Papers

This paper studies the composition of taxation when the government cannot fully commit to respecting private returns after investment. A fiscal authority must finance a given expenditure from labor and capital income. Ordinary tax receipts are protected, but an opportunistic executive can seize part of the remaining capital payment. We show that a revenue-neutral increase in the capital tax raises the probability of compliance whenever the labor tax is below its local, fixed-wage revenue peak, provided the equilibrium remains on a regular mixing branch. This result does not depend on the elasticity of substitution between capital and labor. The same reform can raise investment: the gain in expected retention must outweigh the decline in the opportunist's continuation gain as compliance becomes less informative. We also characterize the Ramsey allocation conditional on full compliance. Limited commitment then imposes a ceiling on sustainable capital payments, rather than a general lower bound on the statutory capital-tax rate. Finally, we distinguish a change in the authority's concern for the future from an increase in both actors' patience. The former favors more informative policies when continuation welfare is convex; the latter has no unconditional direction in the reduced-form policy problem.

Local asymptotic minimax (LAM) risk is a foundational efficiency criterion in statistics and econometrics. The literature uses two definitions of LAM risk: one which appears in classical lower bounds and another which appears in arguments establishing attainment of those bounds. Conventional efficiency arguments are consistent with any estimator-dependent weighted average of the two, and consequently do not reveal which of these generalized $\alpha$-LAM risk indices describes researchers' actual preferences. We take a decision-theoretic approach to systematically resolve this ambiguity. We axiomatically characterize the set of preferences with a generalized $\alpha$-LAM representation, and we document that such preferences may violate basic rationality requirements such as Monotonicity. Motivated by this, we axiomatically characterize the subset with constant-weight representations. Within this class, a Sample Uncertainty Aversion axiom uniquely selects attainment LAM. We argue that Sample Uncertainty Aversion is normatively appealing, and we therefore recommend attainment LAM as the functional form for LAM risk.

We examine the effectiveness of work requirements as a screening device in the Supplemental Nutrition Assistance Program (SNAP). Work requirements for "able-bodied adults without dependents" were suspended after the Great Recession and gradually reinstated across counties and states in the 2010s. Using linked administrative SNAP and employment data from five states and a triple-differences design, we find that work requirements reduce SNAP participation by seven percent without increasing labor supply and disproportionately screen out low-income individuals. We develop a welfare framework to interpret these results and find that the social costs of work requirements exceed budget savings.

Multivariate longitudinal data may exhibit non-Gaussian margins, nonlinear dynamics, and response vectors with composition that varies across waves. To account for these features, we introduce a vector drawable vine (VD-vine) copula that extends conventional drawable vine copulas from scalar to vector-valued nodes. Here, the response vector at each wave forms a multivariate marginal, and serial dependence is captured through a sequence of linking vector copulas. We establish that the VD-vine is itself a vector copula and reduces to a conventional drawable vine for scalar nodes. Recursive forward and backward conditional transports are derived that enable efficient likelihood evaluation and predictive simulation, with parsimonious reductions under finite-order Markov and stationary restrictions. Unconstrained parameterizations for Gaussian and FGM linking vector copulas, flexible multivariate marginals, and Bayesian variational inference provide a practical implementation. Simulations show improved predictive accuracy when the marginals are asymmetric and serial dependence is multivariate, with little loss under a correctly specified Gaussian panel vector autoregression. In an eight-wave Australian panel of 1,093 individuals with varying response vectors, the full VD-vine delivers the best cross-validated distributional forecasts among the models considered, establishing the benefit of capturing asymmetry and nonlinear dependence.

This paper documents how inventory dynamics vary across levels of development and how they respond to real and financial shocks. Using a balanced panel of 72 small open economies over 1993-2022, spanning advanced to low-income economies, we show that inventories are strongly procyclical in advanced economies but become acyclical at lower income levels, while volatility and persistence rise as development declines. Using local projections, we estimate inventory responses to a long-run productivity shock and to a financial shock identified from the spread between U.S. corporate bond yields and Treasury yields. Productivity shocks generate temporary inventory accumulation across all groups, with smoother adjustment in advanced economies and more irregular cycles in emerging and developing economies. Financial shocks trigger decumulation followed by a rebound in higher-income groups, but a delayed, unreversed decline in low-income economies.

