I study transformations of returns in the growth-optimal (Kelly) portfolio problem. In the one-safe-one-risky-asset problem, a return transform f universally produces a more conservative portfolio if and only if f is concave and strictly increasing and r/f is convex. As a corollary, I characterize comparative risk aversion for a rationally-inattentive agent: a more risk-averse agent is one who is sufficiently more risk averse in the Pratt (1964) sense.

This paper presents an implementable framework for tracking Brazil's real neutral-rate proxy, using a block-based ensemble of complementary models. The project begins with daily macro-financial data, converts the series to monthly frequency, computes an ex-ante real Selic rate through the Fisher equation, builds activity-cycle measures from IBC-Br, and then combines five methodological blocks: simple moving averages, statistical trend filters, market-implied curve proxies, a yield-curve state-space model, and a semi-structural IS-Phillips state-space model. The final implementation treats the semi-structural block conservatively: because the IS-Phillips Kalman model falls back to a local-level trend in the current sample, its output is not labeled as structural r-star and receives zero weight in the final ensemble. The latest estimate, for May 2026, places the final operational neutral-rate proxy at 9.48% p.a., with a P25-P75 block range of 8.71%-9.97%. The ex-ante real rate is 10.04%, implying a policy gap of 0.56 p.p. and a neutral stance under the project's thresholds. This neutral classification should be read strictly relative to the project's elevated operational proxy, not relative to conventional long-run structural estimates. The high level of the estimate should not be interpreted as a definitive long-run structural neutral rate: it reflects recent Brazilian real-rate dynamics, market pricing, and trend-based measures in a restrictive cycle. The estimate should be interpreted as a short-to-medium-run shadow neutral-rate proxy under current restrictive monetary and risk-premium conditions, not as a steady-state structural equilibrium rate. The main contribution is therefore methodological and applied: the project offers a transparent, auditable, and extensible measurement system for tracking r-star proxies and monetary-policy stance in Brazil.

In this paper, we study how to rank a finite set of treatment saturations for a target population with clustered network interference. We propose an empirical success (ES) ranking rule that, for each pair of saturations, selects the saturation level with the higher estimated welfare using data from a two-stage randomized saturation design. We adopt the statistical decision theory framework with additively separable regret loss to assess the performance of the ES ranking rule. We derive non-asymptotic upper bounds on the maximum regret of the ES ranking rule that depend on the within-cluster network only through a single combinatorial summary of its dependency structure. We exploit these bounds to characterize a quasi-optimal first-stage saturation distribution within the two-stage randomized saturation design. We further show that the ES ranking rule is asymptotically optimal among threshold ranking rules in the sense of minimizing an upper bound on the worst-case regret.

Estimating causal effects in panel data is a central problem in policy evaluation. Existing methods largely address retrospective questions of the form: what would have happened to a target unit under a different intervention during the observed panel? In many applications, however, decision-makers face prospective questions: what will happen to a target unit under an intervention it has not yet experienced, beyond the observed panel? This article develops a framework for answering such causal forecasting questions by integrating the retrospective counterfactual logic of synthetic-controls-based approaches with the extrapolative structure of multivariate time-series forecasting. Building on the latent factor models that justify unit-side regressions in synthetic controls, we impose low-rank temporal structure on the latent time factors to identify prospective causal forecast estimands. We operationalize this strategy through the Two-Way Synthetic Forecasting estimator, or TWSF, which learns cross-unit relationships from pre-treatment outcomes and combines them with a time-series model learned from treated donor trajectories under the intervention of interest. Under suitable conditions, we establish finite-sample forecasting error bounds that imply pointwise consistency and introduce an orthogonalized correction that yields asymptotic normality and thus enables pointwise inference. We extend the framework to fixed multi-step forecasting horizons through both direct and recursive procedures, each of which inherits analogous pointwise guarantees. We corroborate the theory with simulation studies and illustrate the practical utility of TWSF by studying the public-health impact of opening NFL stadiums during the 2020 season.

