Machine learning systems embed preferences either in training losses or through post-processing of calibrated predictions. Applying information design methods from Strack and Yang (2024), this paper provides decision problem agnostic conditions under which separation training preference free and applying preferences ex post is optimal. Unlike prior work that requires specifying downstream objectives, the welfare results here apply uniformly across decision problems. The key primitive is a diminishing-value-of-information condition: relative to a fixed (normalised) preference-free loss, preference embedding makes informativeness less valuable at the margin, inducing a mean-preserving contraction of learned posteriors. Because the value of information is convex in beliefs, preference-free training weakly dominates for any expected utility decision problem. This provides theoretical foundations for modular AI pipelines that learn calibrated probabilities and implement asymmetric costs through downstream decision rules. However, separation requires users to implement optimal decision rules. When cognitive constraints bind, as documented in human AI decision-making, preference embedding can dominate by automating threshold computation. These results provide design guidance: preserve optionality through post-processing when objectives may shift; embed preferences when decision-stage frictions dominate.

Generative artificial intelligence (Gen-AI) is reshaping content creation on digital platforms by reducing production costs and enabling scalable output of varying quality. In response, platforms have begun adopting disclosure policies that require creators to label AI-generated content, often supported by imperfect detection and penalties for non-compliance. This paper develops a formal model to study the economic implications of such disclosure regimes. We compare a non-disclosure benchmark, in which the platform alone detects AI usage, with a mandatory self-disclosure regime in which creators strategically choose whether to disclose or conceal AI use under imperfect enforcement. The model incorporates heterogeneous creators, viewer discounting of AI-labeled content, trust penalties following detected non-disclosure, and endogenous enforcement. The analysis shows that disclosure is optimal only when both the value of AI-generated content and its cost-saving advantage are intermediate. As AI capability improves, the platform's optimal enforcement strategy evolves from strict deterrence to partial screening and eventual deregulation. While disclosure reliably increases transparency, it reduces aggregate creator surplus and can suppress high-quality AI content when AI is technologically advanced. Overall, the results characterize disclosure as a strategic governance instrument whose effectiveness depends on technological maturity and trust frictions.

The European Central Bank (ECB) is working on the "digital euro", an envisioned retail central bank digital currency for the Euro area. In this article, we take a closer look at the "digital euro FAQ", which provides answers to 26 frequently asked questions about the digital euro, and other published documents by the ECB on the topic. We question the provided answers based on our analysis of the current design in terms of privacy, technical feasibility, risks, costs and utility. In particular, we discuss the following key findings: (KF1) Central monitoring of all online digital euro transactions by the ECB threatens privacy even more than contemporary digital payment methods with segregated account databases. (KF2) The ECB's envisioned concept of a secure offline version of the digital euro offering full anonymity is in strong conflict with the actual history of hardware security breaches and mathematical evidence against it. (KF3) The legal and financial liabilities for the various parties involved remain unclear. (KF4) The design lacks well-specified economic incentives for operators as well as a discussion of its economic impact on merchants. (KF5) The ECB fails to identify tangible benefits the digital euro would create for society, in particular given that the online component of the proposed infrastructure mainly duplicates existing payment systems. (KF6) The design process has been exclusionary, with critical decisions being set in stone before public consultations. Alternative and open design ideas have not even been discussed by the ECB.

We introduce BASTION (Bayesian Adaptive Seasonality and Trend DecompositION), a flexible Bayesian framework for decomposing time series into trend and multiple seasonality components. We cast the decomposition as a penalized nonparametric regression and establish formal conditions under which the trend and seasonal components are uniquely identifiable, an issue only treated informally in the existing literature. BASTION offers three key advantages over existing decomposition methods: (1) accurate estimation of trend and seasonality amidst abrupt changes, (2) enhanced robustness against outliers and time-varying volatility, and (3) robust uncertainty quantification. We evaluate BASTION against established methods, including TBATS, STR, and MSTL, using both simulated and real-world datasets. By effectively capturing complex dynamics while accounting for irregular components such as outliers and heteroskedasticity, BASTION delivers a more nuanced and interpretable decomposition. To support further research and practical applications, BASTION is available as an R package at https://github.com/Jasoncho0914/BASTION

Modern macroeconomic monetary theory suggests that the labor share of income has effectively become a core macroe-conomic parameter anchored by top policymakers through Open Market Operations (OMO). However, the setting of this parameter remains a subject of intense economic debate. This paper provides a detailed summary of these controversies, analyzes the scope of influence exerted by market agents other than the top policymakers on the labor share, and explores the rationality of its setting mechanism.

