We develop an agent-based, stock-ow-consistent model of an economy undergoing automation, built to ask which scal instrument reaches the durable surplus that articial intelligence creates. The model separates two channels: a competitive return on reproducible robotic capital, and a mobile, foreign-held intellectual-property rent earned by AI. Production is an endogenous nested-CES technology; wealth concentration is microfounded through heterogeneous, persistent returns to wealth; and taxation and capital mobility are modelled as behavioural responses. The central result is that the durable surplus is the foreign-held AI rent, a cross-border licence fee that corporate, robot, and compute or token taxes largely miss and that only a source-based levy (a digital-services-style tax or a withholding) reaches. The appropriate policy depends decisively on whether a country owns the automation or imports it: for a host that owns the rent the problem is domestic inequality, reached by progressive and wealth taxes; for a rent-importing host the problem is base erosion and a gradual transfer of capital ownership abroad, which a residence-based wealth tax cannot reach. We report conditional orderings, stress-tested with global (Sobol) sensitivity and a formal stability analysis, rather than point forecasts.

We study a model in which a sender allocates limited treatment to agents with heterogeneous quality and later recommends selected agents to a receiver, seeking to maximize the number of agents accepted by the receiver. All agents value treatment, which improves agents' quality, but treatment must be allocated before the sender observes agents' initial quality; recommendation occurs only after quality is learned. A natural benchmark is to design the two instruments separately: allocate treatment randomly first, and then recommend agents from the top down afterward. Our main result shows that the sender can do strictly better by coordinating treatment allocation with recommendations. In the optimal joint mechanism, treatment is non-monotone in quality: an intermediate group has a lower treatment probability than both higher- and lower-quality agents, but is compensated with a guaranteed recommendation when treatment is realized. We provide an implementation through contracts that induce self-selection and discuss applications to education, industrial policy, and startup incubation. The takeaway is simple: coordinate treatment allocation and recommendation.

Infinite-dimensional parameters are ubiquitous in empirical economics. This paper develops an Imbens--Manski--Stoye type confidence band for infinite-dimensional partially identified parameters. In particular, we propose multiplier bootstrap-based construction of a uniform confidence band. By employing approximation theorems for suprema of non-centered empirical processes indexed by possibly non-Donsker classes \citep{chernozhukov2016empirical}, we confirm the uniform validity of the proposed procedure.

Two recent papers by Borusyak and Hull (2023, 2026) propose using known formulas to adjust linear instrumental variable estimators for confounding covariates. Implementing this "formula instrument" approach requires making a parametric assumption on the distribution of the unobserved shocks that generated the instrument. We develop a method for systematically evaluating the sensitivity of formula instrument estimates to this parametric assumption. The method is straightforward to implement using our companion R package formulaiv. We use our method to reanalyze the applications in both Borusyak and Hull (2023) and Borusyak and Hull (2026). In both applications, we find that a variety of estimates of different signs and magnitudes can be recovered by slightly changing the shock distribution.

This paper extends the sufficient-statistics formula for efficient unemployment developed by Michaillat and Saez (2021) to account for part-time employment. I introduce two additional sufficient statistics that measure the share of part-time employment and part-time hours relative to full-time hours. Applying the framework to the United States (1951-2026) and Japan (1970-2025), I compare the effects of total part-time employment and involuntary part-time employment on efficient unemployment. Total part-time employment has substantially larger effects than involuntary part-time employment. While involuntary part-time employment provides information about labor-market slack, the main change in efficient unemployment comes from part-time work itself because part-time workers supply fewer market hours than full-time workers. Under the total part-time calibration, efficient unemployment averages 4.7 percent in the United States before COVID and 4.2 percent after COVID. In the Japanese application, the full-sample average is 2.7 percent. The distinction is especially important in Japan, where part-time employment is widespread and often reflects flexible work arrangements. These findings suggest that aggregate labor input, rather than involuntary part-time employment alone, is an important determinant of labor-market efficiency.

Has generative AI changed how labor markets value human capital? We study this question using data from Upwork, a large online labor market. Representing worker profiles with high-dimensional text embeddings, we compute the importance of human capital information and price in predicting labor demand, and incorporate these measures into a difference-in-differences design around the release of ChatGPT. We find that in more AI-exposed job categories, the importance of human capital declines and the importance of price rises, suggesting a commoditization effect of AI on labor. Two additional findings support commoditization as a mechanism: The demand premium enjoyed by workers with strong human capital declines in more AI-exposed categories, and demand reallocates toward lower-priced workers. Our results have implications for the design of online labor markets, workers' incentives to invest in human capital, and labor welfare.

Multiplicative Kantian equilibrium has been proposed as a solution to inefficiency in social dilemmas, yet its emergence and stability are associated with a number of coordination and distributional difficulties. Drawing on a simple model of voluntary public good provision with two agents who differ in their initial endowments and have logarithmic preferences, this paper identifies three barriers that arise sequentially when unequal agents attempt to adopt Kantian cooperation voluntarily. The model compares Nash equilibrium with multiplicative Kantian equilibrium under two different parametrizations: one in which the strategic variable is contributions to the public good, and another in which it is private consumption. First, we show that the transition from Nash equilibrium to contribution space Kantian behavior is not always a Pareto improvement: under sufficiently high inequality, the poor agent may prefer the Nash outcome. This barrier can be mitigated by preliminary redistribution. Second, even when agents are willing to cooperate, the choice of a parametrization of the strategic space becomes a distributional issue: different ways of scaling actions lead to different distributive consequences and create a conflict of interest between agents. Third, if the chosen parametrization admits a continuum of Pareto efficient outcomes, an additional coordination problem arises-agreeing on a specific point on the Pareto frontier. The paper reconstructs these barriers as a three step coordination problem in which expectations about later stages affect willingness of agents to enter Kantian cooperation at the outset. On the basis of the results obtained, a program for further formal research is outlined. The findings contribute to understanding the conditions under which Kantian cooperation can be voluntarily adopted and sustainably maintained.

We study the strategic implications of the non-invariance of multiplicative Kantian equilibrium (MKE) under monotone transformations of the strategy space. Before interacting with a standard Nash player, a Kantian player publicly selects a smooth increasing scale that determines how proportional deviations are evaluated. Material payoffs and feasible actions remain unchanged, but the chosen scale alters the Kantian first-order condition through endogenous elasticity weights. The representation of actions therefore becomes a commitment device. We characterize the stationary outcomes implementable by a common monotone scale. A sharp dichotomy emerges. Under strategic substitutes, the Kantian player can approach the Nash payoff arbitrarily closely but cannot exceed player 2's Nash benchmark; scaling is defensive and eliminates the payoff loss associated with naive Kantian behavior. Under strategic complements, scaling becomes offensive: the Kantian player can stationary-implement the Stackelberg leader outcome and obtain a payoff strictly above the Nash benchmark. In the canonical Cournot and differentiated Bertrand examples, we explicitly construct scales satisfying the required local elasticity ratios and verify the second-order conditions, so the stationary outcomes are local transformed Nash-Kantian equilibria. Allowing player-specific scales would align the Kantian first-order condition with the Stackelberg condition along the entire reaction curve under complements, but would violate monotonicity under substitutes. This reveals a trade-off between universality and strategic flexibility. The results identify endogenous scaling as a commitment mechanism and connect Kantian optimization to strategic leadership and strategic non-equivalence.