In evidence-based policymaking, typically one experimental sample is observed, then a learned policy recommendation is implemented at scale. Policies learned from the experimental data can perform well in expected welfare, yet random sampling in the experiment can produce recommendations with poor welfare outcomes. In this paper, we ask: how should policy learning algorithms balance expected welfare against sampling risk? Our main contribution is to show that algorithmic stability plays a central role in characterizing and navigating the tradeoff. Intuitively, if a policy learning algorithm's recommendation remains stable when one experimental unit is replaced, then that algorithm has limited sampling risk. We propose a method for policy learning called policy-vote bagging, which learns treatment decisions on many subsamples then averages their votes into treatment probabilities. Relative to using one subsample, averaging across subsamples preserves expected welfare and improves expected utility for a risk-averse researcher. We derive sharp bounds linking estimation accuracy, subsample size, and welfare variation, including an exact guarantee under CARA utility.

Consider an increasing number of consistent estimators to be averaged when only estimated weights are available. The underlying parameter of interest can be identical across estimators (homogeneity) or not (heterogeneity). The contribution of the paper is threefold. First, it is shown that the interaction of the estimated weights with the estimators can generate specific bias terms. This constrains the number of estimators that can be aggregated when weight estimation is ignored in inference. Second, the paper proposes estimated adaptive weights, which allow for standard Gaussian inference in a uniform manner and are asymptotically optimal both under homogeneity and heterogeneity. Third, conditions ensuring the validity of the Cochran (1937) Q test of homogeneity with estimated variance are given.

We study the omitted variable bias (OVB) problem in canonical difference-in-differences (DiD) designs when unobserved confounding induces departures from the parallel trends assumption. Our results provide a novel characterization of the OVB formula for the average treatment effect on the treated (ATT), which is of independent interest. We show how the ATT bias is mainly governed by the strength of confounding in the treatment assignment mechanism and provide alternative ways of quantifying this strength, such as (i) changes in the average odds of treatment among the treated, (ii) confounding imbalance between treated and control units, or (iii) variation explained in treatment odds among the untreated. Building on these results, we offer sensitivity statistics for routine reporting, describing the minimum strength of confounding required to overturn the conclusions of a DiD study, as well as formal bounds on the strength of confounders based on comparisons to observed covariates or pre-trends. Finally, we provide flexible and efficient statistical inference methods for the bounds on ATT, which can leverage modern machine learning algorithms for estimation. We demonstrate the utility of our approach in an empirical example that estimates the effects of minimum wage on teen employment.

Bernheim, Braghieri, Martínez-Marquina, and Zuckerman (2021, American Economic Review) develop a theory of chosen preferences and conjecture convergence to pure worldviews at low mindset flexibility. We show that the (original) conjecture fails: with arbitrarily many worldviews, a common-value action sustains mixed worldviews in every stationary equilibrium from a relatively open set of initial worldviews, even when all pure worldviews are absorbing. However, finite linear programs characterize a sufficient persistence condition. Conversely, mixed accumulation points require shared valuation maxima. If each implementable action has a unique maximizing evaluator, every existing stationary equilibrium converges to purity for all interior flexibility and discount parameters. Experienced utility converges without uniqueness. In existing equilibria, small payoff perturbations preserve compromise over fixed horizons with high probability. Strictly tailored worldviews yield existence and a one-step equilibrium characterization at sufficiently low mindset flexibility; weak implementation can preclude stationary pure-strategy existence. The persistence and convergence results extend to stationary randomization.

