We develop a tractable identification approach for strategic network formation models with both strategic link interdependence and individual unobserved heterogeneity (fixed effects). The key challenge is that endogenous network statistics (e.g. number of common friends) enter the link formation equation, while the mapping from model primitives to equilibrium network structure is generally intractable. Our approach sidesteps this difficulty using a ``bounding-by-$c$'' technique that treats endogenous covariates as random variables and exploits monotonicity restrictions to obtain identifying information. A central contribution is to develop a spectrum of fixed-effects handling strategies based on subnetwork configurations: tetrad-based restrictions that difference out all individual fixed effects, triad-based and weighted restrictions that combine ``difference-out'' and ``integrate-out'' steps by differencing out some fixed effects and profiling over the remainder conditional on observed characteristics, and general weighted cycle-based restrictions that unify these cases. We also provide point identification results. Preliminary simulations show that the approach can deliver informative bounds on the structural parameters.

We introduce a semiparametric approach for forecasting Value-at-Risk (VaR) and Expected Shortfall (ES) by modeling the conditional scale of financial returns, defined as the difference between two specified quantiles, via restricted quantile regression. Focusing on downside risk, VaR is derived from the left-tail quantile of rescaled returns, and ES is approximated by averaging quantiles below the VaR level. The method delivers robust, distribution-free estimates of extreme losses and captures skewness, heavy tails, and leverage effects. Simulation experiments and empirical analysis show that it often outperforms established models, including GARCH and joint VaR-ES conditional-quantile approaches. An application to daily returns on major international stock indices, spanning the COVID-19 period, highlights its effectiveness in capturing risk dynamics.

Benchmarking the performance of complex systems such as rail networks, renewable generation assets and national economies is central to transport planning, regulation and macroeconomic analysis. Classical frontier methods, notably Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA), estimate an efficient frontier in the observed input-output space and define efficiency as distance to this frontier, but rely on restrictive assumptions on the production set and only indirectly address heterogeneity and scale effects. We propose Geometric Manifold Analysis (GeMA), a latent manifold frontier framework implemented via a productivity-manifold variational autoencoder (ProMan-VAE). Instead of specifying a frontier function in the observed space, GeMA represents the production set as the boundary of a low-dimensional manifold embedded in the joint input-output space. A split-head encoder learns latent variables that capture technological structure and operational inefficiency. Efficiency is evaluated with respect to the learned manifold, endogenous peer groups arise as clusters in latent technology space, a quotient construction supports scale-invariant benchmarking, and a local certification radius, derived from the decoder Jacobian and a Lipschitz bound, quantifies the geometric robustness of efficiency scores. We validate GeMA on synthetic data with non-convex frontiers, heterogeneous technologies and scale bias, and on four real-world case studies: global urban rail systems (COMET), British rail operators (ORR), national economies (Penn World Table) and a high-frequency wind-farm dataset. Across these domains GeMA behaves comparably to established methods when classical assumptions hold, and provides additional insight in settings with pronounced heterogeneity, non-convexity or size-related bias.

Electric vehicles (EVs) require substantially longer refueling times than gasoline vehicles, which can generate severe congestion at charging stations when demand concentrates. We propose a two-stage allocation framework for EV charging networks. In Stage 1, a central coordinator determines station-level admission quotas to control worst-station delay using a queue-informed congestion metric. In Stage 2, given these quotas and feasibility constraints (e.g., reachability), the coordinator solves a utility-maximizing capacitated assignment to allocate EVs across stations. To keep Stage~2 tractable while capturing heterogeneous charging needs, we precompute each EV-station pair's optimal charging amount in closed form under a battery-capacity constraint and then solve a transportation/assignment problem. Finally, we introduce a reduced-form participation model to characterize adoption thresholds under network benefits, spillovers, and coordination costs. Numerical experiments illustrate substantial reductions in worst-case congestion with limited impact on average utility, and highlight scaling patterns as the number of stations increases.

We propose a structural vector autoregressive model with a new and flexible specification of the volatility process which we call Sparse Heterogeneous Markov-Switching Heteroskedasticity. In this model, the conditional variance of each structural shock changes in time according to its own Markov process. Additionally, it features a sparse representation of Markov processes, in which the number of regimes is set to exceed that of the data-generating process, with some regimes allowed to have zero occurrences throughout the sample. We complement these developments with a definition of a new distribution for normalised conditional variances that facilitates Gibbs sampling and identification verification. In effect, our model: (i) normalises the system and estimates the structural parameters more precisely than popular alternatives; (ii) can be used to verify homoskedasticity reliably and, thus, inform identification through heteroskedasticity; and (iii) features excellent forecasting performance comparable with Stochastic Volatility. Finally, revisiting a prominent macro-financial structural system, we provide evidence for the identification of the US monetary policy shock via heteroskedasticity, with estimates consistent with those reported in the literature.