We analyze distributions of historic S&P500 multi-day returns, for the number of days of accumulation from 20 to 120. With the increase of the number of days of accumulation, we observe clear tempering of power-law tails toward a seemingly finite value. To explain this phenomenon, we employ a model that produces a "capped Inverse Gamma" stationary (steady-state) distribution for stochastic volatility which, in turn, produces a "tempered Student-t" distribution for returns. We then employ Jones-Faddy-like symmetry breaking mechanism that produces a "tempered Skew-t" distribution. This distribution provides rather good fits to the distributions of accumulated multi-day S&P500 returns, which exhibit symmetry breaking between gains and losses -- as reflected by positive mean and negative skew. Tempered Skew-t fits are also consistent with near perfect linear dependence on the number of days of accumulation of the mean values and, even more so, of the variances (mean squared realized volatility) of the distributions.

This paper presents a reproducible synthetic benchmark comparing a computational planner, an agent-based market, and a hybrid meta-market within a common simulated economy. The benchmark incorporates input-output production networks, heterogeneous firms, capacity constraints, endogenous prices, welfare metrics, structural shocks, adversarial stress testing, and information-reporting experiments. Across training, holdout, and adversarial scenarios, the planner consistently achieves lower welfare losses than the decentralized alternatives. The main contribution is methodological rather than ideological. While the benchmark demonstrates a falsifiable framework for comparing economic coordination mechanisms, it does not establish the empirical superiority of planning. Several design choices mechanically favor the planner, including informational asymmetries, incomplete market representation, and simplified institutional assumptions. The results should therefore be interpreted as validation of a synthetic experimental architecture and as a prototype for future research. The paper concludes by outlining a validation agenda based on empirical calibration, structural holdouts, sensitivity analysis, uncertainty quantification, mechanism-design tests, and independent replication.

This paper studies the macroeconomic dynamics of climate policy in a multi-sector dynamic general equilibrium model with renewable and non-renewable energy, sector-specific capital adjustment frictions, household energy demand, and endogenous fossil resource dynamics. The central mechanism is that decarbonization requires reallocating energy use and installed capital: fossil energy demand can contract immediately, while renewable capacity and abatement adjust only gradually. The analysis delivers four results. First, gradual policy implementation sharply reduces transition costs: relative to immediate implementation, gradual emissions caps improve welfare by 2.26 percentage points under comprehensive regulation and by 5.06 percentage points under firm-only regulation. Second, renewable energy subsidies and non-renewable energy taxes support renewable capital accumulation and reduce, but do not eliminate, the welfare cost of front-loaded tightening. Third, sectoral coverage changes the welfare ranking across implementation speeds. Firm-only regulation performs better under gradual implementation because it shields utility-relevant household energy services, but becomes nearly as costly as the carbon-price-only transition under immediate implementation. Fourth, endogenous fossil exploration and stock-dependent extraction costs transmit climate policy into lower extraction, fewer discoveries, and a declining shadow value of reserves, providing a structural mechanism for stranded fossil assets. The results show that deep decarbonization can be achieved at substantially lower macroeconomic cost when policy manages the speed and incidence of energy-capital reallocation.

Using average vehicle speed data in 10-minute increments at the Traffic Message Channel (TMC) location level, along with precise crash timing and location information, we analyze driving behavior around five Florida stadiums before and after NFL and NBA regular season games from 2015 to 2019. We find no evidence of emotional driving following NBA games, but strong and consistent effects following NFL games, concentrated in predicted-close games that end in disappointing home-team losses -- combining high pre-game suspense with negative outcome valence. These games are associated with significant increases in average vehicle speed within 3 km of stadiums during the first post-game hour, dissipating with increasing time and distance from the stadium. Average vehicle speed increases by up to 3 mph relative to predicted-close games that ended in a win -- an effect several times larger than the typical game day versus non-game day speed differential. Overall, our results highlight how the combination of sustained suspense and negative outcome valence in close sporting contests can spill over into risky post-game driving behavior, underscoring the behavioral and public safety implications of affective cues in large-scale sporting events.

Previous studies conclude that intermediaries account for a large share of exports. Using Spanish firm-level data, we show that many firms classified as intermediaries are either manufacturer-owned export arms that ship their parent firms' products or vertically integrated firms that control design, production, and distribution and predominantly export goods sold under their own brands. Once we exclude these export arms and vertically integrated firms, the share of intermediaries in exports in our sample falls by about 70%. We also show that pure intermediaries differ markedly from export arms and vertically integrated firms along key firm and export dimensions.

