Papers

States and alliances spend enormous resources signaling resolve to deter adversaries. Two canonical strategies are burning money (sunk costs) and burning bridges (audience costs). Large audience costs can deter effectively, but they may be infeasible and, even when feasible, can increase the likelihood of war relative to burning money. We propose a signaling design in which the defender retains the flexibility to fight or back down but commits ex ante, before learning its resolve, to a rule mapping realized resolve into costly actions. When audience costs are limited, this design raises defender payoffs while reducing the likelihood of war. We discuss implementation through laws and automated algorithms. We also characterize defender payoffs when audience costs are chosen endogenously from a feasible set, showing that lowering the maximum feasible audience cost can raise defender payoffs, and we compare these payoffs with those under the standard burning-money setting without commitment.

This paper studies how Chile's three largest pharmacy chains moved from the price war to collusion, using court-record daily prices and a structural model. After a court-ordered advertisement ban ended the comparison campaign, the estimated gain from loss-leader pricing fell sharply, weakening the incentive to continue the price war. The chains then used an upstream supplier as intermediary to verify a collusive price-leadership procedure. Once verified, they applied it to restore margins on former loss leaders. They then raised prices further to extract rents. These increases spread more slowly than margin restoration. The Adaptive Confidence specification allows a subjective belief about follower participation to update. It more closely matches the cumulative spread of rent extraction than the Unit Confidence specification. Unit Confidence imposes the rational-belief benchmark by fixing the leader's weight at one.

Two frequent approaches for identifying structural VARs are external instruments, which carry economic content but are often weak, and non-Gaussianity of the shocks, which provides statistical identification but carries no economic meaning. We combine the two strategies in a single generalized method of moments framework. This hybrid approach point-identifies the target shocks while also identifying the non-target shocks up to sign and ordering. Under suitable rank conditions, the higher-order moments of the structural shocks anchor the identification uniformly over the instrument strength. Consequently, under local-to-zero proxy relevance, estimators of the dynamic causal effects remain consistent, and standard asymptotic inference remains valid. Moreover, the Anderson-Rubin confidence sets are substantially narrower than their instrument-only counterparts. The hybrid estimator is also more efficient than either source of identification used in isolation: at any fixed proxy relevance, even a weak instrument increases the efficiency of the estimator through its covariance with the non-Gaussian moment block. Under local deviations from proxy exogeneity, we provide asymptotic bias bounds and show that stronger non-Gaussianity of the shocks compresses the bias. Finally, the over-identified structure yields two mutually orthogonal specification tests for proxy exogeneity and the validity of the higher-order moment conditions. We derive their limiting distributions and provide a bootstrap procedure for finite-sample critical values. Monte Carlo simulations and two applications with identification of oil news-shock and a Euro-area MP shock demonstrate the potential of our framework.

Complementary resources are often allocated by agencies that see different coordinates of an individual's needs. If an intervention requires complementary resources, an agency may know if said person lacks its own resource; yet not know if supplying completes a useful bundle. We study allocation of $m$ divisible complementary goods when each agency observes only its own coordinate of a baseline-access profile. To isolate information from incentives, we measure the welfare cost of this split against a generous decentralized benchmark DEC: the best rule that acts on local information alone, with cooperative agencies and known population distribution and capacities. Even so, local observation alone can make optimally coordinated policies arbitrarily inefficient: a factor linear in $m$ (even with equal capacities), and a factor inverse in OPT (with but three agencies). Threshold referrals recover much of this loss: an agency reports if its value lies below a public threshold, and a clearing rule uses only the joint reports. Aggregating types by their reports captures a rectangle under the optimal half-utility survival curve. Our main tool is a profile-level charging certificate: if optimal utility is at least twice a threshold, OPT pays at least that on every deficient coordinate. This yields welfare at least ${\rm OPT}/[4(1+\ln(2/{\rm OPT}))]$ with one bit per agency; and an equal-revenue family shows this log-loss tight for one threshold. A geometric threshold ladder improves this to a constant fraction of OPT with doubly-logarithmic messages: a staircase recovers ${\rm OPT}/8$ with $\Theta(\log\log(1/{\rm OPT}))$ bits, and this is necessary within the class. The results isolate how a simple reporting language turns large local-info losses into constant-factor recovery. In short: One threshold gets a log-approximation. A staircase, with log-of-log bits, a constant-factor.