Market expectations about AI's economic impact may influence interest rates. Previous work has shown that US bond yields decline around the release of a sample of mostly proprietary AI models (Andrews and Farboodi 2025). I extend this analysis to include also open weight AI models that can be freely used and modified. I find long-term bond yields shift in opposite directions following the introduction of open versus closed models. Patterns are similar for treasuries, corporate bonds, and TIPS. The different movements suggest that that markets may anticipate open and closed AI advances to have different economic implications, and that the cumulative impact of AI releases on bond yields may be more muted.

Large-scale AI data center portfolios procure identical SKUs across geographically heterogeneous campuses, yet finance and operations require a single system-level 'world price' per SKU for budgeting and planning. A common practice is deployment-weighted blending of campus prices, which preserves total cost but can trigger Simpson-type aggregation failures: heterogeneous location mixes can reverse SKU rankings and distort decision signals. I formalize cost-preserving blended pricing under location heterogeneity and propose two practical operators that reconcile accounting identity with ranking robustness and production implementability. A two-way fixed-effects operator separates global SKU effects from campus effects and restores exact cost preservation via scalar normalization, providing interpretable decomposition and smoothing under mild missingness. A convex common-weight operator computes a single set of campus weights under accounting constraints to enforce a location-robust benchmark and prevent dominance reversals; I also provide feasibility diagnostics and a slack-based fallback for extreme mix conditions. Simulations and an AI data center OPEX illustration show substantial reductions in ranking violations relative to naive blending while maintaining cost accuracy, with scalable distributed implementation.

We introduce a rational inattention model which produces a unique, interior, weighted multinomial logit conditional choice probability for an agent who acquires costly information about the hedonic characteristics (e.g. whether an insurance contract has high coverage) of their choices and about their payoff-relevant states (e.g. their risk of incurring a loss). As usual, the objective is to choose a joint distribution subject to one marginal constraint (``Bayes plausibility''). We approach the problem by re-writing it in terms of an inner problem of maximizing over \textit{two} constraints and an outer problem of choosing the ``optimal constraint.'' The inner problem is a Schrödinger bridge problem. The outer problem is strictly concave.

Hybrid-quantum classical optimization has emerged as a promising direction for addressing financial decision problems under current quantum hardware constraints. In this work we present a practical end-to-end portfolio optimization pipeline that combines (i) a continuous mean-variance and Sharpe-ratio formulation, (ii) a QUBO/CQM-based discrete asset selection stage solved using D-Wave's hybrid quantum annealing solver, (iii) classical convex optimization for computing optimal asset weights, and (iv) a quarterly rebalancing mechanism. Rather than claiming quantum advantage, our goal is to evaluate the feasibility and integration of these components within a deployable financial workflow. We empirically compare our hybrid pipeline against a fund manager in real time and indexes used in Indian stock market. The results indicate that the proposed framework can construct diversified portfolios and achieve competitive returns. We also report computational considerations and scalability observations drawn from the hybrid solver behaviour. While the experiments are limited to moderate sized portfolios dictated by current annealing hardware and QUBO embedding constraints, the study illustrates how quantum assisted selection and classical allocation can be combined coherently in a real-world setting. This work emphasizes methodological reproducibility and practical applicability, and aims to serve as a step toward larger-scale financial optimization workflows as quantum annealers continue to mature.