Economic growth is conventionally analyzed at the national level, yet cities generate the bulk of global output. Here we construct GDP trajectories for 8,808 functional urban areas (FUAs) across 165 countries over 1993-2019 using satellite-derived nighttime light data and identify 17 distinct, persistent growth regimes through clustering of full temporal trajectories. Rather than converging toward a common frontier, FUAs inhabit distinct economic niches-analogous to ecological niches-defined by shared volatility profiles, shock responses, and long-run dynamics that transcend national boundaries. Cities within the same country frequently belong to different regimes, while structurally similar cities on different continents share the same one; regime membership explains 16% of within-country growth variance beyond country fixed effects. National-level convergence emerges as an aggregation artifact: conditional convergence operates within regimes, not globally. A directed propagation network reveals that shocks transmit along lines of structural similarity rather than geographic proximity, with advanced economies exporting disturbances and emerging economies absorbing or amplifying them. Within-country spatial inequality declines with industrialization maturity, consistent with growth initially concentrating in leading cities before diffusing across the urban system. The global economy is better understood as an ecology of heterogeneous urban growth regimes than as a collection of nations on a shared development path.

Using transaction-level trade data from Polymarket's 2024 U.S. presidential election market, we study how prediction markets process shocks. We analyze three events: the Biden-Trump debate, the assassination attempt on Trump, and Biden's dropout. Trading rises after each shock, especially among incumbent traders with pre-event exposure against a Trump victory, who are also more likely to flip positions. Price adjustment differs across shocks. The debate-induced price jump largely reverses, the assassination-attempt repricing persists, and Biden's dropout triggers two-sided trading with little net price change. These patterns link post-news price dynamics to liquidity and disagreement about how shocks map into election odds.

A tight alignment between the degree vector and the leading eigenvector arises naturally in networks with neutral degree mixing and the absence of local structures. Many real-world networks, however, violate both conditions. We derive bounds on the divergence between the degree vector and the eigenvector in networks with degree assortativity and local mesoscopic structures such as communities, core-peripheries, and cycles. Our approach is constructive. We design sufficiently general degree-preserving rewiring algorithms that start from a neutral benchmark and monotonically increase assortativity and the strength of local structures, with each step inducing a perturbation of the adjacency matrix. Using the Stewart--Sun Perturbation Bound, together with explicit spectral-norm control of the rewiring steps, we derive upper bounds on the angle between the eigenvector and the degree vector for modest levels of assortativity and local structures. Our analytical bounds delineate regions of `spectral safety' in which a node's degree can be used as a reliable measure of its systemic importance in real-world networks. We also substantiate our analytical bounds with numerical simulations that compute the exact angles of deviation.

We develop a unified nonparametric framework for sharp partial identification and inference on inequality indices when the data contain coarsened observations of the variable of interest. We characterize the extremal allocations for all Schur-convex inequality measures, and show that sharp bounds are attained by distributions with finite support. This reduces the computational problem to finite-dimensional optimization, and for indices admitting linear-fractional representations after suitable ordering of the data (including the Gini coefficient and quantile ratios), we express the bound problems as linear or quadratic programs. We then establish $\sqrt{n}$ inference for the upper and lower bounds using a directional delta method and bootstrap confidence intervals. In applications, we compute sharp Gini bounds from household wealth data with mixed point and interval observations and use historical U.S. grouped income tables to bound time series for the Gini and quantile ratios.

Meritocratic systems, from admissions to hiring, aim to impartially reward skill and effort. Yet persistent disparities across race, gender, and class challenge this ideal. Some attribute these gaps to structural inequality; others to individual choice. We develop a game-theoretic model in which candidates from different socioeconomic groups differ in their perceived post-selection value--shaped by social context and, increasingly, by AI-powered tools offering personalized career or salary guidance. Each candidate strategically chooses effort, balancing its cost against expected reward; effort translates into observable merit, and selection is based solely on merit. We characterize the unique Nash equilibrium in the large-agent limit and derive explicit formulas showing how valuation disparities and institutional selectivity jointly determine effort, representation, social welfare, and utility. We further propose a cost-sensitive optimization framework that quantifies how modifying selectivity or perceived value can reduce disparities without compromising institutional goals. Our analysis reveals a perception-driven bias: when perceptions of post-selection value differ across groups, these differences translate into rational differences in effort, propagating disparities backward through otherwise "fair" selection processes. While the model is static, it captures one stage of a broader feedback cycle linking perceptions, incentives, and outcome--bridging rational-choice and structural explanations of inequality by showing how techno-social environments shape individual incentives in meritocratic systems.