We introduce a notion and motivation for very credible auctions. This is a strengthening in the commitment in the credible auctions setting, making it more suitable for a modern digital applications.

Observed choice in a dynamic game mixes current profit with continuation value. A rival adds a second problem: the same comparison averages over the rival's equilibrium policy. Changing the primitive transition rewrites continuation technology; changing the rival's Markov policy, holding that law fixed, rewrites the mixture over rival-contingent payoffs. The two are not substitutes. For a rival-feature payoff of rank $K$, rank identification up to location requires $\Ephi=\lceil(MK-1)/(M-1)\rceil$ policy environments, and a second kernel when payoffs are saturated. Rank can still be restored by arbitrarily small policy differences. Independent private shocks force mixed rival actions to factor, so a payoff that depends jointly on $d$ rivals is visible only at order $\eta^{d}$ near a common interior baseline. Either rank fails or the smallest identified singular value is at most $\kappa\eta^{\dPhi}$, independently of how many kernels are stacked. Oracle-GLS variance in that direction vanishes only if $n\eta^{2\dPhi}$ diverges. An Anderson–Rubin set that carries first-stage error in the design matrix covers without a vanishing-risk condition. On U.S.\ airline entry, even among rank-identified directions, the most favorable rival-dependent contrast is several times wider than observed behavior.

We study strategy-proof social choice where agents have single-dipped preferences and outcomes may be sets of alternatives. While point-valued strategy-proof rules select an endpoint, we ask which outcomes survive when sets are compared through responsive extensions. Under the standard responsive extension, preferences over fixed-length intervals remain single-dipped, so the endpoint restriction persists and anonymity yields a single-threshold rule. Under responsive dominance, the incomplete order shared by all responsive extensions, an interior interval can survive because the two extreme intervals need not be comparable. For arbitrary sets, requiring every chosen alternative to be most preferred by some agent yields voting-by-committees rules, with one committee per endpoint; anonymous rules have a two-threshold quota form. The characterization holds on the entire endpoint-peaked domain, and every such rule is group-strategy-proof.

In social and economic networks linked agents often share connections in common. There are two competing explanations for this phenomenon. First, agents may have a structural taste for transitive links - the returns to linking may be higher if two agents share a common connection. Second, agents may assortatively match on unobserved attributes, a process called homophily. We study parameter identifiability in a simple model of dynamic network formation with both effects. Agents form, maintain, and dissolve links over time to maximize utility. The return to linking may be higher if agents share connections in common. A pair-specific utility component allows for arbitrary homophily on time-invariant agent attributes. We derive conditions under which it is possible to detect the presence of a taste for transitivity in the presence of assortative matching on unobservables. We leave the joint distribution of the initial network and the pair-specific utility component, both high dimensional nuisance parameters, unrestricted. Our identification result is constructive, suggesting an analog estimator, whose finite and (single) large network properties we characterize. We show, via examples, the delicacy of information accumulation in the single (large) network setting.

This paper provides an explicit characterization of the (unique) equilibrium of the two-bidder all-pay auction with asymmetrically distributed, independent private values. The characterization is achieved through recasting the problem into its equivalence in the quantile space and thereby obtaining equilibrium bid functions that involve only integrals and inverses of the primitives. No regularity assumption is required: the value distributions can be continuous, discrete, singular continuous, or any mixture of these. The explicit formula makes comparative statics transparent. Raising one bidder's value distribution in first-order stochastic dominance raises that bidder's equilibrium bid distribution in the same order. Perturbing a symmetric-bidder model has different revenue effects depending on the direction of the perturbation: whereas slightly weakening one of the two bidders reduces expected revenue, slightly strengthening one of the two has an ambiguous effect. The explicit formula also turns some involved arguments in the literature into direct corollaries.

