We prove that computing an $ε$-approximate Nash equilibrium of a win-lose bimatrix game with constant sparsity is PPAD-hard for inverse-polynomial $ε$. Our result holds for 3-sparse games, which is tight given that 2-sparse win-lose bimatrix games can be solved in polynomial time.

The empirical literature on the relationship between income inequality and economic growth has produced highly heterogeneous and often conflicting results. This paper investigates the sources of this heterogeneity using a meta-analytic approach that systematically combines and analyzes evidence from relevant studies published between 1994 and 2025. We find an economically small but statistically significant negative average effect of income inequality on subsequent economic growth, together with strong evidence of substantial heterogeneity and selective publication based on statistical significance, but no evidence of systematic directional bias. To explain the observed heterogeneity, we estimate a meta-regression. The results indicate that both real-world characteristics and research design choices shape reported effect sizes. In particular, inequality measured net of taxes and transfers is associated with more negative growth effects, and the adverse impact of inequality is weaker - or even reversed - in high-income economies relative to developing countries. Methodological choices also matter: cross-sectional studies tend to report more negative estimates, while fixed-effects, instrumental-variable, and GMM estimators are associated with more positive estimates in panel settings.

We study identification of differentiated product demand from market-level data when product characteristics can be endogenous. Past work suggests nonparametric identification may be impossible: that is, in addition to standard price instruments, exogenous characteristic-based instruments are essentially necessary to identify sufficiently flexible demand models with standard index restrictions. We show, however, that price counterfactuals are nonparametrically identified using recentered instruments -- which combine exogenous price instruments with possibly endogenous product characteristics -- under a weaker index restriction and a new condition we term faithfulness. We argue that faithfulness, like the usual completeness condition for nonparametric instrumental variable identification, is best viewed as a technical requirement on the strength of identifying variation rather than a substantive economic or statistical restriction. We show the two conditions are closely related, though generally distinct. We conclude with several practical implications for the parametric estimation of demand counterfactuals.

This paper develops a general concentration inequality for the suprema of empirical processes with dependent data. The concentration inequality is obtained by combining generic chaining with a coupling-based strategy. Our framework accommodates high-dimensional and heavy-tailed (sub-Weibull) data. We demonstrate the usefulness of our result by deriving non-asymptotic predictive performance guarantees for empirical risk minimization in regression problems with dependent data. In particular, we establish an oracle inequality for a broad class of nonlinear regression models and, as a special case, a single-layer neural network model. Our results show that empirical risk minimzaton with dependent data attains a prediction accuracy comparable to that in the i.i.d. setting for a wide range of nonlinear regression models.

In over-identified models, misspecification -- the norm rather than exception -- fundamentally changes what estimators estimate. Different estimators imply different estimands rather than different efficiency for the same target. A review of recent applications of generalized method of moments in the American Economic Review suggests widespread acceptance of this fact: There is little formal specification testing and widespread use of estimators that would be inefficient were the model correct, including the use of "hand-selected" moments and weighting matrices. Motivated by these observations, we review and synthesize recent results on estimation under model misspecification, providing guidelines for transparent and robust empirical research. We also provide a new theoretical result, showing that Hansen's J-statistic measures, asymptotically, the range of estimates achievable at a given standard error. Given the widespread use of inefficient estimators and the resulting researcher degrees of freedom, we thus particularly recommend the broader reporting of J-statistics.

This study addresses the computational challenges of forecasting volatility in high-dimensional commodity markets. Building on the Network log-ARCH framework, we introduce a novel class of network topologies from GARCH-informed correlation weights, obtained from conditional covariance estimates of multivariate GARCH models, rather than relying on the heuristic distance measures commonly used in clustering methods. We evaluate the proposed models forecasting performance through a rolling-window exercise using a panel of OPEC members crude oil prices. The results identify network volatility models incorporating these new GARCH-informed weights as the statistically superior specifications. Remarkably, the proposed framework matches standard DCC-GARCH predictive accuracy while delivering up to 62,000-fold computational gains. By explicitly modeling contemporaneous spillovers through interpretable spatial ARCH-like lags estimated via GMM, the proposed approach offers an optimal trade-off between parsimony, interpretability, and performance. The findings establish GARCH-informed network models as robust, scalable alternatives for systemic risk measurement and volatility forecasting in interconnected financial markets.

