A vocabulary is a list of words designating subsets from a grand set X. We model a vocabulary as a partition of X and study the aggregation of individual vocabularies into a collective one. We characterize aggregation rules when X is linearly ordered and each word of the vocabulary spans an order interval. We allow for individual vocabularies to differ both in the number and in the span of their words. Under a suitable restriction on agents' preferences, we show that our aggregation rules are strategy-proof.

In June 2026, the UK government will set its carbon budget for the period 2038 to 2042, the seventh such carbon budget (CB7) since the Climate Change Act became law in 2008. For the first time, this carbon budget will be accompanied by a macroeconomic assessment of its impact on growth, employment, inflation and inequality. Researchers from the Institute of New Economic Thinking (INET) Oxford are working in partnership with the Department for Energy Security and Net Zero to deliver this assessment using our data-driven macroeconomic agent-based model (ABM). This extended abstract presents the work in progress towards this pioneering policymaking using our data-driven macroeconomic ABM. We are conducting our work in three work packages. By the time of the workshop, we hope to be able to present preliminary findings from the first two work packages. In WP1, we adapt an existing macro-ABM prototype and build a UK macroeconomic baseline. The main task for this is initialising the model with suitable UK household microdata. We present the options considered and the approach settled upon. In WP2, we conduct preliminary modelling that represents UK decarbonisation as an external shock to financial flows and technical coefficients. In order to present results in time to influence the June 2026 policy decision, this second work package exogenously forces the ABM to follow the CB7 green investment and associated technological change projections provided by the Climate Change Committee. Finally, we will implement more sophisticated social and technological learning packages in WP3, building our own projections of likely decarbonisation pathways that may diverge from UK government plans. For the workshop, we will present the progress of WP1 and WP2.

This article's aim is to provide the solution to the equity premium puzzle without using calibrated values. Calibrated values of subjective time discount factor were used in my prior derived models because 4 variables were determined from 3 different equations. Furthermore, calculated values and risk behavior determination of my prior models were compatible with empirical literature. 4 unknown variables are now calculated from 4 different equations in the new derived model in this article. Subjective time discount factor and coefficient of relative risk aversion are found 0.9581 and 1.0319, respectively from the system of equations which are compatible with empirical studies. Micro and macro studies about CRRA value affirm each other for the first time in the literature. Furthermore, equity and risk-free asset investors are pinned down to be insufficient risk-loving, which can be considered a type of risk-averse behavior. Hence it can be said that calculated values and risk attitude determination align with empirical literature. This shows that derived model is valid and make CCAPM work without calibration.

The Growth-at-Risk (GaR) framework has garnered attention in recent econometric literature, yet current approaches implicitly assume a constant Pareto exponent. We introduce novel and robust econometrics to estimate the tails of GaR based on a rigorous theoretical framework and establish validity and effectiveness. Simulations demonstrate consistent outperformance relative to existing alternatives in terms of predictive accuracy. We perform a long-term GaR analysis that provides accurate and insightful predictions, effectively capturing financial anomalies better than current methods.

Compositional data, such as regional shares of economic sectors or property transactions, are central to understanding structural change in economic systems across space and time. This paper introduces a spatiotemporal multivariate autoregressive model tailored for panel data with composition-valued responses at each areal unit and time point. The proposed framework enables the joint modelling of temporal dynamics and spatial dependence under compositional constraints, and is estimated via a quasi-maximum likelihood approach. We build on recent theoretical advances to establish the identifiability and asymptotic properties of the estimator as both the number of regions and the number of time points grow. The utility and flexibility of the model are demonstrated through two applications: analysing property transaction compositions in an intra-city housing market (Berlin), and regional sectoral compositions in Spain's economy. These case studies highlight how the proposed framework captures key features of spatiotemporal economic processes that are often missed by conventional methods.

Scientists agree about the urgency of the problem of climate change. Most citizens, however, pay little attention to gradually increasing temperature levels. Growing numbers of natural disasters in the world might then play a fundamental role as the key signal to alert humanity to the severity of the problem of the changing climate. But is that potential mechanism working? In this empirical examination (N>2 million over three decades in 93 countries), we show for the first time that a typical person's happiness and life satisfaction is barely affected by natural disasters in their region. Yet these are the individuals -- as opposed to the minority literally flooded or literally badly affected by hurricanes -- who effectively shape how governments act. This study's ``psychological near-irrelevance'' result is deeply troubling.