This study examines emission interdependencies within the waste sector and between waste and other economic domains, energy, transport, water, and communications, using Life Cycle Assessment (LCA) methodologies with emphasis on process-based and hybrid approaches. The analysis employs the EXIOBASE multi-regional input-output database. Statistical correlation is applied to identify commonalities and divergences in emission drivers. Results indicate strong correlations among certain landfill waste streams, particularly organic-based materials, as well as links between plastics and wood, suggesting shared decomposition or management pathways. Moderate correlations appear in cross-sectoral interactions, especially between waste, energy, and transport, while weak correlations are observed in processes with distinct treatment mechanisms, such as landfill versus wastewater. Methodologically, the study highlights challenges posed by high-dimensional datasets, including multicollinearity, which limit the effectiveness of linear models. These findings underscore the complexity of sectoral interdependencies and the need for both integrated and material-specific strategies. By demonstrating how systemic tools like EXIOBASE can capture these linkages, the research provides a foundation for constructing more robust emission models and informing targeted mitigation policies. The results contribute to advancing environmental accounting frameworks while offering practical insights for emission reduction planning across interconnected sectors.

A switchback experiment alternates an entire system between treatment and control over time. It is especially useful when interactions between units can undermine standard unit-level experiments. Switchback experiments are commonly implemented on fixed temporal grids, which impose highly structured restrictions on when treatment can switch. We study a broader class of random-duration switchbacks, in which treatment and control alternate across runs whose durations are drawn from a common distribution. Under finite carryover, we show that the mean squared error of the Horvitz-Thompson estimator has a simple frequency-domain representation governed by how temporal outcome patterns align with design-induced imbalance and contamination patterns. This representation yields a tractable worst-case design criterion that can be computed directly from the duration distribution. Optimizing over even a simple two-rate family produces a run-age-dependent switching rule that reduces the asymptotic worst-case mean squared error by at least 32% relative to the standard independently randomized fixed-block switchback.

If a probability measure is a mean-preserving contraction of another, the two measures are said to be in convex order. This paper provides a complete characterization of mean-preserving contractions and their extreme points in the multidimensional setting, extending the results of Kleiner, Moldovanu, Strack, and Whitmeyer (2024) to incorporate fully revealing regions and lower-dimensional pooling regions. A central feature of our characterization is a "concentration " structure: each state can be mapped only to posterior means lying within its own irreducible component. We apply these results to the moment persuasion problem.

In this paper, we study criteria for social evaluation of resource distributions under risk when individuals have expected utility preferences but their utility functions are interpersonally non-comparable. In particular, we focus on cautious evaluation with respect to ex-post distributions. As a key rationality axiom, we adopt Negative Certainty Independence, introduced by Dillenberger (2010). Using this axiom together with Pareto conditions that are compatible with both the rationality axiom and ex-post equity, we characterize a class of social criteria called Cautious Equally Distributed Equivalent (CEDE) criteria. These criteria evaluate risky situations by the lowest certainty equivalent over a set of social utility functions constructed from individual utility functions.

We develop a causal framework for matrix completion under missing not at random (MNAR) data. Drawing on synthetic controls from the econometric panel data literature, our approach relaxes two assumptions common in MNAR matrix completion: positivity and independence of observation indicators. Unlike traditional panel data models, which often require prescribed block-sparse geometries, our framework accommodates flexible, heterogeneous observation patterns through target-specific local information structures. We propose synthetic nearest neighbors (SNN), a local synthetic-controls-inspired estimator, and establish finite-sample entrywise error bounds and consistency for mean recovery under suitable conditions. We further derive asymptotic normality under heteroskedastic noise and develop feasible entrywise inference. To estimate entry-specific noise variances, we apply the same local principle to squared outcomes, obtaining consistency under bounded noise and asymptotic unbiasedness under general subgaussian noise. Simulation studies corroborate the theoretical findings across a range of missingness designs and observation patterns.

