training history to capture temporal change. Results indicate that AI proxies consistently improve out-of-sample discrimination and reduce Type II errors, with the strongest gains in tree-based ensembles. Predictive performance is non-monotonic in training window length; models trained on recent data outperform those using full history, while single-year training proves unreliable. Explainability analyses reveal financial ratios as primary drivers, with AI adoption signals adding incremental forecasting content whose interpretation as a risk factor varies across training regimes. Our findings establish AI proxies as valuable predictors for distress screening and demonstrate that adaptive, temporally pruned forecasting windows are essential for robust early warning models in rapidly evolving technological and economic environments.

Energy imbalance reserve (EIR) product is introduced into the Independent System Operator (ISO) of New England's day-ahead wholesale electricity market to provide a better fuel procurement incentive for generating resources. Different from existing forward reserve products, EIR is a novel real option product, which is settled against real-time energy price rather than reserve prices. This novel product has not been analyzed in the research literature in terms of its effects. In this paper, we develop a stochastic long-run equilibrium model that incorporates the risk preference of generator and demand agents participating in the energy and reserve market in both day-ahead and real-time time frame. In a risk neutral environment, we find that the presence of the EIR product makes little difference on market outcomes. We also conduct a series of numerical simulations with risk-averse generators and demand, and observed increased advanced fuel procurement when the EIR product is present.

Arrow's Impossibility Theorem is a seminal result of Social Choice Theory that demonstrates the impossibility of ranked-choice decision-making processes to jointly satisfy a number of intuitive and seemingly desirable constraints. The theorem is often described as a generalisation of Condorcet's Paradox, wherein pairwise majority voting may fail to jointly satisfy the same constraints due to the occurrence of elections that result in contradictory preference cycles. However, a formal proof of this relationship has been limited to D'Antoni's work, which applies only to the strict preference case, i.e., where indifference between alternatives is not allowed. In this paper, we generalise D'Antoni's methodology to prove in full (i.e., accounting for weak preferences) that Arrow's Impossibility Theorem can be equivalently stated in terms of contradictory preference cycles. This methodology involves explicitly constructing profiles that lead to preference cycles. Using this framework, we also prove a number of additional facts regarding social welfare functions. As a result, this methodology may yield further insights into the nature of preference cycles in other domains e.g., Money Pumps, Dutch Books, Intransitive Games, etc.

This paper analyzes the strategic interactions between a profit-maximizing monopolist and a free, capacity-constrained public option. By restricting its own supply, the monopolist intentionally congests the public option and induces rationing, which increases consumers' willingness to pay for guaranteed access. Counterintuitively, expanding the public option's capacity may raise the monopoly price and lower consumer welfare. However, I derive conditions under which all buyer types benefit from a capacity expansion, and extend these results to a setting where an oligopoly competes with a public option. These findings have implications for mixed public-private markets, such as housing, education, and healthcare.

While the importance of personalized policymaking is widely recognized, fully personalized implementation remains rare in practice, often due to legal, fairness or cost concerns. We study the problem of policy targeting for a regret-averse planner when training data gives a rich set of observables while the assignment rules can only depend on its subset. Our regret-averse criterion reflects a planner's concern about regret inequality across the population. This, in general, leads to a fractional optimal rule due to treatment effect heterogeneity beyond the average treatment effects conditional on the subset of observables. We propose a debiased empirical risk minimization approach to learn the optimal rule from data and establish favorable, new upper and lower bounds for the excess risk, indicating a convergence rate of 1/n and asymptotic efficiency in certain cases. We apply our approach to the National JTPA Study and the International Stroke Trial.