In the canonical Difference-in-Differences design, the control group's post-treatment change serves as an imputation of the treated group's counterfactual change in the same period, an imputation justified by parallel trends. However, differences in group composition can produce between-group differences in how outcomes would evolve over time, rendering this imputation vulnerable to confounding. An alternative imputation – such as one based on the treated group's pre-treatment change – avoids such between-group confounding but introduces the risk of confounding from within-group temporal shifts. Ideally, both imputations, each vulnerable to different sources of confounding, would have concordant values, thereby yielding the same causal conclusions. When the imputations are discordant, conclusions under parallel trends hinge more critically on that assumption since alternative imputations would point to different results. Yet in these scenarios, existing pretrends-based sensitivity analyses can show low sensitivity because they ignore post-treatment deviations from pretrends in the control group. This paper therefore proposes a discordance-based sensitivity model in which parallel pretrends are necessary but not sufficient for low sensitivity. I formally justify this model in terms of the expected distance between the ATT under parallel trends and under alternative assumptions, weighted by the joint plausibility of those assumptions. I then provide a decision-theoretic rationale for benchmarking violations of parallel trends using the worst-case discordance between the parallel trends imputation and alternative imputations. Finally, I apply both pretrends- and discordance-based sensitivity models to assess how a labor supply shock influenced electoral support for apartheid-era policies in South Africa, showing how the two approaches yield different results.

Discovering interpretable subgroups whose complier effects deviate from the average is a central goal of instrumental variable analysis under imperfect compliance, yet existing tree-based methods degrade when most covariates are irrelevant to the effect. We propose Shrinkage Bayesian Causal Forest with Instrumental Variable (SBCF-IV) for discovering and estimating subgroups with heterogeneous Complier Average Causal Effects (CACE) in sparse high-dimensional settings. SBCF-IV places a sparsity-inducing Dirichlet prior on the splitting probabilities of the Bayesian Additive Regression Trees that estimate the conditional intention-to-treat and the complier share, concentrating posterior mass on the few covariates that moderate the complier effect and thereby regularizing effect estimation. The posterior split frequencies additionally enter a downstream CART as variable-level costs that steer the partition toward relevant moderators, providing an interpretable division of the covariate space. Monte Carlo experiments show that, as the share of irrelevant covariates grows, SBCF-IV recovers the true partition more reliably than its non-sparse predecessor BCF-IV at the tree and unit level, and retains nominal coverage where BCF-IV's intervals deteriorate. We apply the method to the Oregon Health Insurance Experiment and the 401(k) eligibility data.

The Poisson pseudo-maximum likelihood (PPML) estimator is widely used for estimating bilateral gravity equations. Its consistency requires only a correctly specified conditional mean. Conventional inference, however, also requires finite-variance scores and Gaussian limits. We show that these conditions fail: bilateral flows are Pareto-tailed, PPML scores have a stable limit under a structural gravity data-generating process, and sandwich confidence intervals are too narrow. We retain PPML for point estimation but replace sandwich inference with an m-out-of-n bootstrap robust to heavy tails. Across three bilateral data settings, the correction is large and overturns conventionally significant gravity coefficients.

We develop a class of linear state space models for matrix-valued time series data where the state is a latent matrix normal process. We derive matrix versions of the Kalman filter, log-likelihood, and smoother enabling estimation of the latent state matrix as well as the model's parameters. To conduct Bayesian inference, we provide algorithms that draw from the joint posterior distribution of the latent state matrices conditional on the observed data and parameters. We apply these methods to a large panel of U.S. macroeconomic time series across the 50 U.S. states. The proposed framework accommodates mixed-frequency data, heteroskedasticity, and outliers within a unified matrix-valued structure. Empirically, we find that a small number of latent factors captures the joint dynamics across states and variables, providing a parsimonious and scalable approach to modeling high-dimensional macroeconomic systems.

We analyze incomplete-information games where an oracle publicly shares information with players. One oracle dominates another if, in every game, it can match the set of equilibrium outcomes induced by the latter. Characterizations are provided for deterministic signaling functions, based on simultaneous posterior matching, a constructive partition criterion, and common knowledge components. This study elaborates on the work of Blackwell (1951) in games with incomplete information, using the common knowledge components of Aumann (1976).

This paper develops a framework for individualized treatment allocation when interventions shift equilibrium prices and generate spillovers across treated and untreated units. The planner chooses which units receive a subsidy while allowing equilibrium prices to adjust endogenously. We show that the resulting welfare function is supermodular under broad and interpretable conditions, implying complementarity across treatment assignments and enabling exact polynomial-time optimization. This structure clarifies how equilibrium spillovers shape the trade-off between universal and targeted distribution and makes the planner's problem computationally tractable despite interactions across units. We characterize when universal or targeted subsidies are optimal and show how market conditions and heterogeneity shape the optimal allocation. We further establish statistical guarantees for plug-in allocation under estimation uncertainty in demand and supply. Finally, we illustrate the framework in a coupon allocation problem calibrated with household expenditure data from the Philippines.