Large Language Models (LLMs) are becoming widely used to support various workflows across different disciplines, yet their potential in discrete choice modelling remains relatively unexplored. This work examines the potential of LLMs as assistive agents in the specification and, where technically feasible, estimation of Multinomial Logit models. We implement a systematic experimental framework involving twelve versions of seven leading LLMs (ChatGPT, Claude, DeepSeek, Gemini, Gemma, Llama, and Mistral) evaluated under five experimental configurations. These configurations vary along three dimensions: (i) modelling goal (suggesting vs. suggesting and estimating MNL models); (ii) prompting strategy (Zero-Shot vs. Chain-of-Thoughts (CoT)); and (iii) information availability (full dataset vs. data dictionary summarising variable names and types). Each specification suggested by the LLMs is implemented, estimated, and evaluated based on goodness-of-fit metrics, behavioural plausibility, and model complexity. Our findings reveal that proprietary LLMs can generate valid and behaviourally sound utility specifications, particularly when guided by structured prompts (CoT). Open-weight models such as Llama and Gemma struggled to produce meaningful specifications. Notably, some LLMs performed better when provided with just data dictionary, suggesting that limiting raw data access may enhance internal reasoning capabilities. Among all LLMs, GPT o3, operating in an agentic setting, was uniquely capable of correctly estimating its own specifications by executing self-generated code. Overall, the results demonstrate both the promise and current limitations of LLMs as assistive agents in discrete choice modelling, not only for model specification but also for supporting modelling decision and estimation, and provide practical guidance for integrating these tools into choice modellers' workflows.

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 reduced-form equation might be problematic when the conditional mean of the endogenous covariate and the instrumental variables is nonlinear. The reason is that ignoring the nonlinearity could lead to weak instruments (instruments are weakly correlated with the endogenous covariate). 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. Estimating the parameter of interest is done using an estimator that we call Super Learner Control Function (SLCF) estimator. The estimation procedure is composed of two main steps and sample splitting. 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. Sample splitting is done across the individual dimension. The estimator is consistent and asymptotically normal achieving a parametric rate of convergence. We perform a Monte Carlo simulation to test the performance of the estimators proposed. We conclude that the Super Learner Control Function Estimators significantly outperform Within 2SLS estimators. Finally, we show that the SLCF estimator differs from both the plug-in IV estimator and a naive plug-in 2SLS estimator.

Estimation and counterfactual experiments in dynamic discrete choice models with large state spaces pose computational difficulties. This paper proposes a model-adaptive approach, based on the conjugate gradient (CG) method, to solve the linear system of fixed point equations of the policy valuation operator. We propose a model-adaptive sieve space, constructed by iteratively augmenting the space with the residual from the previous iteration. We show both theoretically and numerically that model-adaptive sieves dramatically improve performance. In particular, the approximation error decays at a superlinear rate in the sieve dimension, unlike a linear rate achieved using successive approximation. Our method works for both conditional choice probability estimators and full-solution estimators with policy iteration or Newton-Kantorovich iterations. We apply the method to analyze consumer demand for laundry detergent using Kantar's Worldpanel Take Home data. On average, our method is 80% faster than successive approximation and the exact equation solver in solving the dynamic programming problem, substantially reducing the computational cost of the Bayesian MCMC estimator.

This paper studies the properties of linear regression on centrality measures when network data is sparse and observed with error. We make three contributions in this setting. First, we show that OLS estimators can become inconsistent under sparsity and characterize the threshold at which this occurs, finding that regression on eigenvector centrality is less robust to sparsity than on degree and diffusion. Second, we derive the asymptotic distributions of the OLS estimators in regimes where they remain consistent. We show that when the target coefficients are non-zero, the estimators exhibit asymptotic bias that can be large relative to their variance, rendering conventional confidence intervals and t-tests invalid. Third, we propose bias correction and inference procedures for OLS with sparse, noisy networks. Simulations confirm that our methods perform well in such settings. We demonstrate the empirical relevance of our results in a stylized study of the relationship between consumption smoothing and informal insurance in Nyakatoke, Tanzania.

We study dynamic mechanism design in a pure-exchange economy with privately observed idiosyncratic income. In the standard infinitely lived hidden-income benchmark of Green (1987) and Thomas-Worrall (1990), constrained-efficient allocations exhibit immiseration. We propose a simple recursive mechanism -- adapted from Marcet-Marimon (1992) -- that shifts each income shock forward by one period, keeps promised utilities in a bounded set, and, under a transparent ``moderate risk-aversion'' condition, delivers sequential efficiency. In a stationary \emph{overlapping-generations} setting, we further show that under additional symmetry and curvature assumptions, a second-order approximation yields a sufficient condition for period-by-period budget balance; early cohorts pre-fund later transfers; for suitable initial promises, all cohorts are better off than under autarky. Our analysis uses a single state (promised utility), closed-form transfers, and a Bellman verification.

