We construct moment functions that are Neyman-orthogonal to a chosen order in parametric moment condition models. These moment functions reduce sensitivity to nuisance estimation error and, as such, offer a unified and tractable route to higher-order debiasing in a wide range of econometric models. The number of additional nuisance parameters required by our construction, beyond those already present in the original moment conditions, is independent of the order of orthogonalization and can be reduced to a single scalar if desired.

We propose a game-theoretic framework for adaptive multi-agent intelligent systems. Unlike classical game theory, which often treats strategies as primitive objects chosen by perfectly rational agents, the proposed framework provides a mathematical foundation for studying equilibrium in NeuroAI and can be viewed as an extension of game theory under relaxed assumptions, including partial observability, bounded computation, and uncertainty. At its core, Multilevel Interactive Equilibrium (MIE) generalizes the classical Nash equilibrium to intelligent systems with internal computation. Rather than being defined solely at the level of observable behavior, equilibrium emerges when neural learning dynamics, cognitive representations, and behavioral strategies mutually stabilize between interacting agents. This framework applies uniformly to interactions between two biological brains, two artificial agents, or hybrid human-AI systems. We discuss applications of multilevel game theory to human-autonomous vehicle driving, human-machine interaction, human-large language model (LLM) interaction, and computational psychiatry. We also outline experimental strategies and computational methods for estimating MIE and discuss challenges and prospects for future research.

This paper develops a quantitative framework to assess the robustness of Bayes-optimal decisions in finite decision problems under model uncertainty. We introduce two complementary stability notions for acts: the robustness radius, measuring the largest perturbation of a reference prior under which an act remains Bayes-optimal, and the contamination need, quantifying the minimal perturbation required for an act to become Bayes-optimal under some nearby prior. Both concepts are characterized via linear programming formulations and computed efficiently using bisection methods exploiting monotonicity properties. Building on these stability measures, we propose a cost-adjusted stability criterion that integrates robustness considerations with act-specific selection costs, yielding a parametric family of decision rules indexed by a regularization parameter. We analyze how optimal act selection evolves along this parameter and derive selection paths that reveal structural transitions between stability-driven and cost-driven regimes. The framework is applied to a portfolio choice problem under uncertainty between different economic regimes. Concretely, using data on historical ETF returns, we compute robustness and contamination profiles for six portfolio strategies and analyze their behavior under heterogeneous belief specifications. The results illustrate that robustness-based selection refines classical expected utility by accounting for prior misspecification.

The introduction of leverage on prediction-market event contracts raises three structurally distinct questions that have not been addressed jointly: how leverage changes manipulation incentives, how it interacts with informed-trading rents, and how regulatory frameworks should respond. This paper develops a theoretical framework for the first two and a synthesis of the existing regulatory landscape for the third. The principal analytical move is a two-axis manipulation taxonomy distinguishing market-price manipulation from real-world outcome manipulation, where the manipulator affects the underlying event itself. Continuous-underlying derivative markets generally do not make outcome manipulation a venue-level payoff channel; event-linked markets do. Within this taxonomy, leverage plays asymmetric roles: it scales market-price manipulation linearly but shifts the cost-benefit threshold for outcome manipulation, and it scales informed-trading rents in three ways (direct multiplication, Sharpe-ratio preservation, detection-cost amortization). Section 7 connects Paper 1's pre-emption and halt-protocol findings (CC-007b, CC-008) to three manipulation channels: pre-emption introduced by the dynamic-margin engine, halt-arbitrage introduced by the resolution-zone halt protocol, and strategic bad-debt-shifting that no engine in Paper 1's framework family addresses. The framework's manipulation-resistance contribution is a re-allocation of attack surface, not a net reduction. The regulatory synthesis covers principal jurisdictions (US, EU, UK, Singapore, offshore) and identifies three regulatory-arbitrage pathways. The paper concludes with 14 recommendations for venue operators, regulatory bodies, and the research community, separated into framework-independent and framework-conditional categories.

Agent-based models (ABMs) are increasingly used in macroeconomics, but their analysis still often relies on ad hoc Monte Carlo campaigns with heterogeneous statistical effort across parameter settings. We show how statistical model checking (SMC), implemented through MultiVeStA, can provide a principled analysis layer for a realistic macroeconomic ABM without rewriting the simulator in a dedicated formalism. Our case study is the heuristic-switching Keynes+Schumpeter(K+S) model, analysed hrough a transient sensitivity campaign over one-parameter sweeps, two macro observables (unemployment and GDP growth), and one auxiliary micro-level probe (market share) on the post-warmup phase of a 600-step horizon. The analysis is driven by reusable temporal queries, observable-specific precision targets, and confidence-based stopping rules that automatically determine the simulation effort required by each configuration. Results show a clear contrast across parameter families: macro-financial and structural sweeps produce the strongest transient effects, whereas several heuristic-rule sweeps remain much weaker under the same precision policy. More broadly, the paper shows that SMC can support reproducible and informative quantitative analysis of substantively rich economic ABMs, while making uncertainty estimates and simulation cost explicit parts of the reported results.