Some firms export their own products directly, others rely on intermediary firms to export on their behalf, and still others both export their own products and intermediate exports for other producers. To explain this heterogeneity, we develop a model in which firms differ along two dimensions: manufacturing capability and commercial capability. Manufacturing capability lowers the marginal cost of producing a variety, whereas commercial capability lowers the variable cost of reaching foreign customers. Different combinations of these capabilities generate the different types of firms observed in export markets: direct exporters, indirect exporters, pure intermediaries, and hybrid firms. The model predicts that commercially capable intermediaries are matched with more manufacturing-capable producers, and that more commercially capable intermediaries export a broader set of varieties. We provide suggestive evidence for these predictions using Spanish firm-level export data.

Offline policy learning has received growing attention in causal inference. The primary objective is to learn a policy (individualized treatment rule) as a mapping from covariates to treatment that maximizes the empirical welfare defined as the mean of scalar-valued potential outcomes. In this paper, we study offline policy learning with distribution-valued outcomes, where each potential outcome is a probability measure on $\mathbb{R}$ and the reward is defined through a utility functional applied to the Wasserstein barycenter of induced outcome distributions. We establish statistical guarantees for the policy learning framework based on both Inverse Probability Weighting (IPW) and Doubly Robust (DR) estimators. By handling the challenging uniform deviation over the product of the combinatorial policy class and the infinite-dimensional quantile domain, we prove that the finite-sample regret has leading dependence $\widetilde{\mathcal{O}}(\sqrt{\mathrm{N\text{-}dim}(Π)/N})$. In the one-dimensional Wasserstein setting and under the stated regularity conditions, the leading regret rate is still governed by the policy-class complexity. Moreover, we provide a minimax lower bound establishing the sharpness of the leading dependence on $N$ and $\mathrm{N\text{-}dim}(Π)$.

Random allocations are widely used to handle ties and indifferences in two-sided environments. In such environments, commonly used procedures such as random tie-breaking may fail to ensure stability and fairness from an ex ante perspective. We show that when agents have discrete concave (M$^\natural$-concave) valuations, there exists an ex ante stable and fair allocation. To establish this result, we relate our framework to the model of stability introduced by Alkan and Gale. In particular, we show that ex ante stable and fair fractional allocations are exactly characterized as Alkan--Gale stable outcomes under choice functions induced from concave closures together with a symmetric strictly convex tie-breaking rule. We further prove that any ex ante stable fractional allocation can be decomposed into a lottery over stable deterministic allocations, using a generalization of the Birkhoff--von Neumann theorem. Finally, we study a setting that does not rely on cardinal valuations and instead assumes ordinal preferences. Within this ordinal framework, we establish the existence of an ex ante stable and fair fractional allocation. This setting is formulated within the matching-with-contracts framework under matroid constraints. The resulting class includes existing models, such as one-to-many random allocation with responsive choice correspondences, and captures a wide range of applications, including controlled school choice with lotteries.

This volume develops a knowledge theory of capital for economies in which productive capacity increasingly resides in software, data, models, routines, expertise, platforms, organizations, commons, and public epistemic infrastructure. Beginning from Adam Smith's theory of labour, stock, specialization, and market extent, it asks what changes when knowledge becomes stock-like, mobile across forms, scalable, governable, recombinable, and imperfectly visible in accounting. The book introduces knowledge-bearing stock as the central object and analyses how it is generated, converted into governable form, deployed, improved through feedback, enclosed or shared, measured, impaired, and used as input to future production. It distinguishes embodied, disembodied, institutionalized, commons, and public knowledge forms and develops concepts such as first conversion, cognitive enclosure, feedback capture, dark capital, and expected knowledge loss. The argument is conditional and testable: modern wealth depends not only on capital accumulation, but on how productive knowledge is governed.