The declining provision of inertia by synchronous generators in modern power systems necessitates aggregating distributed energy resources (DERs) into virtual power plants (VPPs) to unlock their potential in delivering inertia and primary frequency response (IPFR) through ancillary service markets. To facilitate DER participation in the IPFR market, this paper proposes an aggregation model and market mechanism for VPPs participating in IPFR. First, an energy-reserve-IPFR market framework is developed, in which a VPP acts as an intermediary to coordinate heterogeneous DERs. Second, by taking into account the delay associated with inertial response, an optimization-based VPP aggregation method is introduced to encapsulate the IPFR process involving a variety of DERs. Third, an energy-reserve-IPFR market mechanism with VPP participation is introduced, aiming to minimize social costs, where stochastic deviations of renewable energy generation are explicitly modeled through chance-constrained reformulations, ensuring that the cleared energy, reserve, and IPFR schedules remain secure against forecast errors. Case studies on IEEE 30-bus and IEEE 118-bus systems show that the nadir and quasi-steady-state frequencies are reproduced by the VPP aggregation model with a mean absolute percentage error <= 0.03%, and the proposed market mechanism with VPP participation reduces the total system cost by approximately 40% and increases the net profit by about 30%.

Electricity price forecasting approaches generally fall into two categories: data-driven models, which learn from historical patterns, or fundamental models, which simulate market mechanisms. We propose a novel and highly efficient data-driven merit order model that integrates both paradigms. The model embeds the classical expert-based merit order as a nested special case, allowing all key parameters, such as plant efficiencies, bidding behavior, and available capacities, to be estimated directly from historical data, rather than assumed. We further enhance the model with critical embedded extensions such as hydro power, cross-border flows and corrections for underreported capacities, which considerably improve forecasting accuracy. Applied to the German day-ahead market, our model outperforms both classic fundamental and state-of-the-art machine learning models. It retains the interpretability of fundamental models, offering insights into marginal technologies, fuel switches, and dispatch patterns, elements which are typically inaccessible to black-box machine learning approaches. This transparency and high computational efficiency make it a promising new direction for electricity price modeling.

A group of privately informed agents chooses between two alternatives. How should the decision rule be designed if agents are known to be biased in favor of one of the options? We address this question by considering the Condorcet Jury Setting as a mechanism design problem. Applications include the optimal decision mechanisms for boards of directors, political committees, and trial juries. While we allow for any kind of mechanism, the optimal mechanism is a voting mechanism. In the terminology of the trial jury example: When jurors (agents) are more eager to convict than the lawmaker (principal), then the defendant should be convicted if and only if neither too many nor too few jurors vote to convict. This kind of mechanism accords with a judicial procedure from ancient Jewish law.

In discrete choice panel data, estimation of average effects is crucial for quantifying the effect of covariates, and for policy evaluation and counterfactual analysis. However, in short panels with individual-specific effects, challenges arise due to partial identification and the incidental parameter problem. In particular, estimating the sharp identified set on average effects becomes impractical when covariates have large support sets, such as when they are continuous. This paper proposes a method for estimating outer bounds on the identified set of average effects, which are easy to construct, converge at the parametric rate, and remain computationally feasible even for moderately large samples. Asymptotically valid confidence intervals are also provided.

This paper introduces unit-specific heterogeneity in panel data threshold regression. We develop the asymptotic theory for models with heterogeneous thresholds, heterogeneous slope coefficients, and interactive fixed effects. The estimation methodology employs the Common Correlated Effects approach, which is able to handle heterogeneous parameters while maintaining computational simplicity. We also propose a semi-homogeneous model with heterogeneous slopes but a common threshold, revealing novel mean group estimator convergence rates due to the interaction of heterogeneity with the shrinking threshold assumption. Tests for linearity are provided, as well as a modified information criterion which can select between the fully heterogeneous and semi-homogeneous models. Monte Carlo simulations demonstrate the good performance of the new methods in small samples. The new theory is used to examine the Feldstein-Horioka puzzle, showing that threshold nonlinearity with respect to trade openness occurs only in a small subset of countries.

We introduce a generic class of dynamic nonlinear heterogeneous parameter models that incorporate individual and time fixed effects in both the intercept and slope. These models are subject to the incidental parameter problem, in that the limiting distribution of the point estimator is not centered at zero, and that test statistics do not follow their standard asymptotic distributions as in the absence of the fixed effects. To address the problem, we develop an analytical bias correction procedure to construct a bias-corrected likelihood. The resulting estimator follows an asymptotic normal distribution with mean zero. Moreover, likelihood-based test statistics -- including likelihood-ratio, Lagrange-multiplier, and Wald tests -- follow the limiting chi-squared distribution under the null hypothesis. Simulations demonstrate the effectiveness of the proposed correction method, and an empirical application on the labor force participation of single mothers underscores its practical importance.

