In the linear-in-means model, endogeneity arises naturally due to the reflection problem. A common solution is to use Instrumental Variables (IVs) based on higher-order network links, such as using friends-of-friends' characteristics. We first show that such instruments are unlikely to work well in many applied settings: in very sparse or very dense networks, friends-of-friends may be similar to the original links. This implies that the IVs may be weak or their first stage estimand may be undefined. For a class of random graphs, we use random graph theory and characterize regimes where such instruments perform well, and when they would not. We prove how weak-IV robust inference can be adapted to this environment, and how scaling the network can help. We provide extensive Monte Carlo simulations and revisit empirical applications, showing the prevalence of such issues in empirical practice, and how our results restore valid inference.

This paper examines the impact of introducing a Rank-Dependent Utility (RDU) agent into a von Neumann-Morgenstern (vNM) pure-exchange economy with no aggregate uncertainty. In the absence of the RDU agent, the classical theory predicts that Pareto-optimal allocations are full-insurance, or no-betting, allocations. We show how the probability weighting function of the RDU agent, seen as a proxy for probabilistic risk aversion that is not captured by marginal utility of wealth, can lead to Pareto optima characterized by endogenous betting, despite common baseline beliefs. Such endogenous betting at an optimum leads to uncertainty-generating trade arising purely from heterogeneity in the perception of risk, rather than in beliefs. Our results formalize the intuitive understanding that probability weighting can act as an endogenous source of belief heterogeneity, and provide a new behavioral foundation for the coexistence of common beliefs and speculative behavior, in an environment with no initial aggregate uncertainty. Interpreting the RDU agent's nonlinear weighting function as an ``internality'' prompts the question of whether a social planner should intervene. We show how a benevolent social planner can nudge the RDU agent to behave closer to a vNM agent, through costly statistical or financial education, thereby (partially) restoring the optimality of full-insurance allocations.

We propose a difference-in-differences (DiD) framework with mediation for possibly multivalued discrete or continuous treatments and mediators, aimed at identifying the direct effect of the treatment on the outcome (net of effects operating through the mediator), the indirect effect via the mediator, and the joint effects of treatment and mediator, consistent with the framework of dynamic treatment effects. Identification relies on a conditional parallel trends assumption imposed on the mean potential outcome across treatment and mediator states, or (depending on the causal parameter) additionally on the mean potential outcomes and potential mediator distributions across treatment states. We propose ATET estimators for repeated cross sections and panel data within the double/debiased machine learning framework, which allows for data-driven control of covariates, and we establish their asymptotic normality under standard regularity conditions. We investigate the finite-sample performance of the proposed methods in a simulation study and illustrate our approach in an empirical application to the US National Longitudinal Survey of Youth, estimating the direct effect of health care coverage on general health as well as the indirect effect operating through routine checkups.

This study proposes the General Bayes framework for policy learning. We consider decision problems in which a decision-maker chooses an action from an action set to maximize its expected welfare. Typical examples include treatment choice and portfolio selection. In such problems, the statistical target is a decision rule, and the prediction of each outcome $Y(a)$ is not necessarily of primary interest. We formulate this policy learning problem by loss-based Bayesian updating. Our main technical device is a squared-loss surrogate for welfare maximization. We show that maximizing empirical welfare over a policy class is equivalent to minimizing a scaled squared error in the outcome difference, up to a quadratic regularization controlled by a tuning parameter $ζ>0$. This rewriting yields a General Bayes posterior over decision rules that admits a Gaussian pseudo-likelihood interpretation. We clarify two Bayesian interpretations of the resulting generalized posterior, a working Gaussian view and a decision-theoretic loss-based view. As one implementation example, we introduce neural networks with tanh-squashed outputs. Finally, we provide theoretical guarantees in a PAC-Bayes style.

Congestion pricing has emerged as an effective tool for mitigating traffic congestion, yet implementing welfare or revenue-optimal dynamic tolls is often impractical. Most real-world congestion pricing deployments, including New York City's recent program, rely on significantly simpler, often static, tolls. This discrepancy motivates the question of how much revenue and welfare loss there is when real-world traffic systems use static rather than optimal dynamic pricing. We address this question by analyzing the performance gap between static (simple) and dynamic (optimal) congestion pricing schemes in two canonical frameworks: Vickrey's bottleneck model with a public transit outside option and its city-scale extension based on the Macroscopic Fundamental Diagram (MFD). In both models, we first characterize the revenue-optimal static and dynamic tolling policies, which have received limited attention in prior work. In the worst-case, revenue-optimal static tolls achieve at least half of the dynamic optimal revenue and at most twice the minimum achievable system cost across a wide range of practically relevant parameter regimes, with stronger and more general guarantees in the bottleneck model than in the MFD model. We further corroborate our theoretical guarantees with numerical results based on real-world datasets from the San Francisco Bay Area and New York City, which demonstrate that static tolls achieve roughly 80-90% of the dynamic optimal revenue while incurring at most a 8-20% higher total system cost than the minimum achievable system cost.