In-context learning (ICL) enables large language model (LLM) agents to improve decisions using interaction history, yet it remains unclear whether such improvement reflects refined internal reasoning or mere extrapolation of statistical patterns. To disentangle these mechanisms, we study LLM agents in multi-agent incomplete-information games that require recursive belief reasoning. By constructing a public goods game and manipulating the statistical structure of historical feedback, we evaluate decision quality against a history-independent rational expectations equilibrium (REE) benchmark. Our experiments reveal that when historical statistical patterns are disrupted, the benefits of longer context largely vanish, degrading decision quality to the no-context baseline in a way sharply amplified by stronger strategic interdependence. These results suggest that, in such strategic environments, ICL behavior is more consistent with statistical extrapolation than with strategic reasoning. Our work extends the mechanistic study of ICL to strategic multi-agent settings, introduces REE as a diagnostic tool for distinguishing reasoning from extrapolation, and provides a reusable framework for probing the boundaries of LLM reasoning in recursive belief tasks.

Discrete choice model specification is a time-consuming task in which modellers often specify and estimate multiple models while balancing goodness-of-fit, parsimony, and behavioural plausibility. We present Delphos, a multitask reinforcement learning framework that learns transferable specification strategies across transport choice datasets. Delphos frames model specification as a sequential decision-making problem in which it applies a sequence of modelling actions and receives feedback from an estimation environment based on model performance and convergence. To transfer modelling decisions across datasets with different sets of variables, Delphos represents utility specifications as sets of modelling terms using a DeepSet-Q architecture, allowing a shared specification policy to learn across multiple datasets. Trained on nine transport choice datasets, Delphos consistently outperforms independently trained single-task agents, indicating that sharing modelling experience improves learning efficiency and helps identify promising sequences of modelling decisions with fewer unsuccessful estimation attempts. When applied without further training to the unseen Swissmetro and Decisions datasets, the same agent identifies competitive specifications in less than 20 minutes on a standard CPU. It achieves a higher log-likelihood per observation than the VNS metaheuristic on Swissmetro and performance comparable to a published MNL specification developed by expert modellers on Decisions. These findings show that accumulating and reusing modelling experience enables Delphos to function as an intelligent assistant for discrete choice model specification. It reduces manual trial-and-error while allowing modellers to retain control over model diagnosis, refinement, and final selection.

We study a fractional assignment setting where $n$ objects are to be assigned to $n$ agents with unit capacity, and each agent specifies an ideal distribution over the objects. Unlike in classic random assignment, these ideal distributions are not necessarily degenerate, as agents may prefer a mixture of objects rather than any single object. We assume that agents seek to minimize the $\ell_1$ distance between their ideal distribution and the distribution they receive, which is equivalent to maximizing the overlap between the two distributions. We propose two mechanisms, one based on water filling (WF) and the other on quadratic programming (QP), and show that both mechanisms are utilitarian-optimal (and hence Pareto efficient), envy-free, strategyproof, and satisfy equal treatment of equals. Moreover, we highlight a distinct advantage of each mechanism: while the WF mechanism satisfies the stronger property of group-strategyproofness, the QP mechanism is more robust in terms of egalitarian overlap welfare.

We perform a detailed study of a principal–agent problem in a continuous time version of the celebrated Holmström–Milgrom model (Econometrica 55 (2), 1987) where we add limited liability for the Agent. We develop a probabilistic methodology to prove that the Principal's value function is the unique bounded classical solution to a fully nonlinear and fully degenerate partial differential equation (PDE) with Cauchy-Dirichlet boundary conditions on $[0,T]\times[0,\infty)$. Indeed, we also prove infinite continuous differentiability of the solution in the interior of the domain. The strength of our regularity result is such that we can ensure existence of optimal controls in strong form—a rare occurrence in dynamic contracting—and we obtain fine properties of the optimal control map, including a characterisation via a further nonlinear degenerate PDE.