Dovonon and Hall (Journal of Econometrics, 2018) proposed a limiting distribution theory for GMM estimators for a p - dimensional globally identified parameter vector ϕ when local identification conditions fail at first-order but hold at second-order. They assumed that the first-order underidentification is due to the expected Jacobian having rank p-1 at the true value ϕ_{0}, i.e., having a rank deficiency of one. After reparametrizing the model such that the last column of the Jacobian vanishes, they showed that the GMM estimator of the vector comprising the first p-1 parameters, ϕ_{1}, converges at rate T^{-1/2} and the GMM estimator of the remaining parameter, ϕ_{p}, converges at rate T^{-1/4}. They also provided a limiting distribution of T^{1/4}(ϕ_{p}-hat-ϕ_{0,p}) subject to a (non-transparent) condition which they claimed to be not restrictive in general. However, as we show in this paper, their condition is in fact only satisfied when ϕ is overidentified and the limiting distribution of T^{1/4}(ϕ_{p}-hat-ϕ_{0,p}), which is non-standard, depends on whether ϕ is exactly identified or overidentified. In particular, the limiting distributions of the sign of T^{1/4}(ϕ_{p}-hat-ϕ_{0,p}) for the cases of exact and overidentification, respectively, are different and are obtained by using expansions of the GMM objective function of different orders. Unsurprisingly, we find that the limiting distribution theories of Dovonon and Hall (2018) for Indirect Inference (II) estimation under two different scenarios with second-order identification where the target function is a GMM estimator of the auxiliary parameter vector, are incomplete for similar reasons. We discuss how our results for GMM estimation can be used to complete both theories. We also derive the optimal weight matrices for ϕ_{1}-hat and ϕ_{p}-hat, respectively.

This paper develops a dynamic factor model in which common level and volatility factors evolve jointly, allowing conditional means and variances to interact endogenously within a large-information setting. The joint evolution of these factors provides a tractable framework for modeling risk, as fluctuations in volatility affect both the dispersion and the location of outcomes, generating state-dependent and asymmetric tail risks in predictive distributions. Volatility is captured by latent common factors that drive co-movement in second moments across a large panel, while heavy-tailed idiosyncratic shocks absorb transitory outliers and isolate persistent uncertainty dynamics. The framework embeds these interactions directly within a factor structure, allowing risk to arise endogenously from the joint dynamics of the system rather than being imposed through reduced-form approaches. Empirically, the model delivers systematic improvements in density forecast accuracy, particularly in the tails of the predictive distribution and at medium horizons. An application to international inflation highlights a dominant global level component in advanced economies and stronger regional and volatility contributions in emerging and developing economies, pointing to substantial heterogeneity in the role of uncertainty across countries.

We develop likelihood-based bias reduction for nonlinear panel models with additive individual and time effects. In two-way panels, integrated-likelihood corrections are attractive but challenging because the required integration is high dimensional and standard Laplace approximations may fail when the parameter dimension grows with the sample size. We propose a target-centered full-exponential Laplace--cumulant expansion that exploits the sparse higher-order derivative structure implied by additive effects, delivering a tractable approximation with a negligible remainder under large-$N,T$ asymptotics. The expansion motivates robust priors that yield bias reduction for both common parameters and fixed effects. We provide implementations for binary, ordered, and multinomial response models with two-way effects. For average partial effects, we show that the remaining first-order bias has a simple variance form and can be removed by a closed-form adjustment. Monte Carlo experiments and an empirical illustration show substantial bias reduction with accurate inference.

Repeated interactions are ubiquitous and known to promote social behaviour. While research often focuses on cooperation in the Prisoner's Dilemma, experimental evidence suggests repeated interactions also foster fairness. This study addresses a gap in the literature by theoretically modelling the evolution of fairness within a repeated mini-ultimatum game. Specifically, we construct a repeated-game framework where offerers and accepters interact using reactive strategies. We then investigate whether fair reactive strategy pairs are resilient against unfair mutants in a two-species population. By analyzing short-term evolutionary stability via the concept of two-species evolutionary stable strategy, we identify a critical effective game length: below this value, fairness is promoted by offerers and accepters who comply with their partner's past actions. Above this critical value, fairness is maintained by `complier' offerers and fair accepters. We also show that specific reactive strategies effectively facilitate the emergence and sustenance of fairness in long-term mutation-selection dynamics. To this end, we develop a two-population stochastic dynamics model -- a generalization of classical adaptive dynamics -- that accounts for finite population sizes and non-local mutants in the reactive strategy space.

