This paper investigates the role of complex and negative roots in mixed causal-noncausal autoregressive (MAR) models. Using partial fraction decompositions, we show that seasonal roots can always be isolated in the moving average representation of purely causal and noncausal AR models. We find that this result extends to the MAR model, which means that no new joint seasonal effects can be generated despite the multiplicative structure of the causal and noncausal polynomials. This results has important consequences for the MAR model selection procedure and these are extensively studied in a Monte Carlo simulation study. An empirical application on COVID-19 and soybean data illustrates the main findings of the paper.

This paper develops a unified framework for testing monotonicity of Bayesian Nash equilibrium strategies in unobserved types in games of incomplete information. We show that, under symmetric independent private types, monotonicity of differentiable equilibrium strategies is equivalent to monotonicity of a quasi-inverse strategy identified from observed actions. This allows the problem to be reformulated as testing a countable set of moment inequalities involving unconditional expectations. We propose a Cramer-von Mises-type statistic with bootstrap critical values. The method accommodates covariates and game heterogeneity. Monte Carlo simulations demonstrate finite-sample performance, and an application to procurement auctions illustrates cartel detection.

A principal with cheap capital optimally forces her counterparty to borrow at above-market rates. The reason: the form of finance is a screening device. Advances provide liquidity but pool types; contingent transfers separate types, but, because they are not pledgeable, impose financing costs. The optimal contract preserves outside-finance exposure to maintain screening power. Two sufficient statistics pin down the optimal advance share. With complementary counterparties, a uniform subsidy that cheapens finance across every relationship can reduce the value of each. This explains the coexistence of early payment and contingent compensation in trade credit, venture capital, and internal capital markets.

Addressing the large inefficiencies generated by the Deferred Acceptance (DA) mechanism requires priority violations, but which ones are justifiable? The leading approach is to ask individuals if they consent to waive their priority ex-ante. We develop an alternative question-free solution, in which a priority violation is justifiable whenever the affected student either (i) directly benefits from the improvement, or (ii) is unimprovable under any assignment that Pareto-dominates DA. This endogenous justifiability criterion permits improvements unattainable by the leading consent-based mechanism under any consent structure. We provide a ``just below cutoffs'' mechanism that always finds a strongly justifiable matching whenever DA's outcome is inefficient, and build on it to construct a polynomial-time algorithm that expands justifiable improvements iteratively, converging to a DA improvement that cannot be Pareto-improved by any justifiable matching without strictly expanding the beneficiary set. Finally, we prove theoretically that both the ex-ante consent and the endogenous justifiability frameworks have important limitations in reaching Pareto-efficient outcomes, and use simulations to quantify how binding these constraints are in practice.

In many real-world settings, institutions can and do adjust the consequences attached to algorithmic classification decisions, such as the size of fines, sentence lengths, or benefit levels. We refer to these consequences as the stakes associated with classification. These stakes can give rise to behavioral responses to classification, as people adjust their actions in anticipation of how they will be classified. Much of the algorithmic fairness literature evaluates classification outcomes while holding behavior fixed, treating behavioral differences across groups as exogenous features of the environment. Under this assumption, the stakes of classification play no role in shaping outcomes. We revisit classic impossibility results in algorithmic fairness in a setting where people respond strategically to classification. We show that, in this environment, the well-known incompatibility between error-rate balance and predictive parity disappears, but only by potentially introducing a qualitatively different form of unequal treatment. Concretely, we construct a two-stage design in which a classifier first standardizes its statistical performance across groups, and then adjusts stakes so as to induce comparable patterns of behavior. This requires treating groups differently in the consequences attached to identical classification decisions. Our results demonstrate that fairness in strategic settings cannot be assessed solely by how algorithms map data into decisions. Rather, our analysis treats the human consequences of classification as primary design variables, introduces normative criteria governing their use, and shows that their interaction with statistical fairness criteria generates qualitatively new tradeoffs. Our aim is to make these tradeoffs precise and explicit.