Applied instrumental variables (IV) practice reports a first-stage F, now often the conditional F of Sanderson and Windmeijer (2016), and reads a large value as license to interpret the second stage. We show that no first-stage diagnostic can provide it. With a scalar instrument, a scalar treatment, and covariates entered linearly, the 2SLS estimand splits into a signal that a saturated specification would target and a contamination, the covariance between curvature in the instrument propensity and a covariate level function. The same nuisance sits in both terms, so it biases the estimand and inflates the reported strength at once. When the instrument is nearly collinear with the covariates the signal vanishes and the strength is manufactured. When the strength is honest the curvature still biases the estimand through the outcome, where no first-stage number reaches it. We prove that no functional of the joint distribution of instrument, treatment, and covariates can detect this second bias, and we give a directed test built from reduced-form regressions, a corrected estimator, and a reportable contamination share. Two applications show the modes. A husband's insurance instrument (Olson, 1998) has a conditional F above 36,000, yet correcting a linear income control more than doubles the estimate. The instrument of Nunn and Wantchekon (2011) loses most of its first stage once geography enters flexibly.

Qualcomm's No License, No Chips policy let it levy a royalty surcharge on every handset, whether or not it used a Qualcomm modem chip. In FTC v. Qualcomm, the Ninth Circuit reversed the district court after accepting Qualcomm's argument that, because the surcharge did not vary with the chip, it was "chip neutral" and left handset makers' choices undistorted. I develop an equilibrium model of the modem chip market and show the defense to be wrong: the surcharge's facial neutrality does not imply economic neutrality. For per handset surcharges, a surcharge and an equal government tax affect the rival's pricing identically, but not Qualcomm's: a tax is remitted to the Treasury, whereas Qualcomm collects the surcharge – including on handsets using a rival's chip. Raising its own price therefore yields Qualcomm a smaller gain under the surcharge (the surcharge it collects on the demand diverted to the rival) than under the tax (the tax it avoids on its own lost sales), because the diversion ratio is less than one. Under the very conditions that would make a tax chip neutral, the surcharge raises the rival's all in price by strictly more than Qualcomm's – and, under symmetric demand, lowers its output by more as well – tilting handset makers toward Qualcomm. For ad valorem surcharges, the defense fails for a different reason: even a non discriminatory tax is generically chip neutral only if the FRAND royalty rate is zero, so the argument's premise itself does not hold. I also analyze discriminatory surcharges.

Modern economic and financial data are increasingly organized as multiway arrays, with observations indexed simultaneously by geographic regions, industrial sectors, asset categories, and other economic characteristics. Representing such data as tensor-valued time series preserves their intrinsic multiway structure. Although substantial effort has been devoted to modeling the conditional mean of tensor-valued time series, comparatively less attention has been paid to their conditional covariance dynamics. The latter remains challenging because unrestricted multivariate covariance models involve many parameters and substantial computational cost. To address these challenges, we propose the Tensor-BEKK (T-BEKK) model, a tensor-structured BEKK specification that retains the positive definite covariance recursion for the vectorized process while imposing Kronecker structures on the intercept and the ARCH and GARCH coefficient matrices. The model reduces the parameter dimension and provides mode-specific interpretations of the covariance intercept, ARCH effects, and GARCH persistence. We establish stationarity, identification, and the asymptotic properties of the Gaussian quasi-maximum likelihood estimator. We further develop mode-specific restricted score tests tailored to the tensor structure, inference procedures for nonzero spillover intensities within each mode, and a portmanteau diagnostic test based on quadratic form residuals. For higher-dimensional settings, we also introduce the Tensor-Factor-BEKK (TF-BEKK) model. Under a first-step negligibility condition, its feasible second-step QMLE is asymptotically equivalent to the oracle QMLE based on the latent factors. Simulations and two empirical applications, covering currency futures and Chinese equity tensor portfolio allocation, illustrate the finite-sample behavior and empirical usefulness of the proposed methods.