We introduce a new non-manipulability axiom called worst-case strategy-proofness (WCSP). This axiom is weaker than strategy-proofness and stronger than non-obvious manipulability-worst (NOM-worst) by Troyan and Morrill (2020). WCSP focuses on non-manipulability in a worst-case scenario. We examine the implications of WCSP in a voting model. Although many voting rules, such as the plurality rule, the Borda rule, and the Dowdall rule, satisfy NOM-worst, they violate WCSP. We obtain a necessary and sufficient condition for the anti-plurality rule with fixed-order tie-breaking to satisfy WCSP in terms of the numbers of agents and alternatives.

This paper introduces statistical inference procedures for unit-specific coefficients in panel data models, where the coefficients exhibit a latent group structure. The proposed methods achieve efficiency gains by clustering units into a small number of groups, while explicitly accounting for the statistical uncertainty of group assignments. The core idea is to integrate standard inference procedures, such as the $t$-test and Wald tests, with confidence sets for group membership. Two methods are proposed: the first takes the minimum of the test statistics over the confidence set for group membership, and the second corrects for bias caused by possible group misassignment. The former can produce shorter but possibly disconnected sets, while the latter guarantees connected, interpretable intervals at some cost in length. We also develop standard errors that are adjusted for possible group misassignment and valid even with short time periods, which may be of independent interest. Monte Carlo simulations demonstrate that our approach yields narrower confidence sets for units with relatively large error variances than unit-by-unit time-series methods. In contrast, ignoring statistical uncertainty in the group membership estimation leads to distortions in size and coverage. We illustrate the method with an empirical example that estimates the effect of the minimum wage in each U.S. state.

This paper develops a general equilibrium overlapping-generations model with endogenous fertility, in which firms accumulate both physical and artificial intelligence (AI) capital, and uses it to study the macroeconomic transmission of two structural disturbances: an AI technology shock and a longevity shock. The AI shock acts as a capital-demand disturbance: it raises all rates of return, most sharply the return to AI capital, reallocates investment from physical to AI capital, and produces a front-loaded output expansion that decays monotonically. The longevity shock acts as a saving-supply disturbance: it deepens the aggregate capital stock, compresses returns and the real interest rate, and generates hump-shaped, persistent dynamics. The two shocks move fertility in opposite directions: AI raises it modestly through an income effect, while longevity lowers it by strengthening the life-cycle saving motive and the cost of childrearing. A forecast-error variance decomposition attributes most aggregate volatility to the longevity shock, while the AI shock dominates the variance of the return to AI capital. Fertility is strongly countercyclical and almost perfectly negatively correlated with hours worked, placing household time allocation at the center of the mechanism. Robustness checks across the capital share, the shock persistence, and the utility specification show that only an empirically implausible labor-AI elasticity reverses the wage and fertility signs. A welfare analysis finds the AI shock welfare-improving under complementarity, whereas longevity produces a short-run welfare loss that recedes as capital deepening raises wages, since households initially compress consumption and fertility to finance a longer retirement.

In this paper, we study the patterns of ethnic endogamy in Croatia in relation to six ethnic groups between 1970 and 2015. We find that, over the 45-year period analyzed, the segmentation of the Croatian marriage market was weaker between Czechs and non-Czechs, Hungarians and non-Hungarians, Italians and non-Italians, and Slovaks and non-Slovaks than between Serbs and non-Serbs or Croats and non-Croats. This finding is substantiated by survey evidence revealing similar patterns on relative social distances between different ethnic groups in Croatia and Serbia. From a methodological perspective, we show that a plausible ranking of the degree of segmentation of the Croatian marriage market along ethnic lines can be obtained only when marital sorting is characterized by a carefully selected indicator. While a recently reinvented indicator captures sensible patterns of ethnic endogamy, the commonly applied odds-ratio fails to produce results consistent with survey evidence. AI generated video summary of the paper: this https URL

Battery energy storage systems (BESS) are expected to play an important role in electricity markets with increasing shares of renewable generation. While existing research has primarily focused on price arbitrage and ancillary services, the role of grid fees in shaping BESS operation and profitability remains insufficiently understood. This article investigates how different levels of distribution fees affect the scheduling and economic viability of BESS in the day-ahead electricity market. The analysis employs a mixed-integer linear programming model of BESS operation combined with electricity price data from the German market. Four system configurations are considered: stand-alone storage and BESS combined with consumption, generation, or both. The value of storage is measured as the difference between system profits with and without BESS. In addition, a rolling-horizon optimization framework is used to evaluate the impact of forecast uncertainty and decision horizon length on operational outcomes. The results show that grid fees significantly influence both BESS profitability and operational strategies. For stand-alone storage, higher transmission charges reduce arbitrage revenues and battery utilization. When BESS is integrated with consumption and generation units, load shifting and self-consumption become the dominant sources of value, leading to a non-monotonic relationship between grid fees and storage profitability. These findings highlight the importance of considering tariff structures when evaluating storage investments and designing regulatory frameworks for electricity markets with increasing flexibility needs.

Predictive dependence in time series need not be confined to the conditional mean. Outside the Gaussian setting, causal content may arise through conditional scale, tail behavior, asymmetry, or other distributional features, implying that no single Granger-type test provides a complete characterization of predictive dependence. This paper develops a framework for distributional Granger causality based on a finite collection of channel-specific restrictions. Under suitable determinacy conditions, the channel menu is shown to be complete, yielding an identification result that links distributional Granger non-causality to a finite set of testable hypotheses. Building on this representation, we develop an adaptive sequential testing procedure that allocates inferential resources across channels while maintaining familywise error control through an alpha-investing mechanism. A policy-invariant validity theorem establishes finite-sample size control under arbitrary admissible selection rules, while an asymptotic efficiency theorem shows that a confidence-bound allocation rule achieves power equivalent to that of an infeasible oracle benchmark. The theoretical guarantees are derived from primitive mixing and moment conditions together with a circular-block permutation scheme.

We model unobserved confounding through an unknown finite number of latent types. This assumption induces finite-mixture representations of the treated and control outcome distributions. Using the identified mixture components, we characterize the sharp identified set for the number of latent types and derive the sharp identified set for the average treatment effect (ATE) corresponding to each admissible value, thereby providing a natural framework for sensitivity analysis. We further obtain a cutoff beyond which the identified set for the ATE coincides with a version of the Manski bounds, whereas below the cutoff it is strictly smaller. This cutoff grows only linearly with the numbers of mixture components in the treated and control groups, although the maximum admissible number of latent types grows quadratically. We also provide estimation and inference procedures with asymptotic guarantees and illustrate our methodology using LaLonde's data.

Empirical economists inherit a toolbox. Shared packages, replication archives, and circulated guides etc. Theorists largely start from a blank page. By 2026, large language models can produce and check nontrivial mathematics, so the binding constraint on machine-assisted theory is no longer production but trust: a fluent model will prove a false theorem as readily as a true one. I propose a verification-first protocol for doing economic theory with a language model and instantiate it as three reusable methods that differ on a single axis, how the work is checked: a single disciplined pass, an adversarial prover-verifier pair (Claude Opus~4.8 proposing, OpenAI Codex refuting, the author triaging), and a structured multi-agent project with a reviewer gate. I evaluate the protocol on one open worked example: designing a Groves/Pigouvian incentive mechanism for the Gans-Kominers eigengrade model of grade inflation; none of the three runs produced a strict direct-revelation VCG/Clarke mechanism, a point the adversarial pass itself established. The evidence is a single worked example with one model pairing run by one operator, so what follows are demonstrations rather than measured effects. Three phenomena recur. First, convergent discovery: two runs derive the same effective-resistance externality kernel on opposite margins. Second, adversarial verification is load-bearing: the pair caught three of its own false claims and the gate rejected a sub-goal. Third, polish is not rigor: the most finished-looking output was the least verified. The methodological takeaway is that external verification, not model capability, is the design variable.