Accurate short-term forecasting of agricultural commodity prices is critical for food security planning and smallholder income stabilisation in developing economies, yet machine-learning-ready datasets for this purpose remain scarce in South Asia. This paper makes two contributions. First, we introduce AgriPriceBD, a benchmark dataset of 1,779 daily retail mid-prices for five Bangladeshi commodities - garlic, chickpea, green chilli, cucumber, and sweet pumpkin - spanning July 2020 to June 2025, extracted from government reports via an LLM-assisted digitisation pipeline. Second, we evaluate seven forecasting approaches spanning classical models - naïve persistence, SARIMA, and Prophet - and deep learning architectures - BiLSTM, Transformer, Time2Vec-enhanced Transformer, and Informer - with Diebold-Mariano statistical significance tests. Commodity price forecastability is fundamentally heterogeneous: naïve persistence dominates on near-random-walk commodities. Time2Vec temporal encoding provides no statistically significant advantage over fixed sinusoidal encoding and causes catastrophic degradation on green chilli (+146.1% MAE, p<0.001). Prophet fails systematically, attributable to discrete step-function price dynamics incompatible with its smooth decomposition assumptions. Informer produces erratic predictions (variance up to 50x ground-truth), confirming sparse-attention Transformers require substantially larger training sets than small agricultural datasets provide. All code, models, and data are released publicly to support replication and future forecasting research on agricultural commodity markets in Bangladesh and similar developing economies.

Controversy about the significance of underdetermination of theories persists in the philosophy and conduct of science. The issue has practical import when research is used to inform decision making, because scientific uncertainty yields inductive risk. Seeking to enhance communication between philosophers and researchers who study public policy, this paper describes econometric analysis of partial identification and its use in welfare-economic policy analysis. Study of partial identification finds underdetermination and inductive risk to be highly consequential for credible prediction of important societal outcomes and, hence, for credible public decision making. It provides mathematical tools to characterize a broad class of scientific uncertainties that arise when available data and well-supported assumptions are combined to predict population outcomes. Combining study of partial identification with criteria for reasonable decision making under uncertainty yields coherent approaches to make policy choices without accepting one among multiple empirically underdetermined theories. The paper argues that study of partial identification warrants attention in philosophical discourse on underdetermination and inductive risk.

This paper develops an Afriat-type characterization of concave rationalization with an unknown ideal point. We show that a system of Afriat inequalities - where the unknown peak enters as a virtual observation with the highest utility - is necessary and sufficient for the existence of a continuous concave utility with an ideal point that rationalizes choices from linear budget sets anchored at different corners of the choice space. A stronger characterization adds the requirement that supergradients at observed choices point coordinatewise toward the peak, a necessary condition for single-peaked rationalizability. The resulting peak-oriented Afriat system provides the basis for a Houtman--Maks consistency index that measures the largest fraction of observations jointly rationalizable with a common ideal point. This characterization provides the theoretical foundation for the Priced Survey Methodology (PSM), in which respondents complete the same survey under different linear constraints. A parametric single-peaked specification then sharpens identification into estimates of ideal answers and importance weights. We apply the PSM to study political preferences in a sample of French respondents.

Drafts are sequential round-robin allocation procedures for distributing heterogeneous and indivisible objects among agents subject to some priority order (e.g., allocating players' contract rights to teams in professional sports leagues). Agents report ordinal preferences over objects and bundles are partially ordered by pairwise comparison. We provide a simple characterization of draft rules: they are the only allocation rules that are respectful of a priority (RP), envy-free up to one object (EF1), non-wasteful (NW), and resource monotonic (RM). RP and EF1 are crucial for competitive balance in sports leagues. We also prove two related impossibility theorems showing that the competitive-balance axioms RP and EF1 are generally incompatible with strategy-proofness. Nevertheless, draft rules satisfy maxmin strategy-proofness. If agents may declare some objects unacceptable, then draft rules are characterized by RP, EF1, NW, and RM, in conjunction with individual rationality and truncation invariance.