The Kullback-Leibler divergence, the Kullback-Leibler variation, and the Bernstein "norm" are used to quantify discrepancies among probability distributions in likelihood models such as nonparametric maximum likelihood and nonparametric Bayes. They are closely related to the Hellinger distance, which is often easier to work with. Consequently, it is of interest to characterize conditions under which the Hellinger distance serves as an upper bound for these measures. This article characterizes a necessary and sufficient condition for each of the discrepancy measures to be bounded by the Hellinger distance. It accommodates unbounded likelihood ratios and generalizes all previously known results. We then apply it to relax the regularity condition for the sieve maximum likelihood estimator.

For subvector inference in the linear instrumental variables model under homoskedasticity but allowing for weak instruments, Guggenberger, Kleibergen, and Mavroeidis (2019) (GKM) propose a conditional subvector Anderson and Rubin (1949) (AR) test that uses data-dependent critical values that adapt to the strength of the parameters not under test. This test has correct size and strictly higher power than the test that uses standard asymptotic chi-square critical values. The subvector AR test is the minimum eigenvalue of a data dependent matrix. The GKM critical value function conditions on the largest eigenvalue of this matrix. We consider instead the data dependent critical value function conditioning on the second-smallest eigenvalue, as this eigenvalue is the appropriate indicator for weak identification. We find that the data dependent critical value function of GKM also applies to this conditioning and show that this test has correct size and power strictly higher than the GKM test when the number of parameters not under test is larger than one. Our proposed procedure further applies to the subvector AR test statistic that is robust to an approximate kronecker product structure of conditional heteroskedasticity as proposed by Guggenberger, Kleibergen, and Mavroeidis (2024), carrying over its power advantage to this setting as well.

This paper introduces MarketGAN, a factor-based generative framework for high-dimensional asset return generation under severe data scarcity. We embed an explicit asset-pricing factor structure as an economic inductive bias and generate returns as a single joint vector, thereby preserving cross-sectional dependence and tail co-movement alongside inter-temporal dynamics. MarketGAN employs generative adversarial learning with a temporal convolutional network (TCN) backbone, which models stochastic, time-varying factor loadings and volatilities and captures long-range temporal dependence. Using daily returns of large U.S. equities, we find that MarketGAN more closely matches empirical stylized facts of asset returns, including heavy-tailed marginal distributions, volatility clustering, leverage effects, and, most notably, high-dimensional cross-sectional correlation structures and tail co-movement across assets, than conventional factor-model-based bootstrap approaches. In portfolio applications, covariance estimates derived from MarketGAN-generated samples outperform those derived from other methods when factor information is at least weakly informative, demonstrating tangible economic value.

We study the identification and estimation of long-term treatment effects under unobserved confounding by combining an experimental sample, where the long-term outcome is missing, with an observational sample, where the treatment assignment is unobserved. While standard surrogate index methods fail when unobserved confounders exist, we establish novel identification results by leveraging proxy variables for the unobserved confounders. We further develop multiply robust estimation and inference procedures based on these results. Applying our method to the Job Corps program, we demonstrate its ability to recover experimental benchmarks even when unobserved confounders bias standard surrogate index estimates.

We are delighted to respond to the excellent surveys by Cattaneo et al. (2026) and Hirano (2026). Our discussion will attempt two things: first, we show how statistical decision theory can be applied to situations with partial identification; second, we connect the surveys' themes by applying these insights to an imagined policy experiment in one of Cattaneo et al.'s (2025) applications. To do so, we lay out a stylized scenario of statistical decision making under partial identification and, drawing on our own and others' earlier work, provide a complete solution for that scenario. We then apply these results to a hypothetical reduction (modelled on actual policies) in eligibility for educational subsidies. We will see that something of interest can be said, but also that bringing the theory to the application involves some leaps of faith and leaves some questions open. This leads to the final section, where we discuss what we see as the main open challenges in statistical decision theory under partial identification.