Legal precedents protect computer code as copyrightable expression. They have enabled centralized digital platforms -- operating from corporate servers that hold all user data -- to construct private governance regimes through the interaction of copyright, contract, and technical architecture: people who create virtually all platform value must surrender effective copyright control through Terms of Service agreements as a condition of participation. In contrast, grassroots platforms consist of cryptographically-identified people operating their networked smartphones independently of any server or global resource; each person holds their own data on their own device, with no third party in possession or intermediation. Here, we define the notion of a \textit{digital speech act} -- a deliberate volitional act by a person of cryptographically signing personal content with the person's private key, carried out on the person's own device -- through which the person simultaneously establishes attribution, accountability, and authorship over the signed content. We contend that (\ia) digital speech acts qualify for copyright protection under existing U.S.\ precedent: \textit{Burrow-Giles} locates authorship in volitional creative choices despite mechanical or algorithmic processes, \textit{Feist} supplies the minimal-creativity threshold, and persistent device storage satisfies the Copyright Act's fixation requirement; (\ib) the digital social contract underlying grassroots platforms preserves this copyright by design -- signed content cannot be unbundled from its signature, and the full provenance chain accumulates as content is forwarded -- so that ownership and possession coalesce in the person; and (\ic) copyright in digital speech acts is a prerequisite for digital sovereignty and democratic self-governance.

Electricity markets are inherently complex systems characterised by strong nonlinearities, high-dimensional interactions, and increasing interdependence across regions. While deep neural networks (DNNs) have demonstrated strong predictive capabilities for electricity prices, their lack of interpretability limits their usefulness for understanding the underlying drivers of price formation. This paper addresses this gap by combining DNN models with explainable artificial intelligence (XAI) techniques to analyse the determinants of electricity prices across 39 European bidding zones. We employ SHAP (SHapley Additive exPlanations) to quantify feature contributions and apply and extend SSHAP, an aggregation framework to improve interpretability in high-dimensional settings. The analysis identifies that renewable energy sources, particularly solar, play a disproportionately important role in price formation despite their lower share in total power generation. Gas prices remain a dominant and consistent driver across electricity markets, while interconnections significantly shape price dynamics, highlighting the strong interdependence of European electricity systems. In addition, a synthetic EU-wide electricity market is constructed to explore the counterfactual scenario of a fully integrated market with a single price.

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 ({\sf Actors}, {\sf Actions}, {\sf Ends}, {\sf Things}, {\sf Times}) and six primitive relations ({\em Acts}, {\em Avail}, {\em EndOf}, {\em 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 {\em Lean} companion encodes the language as {\em Lean} type classes and constructs concrete models -- a three-period Robinson Crusoe economy and its infinite-time extension -- whose acceptance by the type-checker is a constructive consistency proof of the full base theory.

How should recommender systems be designed when recommendations shape access to scarce, short-lived opportunities? We study this question in a production setting: Timee, Japan's largest platform for spot work, where workers favorite job templates and receive notifications when firms post shifts from those templates. Maximizing predicted favoriting can generate misdirected concentration: recommendations accumulate on popular templates that create few viable job openings, while templates with unmet labor demand receive too little exposure. We design exposure-control mechanisms for favorite-list management, reallocating template exposure based on posting activity and unfilled capacity. The proposed recommender, thresholded eligibility control (TEC), is fully parallelizable and suitable for large-scale digital platforms. In simulations calibrated to Timee data, TEC raises the per-round job-finding rate from 57.6% to 70.0%. A prefecture-level randomized field experiment increases realized matches and exposure per active template, reduces the share of low-exposure templates, and improves impression-level favoriting and downstream matching.

A game of information concerns two players transmitting messages that are obscured by noise. A receiver digests the combination of the two information sources and makes an assessment rationally. The aim of the players is to generate opposing assessments for the receiver by choosing signal-to-noise ratios of their information. It is shown that this problem can be reduced into an elementary infinite game on the square, thus admitting a complete equilibrium solution. Three generalisations of the game are proposed.

The classical expected utility (EU) axioms are not sufficient for finite datasets. There are a number of anomalies (violations of EU) where axioms are satisfied. This paper studies axioms that are immune to this problem and definitively delineate between EU and non-EU. We discuss implications for experimental design and explore the automatic generation of anomalies.