Recent advances in generative artificial intelligence (AI) are reshaping who enters entrepreneurship, but not who reaches the top of the quality distribution. Using data on over 160,000 product launches on Product Hunt, we find that entrepreneurial entry increased sharply following the public release of ChatGPT-3.5, driven disproportionately by solo entrepreneurs. This shift toward solo entry is particularly pronounced in categories that historically favored team-based ventures. However, much of this growth reflects low-commitment, experimental entry and does not translate into greater representation among the highest-quality outcomes. Team-based ventures are increasingly dominant in the top tiers of platform rankings. These findings suggest that generative AI lowers barriers to solo entrepreneurship while reinforcing team-based advantages.

This paper studies how the organization of production shapes democratic accountability. I propose a model in which learning economies make specialization productively efficient: most workers perform one-domain tasks, while a small set of integrators with cross-domain knowledge keep the system coherent. When policy consequences run across domains, integrators understand them better than specialists. Electoral competition then tilts government policies toward integrators' interests, while low aggregate system knowledge weakens governance and reduces the fraction of public resources converted into citizen-valued services. Labor markets leave these civic margins unpriced, failing to internalize the political returns to system knowledge. Broadening specialists can therefore raise welfare relative to the market allocation. The model speaks to debates on liberal arts education and the effects of AI.

Sampled network data are widely used in empirical research because collecting complete network information is costly. However, empirical analyses based on sampled networks may lead to biased estimators. We propose a nonparametric imputation method for sampled networks and show that empirical analyses based on imputed networks yield consistent estimates. Our approach imputes missing network links by combining a projection onto covariates with a local two-way fixed-effects regression. The method avoids parametric assumptions, does not rely on low-rank restrictions, and flexibly accommodates both observed covariates and unobserved heterogeneity. We establish entrywise convergence rates for the imputed matrix and prove the consistency of generalized method of moments (GMM) estimators based on imputed networks. We further derive the convergence rate of the corresponding estimator in the linear-in-means peer-effects model. Simulations show strong performance of our method both in terms of imputation accuracy and in downstream empirical analysis. We illustrate our method with an application to the microfinance network data of Banerjee et al. (2013).

We conduct a pre-registered randomized controlled trial to test for income targeting in labor supply decisions among sellers of a Swedish street paper. Unlike most workers, these sellers choose their own hours and face severe liquidity constraints and volatile incomes. Treated individuals received a 25 percent bonus per copy sold for the duration of an issue, simulating an increase in earnings potential. Consistent with standard labor supply theory, they sold more papers and, by our measures, worked longer hours and took fewer days off. These findings contrast with studies on intertemporal labor supply that find small substitution effects.

This paper analyzes a cheap-talk model with multiple senders and one receiver. Each sender observes a noisy signal about an unknown state and sends a message; the receiver observes the message tally and chooses a policy. This setting shares certain features with voting models (e.g., Feddersen and Pesendorfer, 1997, 1998). The existing literature (e.g., Levit and Malenko, 2011; Battaglini, 2017) focuses on scenarios in which the receiver and the senders agree on the preferred policy in each state. In contrast, we explore environments in which the receiver and the senders disagree over the preferred policy in some states. We establish an equilibrium no-conflict result: in any non-babbling equilibrium, the senders and the receiver agree on the preferred policy at every realized message tally. We show that information aggregation fails, and the receiver cannot fully learn the state even as the number of senders grows large. We also identify a discontinuity in information transmission relative to the implications of the existing literature. Finally, introducing a mediator can improve information transmission and restore efficiency.

The Global Carbon Budget, maintained by the Global Carbon Project, summarizes Earth's global carbon cycle through four annual time series beginning in 1959: atmospheric CO$_2$ concentrations, anthropogenic CO$_2$ emissions, and CO$_2$ uptake by land and by ocean. We analyze these four time series as a multivariate (cointegrated) system. Statistical tests show that the four time series are cointegrated with rank three and identify anthropogenic CO$_2$ emissions as the single stochastic trend driving the nonstationary dynamics of the system. The three cointegrated relations correspond to the physical relations that the sinks are linearly related to atmospheric concentrations and that the change in concentrations equals emissions minus the combined uptake by land and ocean. Furthermore, likelihood ratio tests show that a parametrically restricted error-correction model that embodies these physical relations cannot be rejected on the data. The model can be used for both in-sample and out-of-sample analysis. In an application of the latter, we demonstrate that projections based on this model, using Shared Socioeconomic Pathways scenarios, yield results consistent with established climate science.

