We study delegated Bayesian persuasion: a principal incentivizes an intermediary to design information via outcome-contingent transfers, while the intermediary privately chooses the experiment subject to convex costs. We characterize first-best implementability through a pair of alignment conditions on the principal's and intermediary's payoff indices. A local condition on the support of the target experiment is necessary; a global affine alignment condition is sufficient. We show that the gap between them is non-empty and provide a partial characterization of the intermediate region. When the first-best is unattainable, the principal's problem admits a virtual Bayesian persuasion representation: the second-best experiment maximizes the same concavified objective as the first-best, with the principal's payoff index distorted by a single scalar shadow price that summarizes the entire agency friction. Under entropy costs, moral hazard compresses posterior dispersion whenever the intermediary's utility differs across the actions it recommends. Explicit closed-form solutions for posteriors, mixing weights, and the optimal transfer schedule are derived for binary environments.

In strategic games such as the prisoner's dilemma, allowing players to make binding offers of utility transfers before play has been shown to alter incentives and potentially support cooperative outcomes. These preplay exchange mechanisms reshape payoffs by transferring utility while being contingent on actions; however, they typically require side payments that can reduce individual benefits relative to joint cooperation. In this paper, we extend the analysis to a finite $n$-player prisoner's dilemma with ordered strategy sets, defined such that any restriction of strategies by any subset of players still yields a prisoner's dilemma. To achieve a robust cooperative outcome that resists group deviations, we introduce a novel class of mechanisms: $\textit{losing contracts}$. Unlike transfer-based preplay mechanisms, losing contracts require players to irrevocably reduce their own utility if they defect, thereby aligning individual incentives with cooperation without inter-player payments. With appropriately chosen loss amounts, losing contracts induce joint cooperation as the unique strong Nash equilibrium in the modified game and in every restricted game within it, ensuring that cooperative incentives persist even under possible external constraints on strategy sets. We show that our contracts can be constructively defined, reducing the preplay stage to a simple and binary decision for each player: whether to sign the contract or not. Furthermore, if the losing contract is only executed when all players sign, signing is a strictly dominant strategy for all. Finally, we extend these results to certain public goods games.

Empirical researchers routinely invoke the no-interference or \textit{individualistic treatment response} (ITR) assumption to identify causal effects in observational studies, despite concerns that interference across units may arise in many economic settings. This paper studies the causal content of standard ITR-based identification formulas when arbitrary interference is present. We show that, under restrictions on dependence between treatment assignments across units, conventional ITR-based identification formulas -- including those underlying selection-on-observables, instrumental variables, regression discontinuity designs, and difference-in-differences -- identify well-defined causal objects: types of \textit{average direct effects} (ADEs). These results do not require knowledge of the interference structure or specification of exposure mappings. We also propose a sensitivity analysis framework that quantifies the robustness of statistical inference to violations of treatment-assignment independence under arbitrary interference.

Human decision-makers often face choices about complex cases with many potentially relevant features, but limited bandwidth to inspect and integrate all available information. In such settings, we study algorithms that highlight a small subset of case-specific features for human consideration, rather than producing a single prediction or recommendation. We model highlighting as a constrained information policy that selects a small number of features to reveal. A central issue is how humans interpret the algorithm's choice of features: a sophisticated agent correctly conditions on the selection rule, while a naive agent updates only on revealed feature values and treats the selection event as exogenous. We show that optimizing highlighting for sophisticated agents can be computationally intractable, even in simple discrete and binary settings, whereas optimizing for naive agents is tractable as long as the maximal bandwidth is fixed. We also show that a highlighting policy that is optimal for sophisticated agents can perform arbitrarily poorly when deployed to naive agents, motivating robust, implementable alternatives. We illustrate our framework in a calibrated empirical exercise based on the American Housing Survey. Overall, our results establish the value of highlighting a context-specific set of features rather than a fixed one as a practically appealing and computationally feasible tool for achieving human-algorithm complementarity.

Benchmark hacking refers to tuning a machine learning model to score highly on certain evaluation criteria without improving true generalization or faithfully solving the intended problem. We study this phenomenon in a generic machine learning contest, where each contestant chooses two types of effort: creative effort that improves model capability as desired by the contest host, and mechanistic effort that only improves the model's fitness to the particular task in contest without contributing to true generalization. We establish the existence of a symmetric monotone pure strategy equilibrium in this competition game. It also provides a natural definition of benchmark hacking in this strategic context by comparing a player's equilibrium effort allocation to that of a single-agent baseline scenario. Under our definition, contestants with types below certain threshold (low types) always engage in benchmark hacking, whereas those above the threshold do not. Furthermore, we show that more skewed reward structures (favoring top-ranked contestants) can elicit more desirable contest outcomes. We also provide empirical evidence to support our theoretical predictions.