This paper develops a model of \textit{identification design} and applies it to robust causal inference in microeconometrics. The decision maker observes the population distribution of signals generated by an information structure and ranks actions by their worst-case payoff over the set of admissible state distributions consistent with those signals. We call an environment \textit{manipulable} if every action is implementable under all true distributions of the state variable, and show this holds if and only if all actions share the same worst-case payoff. We confirm in application that all treatment-effects models are manipulable, and moreover that manipulation is feasible via \textit{almost fully informative} information structures that conceal at most one dimension of information from the decision maker. As in practice, we consider a restriction to \textit{marginal information structures} that disclose the joint distribution of the outcome variable, treatment variable, and a selection of covariates. In that context, we provide necessary and sufficient conditions for exact identification and sharp payoff bounds for disclosures that do not satisfy those conditions. In doing so, we show that the disclosure of a sufficiently rich set of covariates to verify faithful execution of the assignment mechanism eliminates all scope for manipulation in experiments, while observational studies remain partially manipulable via covariate selection.

Commercial fusion energy requires frameworks to assess both the scientific and economic viability of a wide variety of fusion concepts. Inspired by the Lawson criterion's ability to universally describe fusion energy gain, a generalized framework is developed to determine the economic gain of fusion power plants. The model exploits temporal equilibrium, and engineering and cost parameters normalized to the energy capture surface. The derived criteria for economic gain are therefore independent of the power plant's absolute power, impartial to the particulars of its fusion technology, and can be applied to any fusion confinement concept. The derivation of the economic gain factor, $Q_{econ}$, results in nonlinear equations with ten controlling normalized design parameters ranging from fusion power density and surface component lifetime to energy fluence, price of energy, and component efficiency and cost. These ten controlling parameters are varied over a wide range to provide high-level insights in design, finance and operational tradeoffs that improve the prospects for economically viable fusion energy.

We propose a finite-sample risk-optimal selection criterion for Cressie-Read power divergence (CRPD) estimation in overidentified moment-based models. The CRPD family, dual to generalized empirical likelihood, is indexed by the power parameter $γ$. Although $γ$ is conventionally fixed at a researcher-chosen value, we argue that it should be interpreted as a data-tunable curvature parameter governing the finite-sample behavior of the CRPD objective. Through implied probability weights and associated Lagrange multipliers, $γ$ affects how the empirical distribution is reweighted to enforce the moment restrictions, even when population identification is unchanged. The proposed criterion selects $γ$ by minimizing an estimation- and system-oriented risk measure. It combines a structural component, which measures finite-sample distortion in the estimate of the structural parameter relative to a first-order GMM benchmark, with a multiplier-stability component, which measures the cost of moment enforcement in the full estimator-multiplier system. A researcher-specified weight determines the relative importance of the two components, allowing the selection rule to prioritize structural accuracy, multiplier stability, or a balance between them. The resulting selector is designed to reduce second-order finite-sample distortion while discouraging unstable multipliers, concentrated implied weights, and proximity to the feasible-probability boundary. Simulations show that the selected CRPD estimator remains approximately centered around the structural parameter while improving finite-sample stability. An empirical illustration using Owen's dairy-cow data shows that similar point estimates can correspond to different implied weighting schemes, highlighting the practical role of $γ$ as a curvature parameter in moment-based estimation.

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.

Randomized experiments, or A/B testing, are the gold standard for evaluating interventions, yet they remain underutilized in inventory management. This study addresses this gap by analyzing A/B testing strategies in multi-item, multi-period inventory systems with lost sales and capacity constraints. We examine two canonical experimental designs--switchback experiments and item-level randomization--and show that both suffer from systematic bias due to interference: temporal carryover in switchbacks and cannibalization across items under capacity constraints. Under mild conditions, we characterize the direction of this bias in different scenarios. Motivated by two-sided randomization, we propose a pairwise design over items and time and analyze its bias properties. Controlled stochastic simulations verify the theoretical predictions, and trace-driven experiments on real-world fresh-retail data show that the same mechanisms persist in realistic environments with stockout substitution.

This paper focuses on finite-player incomplete information games where players may hold mutually inconsistent beliefs without a common prior. We introduce absolute continuity of beliefs, extending the classical notion of absolute continuity of information in Milgrom and Weber (1985), and prove that Bayesian equilibria exist in a broad class of games, including those with discontinuous payoffs. Examples illustrate the scope and implications of our findings.