In the value-added literature, it is often claimed that regressing on empirical Bayes shrinkage estimates corrects for the measurement error problem in linear regression. We clarify the conditions needed; we argue that these conditions are stronger than the those needed for classical measurement error correction, which we advocate for instead. Moreover, we show that the classical estimator cannot be improved without stronger assumptions. We extend these results to regressions on nonlinear transformations of the latent attribute and find generically slow minimax estimation rates.

Economists are often interested in the mechanisms by which a treatment affects an outcome. We develop tests for the "sharp null of full mediation" that a treatment $D$ affects an outcome $Y$ only through a particular mechanism (or set of mechanisms) $M$. Our approach exploits connections between mediation analysis and the econometric literature on testing instrument validity. We also provide tools for quantifying the magnitude of alternative mechanisms when the sharp null is rejected: we derive sharp lower bounds on the fraction of individuals whose outcome is affected by the treatment despite having the same value of $M$ under both treatments (``always-takers''), as well as sharp bounds on the average effect of the treatment for such always-takers. An advantage of our approach relative to existing tools for mediation analysis is that it does not require stringent assumptions about how $M$ is assigned. We illustrate our methodology in two empirical applications.

We study prior-independent pricing for selling a single item to a single buyer when the seller observes only a single sample from the valuation distribution, while the buyer knows the distribution. Classical robust pricing approaches either rely on distributional statistics, which typically require many samples to estimate, or directly use revealed samples to determine prices and allocations. We show that these two regimes can be bridged by leveraging the buyer's informational advantage: pricing policies that conventionally require the seller to know statistics such as the mean, $L^η$-norm, or superquantile can, in our framework, be implemented using only a single hidden sample. We introduce hidden pricing mechanisms, in which the seller commits ex ante to a pricing rule based on a single sample that is revealed only after the buyer's participation decision. We show that every concave pricing policy can be implemented in this way. To evaluate performance guarantees, we develop a general reduction for analyzing monotone pricing policies over $α$-regular distributions, enabling a tractable characterization of worst-case instances. Using this reduction, we characterize the optimal monotone hidden pricing mechanisms and compute their approximation ratios; in particular, we obtain an approximation ratio of approximately $0.79$ for monotone hazard rate (MHR) distributions. We further establish impossibility results for general concave pricing policies and for all prior-independent mechanisms. Finally, we show that our framework also applies to statistic-based robust pricing, thereby unifying sample-based and statistic-based approaches.

We study independent private values auction environments in which the auctioneer's revenue depends nonlinearly on bidders' interim winning probabilities. Our framework accommodates heterogeneity among bidders and places no ad hoc constraints on the mechanisms available to the auctioneer. Within this general setting, we show that feasibility of interim winning probabilities can be tested along a unidimensional curve -- the principal curve -- and use this insight to explicitly characterize the extreme points of the feasible set. We then combine our results on feasibility and extremality to solve for the optimal auction under a natural regularity condition. We show that the optimal mechanism allocates the good based on principal virtual values, which extend Myerson's virtual values to nonlinear settings and are constructed to equalize bidders' marginal revenue along the principal curve. We apply our approach to the classical linear model, settings with endogenous valuations due to ex ante investments, and settings with non-expected utility preferences, where previous results were largely limited either to symmetric environments with symmetric allocations or to two-bidder environments.