The rise of foundation models has driven the emergence of AI supply chains, where upstream foundation model providers offer fine-tuning and inference services to downstream firms developing domain-specific applications. Downstream firms pay providers to use their computing infrastructure to fine-tune models with proprietary data, creating a co-creation dynamic that enhances model quality. Amid concerns that foundation model providers and downstream firms may capture excessive consumer surplus, along with increasing regulatory measures, this study employs a game-theoretic model involving a provider and two competing downstream firms to analyze how policy interventions affect consumer surplus in the AI supply chain. Our analysis shows that policies promoting price competition in downstream markets (i.e., pro-price-competitive policies) boost consumer surplus only when compute or data preprocessing costs are high, while compute subsidies are effective only when these costs are low, suggesting these policies complement each other. In contrast, policies promoting quality competition in downstream markets (i.e., pro-quality-competitive policies) always improve consumer surplus. We also find that under pro-price-competitive policies or compute subsidies, both the provider and downstream firms can achieve higher profits along with greater consumer surplus, creating a win-win-win outcome. However, pro-quality-competitive policies increase the provider's profits while reducing those of downstream firms. Finally, as compute costs decline, pro-price-competitive policies may lose their effectiveness, whereas compute subsidies may shift from ineffective to effective. These findings offer insights for policymakers seeking to foster AI supply chains that are economically efficient and socially beneficial.

Economists often interpret estimates from linear regressions with log dependent variables as elasticities. However, the coefficients from log-log regressions estimate the elasticity of the geometric mean of $y_i|x_i$, not the arithmetic mean. The unbounded difference between the two is known as retransformation bias and can take either sign. We develop a specification-robust debiased estimator of the average arithmetic elasticity and re-estimate 50 results from top 5 papers published in 2020. We find that 19 are significantly different, with the median absolute difference being 65% of the OLS elasticity estimate. Furthermore, we show standard instrumental variables assumptions with log dependent variables do not identify the elasticity. We specify a control function approach and re-estimate papers that use 2SLS with log dependent variables. We find that 13 of 19 results from top 5 papers are significantly different between the two approaches. Retransformation bias arises as a result of heterogeneous responses. The geometric mean elasticity corresponds to the average response. Arithmetic and geometric means are elements of the power mean family. We show power mean elasticities are sufficient statistics for a common class of decision problems.

This paper studies mechanism design environments in which the designer does not know the distribution of agents' private information a priori and instead learns from agents' behavior induced by the mechanism itself. We formalize a notion of self-confirming mechanisms and a refinement thereof, capturing the idea that an equilibrium mechanism is optimal given the designer's belief and that this belief is consistent with the information produced by the mechanism. We establish a fictitious revelation principle, showing that any incentive-compatible mechanism can be represented as a direct mechanism with filtered type reports that preserve the original mechanism's informational content. Applying the framework to a monopoly problem, we show that, subject to an equilibrium refinement, dominant-strategy self-confirming mechanisms are exactly posted-price mechanisms with locally revenue-maximizing prices.

A central challenge in financial economics is understanding how credit networks form under informational noise. We introduce the concept of topological capital, arguing that banks increasingly rely on topological certification, interpreting a borrower's connectivity as a primary proxy for creditworthiness. Using a novel dataset of bank-firm relationships manually extracted from Italian financial statements, we implement a multi-stage empirical framework, benchmarking empirical patterns against a maximum-entropy benchmark, to separate the determinants of credit access from those of loan volumes. Our results indicate that network topology systematically outperforms traditional fundamentals. In the link-formation stage, connectivity breeds further connectivity through an amplified preferential attachment mechanism. In the loan-sizing stage, network strength absorbs the explanatory power of balance-sheet metrics, documenting a profound network substitution effect where topological signals effectively replace physical collateral across all corporate segments. For SMEs, we identify a critical signal divergence: reported debt acts as a risk signal, while network footprint serves as market validation. Furthermore, we reveal a diversification paradox: while firms fragment debt to avoid hold-up risks, over-diversification leads to a complexity penalty that stagnates credit depth and inflates systemic Loss Given Default. Ultimately, our findings signal the twilight of the balance sheet as the primary anchor of corporate lending, calling for a shift toward topological macro-prudential supervision to manage vulnerabilities invisible to traditional bilateral indicators.

Firms collect vast amounts of behavioral and geographical data on individuals. While behavioral data captures an individual's digital footprint, geographical data reflects their physical footprint. Given the significant privacy risks associated with combining these data sources, it is crucial to understand their respective value and whether they act as complements or substitutes in achieving firms' business objectives. In this paper, we combine economic theory, machine learning, and causal inference to quantify the value of geographical data, the extent to which behavioral data can substitute for it, and the mechanisms through which it benefits firms. Using data from a leading in-app advertising platform in a large Asian country, we document that geographical data is most valuable in the early cold-start stage, when behavioral histories are limited. In this stage, geographical data complements behavioral data, improving targeting performance by almost 20%. As users accumulate richer behavioral histories, however, the role of geographical data shifts: it becomes largely substitutable, as behavioral data alone captures the relevant heterogeneity. These results highlight a central privacy-utility trade-off in ad personalization and inform managerial decisions about when location tracking creates value.