As LLMs increasingly function as economic agents, the specific mechanisms LLMs use to update their belief with heterogeneous signals remain opaque. We design experiments and develop a Behavioral Kalman Filter framework to quantify how LLM-based agents update expectations, acting as households or firm CEOs, update expectations when presented with individual and aggregate signals. The results from experiments and model estimation reveal four consistent patterns: (1) agents' weighting of priors and signals deviates from unity; (2) both household and firm CEO agents place substantially larger weights on individual signals compared to aggregate signals; (3) we identify a significant and negative interaction between concurrent signals, implying that the presence of multiple information sources diminishes the marginal weight assigned to each individual signal; and (4) expectation formation patterns differ significantly between household and firm CEO agents. Finally, we demonstrate that LoRA fine-tuning mitigates, but does not fully eliminate, behavioral biases in LLM expectation formation.

Standard Distributional Synthetic Controls (DSC) estimate counterfactual distributions by minimizing the Euclidean $L_2$ distance between quantile functions. We demonstrate that this geometric reliance renders estimators fragile: they lack informative gradients under support mismatch and produce structural artifacts when outcomes are multimodal. This paper proposes a robust estimator grounded in Optimal Transport (OT). We construct the synthetic control by minimizing the Wasserstein-1 distance between probability measures, implemented via a Wasserstein Generative Adversarial Network (WGAN). We establish the formal point identification of synthetic weights under an affine independence condition on the donor pool. Monte Carlo simulations confirm that while standard estimators exhibit catastrophic variance explosions under heavy-tailed contamination and support mismatch, our WGAN-based approach remains consistent and stable. Furthermore, we show that our measure-based method correctly recovers complex bimodal mixtures where traditional quantile averaging fails structurally.

We develop an integrated framework for information design and mechanism design in screening environments with quasilinear utility. Using the tools of majorization theory and quantile functions, we show that both information design and mechanism design problems reduce to maximizing linear functionals subject to majorization constraints. For mechanism design, the designer chooses allocations weakly majorized by the exogenous inventory. For information design, the designer chooses information structures that are majorized by the prior distribution. When the designer can choose both the mechanism and the information structure simultaneously, then the joint optimization problem becomes bilinear with two majorization constraints. We show that pooling of values and associated allocations is always optimal in this case. Our approach unifies classic results in auction theory and screening, extends them to information design settings, and provides new insights into the welfare effects of jointly optimizing allocation and information.

In an era of accelerating change, urban water infrastructure systems increasingly operate outside of their design conditions, putting new pressure on systems' institutional designs to weather emerging challenges. Water management institutions must therefore be designed to exhibit dynamic fitness, defined by anticipatory capacity and responsiveness. However, we do not yet understand the specific features of institutional design that enable dynamic fitness, especially in relation to the diverse biophysical characteristics of systems that such fitness is contingent upon. We advance research on dynamic fitness in the context of urban water supply systems by drawing on 35-year data sets of stressors and responses for 16 U.S. urban water utilities using archetype analysis. Here we find that institutional archetypes capable of coping with higher biophysical complexity invest in both information processing capacity and response diversity. While dynamic fitness comes at a cost, balance between information processing capacity and response diversity promotes efficiency, which can be expanded through polycentric regional institutional structures that facilitate information sharing. Lastly, careful consideration should be given to tradeoffs across levels of governance, as institutional structures that facilitate dynamic fitness at the utility level may reduce the control and flexibility of higher levels of governance.

Suppose we need a deep collective analysis of an open scientific problem: there is a complex scientific hypothesis and a large online group of mutually unrelated experts with relevant private information of a diverse and unpredictable nature. This information may be results of experts' individual experiments, original reasoning of some of them, results of AI systems they use, etc. We propose a simple mechanism based on a self-resolving play-money prediction market entangled with a chat. We show that such a system can easily be brought to an equilibrium where participants directly share their private information on the hypothesis through the chat and trade as if the market were resolved in accordance with the truth of the hypothesis. This approach will lead to efficient aggregation of relevant information in a completely interpretable form even if the ground truth cannot be established and experts initially know nothing about each other and cannot perform complex Bayesian calculations. Finally, by rewarding the experts with some real assets proportionally to the play money they end up with, we can get an innovative way to fund large-scale collaborative studies of any type.