Coping with prolonged periods of low availability of wind and solar power, also referred to as variable renewable energy droughts or "Dunkelflaute", emerges as a key challenge for realizing decarbonized energy systems based on renewable energy. Here we investigate the role of long-duration electricity storage and geographical balancing through transmission in dealing with such events in Europe, combining a time series analysis of renewable availability with power sector modeling of 35 historical weather years. We find that extreme droughts define long-duration storage operation and investment. Assuming policy-relevant interconnection, the least-cost system in our model capable of coping with the most extreme event requires 351 terawatt hours long-duration storage capacity, corresponding to 7% of yearly European electricity demand. While nuclear power can partially reduce storage needs, the storage-mitigating effect of fossil backup plants in combination with carbon removal is limited. Policymakers and system planners should prepare for a rapid expansion of long-duration storage to safeguard the renewable energy transition in Europe.

As an alternative to synthetic control, the distributional Synthetic Control (DSC) proposed by Gunsilius (2023) provides estimates for quantile treatment effect and thus enabling researchers to comprehensively understand the impact of interventions in causal inference. But the asymptotic properties of DSC have not been built. In this paper, we first establish the DSC estimator's asymptotic optimality in the essence that the treatment effect estimator given by DSC achieves the lowest possible squared prediction error among all potential estimators from averaging quantiles of control units. We then establish the convergence rate of the DSC weights. A significant aspect of our research is that we find the DSC synthesis forms an optimal weighted average, particularly in situations where it is impractical to perfectly fit the treated unit's quantiles through the weighted average of the control units' quantiles. Simulation results verify our theoretical insights.

In this paper, we use tools from network theory to trace the properties of the matching function to the structure of granular connections between applicants and vacancies. We unify seemingly disparate parts of the literature by recovering multiple functional forms as special cases including the CES. We derive a testable condition under which matching in any network from the broad class we analyze can be thought "as if" it comes from a CES matching function, up to a first-order approximation. We provide a theory of match efficacy in which inequality in search intensities is the key determinant of how well the matching process works. A robust finding of our analysis is that dispersion of search intensities on either side of the market is bad for the matching process. We also show that a rise in the market's mean search intensity can reduce match efficacy when it is associated with a higher Gini coefficient of search intensities.

Needless to say, linear dynamics are pervasive in economic time series, particularly autoregressive ones. While gradient boosting with trees excels at capturing nonlinearities, it is inefficient in small samples when much of the predictive content is linear, expending splits to approximate relationships better captured by simple linear terms. This paper proposes LGB+, a boosting procedure operating on a more inclusive set of basis functions. The idea comes in two flavors. LGB+ evaluates a tree and a linear candidate at each step against out-of-bag data; only the winner advances. The simpler variant, LGB^A+, alternates on a fixed schedule: a block of tree updates, then a greedy linear correction, repeat. Both designs avoid ex ante commitments to any particular functional form or predictor selection. Because the prediction is the sum of a linear and a tree component, forecasts decompose natively into linear and nonlinear contributions, and so does permutation-based variable importance and historical proximity weights. In a quarterly U.S. macroeconomic forecasting exercise, LGB+ delivers strong gains for targets with pronounced autoregressive dynamics or mixed linear-nonlinear signals. Variables dominating the linear channel are those operating through autoregressive persistence or near-accounting relationships to the target (e.g., initial claims for unemployment and building permits for housing starts).

Average forecast accuracy is not the same as forecast reliability. I treat forecast loss differentials relative to a benchmark as a return series. I then evaluate these returns using risk-adjusted performance measures from finance, including the Sharpe ratio, Sortino ratio, Omega ratio, and drawdown-based metrics. I also introduce the Edge Ratio capturing a model's propensity to deliver uniquely informative predictions relative to the forecasting frontier. I apply this framework to U.S. macroeconomic forecasting, comparing econometric benchmarks, machine learning models, a foundation model (TabPFN), and the Survey of Professional Forecasters. While it is often feasible to beat professional forecasters in terms of average accuracy, it is much harder to beat them on a risk-adjusted basis. They rarely exhibit catastrophic failures and often achieve high Edge Ratios, plausibly reflecting the value of contextual judgment. Nonetheless, selected machine learning methods deliver attractive risk profiles for specific targets. The framework naturally extends to meta-analyses across targets, horizons, and samples, illustrated with a density forecast evaluation and the M4 competition.