We construct a thin double category HS (Hub-and-Spoke) whose objects are closed subsets of standard simplices, horizontal morphisms are continuous maps representing portfolio re-implementation processes, and vertical morphisms are closed relations representing alignment constraints. This framework models industrial portfolio construction pipelines -- hierarchical structures in which a single investment strategy is translated through multiple stages into thousands of client portfolios. We establish four structural theorems: compositionality of alignment (functoriality), a pre-trade safety guarantee (adjunction), an order-independence result for compliance checking (lax Beck--Chevalley), and a filter-commutation law (Frobenius reciprocity). The topological requirement that permissible portfolio spaces be closed and compact -- ruling out ``phantom portfolios'' that arise from open constraint specifications -- is shown to be essential for coherence. Extensions to set-valued re-implementations via the Double Operadic Theory of Systems, stochastic re-implementations via Markov kernels on Polish spaces, and transport-based safety metrics via Wasserstein distances are developed. An abstract axiomatic treatment identifies the equipment axioms sufficient for the main results. The mathematical content is elementary -- no novel category theory is required. The contribution is the modelling claim: that these particular objects and morphisms formalise portfolio re-implementation correctly.

We study settings in which a researcher has an instrumental variable (IV) and seeks to evaluate the effects of a counterfactual policy that alters treatment assignment, such as a directive encouraging randomly assigned judges to release more defendants. We develop a general and computationally tractable framework for computing sharp bounds on the effects of such policies. Our approach does not require the often tenuous IV monotonicity assumption. Moreover, for an important class of policy exercises, we show that IV monotonicity -- while crucial for a causal interpretation of two-stage least squares -- does not tighten the bounds on the counterfactual policy impact. We analyze the identifying power of alternative restrictions, including the policy invariance assumption used in the marginal treatment effect literature, and develop a relaxation of this assumption. We illustrate our framework using applications to quasi-random assignment of bail judges in New York City and prosecutors in Massachusetts.

As large language models (LLMs) increasingly act as autonomous agents in markets and organizations, their behavior in strategic environments becomes economically consequential. We document that off-the-shelf LLM agents exhibit systematic deviations from payoff-sensitive behavior in canonical economic games, including excessive cooperation and limited responsiveness to incentives. We introduce a supervised fine-tuning approach that aligns agent behavior with explicit economic preferences. Specifically, we generate optimal strategies under two stylized utility specifications, homo economicus, which maximizes self-interest, and homo moralis, which incorporates Kantian universalizability, and use these utility-implied reasoning and strategies to guide fine-tuning. Fine-tuning on a small, theory-driven synthetic dataset induces persistent and interpretable shifts in strategic behavior. In applications to moral dilemmas and repeated duopoly pricing, agents aligned to different preference structures produce systematically distinct equilibrium outcomes and pricing dynamics. These results frame AI alignment in multi-agent settings as an objective-design problem and illustrate how economic theory can guide the design of strategically coherent AI agents.

We compare the total capital efficiency of secure restaking and Proof-of-Stake (PoS) protocols. First, we consider the sufficient condition for the restaking graph to be secure. The condition implies that it is always possible to transform such a restaking graph into separate secure PoS protocols. Next, we derive two main results: upper and lower bounds on the required extra stakes to add to the validators of the secure restaking graph to be able to transform it into secure PoS protocols. In particular, we show that the restaking savings compared to PoS protocols can be very large and can asymptotically grow as a square root of the number of validators. We also study a complementary question of aggregating secure PoS protocols into a secure restaking graph and provide matching lower and upper bounds on the PoS savings.

This paper investigates the optimal control of an epidemic governed by a SEIR model with an operational delay in vaccination. We address the mathematical challenge of imposing hard healthcare capacity constraints (e.g., ICU limits) over an infinite time horizon. To rigorously bridge the gap between theoretical constraints and numerical tractability, we employ a variational framework based on Moreau--Yosida regularization and establish the connection between finite- and infinite-horizon solutions via $Γ$-convergence. The necessary conditions for optimality are derived using the Pontryagin Maximum Principle, allowing for the characterization of boundary-maintenance arcs where the optimal strategy maintains the infection level precisely at the capacity boundary. Numerical simulations illustrate these theoretical findings, quantifying the shadow prices of infection and costs associated with intervention delays.

In non-asymptotic learning, variance-type parameters of sub-Gaussian distributions are of paramount importance. However, directly estimating these parameters using the empirical moment generating function (MGF) is infeasible. To address this, we suggest using the sub-Gaussian intrinsic moment norm [Buldygin and Kozachenko (2000), Theorem 1.3] achieved by maximizing a sequence of normalized moments. Significantly, the suggested norm can not only reconstruct the exponential moment bounds of MGFs but also provide tighter sub-Gaussian concentration inequalities. In practice, we provide an intuitive method for assessing whether data with a finite sample size is sub-Gaussian, utilizing the sub-Gaussian plot. The intrinsic moment norm can be robustly estimated via a simple plug-in approach. Our theoretical findings are also applicable to reinforcement learning, including the multi-armed bandit scenario.