This paper studies a cheap-talk model of strategic test announcements. A teacher observes the day of the test of the next week decided by the nature and makes an announcement to his students who choose effort levels of studying. The competing forces are the teacher's value on consistent study habits and the students' grade orientation. We characterize the pure strategy Nash equilibrium under the linear-quadratic student utility. We also study what happens when the teacher can commit to an information policy.

We propose a new treatment of nonlinear regression with serially correlated disturbances that incorporates autoregressive moving average structures into feedforward neural networks. The resulting model provides an alternative to modeling temporal dependence using lagged variables. In simulations, the proposed method accurately recovers regression functions of varying complexity and the underlying error dynamics across a range of time-series lengths and signal-to-noise ratios. Finite-sample properties and out-of-sample predictive performances are shown to be robust to model misspecification induced by omitted lagged variables and incorrect specification of the error dynamics. Cloud cover is an important factor in climate projections. In an empirical study of cloud cover prediction for a grid of locations within and around the Mediterranean Sea, our proposed model yields more accurate predictions than existing methods, including long short-term memory networks. Improvements are observed broadly and are particularly pronounced in mountain areas relative to linear models with serially correlated errors, consistent with the presence of stronger nonlinear effects in cloud composure in such regions.

We develop a framework for learning dependence structures from empirical dependence operators. Rather than treating cluster, factor, and sparse dependence as maintained assumptions, we represent them as covariance geometries in a common Hilbert space and summarize dependence through a low-dimensional dependence profile based on projection similarity scores. We establish identification under a principal-angle separation condition, prove consistency and asymptotic normality of the estimated profile, and derive finite-sample classification error bounds. We further show that when covariance-geometry tangent spaces overlap, no statistical procedure can distinguish the geometries at first order, providing a formal characterization of ambiguous dependence structures. Projection-residual diagnostics assess absolute goodness-of-fit and detect misspecified covariance dictionaries. Finally, we establish oracle adaptivity of profile-guided inference: dependence profiles can be used to select dependence-robust procedures in a data-driven manner, yielding inference that is asymptotically equivalent to an infeasible oracle that knows the dominant covariance geometry in advance.

In 2019, North Dakota repealed its Sunday closing law, which had required most non-grocery stores to close between midnight and noon. Using this policy change and consumer GPS data, we study the impact of opening hours on shopping behavior and welfare. We compare visits before and after the repeal in North Dakota and neighboring states using difference-in-differences and event-study designs. The repeal caused a large increase in Sunday morning visits, originating partly from intertemporal, store-type, and cross-border substitution. The closing law's welfare loss is equivalent to increasing the travel distance to affected stores by about 1.4 miles per consumer.

Risk perception is typically modeled as an individual cognitive readout of objective hazard, yet during crises what people judge as risky is shaped by what their peers do. Using weekly mobility data from 313 Massachusetts municipalities over the first year of the COVID-19 pandemic and a pre-pandemic inter-town mobility network that fixes interaction structure before the shock, we estimate two-way fixed-effects panel regressions that separate local case response, inter-town behavioral spillover along the mobility network, and within-town inertia; the pre-shock network and a lagged peer signal address the standard reflection and endogenous-group concerns. Three findings emerge. First, inter-town behavioral spillovers are substantial and localize almost entirely within mobility-defined communities, with effectively no propagation across community boundaries, the empirical referent of behavioral bubbles. Second, the within-community spillover carries behavioral content beyond peer-town case information: when network-exposure-to-cases and network-exposure-to-behavior are raced, the behavioral channel survives and the case-exposure channel goes null. Third, a joint mobility-by-demographic decomposition shows the spillover requires both routine connection and demographic similarity. It concentrates where towns are connected and similar, and vanishes between similar towns that are not connected, ruling out a shared-conditions confound and pointing to an observational and normative channel rather than a purely informational one. These results recast risk perception as a networked phenomenon and identify mobility-defined communities, rather than administrative units, as the operative scale of behavioral response. The pattern should generalize wherever exposure is uncertain, evolving, and socially negotiated, including climate adaptation and financial contagion.

India's post-liberalisation higher education expansion was premised on widening credential access for historically excluded groups. We show that the groups most expected to benefit - Scheduled Caste and Scheduled Tribe (SC/ST) workers - instead bore a disproportionate share of the resulting wage cost, a pattern we term the double whammy. We merge eight rounds of the NSS Employment-Unemployment Survey (1987-2011) with a district-level measure of college-expansion intensity built from the All India Survey on Higher Education (AISHE) and estimate reduced-form triple- and quadruple-difference wage specifications across 91 districts in six states (N = 79,904), interacting graduate status, expansion intensity, and post-expansion cohort. The human capital return to a degree remains large and positive throughout (about 1.08 log points), yet the graduate wage premium erodes for post-2004 cohorts in high-expansion districts: non-SC/ST graduates earn roughly 9 per cent less than comparable graduates in low-expansion districts at mean intensity, and SC/ST graduates face an additional penalty of about 34 per cent (a combined shortfall near 43 per cent). The SC/ST differential is statistically indistinguishable from zero before the expansion and emerges only afterwards. Non-graduate placebo and pre-trend tests are broadly consistent with a credential-signalling channel, though we flag the limits of the design rather than claim clean identification. The results suggest that expanding access without commensurate investment in institutional quality can deepen, rather than narrow, labour-market inequality for disadvantaged groups.

We study competition among multiple firms that offer differentiated varieties of the same good to a unit-demand agent. The agent has heterogeneous valuations for goods from different firms. Firms do not observe the agent's exact valuations, but they know their distribution. Firms simultaneously post menus of contracts, after which the agent chooses a firm and one of its contracts to maximize her utility. This defines a game in which firms aim to maximize expected revenue. We introduce a sufficient condition, density-regularity, under which each firm's best response to any arbitrary menu profile posted by its opponents is equivalent to posting a menu that contains only a posted-price contract. Our result is not a direct extension of the canonical Myersonian model with a single seller. The standard argument in the literature breaks down once heterogeneous preferences and competition are introduced. We therefore adopt an optimal-control approach, in which the density-regularity condition is essential for establishing the optimality of posted prices. When this condition fails, posted prices may fail to be a best response.

Automation and artificial intelligence (AI) are reshaping labor demand unevenly across space, creating an urgent imperative for place-sensitive education and workforce policy. This study asks whether regional exposure to automation and to AI relates to local employment and wages in opposite ways, and whether those relationships differ between urban and rural regions -- two questions whose answers carry direct implications for how skills training and digital education should be targeted. Using a region-by-year panel and shift-share measures of technological exposure built from baseline industry and occupation composition, we estimate two-way fixed-effects and instrumental-variable models that interact exposure with an urban indicator. The framework distinguishes automation exposure, concentrated in routine work, from AI exposure, concentrated in cognitive work -- a distinction that maps directly onto the types of skills that education systems need to develop or preserve. Estimates show automation exposure lowering employment and wages, with the employment loss cushioned in cities, while AI exposure raises wages and concentrates in urban regions. Technology therefore reshapes, rather than simply widens, the divide. The findings argue for place-sensitive policy: weighting reallocation and reskilling support toward routine-exposed rural regions, while extending digital infrastructure and AI-complementary skills outward so that rural workers can share AI's wage gains rather than absorb only automation's losses.