We propose a novel framework for conducting causal inference based on counterfactual densities. While the current paradigm of causal inference is mostly focused on estimating average treatment effects (ATEs), which restricts the analysis to the first moment of the outcome variable, our density-based approach is able to detect causal effects based on general distributional characteristics. Following the Oaxaca-Blinder decomposition approach, we consider two types of counterfactual density effects that together explain observed discrepancies between the densities of the treated and control group. First, the distribution effect is the counterfactual effect of changing the conditional density of the control group to that of the treatment group, while keeping the covariates fixed at the treatment group distribution. Second, the covariate effect represents the effect of a hypothetical change in the covariate distribution. Both effects have a causal interpretation under the classical unconfoundedness and overlap assumptions. Methodologically, our approach is based on analyzing the conditional densities as elements of a Bayes Hilbert space, which preserves the non-negativity and integration-to-one constraints. We specify a flexible functional additive regression model estimating the conditional densities. We apply our method to analyze the German East--West income gap, i.e., the observed differences in wages between East Germans and West Germans. While most of the existing studies focus on the average differences and neglect other distributional characteristics, our density-based approach is suited to detect all nuances of the counterfactual distributions, including differences in probability masses at zero.

We study the deployment performance of machine learning based enforcement systems used in cryptocurrency anti money laundering (AML). Using forward looking and rolling evaluations on Bitcoin transaction data, we show that strong static classification metrics substantially overstate real world regulatory effectiveness. Temporal nonstationarity induces pronounced instability in cost sensitive enforcement thresholds, generating large and persistent excess regulatory losses relative to dynamically optimal benchmarks. The core failure arises from miscalibration of decision rules rather than from declining predictive accuracy per se. These findings underscore the fragility of fixed AML enforcement policies in evolving digital asset markets and motivate loss-based evaluation frameworks for regulatory oversight.

Text-based measurement in political research often treats classi6ication disagreement as random noise. We examine this assumption using con6idence-weighted human annotations of 5,000 social media messages by U.S. politicians. We 6ind that political communication is generally highly legible, with mean con6idence exceeding 0.99 across message type, partisan bias, and audience classi6ications. However, systematic variation concentrates in the constituency category, which exhibits a 1.79 percentage point penalty in audience classi6ication con6idence. Given the high baseline of agreement, this penalty represents a sharp relative increase in interpretive uncertainty. Within messages, intent remains clear while audience targeting becomes ambiguous. These patterns persist with politician 6ixed effects, suggesting that measurement error in political text is structured by strategic incentives rather than idiosyncratic coder error.

This paper studies whether behavioral interventions designed to promote resource conservation in one domain generate spillovers in another. Using a natural field experiment involving over 2,000 residents, we identify the direct and spillover effects of real-time feedback and social comparisons on water and energy consumption. We implement three interventions: two targeting shower use and one targeting air-conditioning use. We find significant reductions in shower use from both water-saving interventions, but no direct effect of the energy-saving intervention on air-conditioning use. For spillovers, we estimate precise null effects of water-saving interventions on air-conditioning use, and of the energy-saving intervention on shower use.

I study linear panel data models with predetermined regressors (such as lagged dependent variables) where coefficients are individual-specific, allowing for heterogeneity in the effects of the regressors on the dependent variable. I show that the model is not point-identified in a short panel context but rather partially identified, and I characterize the identified sets for the mean, variance, and CDF of the coefficient distribution. This characterization is general, accommodating discrete, continuous, and unbounded data, and it leads to computationally tractable estimation and inference procedures. I apply the method to study lifecycle earnings dynamics among U.S. households using the Panel Study of Income Dynamics (PSID) dataset. The results suggest the presence of unobserved heterogeneity in earnings persistence, implying that households face varying levels of earnings risk which, in turn, contribute to heterogeneity in their consumption and savings behaviors.

Probabilistic electricity price forecasting (PEPF) is vital for short-term electricity markets, yet the multivariate nature of day-ahead prices - spanning 24 consecutive hours - remains underexplored. At the same time, real-time decision-making requires methods that are both accurate and fast. We introduce an online algorithm for multivariate distributional regression models, allowing efficient modeling of the conditional means, variances, and dependence structures of electricity prices. The approach combines multivariate distributional regression with online coordinate descent and LASSO-type regularization (absolute shrinkage and selection operator), enabling scalable estimation in high-dimensional covariate spaces. Additionally, we propose a regularized estimation path over increasingly complex dependence structures, allowing for early stopping and avoiding overfitting. In a case study using historical data from the German day-ahead market, the proposed method yields interpretable and well-calibrated joint prediction intervals for the 24-dimensional price distribution and provides robust performance across a range of proper scoring rules. The results underscore the importance of modeling the dependence structure of electricity prices. Furthermore, we analyze the trade-off between predictive accuracy and computational costs for batch and online estimation and provide a high-performing open-source Python implementation in the ondil package.