We introduce capital games, which generalize the definition of standard games to incorporate dynamics. In capital games, payoffs are in units of capital which are not assumed to be units of utility. The dynamics allow us to infer player utilities from their individual payoffs and linearizable capital dynamics under the assumption that players aim to maximize the time-average growth rate of their capital.

The Difference-in-Differences (DiD) method is a fundamental tool for causal inference, yet its application is often complicated by missing data. Although recent work has developed robust DiD estimators for complex settings like staggered treatment adoption, these methods typically assume complete data and fail to address the critical challenge of outcomes that are missing at random (MAR) -- a common problem that invalidates standard estimators. We develop a rigorous framework, rooted in semiparametric theory, for identifying and efficiently estimating the Average Treatment Effect on the Treated (ATT) when either pre- or post-treatment (or both) outcomes are missing at random. We first establish nonparametric identification of the ATT under two minimal sets of sufficient conditions. For each, we derive the semiparametric efficiency bound, which provides a formal benchmark for asymptotic optimality. We then propose novel estimators that are asymptotically efficient, achieving this theoretical bound. A key feature of our estimators is their multiple robustness, which ensures consistency even if some nuisance function models are misspecified. We validate the properties of our estimators and showcase their broad applicability through an extensive simulation study.

We present simple to implement Wald-type statistics that deliver a general nonparametric inference theory for linear restrictions on varying coefficients in a range of regression models allowing for cross-sectional or spatial dependence. We provide a general central limit theorem that covers a broad range of error spatial dependence structures, allows for a degree of misspecification robustness via nonparametric spatial weights and permits inference on both varying regression and spatial dependence parameters. Using our method, we first uncover evidence of constant returns to scale in the Chinese nonmetal mineral industry's production function, and then show that Boston house prices respond nonlinearly to proximity to employment centers. A simulation study confirms that our tests perform very well in finite samples.

We study a portioning setting in which a public resource such as time or money is to be divided among a given set of candidates, and each agent proposes a division of the resource. We consider two families of aggregation rules for this setting -- those based on coordinate-wise aggregation and those that optimize some notion of welfare -- as well as the recently proposed independent markets rule. We provide a detailed analysis of these rules from an axiomatic perspective, both for classic axioms, such as strategyproofness and Pareto optimality, and for novel axioms, some of which aim to capture proportionality in this setting. Our results indicate that a simple rule that computes the average of the proposals satisfies many of our axioms and fares better than all other considered rules in terms of fairness properties. We complement these results by presenting two characterizations of the average rule.

This paper addresses the methodology for the quarterly estimation of Compensation of Employees paid by the General Government (GG) sector, in accordance with the European System of Accounts (ESA 2010). Due to the limited high-frequency data availability and the need to guarantee the consistency with annual constraints, quarterly estimation relies on indirect temporal disaggregation techniques. These methods use specific infra-annual indicators as proxies for the variables being estimated. The specific case of the quarterly estimation of Compensation of employees presents several additional challenges. Firstly, the information provided by the sources, based on cash or legal-accrual data, is elaborated to define indicators which respect the accrual ESA 2010 principle as the annual estimates, based on more compliant data sources such as final budgets of public entities. Secondly, at a quarterly level the extraordinary events - such as the recording of delayed collective bargaining agreements which result in arrears - have a strong impact on quarterly indicators, whereas their effect is mitigated at annual level. To attribute these flows to the period when the work is performed, multi-source data harmonization techniques are employed. Thirdly, to accurately reflect intra-annual dynamics, information is collected for specific groups of GG entities (e.g., regions and provinces) and aggregated into ESA 2010 GG sub-sectors (Central Government, Local Government, Social Security Funds) leading to three specific estimates. To validate temporal disaggregation models and ensure methodological rigor and data quality, statistical tests are applied throughout the process. The results confirm the effectiveness of this methodology in providing accurate and timely quarterly estimates of Compensation of employees for the GG sector, thereby supporting reliable short-term economic analysis and policy making.