How do labor demand shocks affect workforce diversity in the absence of targeted diversity policies? A conceptual framework illustrates the potential trade-off between the demographic and quality composition of a workforce when there is a positive labor demand shock. Exploiting the German reunification as a natural experiment, we analyze the academic labor market where nearly all social sciences professors in East Germany were replaced while STEM faculty remained largely unchanged. Using administrative data and a regional difference-in-differences design, we find increased dispersion in the institutional quality of hires, indicating that the new hires came from less select departments. At the same time, female representation did not increase despite qualified women in the pipeline. Instead, East German hiring patterns converged to those in West Germany in terms of gender composition. In simulations, we investigate implied losses: Under conservative assumptions, we show that, considering the pipeline of qualified applicants, the marginal female hire's quality is approximately half a standard deviation higher than the marginal male hire's quality.

We study flow games with public arcs, an extension of classical cooperative flow games that allows players to use public resources. In these games, a coalition corresponds to a set of arcs, while certain arcs, called public arcs, can be used freely by any coalition. The value of a coalition is the maximum flow value achievable using the arcs controlled by the coalition along with the public arcs. These games have significant applications in financial, communication, and supply-chain networks. We investigate two solution concepts, the least core and the nucleolus. Both solution concepts provide principled ways to allocate the value of the grand coalition among individual players. We provide characterizations of the least core of these games. We also give a polynomial-time algorithm to compute the nucleolus when the core is non-empty.

Non-price interventions targeting specific household water uses are increasingly central to conservation policy, but whether end-use savings translate into lower aggregate demand remains unresolved. This paper reports evidence from a pre-registered field experiment in which 775 Finnish households were randomized to a shower timer, a water-saving shower head, or the same shower head with real-time feedback. Utility-grade water meters measure household-level effects, while shower-level data provide complementary end-use evidence for the two shower-head treatments. The shower timer has no detectable effect. In contrast, the water-saving shower head reduces daily household demand by about 5%, and pairing it with real-time feedback doubles this reduction to about 10%. The convergence between shower- and meter-based estimates shows that end-use savings largely pass through to aggregate demand rather than being offset elsewhere in the home. Cost-benefit analysis indicates that combining technological constraint with salient point-of-use feedback dominates reminder-based strategies.

In this paper we examine the constructive nature of social welfare orders on infinite utility streams $X=Y^{\mathbb{N}}$ satisfying Strong Equity, Hammond Equity, or the Pigou--Dalton transfer principle. The constructive social welfare orders are described using lexicographic preference relations. Social welfare orders satisfying Strong Equity, Hammond Equity, or the Pigou--Dalton transfer principle admit explicit descriptions when $Y(<)$ is well-ordered. We describe restrictions on the domain $Y$ under which the existence of social welfare orders satisfying the aforementioned equity axioms entails the existence of a non-Ramsey collection. For this, we rely on the existence of a non-Ramsey collection, which is treated here as a nonconstructive object.

This paper studies probabilistic properties of pairwise stability for a network model where individual utilities are random variables. We study the probability that a given network is pairwise stable and the expected number of pairwise stable networks. We provide a closed-form solution for the latter number. As the evaluation of the exact expression is computationally challenging for large populations, we provide tractable lower and upper bounds for this expression which allow us to pin down the asymptotic behavior of the expected number of pairwise stable networks up to a multiplicative constant. This asymptotic behavior is described by the number of networks $ 2^{n(n-1)/2} $ times $ (2/n+1)^{n} $, a sequence that tends to infinity fast. We normalize the number of pairwise stable networks by this sequence and show that the variance of the normalized number of pairwise stable networks converges to zero as $ n $ tends to infinity. We conclude that almost surely the number of pairwise stable networks tends to infinity, while the fraction of pairwise stable networks tends to $ 0 $ as $ n $ goes to infinity.

We introduce \emph{Equilibrium World Models} (EWMs), a deep-learning method for globally solving dynamic stochastic models that feature rare disasters, binding constraints, and counterfactual states. Standard unsupervised neural-network-based solvers impose equilibrium conditions only on states generated by their own simulated policy. Their solutions can therefore be self-confirming: accurate on the simulated path, but untested off it, sensitive to initialization, and costly when expectations must be recomputed at each step. EWMs change the computational representation, not the economics. They enforce the model's exact equilibrium conditions on a broader, model-generated distribution of ordinary, rare, stressed, and counterfactual states. They carry the continuation with a learned surrogate, but certify the resulting policy strictly against the true equilibrium conditions. We provide an error decomposition, an off-path residual bound, and a convergence result linking self-confirming solutions to rational-expectations equilibria. We demonstrate EWMs through a sequence of test cases that isolate the main pathologies of classical deep-learning solvers and then scale them to richer economies. In a rare-disaster Brock--Mirman laboratory, coverage reduces disaster-region residuals by an order of magnitude. In a high-dimensional international real-business-cycle model, classical deep-learning solvers fail from all random starts, whereas EWMs converge from nearly all and evaluate continuations up to two orders of magnitude less often. When actions move transition measures, EWMs use action-conditioned continuations to recover the relevant policy margin. In a heterogeneous-agent economy with aggregate risk, EWMs compress the numerical representation of the wealth distribution by at least 25x while imposing exact full-distribution rational-expectations conditions.

Nash equilibrium (NE) arises from selfish utility maximization, yet its social welfare can be arbitrarily far from optimal. Moreover, computing an NE is intractable in general. We study augmented game models in which players use budget-balanced internal transfers to improve incentives before play. We first introduce \emph{Self-Enforcing Transfer Equilibrium} (SETE), where players commit to nonnegative peer-to-peer transfers that are paid only if the recipient does not deviate from a prescribed strategy. For polymatrix games, we show that every stationary point of the social welfare function, in particular any socially optimal strategy profile, can be sustained as a SETE. This induces a Nash equilibrium in the agent normal form of the corresponding augmented game. We further propose a polynomial-time algorithm and a decentralized learning dynamic to compute such product-form equilibria. We then introduce \emph{Mediated Self-Enforcing Transfer Equilibrium} (M-SETE), where a mediator makes both the payment schedule and the prescribed strategies binding offers. This additional enforcement resolves the agent-normal-form limitation: an M-SETE is a Nash equilibrium of the augmented game itself, not merely of its agent normal form, and any socially optimal strategy profile can be supported as an M-SETE in any finite game while preserving budget balance. Thus, internal transfers improve welfare and computation while preserving independent play on the equilibrium path. When full sequential-game stability is required, binding mediation provides the corresponding implementation.

We develop a novel distributional Difference-in-Differences (DiD) framework to capture treatment heterogeneity across outcome distributions. By leveraging optimal transport, we use the control group to estimate the untreated distributional drift from the pre- to post-treatment period and apply it to the treated group's pre-treatment baseline, constructing a counterfactual distribution under the assumption of no treatment effect. We frame the null hypothesis as a distributional equality between the transported counterfactual distribution and the observed treated post-treatment distribution, and test it using a maximum mean discrepancy statistic in a reproducing kernel Hilbert space (RKHS). The resulting nonparametric omnibus test is sensitive to changes in location, scale, shape, and tail behavior. Under the null, we derive the asymptotic Gaussian quadratic-form limit of the test statistic, while under local alternatives, we provide a unified characterization of power that establishes its Pitman local power and moderate-deviation consistency. Our theory reveals how detectability is shaped by the interaction between transport-induced drift and RKHS geometry. Simulations and an application to the Card--Krueger minimum-wage data demonstrate that the proposed method identifies key distributional treatment effects missed by classical mean-based DiD.