In rank aggregation, the task is to aggregate multiple weighted input rankings into a single output ranking. While numerous methods, so-called social welfare functions (SWFs), have been suggested for this problem, all of the classical SWFs tend to be majoritarian and are thus not acceptable when a proportional ranking is required. Motivated by this observation, we design SWFs that guarantee that every input ranking is proportionally represented by the output ranking. Specifically, our central fairness condition requires that the number of pairwise comparisons between candidates on which an input ranking and the output ranking agree is at least proportional to the weight of the input ranking. As our main contribution, we present a simple SWF called the Proportional Sequential Borda rule which satisfies this condition. Moreover, we introduce a more involved variant of this rule, the Flow-adjusting Borda rule, which satisfies a stronger fairness condition that applies to arbitrary groups of rankings. Many of our axioms and techniques are inspired by results in approval-based committee voting and participatory budgeting, where the concept of proportional representation has been studied in depth.

We derive a novel canonical decomposition of factor models encompassing both the static factor model - where factors are loaded only contemporaneously - and the Generalised Dynamic Factor Model - where factors are loaded with lags. This decomposition features a new term: the weak common component, defined as the difference between the dynamic and static common components. It is driven by (possibly infinitely many) non-pervasive weak factors which belong to the dynamically common space. Through theoretical and empirical examples - both on U.S. macroeconomic indicators and global financial volatilities - we show that, in general, the weak common component shall not be neglected. Furthermore, we show that, by accounting for the presence of weak common components, we are likely to obtain Impulse Response Functions with more plausible shapes than those obtained from purely static approaches. In addition, we provide consistent estimators for all terms of the canonical decomposition and for the weak factors.

We identify the distributional and quantile marginal treatment effect functions when the outcome is right-censored. Our method requires a conditionally exogenous instrument and random censoring. We propose asymptotically consistent semi-parametric estimators and valid inferential procedures for the target functions. To illustrate, we evaluate the effect of alternative sentences (fines and community service vs. no punishment) on recidivism in Brazil. Our results highlight substantial treatment effect heterogeneity: we find that people whom most judges would punish take longer to recidivate, while people who would be punished only by strict judges recidivate at an earlier date than if they were not punished.

A triangular structural panel data model with additive separable individual-specific effects is used to model the causal effect of a covariate on an outcome variable when there are unobservable confounders with some of them time-invariant. In this setup, a linear specification for the reduced-form equation might be problematic when the conditional mean of the endogenous covariate and the instrumental variables is nonlinear in the population. The reason is that ignoring the nonlinearity could lead to weak instruments (instruments are weakly correlated with the endogenous covariate) due to misspecification as shown using a generalized concentration parameter for panel data. As a solution, we propose a triangular simultaneous equation model for panel data with additive separable individual-specific fixed effects composed of a linear structural equation with a nonlinear reduced form equation. The parameter of interest is the structural parameter of the endogenous variable. The identification of this parameter is obtained under the assumption of available exclusion restrictions and using a control function approach. We provide an estimator that we call Super Learner Control Function estimator (SLCFE). The estimation procedure is composed of two main steps and cross-fitting. First, we estimate the control function using a super learner. In the following step, we use the estimated control function to control for endogeneity in the structural equation. Cross-fitting is done across the individual dimension. The estimator is consistent and asymptotically normal achieving a parametric rate of convergence. We show that the SLCF estimator differs from both the plug-in IV estimator and a naive plug-in 2SLS estimator, with the former not being consistent without cross-fitting, and the latter not being consistent even with cross-fitting.

Allocating indivisible goods is a ubiquitous task in fair division. We study additive welfarist rules, an important class of rules which choose an allocation that maximizes the sum of some function of the agents' utilities. Prior work has shown that the maximum Nash welfare (MNW) rule is the unique additive welfarist rule that guarantees envy-freeness up to one good (EF1). We strengthen this result by showing that MNW remains the only additive welfarist rule that ensures EF1 for identical-good instances, two-value instances, as well as normalized instances with three or more agents. On the other hand, if the agents' utilities are integers, we demonstrate that several other rules offer the EF1 guarantee, and provide characterizations of these rules for various classes of instances.