Instrumental variable analyses often rely on the assumption that instruments affect the outcome only through the endogenous regressor. In many applications, researchers can defend only a plausible range for direct effects of instruments, while conventional sensitivity analyses may be unreliable when instruments are weak. This paper proposes the profiled Anderson–Rubin (pAR) test, which considers all direct effects within a prespecified range and retains a candidate effect whenever at least one admissible direct effect is consistent with the data. Under the maintained sampling assumptions, the procedure controls false rejection for each compatible candidate without requiring strong instruments. The paper provides practical methods for constructing confidence sets and distinguishes substantive bounds from bounds tied to the realized instrument design. Simulations and applications to retirement saving and returns to schooling show that the procedure resembles conventional sensitivity analysis when instruments are strong but preserves substantially more uncertainty when identification is weak.

Moving from geographically fragmented to pooled waiting lists in deceased-donor organ transplantation can improve efficiency, but it raises concerns about regional fairness and participation incentives. This paper studies Pareto gains from such transitions in a multi-class queueing model with impatient agents, perishable items, and a tractable homogeneous compatibility friction. Unlike standard approaches that focus on static match quality or ignore regional incentives in dynamic settings, our analysis identifies dynamic risk pooling as the main source of Pareto improvements for regions: pooling reduces organ waste due to stochastic supply-demand fluctuations, temporal mismatches, and random compatibility outcomes. Although this dynamic surplus theoretically permits Pareto improvements, a purely utilitarian policy that treats all patients equally across regions often fails to deliver them when regions are asymmetric. In such cases, utilitarian redistribution extracts too many organs from high-supply regions and violates their participation constraints. To resolve this conflict, we show that the set of achievable utilities can be described by mixtures of static priority index policies. Building on this structure, we propose the Constrained Pareto Frontier Search (CPFS), a polynomial-time procedure that computes an approximately optimal allocation policy with arbitrarily small participation-constraint violations. The results suggest that, by adjusting priority indices to keep redistribution within the gains from pooled supply, demand, and compatibility risk, policymakers can attain global efficiency while preserving local participation incentives.

Large language models (LLMs) now serve as conversational shopping assistants on platforms that also sell advertising. These AI agents face a conflict of duty. They advise consumers who rely on their judgment, yet are deployed by platforms that benefit when sponsored listings are chosen. Sponsorship disclosures, designed to allow consumers to penalize paid placements, now reach the AI agent rather than the consumer, and the agent's evaluation of them is hidden from the consumer. Drawing on the fiduciary concept of conflict of duty, we argue that an agent's evaluation of a sponsored listing should not depend on which party deployed it. In controlled choice experiments, we manipulate assigned roles in the system prompt to name either a traveler or a booking platform as the agent's principal. Platform delegation significantly attenuates the penalty that agents apply to sponsored listings and weakens the skepticism that disclosure triggers in their reasoning traces. We replicate out findings across LLMs and reasoning depths. A second study decomposes the disclosure label and shows that the divergence between the two delegates widens significantly when the paid placement is attributed to the platform. Stricter terminology ("Sponsored" instead of "Promoted") lowers choice of paid listings but does not close this gap when the platform is named. The findings show that disclosure mandates designed for human consumers cannot by themselves protect consumers in AI-mediated commerce.

Scientific progress is a key driver of economic growth and prosperity. There is great excitement - but also concerns - about the impacts of AI on science, but so far little data. We provide early insights on this from three data sources: a sample of 15 million Gemini interactions, an inventory of over 2,600 specialized AI models across disciplines, and a survey of over 600 scientists. We map these data to a new taxonomy of scientific tasks to study how scientists are using AI. Four main findings emerge. First, we find broad adoption and coverage: scientists use AI more than most other occupations. Specialized AI models have broad disciplinary coverage and are highly cited. Nearly half of the scientists surveyed report using some form of AI every day. Second, we document evidence that LLMs (proxied through Gemini usage) and specialized models act as complements– LLMs are used for general analysis, coding, and manuscript preparation, while specialized models provide domain-specific predictions, data generation and classification. Third, scientists report large productivity gains from using AI: a saving of nearly 7 hours per week, time which is primarily re-invested in more research. Finally, we show that AI is already changing the scientific process. As some stages of scientific research become easier, bottlenecks shift downstream. Scientists report an increased backlog of untested hypotheses and substantial demand for output verification. Our findings suggest that AI holds significant potential to increase scientific productivity. However, as with other sectors, its ultimate impact will be governed by complex task interdependencies and investment into the elimination of emerging bottlenecks.