We develop a framework for quantifying omitted variable bias (OVB) in nonlinear instrumental variable (IV) estimators, including the local average treatment effect (LATE), the LATE for the treated (LATT), and the partially linear IV model (PLIVM). Extending sensitivity analysis beyond linear settings, we derive bias decompositions, establish partial identification bounds, and construct OVB-adjusted confidence intervals. We estimate OVB bounds and conduct inference using double machine learning (DML), allowing flexible control for high-dimensional covariates. An application to the U.S. Job Training Partnership Act (JTPA) experiment shows that, at conventional significance levels, first-stage compliance estimates are robust to omitted variables, whereas intention-to-treat and treatment effects are more sensitive. Program impacts are robust and significant for females but fragile for males.

Autonomous AI systems can now generate complete economics research papers, but they substantially underperform human-authored publications in head-to-head comparisons. This paper decomposes the quality gap into two independent components: research idea quality and execution quality. Using a two-model ensemble of fine-tuned language models trained on publication decisions (Gong, Li, and Zhou, 2026) to evaluate idea quality and a comprehensive six-dimension rubric assessed by Gemini 3.1 Flash Lite -- the same model family used as the APE tournament judge, ensuring methodological consistency -- to evaluate execution quality, we analyze 953 economics papers -- 912 AI-generated papers from the APE project and 41 human papers published in the American Economic Review and AEJ: Economic Policy. The idea quality gap is large (Cohen's d = 2.23, p < 0.001), with human papers achieving 47.1% mean ensemble exceptional probability versus 16.5% for AI. The execution quality gap is also significant but smaller (d = 0.90, p < 0.001), with human papers scoring 4.38/5.0 versus 3.84. Idea quality accounts for approximately 71% of the overall quality difference, with execution contributing 29%. The largest execution weakness is mechanism analysis depth (d = 1.43); no significant difference is found on robustness. We document that 74% of AI papers employ difference-in-differences, and only 7 AI papers (0.8%) surpass the median human paper on both idea and execution quality simultaneously. The primary bottleneck to competitive AI-generated economics research remains ideation.

There are relatively few comparative cross-European studies on segregation, and those that do exist often use a single measure of segregation at a single spatial scale. This paper investigates ethnic segregation in seven European capitals (Amsterdam, Berlin, Lisbon, London, Madrid, Paris, and Rome) using the five dimensions of segregation (centralisation, evenness, exposure, clustering, and concentration) at multiple spatial scales. For each dimension, we found very different levels of segregation. Moreover, the impact of scale was different in both between and within cities relative to their cores and hinterlands. Crucially, we found that segregation does not necessarily decrease with spatial scale.

Specifications that impose constant treatment effects are common but biased, while fully flexible alternatives can be imprecise or infeasible. Under a bound on treatment effect heterogeneity, we propose a generalized ridge estimator, $\texttt{regulaTE}$, that yields heterogeneity-aware confidence intervals (CIs). The ridge penalty is chosen to optimally trade off worst-case bias and variance in a Gaussian homoskedastic setting; the resulting CIs remain tight more generally and are valid even under lack of overlap. Varying the bound enables sensitivity analysis to departures from constant effects, which we illustrate in leading empirical applications of unconfoundedness and staggered adoption designs.

This paper introduces the Eigenvalue-Based Randomness (EBR) test - a novel approach rooted in the Tracy-Widom law from random matrix theory - and applies it to the context of residual analysis in panel data models. Unlike traditional methods, which target specific issues like cross-sectional dependence or autocorrelation, the EBR test simultaneously examines multiple assumptions by analyzing the largest eigenvalue of a symmetrized residual matrix. Monte Carlo simulations demonstrate that the EBR test is particularly robust in detecting not only standard violations such as autocorrelation and linear cross-sectional dependence (CSD) but also more intricate non-linear and non-monotonic dependencies, making it a comprehensive and highly flexible tool for enhancing the reliability of panel data analyses.

This paper studies the persuasion of a receiver who accesses information only if she exerts costly attention effort. A sender designs an experiment to persuade the receiver to take a specific action. The experiment affects the receiver's attention effort, that is, the probability that she updates her beliefs. Persuasion has two margins: an extensive (effort) and an intensive (action). The receiver's utility exhibits a supermodularity property in information and effort. By leveraging this property, we establish an equivalence between experiments and persuasion mechanisms à la Kolotilin et al.~(2017). In applications, the sender's optimal strategy involves censoring favorable states.