In this paper, we characterize the extreme points of a class of multidimensional monotone functions. This result is then applied to large contests, where it provides a useful representation of optimal allocation rules under a broad class of distributional preferences of the contest designer. In contests with complete information, the representation significantly simplifies the characterization of the equilibria.

This paper considers estimation and model selection of quantile vector autoregression (QVAR). Conventional quantile regression often yields undesirable crossing quantile curves, violating the monotonicity of quantiles. To address this issue, we propose a simplex quantile vector autoregression (SQVAR) framework, which transforms the autoregressive (AR) structure of the original QVAR model into a simplex, ensuring that the estimated quantile curves remain monotonic across all quantile levels. In addition, we impose the smoothly clipped absolute deviation (SCAD) penalty on the SQVAR model to mitigate the explosive nature of the parameter space. We further develop a Bayesian information criterion (BIC)-based procedure for selecting the optimal penalty parameter and introduce new frameworks for impulse response analysis of QVAR models. Finally, we establish asymptotic properties of the proposed method, including the convergence rate and asymptotic normality of the estimator, the consistency of AR order selection, and the validity of the BIC-based penalty selection. For illustration, we apply the proposed method to U.S. financial market data, highlighting the usefulness of our SQVAR method.

Contemporary AI regulation, including the EU Artificial Intelligence Act and related governance frameworks, increasingly requires institutions to justify the training data used in automated decision-making. Yet existing governance regimes provide limited operational methods for selecting, weighting, and explaining data inputs. We introduce the Smart Data Portfolio (SDP) framework, which treats data categories as productive but risk-bearing assets, formalizing input governance as an information-risk trade-off. Within this framework, we define two portfolio-level quantities, Informational Return and Governance-Adjusted Risk, whose interaction characterizes attainable data mixtures and yields a Governance-Efficient Frontier. Regulators shape this frontier through risk caps, admissible categories, and weight bands that translate fairness, privacy, robustness, and provenance requirements into measurable constraints on data allocation while preserving model flexibility. A sectoral illustration shows how different AI services require distinct portfolios within a common governance structure. The framework provides an input-level explanation layer through which institutions can justify governed data use in large-scale AI deployment.

This paper studies nonparametric local (over-)identification and the semiparametric efficiency in modern causal frameworks. We develop a unified approach that begins by translating structural models with latent variables into their induced statistical models of observables and then analyzes local overidentification through conditional moment restrictions. We apply this approach to three popular classes of causal models: (1) the general treatment model under unconfoundedness; (2) the negative control model, and (3) the long-term causal inference model under unobserved confounding. The first model yields a locally just-identified statistical model, implying that all regular asymptotically linear estimators of the treatment effect have the same asymptotic variance, which equals the (trivial) semiparametric efficient variance bound. In contrast, the latter two models involve nonparametric endogeneity and are naturally locally overidentified; consequently, some doubly robust orthogonal moment estimators of the average treatment effect are inefficient. Whereas existing work typically imposes strong conditions to restore local just-identification to justify the efficiency of their doubly robust orthogonal moment estimators, we characterize the semiparametric efficient variance bounds, along with efficient estimators, for the (locally) overidentified models (2) and (3). A small real data application, along with a simulation study, illustrates the semiparametric efficiency gains in model (3).

Instrumental variables are a popular tool to infer causal effects under unobserved confounding, but choosing suitable instruments is challenging in practice. We propose gIVBMA, a Bayesian model averaging procedure that addresses this challenge by averaging across different sets of instrumental variables and covariates in a structural equation model. This allows for data-driven selection of valid and relevant instruments and provides additional robustness against invalid instruments. Our approach extends previous work through a scale-invariant prior structure and accommodates non-Gaussian outcomes and treatments, offering greater flexibility than existing methods. The computational strategy uses conditional Bayes factors to update models separately for the outcome and treatments. We prove that this model selection procedure is consistent. In simulation experiments, gIVBMA outperforms current state-of-the-art methods. We demonstrate its usefulness in two empirical applications: the effects of malaria and institutions on income per capita and the returns to schooling. A software implementation of gIVBMA is available in Julia.