This paper considers filtering, parameter estimation, and testing for potentially dynamically misspecified state-space models. When dynamics are misspecified, filtered values of state variables often do not satisfy model restrictions, making them hard to interpret, and parameter estimates may fail to characterize the dynamics of filtered variables. To address this, a sequential optimal transportation approach is used to generate a model-consistent sample by mapping observations from a flexible reduced-form to the structural conditional distribution iteratively. Filtered series from the generated sample are model-consistent. Specializing to linear processes, a closed-form Optimal Transport Filtering algorithm is derived. Minimizing the discrepancy between generated and actual observations defines an Optimal Transport Estimator. Its large sample properties are derived. A specification test determines if the model can reproduce the sample path, or if the discrepancy is statistically significant. Empirical applications to DSGE models, affine term structure models, and trend-cycle decomposition illustrate the methodology and the results.

We consider the problem of allocating heterogeneous and indivisible goods among strategic agents, with preferences over subsets of goods, when there is no medium of exchange. This model captures the well studied problem of fair allocation of indivisible goods. Serial-quota mechanisms are allocation mechanisms where there is a predefined order over agents, and each agent in her turn picks a predefined number of goods from the remaining goods. These mechanisms are clearly strategy-proof, non-bossy, and neutral. Are there other mechanisms with these properties? We show that for important classes of strict ordinal preferences (as lexicographic preferences, and as the class of all strict preferences), these are the only mechanisms with these properties. Importantly, unlike previous work, we can prove the claim even for mechanisms that are not Pareto-efficient. Moreover, we generalize these results to preferences that are cardinal, including any valuation class that contains additive valuations. We then derive strong negative implications of this result on truthful mechanisms for fair allocation of indivisible goods to agents with additive valuations.

In a satisficing equilibrium each agent $i$ plays one of her top $k_i$ actions in response to the actions of the other agents. Our concept unifies models of bounded rationality and yields predictions that differ from canonical solution concepts. We study its theoretical properties and show that it provides sharp predictions, exists in most games as well as in a broad new class of economic environments, admits standard epistemic and dynamic foundations, and is empirically falsifiable.

Large-scale streaming data are common in modern machine learning applications and have led to the development of online learning algorithms. Many fields, such as supply chain management, weather and meteorology, energy markets, and finance, have pivoted toward probabilistic forecasting. This results in the need not only for accurate learning of the expected value but also for learning the conditional heteroskedasticity and conditional moments. Against this backdrop, we present a methodology for online estimation of regularized, linear distributional models. The proposed algorithm combines recent developments in online estimation of LASSO models with the well-known GAMLSS framework. We provide a case study on day-ahead electricity price forecasting, in which we show the competitive performance of the incremental estimation combined with strongly reduced computational effort. Our algorithms are implemented in a computationally efficient Python package ondil.

We consider the problem of designing prices for public transport where payment enforcing is done through random inspection of passengers' tickets as opposed to physically blocking their access. Passengers are fully strategic such that they may choose different routes or buy partial tickets in their optimizing decision. We derive expressions for the prices that make every passenger choose to buy the full ticket. Using travel and pricing data from the Washington DC metro, we show that a switch to a random inspection method for ticketing while keeping current prices could lead to more than 59% of revenue loss due to fare evasion, while adjusting prices to take incentives into consideration would reduce that loss to less than 20%, without any increase in prices.

Many events and policies (treatments) occur at specific spatial locations, with researchers interested in their effects on nearby units. I approach the spatial treatment setting from an experimental perspective: What ideal experiment would we design to estimate the causal effects of spatial treatments? This perspective motivates a comparison between units near realized treatment locations and units near counterfactual (unrealized) candidate locations, which differs from current empirical practice. I derive design-based standard errors that are straightforward to compute. For observational data, I propose machine learning methods to find counterfactual candidate locations when observable characteristics, rather than potential outcomes, determine treatment probabilities. To accommodate methods for high-dimensional data in the theory, I extend a double machine learning result to the design-based framework with spatial correlations. I apply the proposed methods to study the causal effects of grocery stores on foot traffic to nearby businesses during COVID-19 shelter-in-place policies, finding a large positive effect at very short distances, with no effect at larger distances.