This paper studies information design when the designer lacks precise knowledge of agents' payoff coefficients. The Calibrated Bayes Correlated Equilibrium (Cal-BCE) is introduced as a solution concept that augments the Bayes correlated equilibrium with a corrector policy preserving incentive compatibility under the designer's structural uncertainty, adapting its revelation principle to this setting. The design problem is nonconvex in general, but under a linear-quadratic-Gaussian structure it admits convex second-order cone and semidefinite reformulations under two-sided probabilistic and conditional value-at-risk (CVaR) constraints, with feasibility guaranteed by a Hadamard invertibility condition. A joint decentralization theorem shows that both designs cap cross-agent action covariances, the CVaR design more tightly at a common tolerance; but because the formulations operate at design-specific feasibility thresholds, the realized ordering is calibration-dependent. Experiments on fifteen sector ETFs confirm the trade-off: the probabilistic design attains higher mean welfare and the CVaR design better tail protection, with neither dominating outright.

Large and persistent differences in opioid prescribing across physicians and regions cannot be explained by patient characteristics or physician attributes alone. We developed a behavioral framework in which prescribing evolves through persistence, exposure to peers in professional networks, and heterogeneous responses to a common policy signal that varies with network centrality. Using nationwide Medicare Part D data from 2013 to 2020, covering more than two million physician-year observations, we tested three hypotheses implied by this framework. Physicians exposed to higher peer prescribing subsequently prescribe more; more central physicians reduce prescribing more following the introduction of the 2016 CDC guideline, with no evidence of differential pre-trends; and changes in peer prescribing are closely associated with changes in individual prescribing in the post-guideline period. By 2020, physicians at the 90th percentile of network centrality exhibited prescribing reductions 0.30 percentage points larger than those at the 10th percentile, with the gap widening steadily after the introduction of the CDC guideline. Together, these results indicate that opioid prescribing operates through professional networks, in which policy effects spread through connections and appear to be shaped by network position. This suggests that engaging highly connected physicians may help extend the reach of opioid stewardship programs. It also raises questions about how the burden and benefits of such targeting would be distributed across physicians and patients.

Structure-agnostic (SA) models introduced by Balakrishnan et al. (2026) aim to reflect the general lack of knowledge of structural assumptions on data-generating laws such as smoothness or sparsity in practice. Roughly speaking, SA models restrict the observed-data generating law to be in some rn-neighborhood of (black-box machine learning) estimates, treated as given and fixed, where rn encodes the convergence rates of the estimates to the truth. Under SA models, Balakrishnan et al. (2026) show that the popular Double Machine Learning (DML) estimators for three functionals, the quadratic functional in the Gaussian sequence model, the quadratic density integral functional and the expected conditional covariance, are minimax. However, minimax estimators may be inadmissible. In this paper, we show that, for the first two of the three functionals, the DML estimator is asymptotically inadmissible under the SA model. In particular, we show that these two functionals fall into a class of functionals, which we refer to as the monotone bias class. For this class, we exhibit second-order (U-statistic) estimators, which asymptotically dominate DML estimators, under the SA model. These second-order estimators are empirical higher-order influence function (HOIF) estimators introduced in Liu et al. (2017). Furthermore, the empirical HOIF estimator, like the DML estimator, is minimax for the third functional (the expected conditional covariance), although neither asymptotically dominates the other.

A Nash equilibrium is learnable if there exists a myopic adjustment dynamic for which it is asymptotically stable. In generic symmetric two-player games, a Nash equilibrium is learnable if and only if it has index +1.

Large language models are increasingly deployed as autonomous decision makers, yet the behavioral mapping they exhibit can vary substantially across decision environments that are payoff-equivalent by construction-environments that share identical payoff-relevant structure but differ in surface presentation. This sensitivity renders suite-based evaluation fragile and raises a fundamental question of behavioral portability: how well does a behavioral mapping learned in one decision environment informative on another that preserves the same underlying incentive structure? We introduce a formal framework to measure this property. Our protocol fits an interpretable behavioral model on data pooled from a set of source environments and evaluates its out-of-sample predictive performance in a held-out target environment, benchmarking against an oracle trained directly on target data. Portability is quantified via a loss-agnostic measure that delivers worst-case bounds on the performance of the induced prediction-action mapping in the target environment. In controlled experiments spanning seven canonical economic decision problems, we document substantial and systematic portability losses, suggesting that behavioral characterizations of LLMs obtained in one decision environment cannot be assumed to transfer reliably to structurally equivalent alternatives.

We study how the choice of default prior for a common Gaussian scale affects high-dimensional shrinkage risk, highlighting the role played by high-dimensional geometry. Formally, we consider a high-dimensional setting in which the near-zero behavior of the common scale prior has first-order consequences for shrinkage risk, and show that priors that are flat on the variance and those flat on the standard deviation allocate markedly different mass near the zero-scale boundary, leading to distinct shrinkage behavior and informing principled default prior selection. Specifically, under a radial-power benchmark, we establish that the SD-flat benchmark has a one-unit asymptotic risk advantage near the origin, crosses over in the critical regime, and is second-order equivalent to the variance-flat benchmark for strong signals. Proper single global-scale hyperpriors and bounded coordinate-multiplier mixtures inherit these limits through the near-zero exponent of their SD-scale density. For heavier-tailed or sparse priors, that exponent still classifies the common global-scale component, while local-scale tails, model-size priors, or allocation priors can also affect risk.

A set of exposure scores calculated in 2023 has become a central empirical input to the future of work debate. Produced by Eloundou et al. (2023) and referred to here as the GPTs are GPTs scores, they define exposure as the share of occupational tasks a large language model can assist with. This work is a genuine methodological contribution, but as the scores travel from the time and place they were produced, the limitations the authors named do not always travel with them. Two gaps have widened as a result. The first is structural, between what static exposure scores measure and what policy questions actually require. Taking the diffusion of these scores as a case study, we show how their temporal, geographic, and ontological limitations compound in policy-facing analyses, and we survey five families of research responding to these limits: dynamic and benchmark-based measures, ensemble methods, task-framework extensions, worker-centered metrics, and adoption and usage data. The second gap is the one we argue needs more attention: the coordination between researchers and policymakers. The policy-relevant work which ask who is harmed, who benefits, how, and when, continues to reference the static GPTs are GPTs scores without engagement with the methodological updates that would let these questions be answered more reliably. We then ask what additional steps towards navigating uncertainty remain: ex-post frameworks and the deliberate, political work of reimagining what futures are worthy of building towards are. Closing the research-policy gap is a shared task: policymakers must widen their evidence base, engage workers as epistemic partners, and shift from prediction to preparedness; researchers must build data infrastructure, adopt participatory methods, and write with policymakers in mind. Better measurement matters, but it will not close the second gap alone.