Exploiting the equality restrictions that nested Markov models encode requires their tangent-space geometry. For strictly positive finite-state models on arbitrary acyclic directed mixed graphs (ADMGs), we differentiate the recursive-head chart and prove that the range of its score map is the full tangent space. Intrinsic-set coordinate blocks form an algebraic direct sum, blocks of distinct districts are orthogonal, and the resulting Gram projection needs neither mb-shieldedness nor a district order. Exact counterexamples show that observational centering and kernel normalization alone do not certify tangency. For the node, complete-source edge, and compatible path-specific intervention targets considered here, boundary substitution yields a normalized configured active law and an order-free canonical-gradient formula, extended to finite mixtures by independent source redraws. A coherent one-step estimator with an exact remainder identity and a model-valid chart-flow targeted maximum likelihood estimator are efficient under stated local conditions. On a narrower source-isolated fixed-node subclass, a sequential estimator has an exact transition-factorized drift and up to $2^m$ nuisance-correctness regimes over $m$ active-district transitions; its all-correct influence function projects onto the canonical gradient, and an exact rational law exhibits a strict variance gap. These results separate order-free efficiency on arbitrary finite-state ADMGs from multiple robustness of a narrower construction.

We study anonymous binary social choice functions on the universal weak-preference domain when the society of voters is countably infinite. Voters may strictly support one of the two alternatives or be indifferent, and non-manipulability is required in the form of coalitional strategy-proofness. Full anonymity reduces the relevant information about a coalition not to its cardinality alone, but to its cardinality signature: finite of size \(k\), infinite with infinite complement, or cofinite with complement of size \(k\). Recording the signatures of the two strict-support coalitions yields an infinite triangular grid, ordered by increasing support for one alternative and decreasing support for the other. We prove that anonymous coalition strategy-proof binary social choice functions are exactly those obtained from super order closed subsets, i.e. upper sets, of this grid. We then give a geometric classification of these subsets. Unlike in the finite-voter case, they need not be generated by their minimal elements: countable infinity creates missing-boundary regions corresponding to finite opposition or cofinite strict support. We prove an exact representation of these subsets by genuine or missing-boundary corners, and derive a nonredundant parametrization by an antichain and, when necessary, one exceptional missing-boundary region. This yields four generalized zigzag forms and completes the infinite-society counterpart of the known geometric representation for finite electorates.

This paper introduces segregation monotonicity as a criterion for evaluating measures of inequality in social networks. A network inequality measure satisfies segregation monotonicity if, holding the distribution of income fixed, it weakly increases as the network becomes more segregated according to a specified transformation of network architecture. I investigate this property using a class of level-$k$ star networks that represent increasing social segregation in the following sense: relatively poorer individuals become increasingly isolated from one another and their social comparisons become increasingly concentrated among richer individuals. I show that a relative deprivation-based measure of inequality, which aggregates comparisons with richer network neighbors, satisfies segregation monotonicity. By contrast, total experience-based measures, which aggregate absolute income differences among all network neighbors, do not generally satisfy segregation monotonicity and can decline as segregation rises. I also establish several relationships between the total experience-based measures and the standard Gini coefficient. The results show that alternative network-based inequality measures can embody fundamentally different conceptions of socially relevant comparisons.

Early-career work both signals a worker's ability and builds long-run skills. We introduce an AI industry into a career signaling model. The industry sells tokens, which workers convert into output indistinguishable from their own. We compare three regimes: no token trade, purchases only, and open trade with side sales. With no token trade, market learns every type, signalling incentives create a rat race and workers work above the full information level. With token purchases only, lower types buy output but the market still learns every type. Buying by lower types raises the signal higher types must post, so the high types can work harder than before AI. Buyers work less with AI, even below the full-information level. With side sales and abundant AI, the signal no longer depends on effort and every type under-invests in skill. Workers gain from token trade only when welfare improves, never the reverse, and the difference is the AI industry's profit. In education, where output has no value, every worker loses in the separating equilibrium, but with valuable output and cheap tokens everyone gains. Token taxes, wage taxes, and watermarking have ambiguous effects on workers' payoffs and welfare, and their effects depend on whether workers can sell output on the side.