Probabilistic forecasting is central to decision-making under uncertainty, yet its methodological landscape has become increasingly fragmented across temporal and spatiotemporal forecasting, statistical modeling, machine learning, and deep generative modeling. This survey develops a unified perspective by organizing probabilistic forecasting methods according to where and how uncertainty is introduced into the forecasting pipeline. Our taxonomy connects model-agnostic approaches including ensembles and distribution-free calibration, with model-intrinsic approaches spanning Bayesian modeling, parametric predictive distributions, distributional regression, and modern generative models, and further examines the emerging role of time series foundation models. Beyond methodological synthesis, we identify the assumptions, computational demands, and forms of uncertainty represented by different paradigms, and translate these distinctions into data-driven and domain-specific guidance for method selection. We complement the survey with a cross-paradigm empirical study on univariate, multivariate, and spatiotemporal forecasting tasks. The results reveal that no single uncertainty-quantification paradigm dominates across settings. Calibration, sharpness, predictive accuracy, and computational efficiency can lead to substantially different model preferences, while expressive generative models and zero-shot foundation models exhibit markedly different accuracy-efficiency trade-offs. Lastly, we identify unresolved challenges surrounding uncertainty in evolving dependency structures, physics-informed predictive distributions, forecasting extreme events, handling count-valued, directional, and continuous-time series, and the development of unified software resources. Our survey provides both a conceptual framework and a practical roadmap for probabilistic forecasting research.

Empirical researchers often use binary classification trees to identify subgroups at risk of adverse outcomes. We compare two classification tree algorithms in this policy-targeting context: classical classification and regression trees (CART) and the maximizing-distance final-split approach (MDFS). We establish a theoretical setting in which MDFS identifies a high-risk subgroup while CART identifies none. Applied to rural hospital closure data, MDFS targets a high-closure-probability subgroup: for-profit hospitals with more than 63 days in accounts receivable. CART misses this subgroup. To facilitate further application of these classification tree algorithms, we provide targetree package in Python, R, and Stata.

This paper studies identification and inference in a triangular system with an endogenous regressor when exclusion restrictions are unavailable and the dependence between structural disturbances is modeled through an unrestricted control function. In this setting, standard orthogonality conditions do not deliver point identification, as the unknown control function can rationalize a wide range of structural coefficients. We show that identifying information can be extracted from distributional shifts in the first-stage disturbance induced by an auxiliary variable that may directly affect the outcome. Imposing a local restriction on the log density ratio, together with an explicit bound on the sieve approximation error of the control function, we derive moment inequalities that restrict the structural parameter. We develop a practical inference procedure based on test inversion and multiplier bootstrap that accommodates generated regressors, cross-fitted sieve estimation, and locally estimated density-ratio nuisances. The results clarify how identification can be recovered from weak local distributional structure in the absence of classical instruments.

We derive the exact likelihood of the Berry (1994) share-form nested logit and show it contains a Jacobian term that depends on nest size and the nesting parameter. Omitting the term biases within-nest substitution estimates wherever choice sets vary across markets. Commonly-used count instruments for the within-nest share fail exclusion when product counts enter demand directly. The corrected likelihood identifies substitution without them, making crowding estimable. We apply the estimator to Medicare Advantage plan proliferation after 2019 elimination of the “meaningful difference” requirement. Estimates indicate plan proliferation raised consumer surplus in most markets, but ignoring crowding overstates the gains.

Whether medical technology reduces or increases demand for professional care is central to understanding its effects on healthcare utilization and costs. We study automated insulin delivery (AID) adoption among 1,608 adults with type 1 diabetes treated in four specialist clinics of the Italian National Health Service, 283 of whom adopt AID. Because adoption is clinically targeted and staggered, we combine risk-set coarsened exact matching with a staggered event-study design. Matching retains 181 adopters with comparable untreated controls. We further adjust for differential pre-adoption trends by extrapolating the untreated trajectory in event time. After adjustment, AID adoption is associated with greater routine outpatient engagement. The estimated effect on the probability of a diabetologist visit is 16.3 percentage points one semester after adoption and 39.3 percentage points four semesters after adoption, relative to a 55.2% visit probability in the semester before adoption. HbA1c testing and a broader process-of-care index show similar positive patterns, although the evidence is less precise. The visit estimates remain sensitive to the trend-extrapolation assumption and should therefore be interpreted conditionally on that restriction. The findings are consistent with a task-based view in which automation substitutes for routine dosing decisions while complementing clinical labor through interpretive, adjustment, and supervisory tasks. Patient-facing automation may therefore reorganize rather than simply reduce healthcare use.