The value-loading problem is a significant challenge for researchers aiming to create artificial intelligence (AI) systems that align with human values and preferences. This problem requires a method to define and regulate safe and optimal limits of AI behaviors. In this work, we propose HALO (Hormetic ALignment via Opponent processes), a regulatory paradigm that uses hormetic analysis to regulate the behavioral patterns of AI. Behavioral hormesis is a phenomenon where low frequencies of a behavior have beneficial effects, while high frequencies are harmful. By modeling behaviors as allostatic opponent processes, we can use either Behavioral Frequency Response Analysis (BFRA) or Behavioral Count Response Analysis (BCRA) to quantify the hormetic limits of repeatable behaviors. We demonstrate how HALO can solve the 'paperclip maximizer' scenario, a thought experiment where an unregulated AI tasked with making paperclips could end up converting all matter in the universe into paperclips. Our approach may be used to help create an evolving database of 'values' based on the hedonic calculus of repeatable behaviors with decreasing marginal utility. This positions HALO as a promising solution for the value-loading problem, which involves embedding human-aligned values into an AI system, and the weak-to-strong generalization problem, which explores whether weak models can supervise stronger models as they become more intelligent. Hence, HALO opens several research avenues that may lead to the development of a computational value system that allows an AI algorithm to learn whether the decisions it makes are right or wrong.

We propose a method for defining, identifying, and estimating the marginal treatment effect (MTE) without imposing the instrumental variable (IV) assumptions of independence, exclusion, and separability (or monotonicity). Under a new definition of the MTE based on reduced-form treatment error that is statistically independent of the covariates, we find that the relationship between the MTE and standard treatment parameters holds in the absence of IVs. We provide a set of sufficient conditions ensuring the identification of the defined MTE in an environment of essential heterogeneity. The key conditions include a linear restriction on potential outcome regression functions, a nonlinear restriction on the propensity score, and a conditional mean independence restriction that will lead to additive separability. We prove this identification using the notion of semiparametric identification based on functional form. And we provide an empirical application for the Head Start program to illustrate the usefulness of the proposed method in analyzing heterogenous causal effects when IVs are elusive.

This paper develops a unifying theory of peer effects that treats the peer aggregator (the social norm mapping peers' actions into a scalar exposure) as the central behavioral primitive. We formulate peer influence as a norm game in which payoffs depend on own action and an exposure index, and we provide equilibrium existence and uniqueness for a broad class of aggregators. Using economically interpretable axioms, we organize commonly used exposure maps into a small taxonomy that nests linear-in-means, CES (peer-preference) norms, and smooth ``attention-to-salient-peers'' aggregators; rank-based quantile norms are treated as a complementary class. Building on this unification, we show that each aggregator induces an operator that governs how exogenous variation propagates through the network. Linear-in-means corresponds to constant transport (adjacency matrix), recovering the classic (friends-of-friends) instrument families. For nonlinear norms, operator becomes state- and preference-dependent and is characterized by the Jacobian of the exposure map evaluated at an exogenous predictor. This perspective yields geometry-induced instrument that exploit heterogeneity in marginal influence and nonredundant paths, and can remain informative when one-step moments or adjacency-power instruments become weak. Monte Carlo evidence and an application to NetHealth illustrate the practical implications across alternative aggregators and outcomes.

This paper develops inference methods for ratios of deterministic trend slopes in systems of pairs of time series. Hypotheses based on linear cross-equation restrictions are considered with particular interest in tests that trend ratios are equal across pairs of trending series. Tests of equal ratios can be used for the empirical assessment of climate models through comparisons of trend ratios (amplification ratios) of model generated temperature series and observed temperature series. The analysis in this paper builds on the estimation and inference methods developed by Vogelsang and Nawaz (2017, Journal of Time Series Analysis) for a single pair of trending time series. Because estimators of ratios can have poor finite sample properties when the trend slope are small relative to variation around the trends, tests of equal trend ratios are restated in terms of products of trend slopes leading to inference that is less affected by small trend slopes. Asymptotic theory is developed that can be used to generate critical values. For tests of equal trend ratios, finite sample performance is assessed using simulations. Practical advice is provided for empirical practitioners. An empirical application compares amplification ratios (trend ratios) across a set of five groups of observed global temperature series.