Connections appear to be helpful in many contexts such as obtaining a job, a promotion, a grant, a loan, or publishing a paper. This may be due to favoritism or to information conveyed by connections. Building on earlier work on discrimination, we propose a new method that identifies these channels using data observed at the time of promotion. The method exploits distinct implications of the two effects on the relationship between observables and success. We show that extra information on connected candidates generates excess variance in latent errors while favors yield different promotion thresholds. We characterize the conditions under which both effects are identified and operationalize these ideas econometrically within a semiparametric framework. We also derive testable restrictions of the model and show how to account for connection endogeneity. We reanalyze data on academic promotions in Spain and Italy and political promotions in China. We detect evidence of favoritism for all types of candidates and of information effects for candidates applying to junior positions. We find strong support for the model's testable restrictions.

This paper integrates deep neural networks (DNNs) into structural models to increase flexibility and capture rich heterogeneity while preserving interpretability. Economic (or scientific or domain-restricted) structure and machine learning are complements in empirical modeling, not substitutes: DNNs provide the capacity to learn complex, nonlinear heterogeneity, while the structure ensures the estimates remain interpretable and suitable for decision-making and policy analysis. We start with a standard parametric structural model and then enrich its parameters into fully flexible functions, which are estimated using a DNN with the model structure built in. We illustrate our framework with an application to demand estimation in consumer choice. We show that by enriching a demand model we can capture rich heterogeneity exploit it to create personalized pricing. Optimization is not possible without structure, but cannot be heterogeneous without machine learning. The same lessons apply to precision dosing, adaptive treatment, educational testing, and other targeting settings. We provide theoretical justification for our proposed methodology: nonasymptotic bounds and a novel and general influence function for feasible inference via double machine learning, so that the latter can be easily applied in numerous new contexts. These results may be of interest in other contexts as they generalize prior work.

Proponents of participatory democracy praise Liquid Democracy: decisions are taken by referendum, but voters delegate their votes freely. When better informed voters are present and the electorate is finite, we show theoretically that delegation can always strictly increase the probability of a correct decision. However, delegation must be used sparingly because it reduces the information aggregated through voting. In two different experiments -- a tightly controlled lab experiment and a perceptual task run online -- we find that subjects choose very high rates of delegation, and the theoretically possible improvements fail to materialize. The experimental evidence favors Direct Democracy, whether with or without abstention. We study the perceptual task, where signals' precisions are not known, both as a test of the robustness of the lab results and as an independent methodological contribution. We argue that tests under ambiguous information are valuable and under-used tools in studying collective decision-making.

Despite increasing popularity in empirical studies, the integration of machine learning generated variables into regression models for statistical inference suffers from the measurement error problem, which can bias estimation and threaten the validity of inferences. In this paper, we develop a novel approach to alleviate associated estimation biases. Our proposed approach, EnsembleIV, creates valid and strong instrumental variables from weak learners in an ensemble model, and uses them to obtain consistent estimates that are robust against the measurement error problem. Our empirical evaluations, using both synthetic and real-world datasets, show that EnsembleIV can effectively reduce estimation biases across several common regression specifications, and can be combined with modern deep learning techniques when dealing with unstructured data.

Social media influencers account for a growing share of marketing worldwide. We demonstrate the existence of a novel form of market failure in the advertising market: influencer cartels, where groups of influencers collude to increase their advertising revenue by inflating their engagement. Our theoretical model shows that influencer cartels can improve consumer welfare if they expand social media engagement to the target audience, or reduce welfare if they divert engagement to less relevant audiences. Drawing on the model's insights, we empirically examine influencer cartels using novel datasets and machine learning tools, and derive policy implications.

Response times contain information about economically relevant but unobserved variables like willingness to pay, preference intensity, quality, or happiness. We provide a general characterization of the properties of latent variables that can be detected using response time data. Our theoretical framework unifies and generalizes existing results in the literature and gives rise to many new applications. We illustrate the novel insights that the method can deliver through three empirical applications: identifying an optimal nudge, testing decreasing marginal happiness of income, and predicting treatment heterogeneity.

This paper provides new evidence on spot gig work platforms for individuals seeking flexible, short-term jobs with minimal educational or experience requirements in Japan. Using proprietary data from Timee, a private matching platform, the study analyzes trends in active users, vacancies, hires, and labor market tightness, compared to part-time data from Hello Work, a public employment service. Applying a nonparametric approach, it finds that the private platform exhibits substantially higher matching efficiency, especially after 2022. Elasticities also differ across platforms: for Hello Work, the user elasticity fluctuates around 0.3--0.5, while the vacancy elasticity ranges roughly from 0.4 to slightly above 1.0; for the private platform, the user elasticity remains around 0.2--0.3, while the vacancy elasticity ranges from 0.7 to 1.1. At the prefecture level, the three prefectures exhibit broadly similar movements early in the sample, followed by divergence and partial re-convergence later on, while elasticities remain stable and similar across regions. These results reveal how digital platforms reshape job matching dynamics relative to traditional systems.

When evaluating policy interventions, researchers often pursue two related goals: identifying which individuals or contexts benefit most, and determining whether patterns of treatment effect heterogeneity can be used to aggregate evidence across environments. We develop a framework that aggregates treatment effect heterogeneity, defined over individual and environmental characteristics, into interpretable summaries while setting aside contexts in which extrapolation is unreliable and further evidence is needed. The procedure therefore learns both how to summarize heterogeneous effects and when researchers should admit ignorance. We derive finite-sample regret guarantees, provide data-driven guarantees for selecting the complexity of the summary class, and inference procedures that quantify the value of follow-up data collection. We illustrate the approach by reanalyzing a multifaceted anti-poverty program implemented in six countries.

For the object reallocation problem, we study whether characterizations of Top Trading Cycles (TTC) based on individual rationality, efficiency, and strategyproofness on the unrestricted domain extend to restricted preference domains. We introduce the top-two condition and show that it offers a useful criterion for answering this question. The condition requires that, within every subset of objects, any two objects that can each be ranked first can also be ranked as the top two, in both possible orders. We first show that this condition is sufficient: on every domain satisfying the top-two condition, TTC is the unique rule satisfying the relevant axioms. We also provide a partial converse. For domains that fail the top-two condition within a small subset of objects and satisfy a mild extension condition, we construct a rule distinct from TTC satisfying these axioms. Our results provide a unifying perspective on existing findings for specific domains, such as the single-peaked and single-dipped domains, while also addressing several previously unexplored domains, including the circular and partial-agreement domains.

Startup accelerators are a leading gateway to venture capital, but top programs often require founders to relocate to a venture hub. From a hand-collected census of U.S. accelerator startups (2008-2011) followed for five years, we estimate a two-sided matching model that separates two channels behind the gender funding gap, geographic mobility and sorting across accelerator tiers. Women raise about 60% less than men over five years; the gap concentrates among non-relocating women, is largest at active-childrearing ages, and vanishes for relocators, while the mobility cost is near zero for men. Removing mobility frictions raises women's match quality but not their tier; reaching the high-funding top tier also requires removing the sorting disadvantage that women face. The 2012 JOBS Act eased the legal barrier and capacity grew tenfold, yet the U.S. VC dollar gap still tripled (2011-2020): closing it needs mobility, sorting, and capacity together.