The favorite–longshot bias (FLB) is one of the most persistent return patterns in betting markets, but its prevalence in modern prediction markets and its relation to recurrent longshot demand remain unclear. We study these questions in Polymarket, a large and increasingly important prediction market, using 588 million trades by 2.48 million accounts. In observed transaction flows, purchases below 10 cents lose 19.3 cents per dollar, while purchases at or above 90 cents earn 0.83 cents. How contracts are grouped changes the result: longshots lose 6.3 cents per dollar when each contract is weighted equally but gain 4.1 cents when related contracts are first grouped by parent event; the two-sided pattern is robust in Crypto and Politics but surprisingly absent in Sports. The top decile of accounts with the strongest past tendency to buy longshots accounts for 26.6 percent of next-month low-price purchases, but earns similar returns to others. The top decile of accounts with the strongest past tendency to buy favorites accounts for 15.1 percent of next-month high-price purchases but earns less than others. These findings provide evidence of an aggregate FLB on Polymarket, but its magnitude depends on how contracts are grouped.

Many digital platforms earn revenue by selling content access and displaying ads. We study monopoly screening by a platform allocating heterogeneous content and ads to heterogeneous consumers. Advertising generates revenue and affects information rents through nuisance, which alters the platform's incentives to allocate content. The optimal mechanism balances a trade-off between advertising and rent extraction: Expanding content access increases advertising revenue but reduces sales revenue by raising information rents. The mechanism features novel distortions in content access and ad exposure, rationalizes contracts across ad-supported platforms, and explains why greater ad profitability may weaken incentives to invest in content quality.

We study optimal growth in a Ramsey economy with irreversible pollution, where the natural absorption capacity is non-monotonic and non-concave a la Forster. In the absence of pollution control, the capital dynamics decouple from pollution, and we characterize a simple threshold on the maximal absorption capacity above which the optimal path is sustainable and below which an optimal regime of irreversible pollution sets in. We then introduce an optimal abatement pollution control to assess whether irreversible pollution ceases to be optimal. We derive a four-dimensional dynamical system for capital, consumption, pollution and the (shadow) cost of pollution, coupled with an algebraic rule for optimal abatement. First, we show that while optimal abatement does shift the irreversibility threshold, it may not rule out optimal irreversible pollution paths. Second, and more importantly, we show that embedding the Forster's pollution dynamics into a Ramsey growth model generates a novel and robust hybrid ecological-economic irreversibility condition that is invisible in pollution-only frameworks. Coupling ecosystem curvature with the social discount rate, it is structurally robust and preeminent over all feasibility conditions amenable to policy intervention, and defines the boundary between a world where sustainability is achievable and one where it is not.

This paper studies school choice when each school has an original priority order and an adjusted priority order reflecting policies such as affirmative action. We introduce a weak notion of stability that permits justified envy under one priority order only when the opposite priority relation is supported by the other. We characterize weakly stable matchings as stable matchings under the intersection of the two priority profiles. Using the efficiency-adjusted deferred acceptance algorithm, we obtain a weakly stable matching that cannot be Pareto improved upon, within the set of weakly stable matchings, for any group containing all improved students by the adjustment. We also show that any Pareto improvement over this outcome necessarily creates justified envy under both priority profiles. Finally, our mechanism is responsive to stronger priority adjustments: the outcome under a stronger affirmative action policy is not Pareto dominated by that under a weaker policy for any group containing all students improved by the stronger adjustment.

This paper investigates the construction of moment restrictions in dyadic network formation models with unobserved individual heterogeneity under nontransferable utility. Using observed links and covariates from five-node pentads, we construct moment restrictions that do not depend on individual fixed effects. For a broad class of covariate specifications, the construction is minimal in the sense that it uses the least possible number of nodes and dyads. Based on these moment restrictions, we propose the pentad-GMM estimator. We establish asymptotic normality of the pentad-GMM estimator in dense, sparse, and ultra-sparse network regimes, with regime-specific convergence rates and asymptotic variances. These results provide a basis for inference across all three regimes. To make our method computationally efficient, we develop an algorithm that reduces the computational cost of the estimator from naïve \(O(N^5)\) to \(O(N^3)\). We apply the proposed method to an academic-discussion network, and find academic homophily and a positive association between link formation and a potential partner's openness to different perspectives.