Background: Many workers with disabilities face negative stereotypical attitudes, pay gaps, and a lack of respect in the workplace, contributing to substantially lower job satisfaction compared to people without disabilities. Work from home may help to increase job satisfaction for people with disabilities. Objective: This study analyzes how different measures of job satisfaction vary between people with and without disabilities, and the extent to which working from home moderates the relationship between disability and job satisfaction. Methods: We use multivariable regression analysis to examine if the ability to work from home moderates the relationship between disability and indicators related to job satisfaction. The dataset draws on a novel survey of healthcare professionals. Results: Results show that people with disabilities have relatively greater turnover intentions, lower sense of organizational commitment and support, weaker perceptions of openness and inclusion in the workplace, and worse relations with management and coworkers. Regressions indicate that working from home helps to improve most perceptions of work experiences but does so more for people without disabilities than for people with disabilities. Conclusions: The findings suggest that (a) some accommodations typically viewed as exceptions to meet the needs of people with disabilities have even greater benefits for the workforce at large and (b) because workers with and without disabilities benefit from remote work, we cannot expect those accommodations to close the gaps caused by inequities.

We examine the joint investment and operational decisions of a prosumer, a customer who both consumes and generates electricity, under net energy metering (NEM) tariffs. Traditional NEM schemes provide temporally flat compensation at the retail price for net energy exports over a billing period. However, ongoing reforms in several U.S. states are introducing time-varying prices and asymmetric import/export compensation to better align incentives with grid costs. While prior studies treat PV capacity as exogenous and focus primarily on consumption behavior, this work endogenizes PV investment and derives the marginal value of solar capacity for a flexible prosumer under asymmetric NEM tariffs. We characterize optimal investment and show how optimal investment changes with prices and PV costs. Through this analysis, we identify a PV effect: changes in NEM pricing in one period can influence net demand and consumption in generating periods with unchanged prices through adjustments in optimal PV investment. The PV effect weakens the ability of higher import prices to increase prosumer payments, with direct implications for NEM reform. We validate our theoretical results in a case study using simulated household and tariff data derived from historical conditions in Massachusetts.

This paper examines how household-targeted government policies influence financial market participation conditional on financial literacy, focusing on potential Central Bank Digital Currency (CBDC) adoption. Due to the lack of empirical CBDC data, I use the 2012 introduction of retail Treasury bonds in Italy as a proxy to study how financial literacy affects households' likelihood to engage with a new government-backed retail instrument. Using the Bank of Italy's Survey on Household Income and Wealth, I show that households with some but low financial literacy are more likely to participate in the Treasury bond market than other groups following the introduction of the new instrument. Based on these findings, I develop a theoretical model to study how financial literacy affects CBDC demand through portfolio choice: low-literate households with limited access to risky assets allocate more wealth to CBDC, while high-literate households use risky assets to safeguard against income risk. These results highlight the role of financial literacy in shaping portfolio choices and CBDC adoption.

This paper analyses the impact of credit expansions arising from decreases in collateral requirements or more expansionary monetary policies on long-term productivity in a model with endogenous growth. Credit expansions associated with relaxation of land collateral financing (capital collateral financing) will be productivity-and growth-retarding (enhancing). Without appropriate financial regulation, expansionary monetary policy may so encourage land speculation using leverage that productive capital investment is decreased; there is a temporary asset boom, but slower economic growth. The generation that experienced the asset price boom is better off, but subsequent generations are worse off because of low growth.

This paper experimentally evaluates four mechanisms intended to achieve the Uniform outcome in rationing problems (Sprumont, 1991). Our benchmark is the dominant-strategy, direct-revelation mechanism of the Uniform rule. A strategically equivalent mechanism that provides non-binding feedback during the reporting period greatly improves performance. A sequential revelation mechanism produces modest improvements despite not possessing dominant strategies. A novel, obviously strategy-proof mechanism, devised by Arribillaga et al. (2023), does not improve performance. We characterize each alternative to the direct mechanism, finding general lessons about the advantages of real-time feedback and sequentiality of play as well as the potential shortcomings of an obviously strategy-proof mechanism.

We study efficient risk sharing among risk-averse agents in an economy with a large, finite number of states. Following a random shock to an initial agreement, agents may renegotiate. If they require a minimal utility improvement to accept a new deal, we show the probability of finding a mutually acceptable allocation vanishes exponentially as the state space grows. This holds regardless of agents' degree of risk aversion. In a two-agent multiple-priors model, we find that the potential for Pareto-improving trade requires that at least one agent's set of priors has a vanishingly small measure. Our results hinge on the ``shape does not matter'' message of high-dimensional isoperimetric inequalities.