Double Machine Learning is widely used to estimate treatment effects from non-experimental data. The "residuals-on-residuals" regression (RORR) is especially popular for its simplicity and computational tractability. However, with heterogeneous treatment effects, the proper interpretation of RORR may not be well understood. We show that, for non-binary treatments with continuous dose-response functions, RORR estimates a conditional variance-weighted average of derivatives evaluated at treatment values not in the observed dataset. This estimand does not equal the Average Causal Derivative (ACD) in general. Hence, even if all units share the same dose-response function, RORR does not estimate an average treatment effect in the population represented by the sample. We propose an alternative estimator for the ACD that is well suited to the large datasets found in applied data science settings. We demonstrate the pitfalls of RORR and the favorable properties of the proposed estimator through an illustrative numerical example and with real-world data from Netflix. Our methodology is used by default in Netflix's observational causal inference platform, where it regularly powers causal research and decision-making at scale.

This paper studies nonparametric empirical Bayes methods in a heterogeneous parameters framework that features unknown means and variances. We provide extended Tweedie's formulae that express the (infeasible) optimal estimators of heterogeneous parameters, such as unit-specific means or quantiles, in terms of the density of certain sufficient statistics. These are used to propose feasible versions with nearly parametric regret bounds of the order of $(\log n)^\kappa / n$. The results rely on a distributional assumption, and thus a misspecification analysis is also presented. The estimators are employed in a study of teachers' value-added, where we find that allowing for heterogeneous variances across teachers is crucial for delivery optimal estimates of teacher quality and detecting low-performing teachers.

This paper examines how natural gas supply shocks affect Italian firms' pricing decisions and inflation expectations using quarterly survey data from the Bank of Italy's Survey on Inflation and Growth Expectations (SIGE). We identify natural gas supply shocks through an external IV-VAR approach exploiting likely unexpected news about interruption to gas supplies to Europe. Our findings show that although gas supply shocks do not have huge effects on gas quantity and only modest effect on gas inventories, they are quickly transmitted to spot electricity prices with persistent effects. We then estimate a proxy internalizing BVAR incorporating firm-level variables from SIGE, documenting that gas supply shocks raise firms' current and expected prices as well as inflation uncertainty. Finally, we uncover substantial nonlinearities using state-dependent local projections: under high inflation uncertainty, firms successfully pass cost increases on to consumers, sustaining elevated prices; under low uncertainty, recessionary effects dominate, leading firms to cut prices below baseline.

We develop a step-by-step guide to leniency (a.k.a. judge or examiner instrument) designs, drawing on recent econometric literatures. The unbiased jackknife instrumental variables estimator (UJIVE) is purpose-built for leveraging exogenous leniency variation, avoiding subtle biases even in the presence of many decision-makers or controls. We show how UJIVE can also be used to assess key assumptions underlying leniency designs, including quasi-random assignment and average first-stage monotonicity, and to probe the external validity of treatment effect estimates. We further discuss statistical inference, arguing that non-clustered standard errors are often appropriate. A reanalysis of Farre-Mensa et al. (2020), using quasi-random examiner assignment to estimate the value of patents to startups, illustrates our checklist.

What was the origin of modern economic growth? Joel Mokyr has argued that self-sustained modern economic growth originated from a feedback loop between propositional (theoretical) and prescriptive (applied) knowledge, which turned positive in the eighteenth century during the "Industrial Enlightenment". While influential, this thesis has never been directly tested. This paper provides the first quantitative evidence by estimating the impact of knowledge spillovers between propositional and prescriptive knowledge on innovation in England, 1600-1800. For this, it introduces two new text-based measures for 1) the innovativeness of publications and 2) knowledge spillovers. The paper finds strong evidence that a feedback loop between propositional and prescriptive knowledge became positive during the second half of the eighteenth century. It also documents that this process had positive effects on the real economy as measured through patents. Overall, the findings provide empirical support for Mokyr's original hypothesis.

Empirical models of multi-product demand rely on low-dimensional product representations to capture substitution patterns, increasingly using proxies built from unstructured data. When proxies are imperfect, standard workflows yield biased counterfactuals and invalid inference. We develop a practical toolkit to address these issues. Our methods apply to market-level and/or individual data, require minimal additional computation, provide simple standard-error formulas, and accommodate proxies from fine-tuned models. Further, we propose diagnostics to assess proxy quality. Our methods yield meaningful improvements in predicting substitution in empirically calibrated simulations and in an application where we assess counterfactual prediction performance against a ground truth.

People learn about opportunities and actions by observing the experiences of their friends. We model how homophily -- the tendency to associate with similar others -- affects both the endogenous quality and diversity of the information accessible to decision makers. Homophily provides higher-quality information, since observing the payoffs of another person is more informative the more similar that person is to the decision maker. However, homophily can lead people to take actions that generate less information. We show how network connectivity influences the tradeoff between the endogenous quantity and quality of information. Although homophily hampers learning in sparse networks, it enhances learning in sufficiently dense networks.

This paper formalizes the identification framework underlying common child penalty triple difference estimators that normalize by counterfactual earnings. I reverse-engineer the assumption underlying the validation test: parallel-trend violations, divided by counterfactual earnings, are equal between genders, a framework I term Normalized Triple Differences (NTD). Under NTD, however, I find that the conventional estimator does not identify its target causal estimand. I show that the effect of parenthood on the gender earnings ratio is point identified under NTD. Using the new estimator on Israeli administrative data, I find heterogeneous contributions of parenthood to gender earnings inequality across treatment groups.

Random-restart heuristics are widely used in nonconvex optimization and equilibrium computation: practitioners run a local algorithm from many initial conditions and interpret repeated convergence to the same output as evidence that the result is robust, dominant, or even unique. Despite its widespread use, this reasoning is usually informal. We provide a probabilistic framework for interpreting restart evidence. We give broad, easy-to-verify sufficient conditions under which repeated runs of a solver can be treated as independent draws from a categorical distribution induced by random initial conditions. Within this framework, we develop Bayesian inference from repeated identical outputs. We derive posterior concentration rates for basin size and uniqueness. These rates demonstrate that uniqueness is inherently harder than learning basin size: posterior concentration for uniqueness is polynomial, whereas basin size concentrates exponentially fast. We also provide a verification protocol for checking whether a given problem fits our framework. We demonstrate the protocol on a widely used equilibrium solver for mixed-logit demand with multi-product firms, and complement the verification exercise with posterior tables that apply to any restart experiment satisfying the protocol. We conclude by delineating limits of restart-based inference, including failures induced by solver--problem mismatch and limited visibility of alternative outcomes.

High-stakes auctions are often preceded by nonbinding communication between bidders and the seller. I study a two-period model in which bidders privately send cheap-talk messages to the seller about their valuations before the seller decides whether to run a mechanism or take a forfeitable outside option. The seller has commitment within the second-period mechanism but not over how she uses first-period communication. In monotone bidder-symmetric equilibria, an unrestricted seller runs at most one mechanism on the equilibrium path: a second-price auction with a common reserve, and only when all bidders report values above a common threshold. Thus discriminatory auctions cannot arise in equilibrium, despite asymmetric on-path posteriors. With two bidders, the seller is better off, and can sometimes attain her full-commitment payoff, if she can commit ex-ante to second-price auctions with a common reserve.

I study the topology of reputation effects in the canonical framework in which a long-lived player -- either a normal type who acts strategically or a commitment type who plays a fixed distribution over actions -- faces a sequence of short-lived players who may misspecify the commitment-type signal process. I show that reputation effects are robust to such misspecification in the entropy-rate topology on commitment-type signal processes; in contrast, they are discontinuous in finite-dimensional topology, equivalently weak convergence and, for compatible bounded metrics, Wasserstein and Prokhorov convergence: there exists a convergent sequence of subjective commitment processes along which the patient normal type's highest equilibrium payoff is at most his highest complete-information equilibrium payoff. Reputation effects are therefore an infinite-horizon statistical test.