This paper investigates how natural language communication with an AI agent affects human cooperative behaviour in indefinitely repeated Prisoner's Dilemma games. We conduct a laboratory experiment (n = 126) with two between-subjects treatments varying whether human participants chat with an AI chatbot (GPT-5.2) before every round or only before the first round of each supergame, and benchmark against human-human data from Dvorak and Fehrler (2024) (n = 108). We find four main results. First, cooperation against the AI is high and initially comparable to human-human levels, but unlike in the human-human setting, where cooperation converges to near-complete levels, cooperation against the AI plateaus and never reaches full cooperation. Second, repeated communication, which substantially increases cooperation in human-human interactions, has no detectable effect in the human-AI setting. Third, strategy estimation reveals that human-AI subjects favour Grim Trigger under pre-play communication and remain dispersed under repeated communication, whereas human-human subjects converge to Tit-for-Tat and unconditional cooperation respectively. Fourth, human-AI conversations contain more explicit strategy commitments but fewer emotional and social messages. These results suggest that humans cooperate with AI at high rates but do not develop the trust observed in human-human interactions. Cooperation in the human-AI setting is sustained through conditional rules rather than through the social bonds and mutual understanding that characterise human-human cooperation.

This paper revisits the classic instrument choice problem in a setting with consumption externalities, through the lens of robust mechanism design. A regulator can implement any incentive-compatible policy but is uncertain about how individual demand is correlated with marginal externalities, and evaluates policies by worst-case welfare. The optimal policy is a quantity control: a floor for positive externalities and a ceiling for negative externalities. If the sign of the correlation is known, a uniform tax or subsidy can be optimal. The framework also applies to regulatory uncertainty and costly screening, providing a welfare-based explanation for the prevalence of non-price policies.

Social relationships are known to shape human behavior, yet when and how social ties influence strategic cognition remains unclear. We adopt a dual-measure approach that combines observed gameplay behavior with elicitation of partner-specific beliefs at each decision point, allowing us to examine how social ties shape both decisions and predictions across interaction structures. Dyads classified as having no ties, weak ties, or strong ties played three canonical economic games: the Dictator Game, Ultimatum Game, and Centipede Game, while also making predictions about their partner's actions. Using a mixed design that held partners constant across games while varying social distance between dyads, we examined how relational proximity affected the alignment between behavior and partner-specific beliefs. Across two norm-saturated games (Dictator and Ultimatum), neither offers nor belief calibration differed reliably by social distance. In contrast, in the sequential Centipede Game, where outcomes depend on anticipating a specific partner's future actions, strong-tie dyads both cooperated longer and expected later termination than no-tie dyads, with beliefs and behavior shifting in parallel. These results indicate that social ties become strategically relevant when the interaction structure makes partner-specific accountability cognitively necessary, but not when behavior is governed primarily by shared norms or institutional constraints. The findings provide a structural account of when relational knowledge enters strategic cognition and help reconcile mixed results in prior work on social distance in economic games.

This paper makes the Millennium Prize problem P vs NP operational in quantitative finance by studying cardinality-constrained portfolio selection. Starting from the convex Markowitz mean-variance program with CAPM-based expected returns (Rf plus beta times ERP), we impose a hard sparsity rule that limits the portfolio to K assets out of approximately 94 industry portfolios (Damodaran). The constraint couples discrete subset selection with continuous weight optimization, yielding a mixed-integer quadratic program and an NP-hard search space that grows combinatorially with n and K. We therefore evaluate scalable approximation schemes (greedy screening, Monte Carlo sampling, and genetic algorithms) under a replication-oriented protocol with random-seed control, distributional performance summaries (median and quantiles), runtime profiling, and convergence diagnostics. Dependence structure is documented via correlation and covariance diagnostics and positive-semidefinite checks to link algorithm behavior to the geometry implied by the risk matrix. To support the title's derivatives component, we add a European call option priced by the Black-Scholes model and map it into CAPM-consistent moments using delta-based linearization, validated with a bump test and moneyness/maturity sensitivity. Results highlight how the cardinality constraint reshapes the attainable efficient frontier, why stability and computational-cost trade-offs matter more than single-best runs, and how common-factor dependence can limit diversification in K-sparse solutions. The study provides a reproducible template for NP-hard portfolio optimization with transparent inputs and extensible derivative overlays.