This paper compares the stable improvement cycles (SIC) mechanism of Erdil and Ergin (2008) with the efficiency-adjusted deferred acceptance (EADA) mechanism of Kesten (2010) in school choice problems with incomplete priorities. When school priorities are strict partial orders, we show that the EADA mechanism produces a constrained efficient matching. Combined with earlier results for the SIC mechanism, this establishes the outcome equivalence of the two mechanisms: the sets of matchings attainable under them coincide. We then move beyond transitivity and consider acyclic priority relations. On this broader domain, neither mechanism is guaranteed to produce a constrained efficient matching, but their failures take opposite forms. The SIC mechanism may under-improve: its outcome is always stable but may be Pareto dominated by another stable matching. By contrast, the EADA mechanism may over-improve: its outcome is never Pareto dominated by any stable matching but may itself be unstable.

Including covariates alongside strictly monotone transformations can change a causal forest's treatment decisions without adding information. Random feature selection favors covariates represented by these multiple columns. Under stated conditions, I show that this imbalance can persist as samples grow. Treatment effect components associated with other covariates are omitted, attenuated, or recovered depending on their inclusion probabilities and tree depth. Simulations and a job-training replication illustrate sensitivity to redundant transformations. Sampling groups of variables that generate identical splits restores prediction invariance on the grouping data when fitting and randomization are held fixed.

Using a balanced panel of 129 countries from 2000 to 2024, we estimate the macroeconomic costs of sanctions on Russia. To that end, we employ a novel two-wave common-correlated-effects imputation design that separates the 2014 sanctions from the 2022 escalation and accounts for heterogeneous exposure to global shocks. We find the main boomerang effect of these sanctions operates through prices rather than output. Specifically, relative to 2019-2021, we find a significant post-2022 increase in prices among sanctioning countries that remains robust under alternative counterfactuals, reference windows, and inference procedures. Conversely, we find no robust evidence of aggregate GDP-per-capita losses.

Past research highlights failures of "procedural invariance" when measuring economic preferences using choices versus valuations. We reassess these failures by examining theoretical connections between choices and valuations when preferences are stable but measurements are noisy and individuals are heterogeneous. Even under strong assumptions governing noise and heterogeneity, stability does not generally imply identical measurements. We develop new tests of stable preferences in conjunction with various ancillary assumptions about heterogeneity and noise. We implement these tests using existing data to understand if, in the domain of risk preferences, choices and valuations truly differ and to provide quantitative assessments of any deviations. Limiting to the types of data used in the prior literature, we rarely reject the null of stable preferences. With richer data linking individual choices and valuations and structural assumptions, we find evidence of instability which differs qualitatively from the received wisdom that choices implicate greater risk aversion than valuations.

Identification in vector autoregressions involves two distinct choices: how extensively to orthogonalize shocks and whether orthogonality is imposed sequentially or simultaneously. Generalized identification imposes no orthogonality; Sims (1980} imposes full orthogonality sequentially; Francis et al. (2026) impose full orthogonality simultaneously; and Buchwalter et al. (2026a) provide clustered partial orthogonalization sequentially. We fill the remaining case by developing simultaneous clustered orthogonalization (SCO). SCO preserves contemporaneous dependence within economically meaningful clusters while imposing orthogonality across clusters jointly, thereby eliminating dependence on cluster ordering. We formulate the associated correlation-maximizing identification problem and show that, in correlation space, it reduces to a quadratic matrix equation. This yields a closed-form solution, and we prove that the associated identification matrix is the unique global maximizer. SCO is order- and scale-invariant and nests generalized identification and full simultaneous orthogonalization as special cases, yielding a flexible family of structural decompositions indexed by the number and composition of clusters.

We establish a sharp pathwise signal-to-noise criterion for quasi-maximum-likelihood (QML) estimation of a dominant breakpoint in the second-moment structure of a multivariate time series: the QML estimator is consistent whenever the between-regime contrast exceeds the within-regime fluctuation by an explicit factor, and below this threshold global recovery can fail. Two innovations drive the result. First, the framework is pathwise: no stochastic model is imposed on the data. Second, the log-determinant objective carries an additive ridge regularization: it removes the endpoint boundary layers, so no trimming of the candidate set is required, and tuning the ridge weakens the consistency condition. As an application of the main theorem, we establish consistency of QML breakpoint estimation in pervasive factor models whose dimension diverges with the sample size, for completely general error terms – not necessarily independent, idiosyncratic, or even random.