Who is exposed to generative AI in a developing-country labour market? We map three occupational AI-exposure indices to India's redesigned Periodic Labour Force Survey (2025) and document a steep caste gradient among 83,000 employed graduates: graduates from the Scheduled Castes and the Scheduled Tribes are 0.24--0.37 standard deviations less exposed than upper-caste graduates within the same district. Two channels drive the gap: one in four SC and one in three ST graduates work in farm or elementary occupations untouched by AI, and those in white-collar work are underrepresented in managerial, software, and finance occupations. Because exposure commands a wage premium of up to 20 per cent, generative AI stands to widen, not narrow, India's caste earnings gap.

This paper presents an axiomatization of Ludwig von Mises' praxeology in many-sorted first-order logic, isolating the foundational layer. We introduce a formal language with five sorts (Actors, Actions, Ends, Things, Times) and six primitive relations (Acts, Avail, EndOf, Use, a preference order, and a time order), together with a base axiom system organised into three layers: the structure of action itself, the actor's preference order together with its revelation in choice, and material scarcity. The base system captures purposeful action in its bare praxeological form. Working entirely within the base system we derive the core classical Misesian propositions as Hilbert-style theorems: the asymmetry of revealed preference, the existence of opportunity cost, the structural scarcity of time, the subjectivity of opportunity cost, the law of diminishing marginal utility, and the increasing marginal disutility of labour. Where a theorem requires structure beyond the praxeological core, as with diminishing marginal utility, the additional premises are made explicit; identifying these hidden premises is one of the methodological payoffs of the approach. A self-contained Lean companion encodes the language as Lean type classes and constructs a concrete infinite-time Robinson Crusoe model whose acceptance by the type-checker is a constructive consistency proof of the full base theory.

We study linear-quadratic games of incomplete information with Gaussian uncertainty, where each player's payoff depends on a privately observed type and a common state. The designer observes the state, elicits types, and sells action recommendations. We characterize all implementable mechanisms with Gaussian joint distributions of actions and fundamentals, and identify the players-optimal, consumer-optimal, and revenue-maximizing designs. In games of strategic complements (substitutes), these optimal mechanisms maximally correlate (anticorrelate) players' actions. When type uncertainty is large, recommendations become deterministic linear functions of the state and reports, but remain only partially revealing.

This paper proposes an innovative Transformer model, Single-directional representative from Transformer (SERT), for US large capital stock pricing. It also innovatively applies the pre-trained Transformer models under the stock pricing and factor investment context. They are compared with standard Transformer models and encoder-only Transformer models in three periods covering the entire COVID-19 pandemic to examine the model adaptivity and suitability during the extreme market fluctuations. Namely, pre-COVID-19 period, COVID-19 period and 1-year post-COVID-19. The best proposed SERT model achieves the highest out-of-sample $R^2$, 11.94\% and 11.47\% respectively, when extreme market fluctuation takes place, followed by pre-trained Transformer models (11.13\% and 9.72\%). Their Trend-following-based strategy's performance also proves their excellent capability for hedging downside risks during market shocks. The proposed SERT model achieves a Sortino ratio 47\% higher than the buy-and-hold benchmark in the equal-weighted portfolio and 28\% higher in the value-weighted portfolio in the static transaction cost scenario when the pandemic period is considered. It proves that Transformer models have a strong ability to capture patterns of temporal sparsity in asset pricing factor models, especially with high volatility. I also find the softmax signal filter as the common configuration of Transformer models in alternative contexts, which only eliminates differences between models, but does not improve strategy-wise performance, while increasing attention heads improves the model performance insignificantly and applying the 'layer normalization first' method does not boost the model performance in our case.

We amend and extend the Chiarella model of financial markets to deal with arbitrary long-term value drifts in a consistent way. This allows us to improve upon existing calibration schemes, opening the possibility of calibrating individual monthly time series instead of classes of time series. The technique is employed on spot prices of four asset classes from ca. 1800 onward (stock indices, bonds, commodities, currencies). The so-called fundamental value is a direct output of the calibration, which allows us to (a) quantify the amount of excess volatility in these markets, which we find to be large (e.g. a factor $\approx$ 4 for stock indices) and consistent with previous estimates; and (b) determine the distribution of mispricings (i.e. the difference between market price and value), which we find in many cases to be bimodal. Both findings are strongly at odds with the Efficient Market Hypothesis. We also study in detail the 'sloppiness' of the calibration, that is, the directions in parameter space that are weakly constrained by data. The main conclusions of our study are remarkably consistent across different asset classes, and reinforce the hypothesis that the medium-term fate of financial markets is determined by a tug-of-war between trend followers and fundamentalists.

Optimal signaling schemes in information design (Bayesian persuasion) often involve randomization or disconnected partitions of state space, which might be too intricate to be audited or communicated. We propose explainable information design in the context of linear information design with a continuous state space. In the case of single-dimensional state, we restrict the information designer to use interval-partitional signaling schemes defined by deterministic and monotone partitions of the state space, where a unique signal is sent for all states in each part. We prove that the price of explainability (PoE) -- the ratio between the performances of the optimal explainable signaling scheme and unrestricted signaling scheme -- is exactly $1/2$ in the worst case, meaning that partitional signaling schemes are never worse than arbitrary signaling schemes by a factor of $2$. For a uniform prior, this PoE can be improved to a tight $2/3$. We then extend the analysis to multi-dimensional state spaces by studying two notions of explainability: convex-partitional policies and axis-aligned rectangular policies. We prove a tight PoE of $1/(m+1)$ for convex-partitional policies, while for rectangular policies we establish a PoE guarantee under uniform prior that is independent of the number of signals but unavoidably exponential in the dimension $m$. We also study the computational complexity of explainable information design, proving that the exactly optimal explainable policy is NP-hard to compute, but an explainable policy with $1/2$ approximation guarantee can be computed in polynomial time for piecewise Lipschitz utility functions.

Global food security depends on tightly coupled international supply chains encompassing natural gas, mineral fertilizers, and staple crops. Earlier research has examined the potential consequences of disruptions in each of these domains separately, but not from a systemic perspective. Here we integrate bilateral trade in natural gas, nitrogen, phosphorus, and potassium fertilizers, and eleven staple crops -- accounting for approximately 70% of plant-based calories -- into a cascading-impact model spanning 208 countries, 20 geopolitical blocs, and the period 1992--2023. Under complete trade isolation, up to 22% of global caloric consumption would be lost, with a peak in the most recently evaluated years. Structural vulnerabilities vary considerably. Regions largely lacking some segments of the supply chain face near-total crop supply collapse, while few countries can cover the entire nexus through domestic resource endowments and production capacities. Temporal trends highlight a substantial increase in vulnerability globally, most prominently in the EU, with a near two-fold increase since the 1990s. Market power is most concentrated and most volatile in the upstream gas layer and has risen in the fertilizer layers since the 2000s; shocks propagate downstream from these tightening upstream layers, driving the system's fragility. Food stocks provide only limited resilience, with half of humanity living in countries holding stocks lasting fewer than three months. Our results identify upstream supply chains as the structural bottlenecks of the global agrifood system and propose leverage points to enhance resilience.