We construct a stochastic dynamical systems theory in which sustainability is a structural boundary property of a fully coupled Earth--Human--Production system. Each subsystem is modelled as a vector-valued process governed by stochastic differential equations with multiplicative noise and absolute bidirectional cross-subsystem flows. Biodiversity is endogenous, and societal evaluation is represented by a reflexive functional whose weights depend on evolving human capabilities. Sustainability, development, and sustainable development are defined as trajectory properties. Sustainability corresponds to boundary non-attainment with positive or unit probability; development corresponds to local ascent in the evaluation functional; sustainable development requires directional alignment under strictly positive survival probability. No optimisation problem is imposed. Necessary and sufficient conditions are derived using Feller boundary classification and stochastic Lyapunov methods. A central result identifies the sign of the net absolute cross-subsystem flow on each component as a phase-transition parameter: if negative near zero, the boundary is of exit type and almost-sure persistence is structurally impossible, independent of intrinsic regeneration, capability accumulation, or productivity parameters. Because flows are absolute, any perturbation diffuses through the entire coupled system without requiring correlated exogenous shocks. The reflexive evaluation structure generically induces non-transitive development relations, providing a formal mechanism for path-dependent welfare comparisons. Sustainability emerges as a geometric property of boundary structure and vector-field alignment, not as a corollary of intertemporal optimality.

Climate-driven flood risk increasingly necessitates managed retreat through government buyout programmes, yet empirical evidence documents substantial racial and economic disparities in programme implementation. Here we develop a three-level Stackelberg game to analyse how federal-local cost-sharing arrangements generate inequitable outcomes through strategic interactions among federal authorities, local governments, and heterogeneous homeowners. Our model reveals three distinct mechanisms driving inequity: differential discount rates across income groups, local governments' tax-base preservation incentives, and participation thresholds that exclude fiscally constrained communities. Numerical analysis of 34,493 households across nine flood-prone US regions demonstrates that the current Federal Emergency Management Agency 75/25 cost-sharing arrangement produces a relocation ratio gap of 0.26--low-income households relocate at roughly one-quarter the rate of high-income households. Achieving near-equity requires federal cost shares of at least 85%, though equity-weighted mechanisms can attain similar outcomes at 25% lower cost. These findings provide a theoretical foundation for understanding observed disparities and identify policy levers for more equitable climate adaptation.

I consider an environment in which a decision maker faces uncertainty and privately holds information in the form of a signal about the true state of the world. The decision maker purchases additional information from a data broker before receiving the signal realization. I characterize the data broker's optimal selling mechanism, which involves screening over all possible signals. I allow the space of all signals the data broker can sell to be arbitrarily correlated with the signal the decision maker owns. This plays a key role in designing the optimal menu. In the binary action setting, the data broker extracts the efficient surplus by offering a distinct binary signal for each type. Moreover, this result holds even when the broker does not know the prior distribution over states. In more general environments, I provide conditions on the payoff structure and the decision maker's type space under which the data broker extracts the efficient surplus. I discuss scenarios in which efficient surplus extraction is not possible.

We study how increases in remote work opportunities for men affect their spouses' labor supply. Exploiting variation in the change in work-from-home (WFH) exposure across occupations before and after the COVID-19 pandemic, we find that increases in men's WFH exposure led to sizable improvements in their wives' labor-market outcomes: annual employment rose by roughly 2.5 percentage points (from a 69% pre-treatment mean), earnings increased by about 5%, weekly hours worked rose by roughly half an hour, weeks worked increased by about 1.3%, and the likelihood of part-time work declined by approximately 9%. Evidence from time-use diaries and childcare questionnaires suggests these effects are driven by intra-household reallocation of child-caring time: women are less likely to engage in primary childcare activities, while men working at home partially compensate by covering more for their spouse. These results highlight the role of households in shaping the labor market consequences of remote work.

How does transport cost affect the spatial organization of economic activities? This study develops a theoretical framework that distinguishes between two types of dispersion forces in spatial models: "local" dispersion forces acting within cities, and "global" dispersion forces acting across them. The distinction leads to a systematic classification of spatial models into a few fundamental types, each with distinct endogenous spatial patterns and comparative statics in response to changes in transport costs. The framework reconciles empirical findings and clarifies how transport-induced reorganization of economic activities can depend on the spatial scale of dominant dispersion forces.