Empirical research shows that individuals' responses to treatments vary along latent characteristics, such as innate ability or motivation. Therefore, a policymaker seeking to maximize welfare may consider designing policies based on observed characteristics and estimated latent traits. I characterize how the estimates' precision affects the worst-case performance of policies, deriving rate-sharp regret bounds for assignment rules that include or exclude them, highlighting new trade-offs with the policy space complexity. I then study how a policymaker can solve such trade-offs by designing tailored data collections, and derive the minimax optimal collection plan. In an empirical application in development economics, I show that including a proxy for entrepreneurs' business skills in targeting cash transfers increases welfare by 5%, and halves the probability of generating welfare losses. Moreover, I estimate the optimal allocation of resources between improving the precision of the proxy via repeated measurements and increasing sample size.

Under heterogeneous treatment effects, the GMM weighting matrix in overidentified IV models dictates the estimand. We show that efficient GMM downeights high-variance instruments and frequently assigning negative weights that undermine causal interpretation. Moreover, GMM cannot simultaneously achieve efficiency and accommodate researcher-specified weights. We resolve this trade-off by developing the Representative Targeting (RT) estimator. By averaging instrument-specific Wald estimators under Positive Regression Dependence, RT ensures non-negative weights while achieving the semiparametric efficiency bound for its targeted estimand. We demonstrate the heterogeneity penalty empirically in a class-size experiment and apply RT to recover the Policy-Relevant Treatment Effect within a patent leniency design.

Normalization is ubiquitous in economics, and a growing literature shows that ``normalizations'' can matter for interpretation, counterfactual analysis, misspecification, and inference. This paper provides a general framework for these issues, based on the formalized notion of modeling equivalence that partitions the space of unknowns into equivalence classes, and defines normalization as a WLOG selection of one representative from each class. A counterfactual parameter is normalization-free if and only if it is constant on equivalence classes; otherwise any point identification is created by the normalization rather than by the model. Applications to discrete choice, demand estimation, and network formation illustrate the insights made explicit through this criterion. We then study two further sources of fragility: an extension trilemma establishes that fidelity, invariance, and regularity cannot simultaneously hold at a boundary singularity, while a normalization can itself introduce a coordinate singularity that distorts the topological and metric structures of the parameter space, with consequences for estimation and inference.

Collective decision-making requires aggregating multiple noisy information channels about an unknown state of the world. Classical epistemic justifications of majority rule rely on homogeneity assumptions often violated when individual competences are heterogeneous. This paper studies endogenous epistemic weighting in binary collective decisions. It introduces the Epistemic Shared-Choice Mechanism (ESCM), a lightweight and auditable procedure that generates bounded, issue-specific voting weights from short informational assessments. Unlike likelihood-optimal rules, ESCM does not require ex ante knowledge of individual competences, but infers them endogenously while bounding individual influence. Using a central limit approximation under general regularity conditions, the paper establishes analytically that bounded competence-sensitive monotone weighting strictly increases the mean quality of the aggregate signal whenever competence is heterogeneous. Numerical comparisons under Beta-distributed and segmented mixture competence environments show that these mean gains are associated with higher signal-to-noise ratios and large-sample accuracy relative to unweighted majority rule.

We show that all finite lattices, including non-distributive lattices, arise as stable matching lattices when all agents have path-independent choice functions. This result answers an open question of Blair~\cite{blair1988lattice}. In the process, we introduce new tools to reason on general lattices for optimization purposes: the \emph{partial representation} of a lattice, which partially extends Birkhoff's representation theorem to non-distributive lattices; the \emph{distributive closure} of a lattice, which gives such a partial representation; and \emph{join constraints}, which can be added to the distributive closure to obtain a representation for the original lattice. Then, we use these techniques to show that the minimum cost stable matching problem under the same standard assumptions on choice functions is NP-hard, by establishing a connection with antimatroid theory.