This paper studies a structural failure of subsample-based estimation in dynamic time series models. Even under oracle knowledge of contamination locations, removing contaminated observations does not restore the uncontaminated objective. In such settings, contamination propagates through the residual filter and distorts the estimation criterion. As a result, subsample-based estimators are generically inconsistent for the clean-data parameter. We characterise this failure as a structural incompatibility between pointwise subsampling and residual propagation. More generally, the failure arises whenever contamination propagates through transformations that enter the estimation criterion, with dynamic time series models as a leading example. To address it, we propose a propagation-compatible transformation of index sets via a patch removal operator. Under general high-level conditions, this transformation leaves the estimator asymptotically unchanged under the uncontaminated model while restoring consistency under contamination. The results apply to a broad class of residual-based estimators and do not rely on modelling the contamination process.

We present a novel framework for high-resolution forecasting of residential heating demand and non-heating electricity demand using probabilistic deep learning models. Because our models are trained on electricity consumption from a predominantly gas-heated region, the learned electricity demand patterns primarily reflect non-heating end uses such as lighting, appliances, and cooling. We focus specifically on providing hourly building-level electricity and heating demand forecasts for the residential sector. Leveraging multimodal building-level information -- including data on building footprint areas, heights, nearby building density, nearby building size, land use patterns, and high-resolution weather data -- and probabilistic modeling, our methods provide granular insights into demand heterogeneity. Validation at the building level underscores a step change improvement in performance relative to NREL's ResStock model, which has emerged as a research community standard for residential heating and electricity demand characterization. In building-level heating and electricity estimation backtests, our probabilistic models respectively achieve RMSE scores 18.8% and 27.6% lower than those based on ResStock, with probabilistic forecast quality measured via WIS improving by 59% for both applications. By offering an open-source, scalable, high-resolution platform for demand estimation and forecasting, this research advances the tools available for policymakers and grid planners, contributing to the broader effort to decarbonize the U.S. building stock and meeting climate objectives.

This paper studies preference aggregation under uncertainty in the multi-profile framework and characterizes a new class of aggregation rules that address classical concerns about Harsanyi's (1955) utilitarian rules. Our aggregation rules, which we call relative fair aggregation rules, are grounded in three key ideas: utilitarianism, egalitarianism, and the 0--1 normalization of individual utilities. These rules are parameterized by a set of weight vectors over individuals and evaluate each ambiguous alternative by taking the minimum weighted sum of 0--1 normalized utility levels over the weight set. For the characterization, we propose two novel axioms -- weak preference for mixing and restricted certainty independence -- developed by using a new method of objectively randomizing outcomes within the Savagean setting. Additional results clarify how these axioms capture the utilitarian and egalitarian attitudes of the rules.

Eradicating extreme poverty and inequality are the key leverage points to achieve the seventeen Sustainable Development goals. Yet, the reduction in extreme poverty and inequality are vulnerable to shocks such as the pandemic and climate change. We find that that these vulnerabilities emerge from the interaction between individual and institutional mechanisms. Individual characteristics like risk aversion, attention, and saving propensity can lead to sub-optimal diversification and low capital accumulation. These individual drivers are reinforced by institutional mechanisms such as lack of financial inclusion, access to technology, and economic segregation, leading to persistent inequality and poverty traps. Our experiments demonstrate that addressing above factors yields 'double dividend' - reducing poverty and inequality within-and-between communities and create positive feedback that can withstand shocks.

A sustainable solution to negative externalities imposed by road transportation is replacing internal combustion vehicles with electric vehicles (EVs), especially plug-in EV (PEV) encompassing plug-in hybrid EV (PHEV) and battery EV (BEV). However, EV market share is still low and is forecast to remain low and uncertain. This shows a research need for an in-depth understanding of EV adoption behavior with a focus on one of the main barriers to the mass EV adoption, which is the limited electric driving range. The present study extends the existing literature in two directions; First, the influence of the psychological aspect of driving range, which is referred to as range anxiety, is explored on EV adoption behavior by presenting a nested logit (NL) model with a latent construct. Second, the two-level NL model captures individuals' decision on EV adoption behavior distinguished by vehicle transaction type and EV type, where the upper level yields the vehicle transaction type selected from the set of alternatives including no-transaction, sell, trade, and add. The fuel type of the vehicles decided to be acquired, either as traded-for or added vehicles, is simultaneously determined at the lower level from a set including conventional vehicle, hybrid EV, PHEV, and BEV. The model is empirically estimated using a stated preferences dataset collected in the State of California. A notable finding is that anxiety about driving range influences the preference for BEV, especially as an added than traded-for vehicle, but not the decision on PHEV adoption.

Daniel Kahneman and Amos Tversky argued for challenging inside views (informed by contextual specifics) with outside views (based on historical "base rates" for certain event types). A reasonable inside view of the prospects for the global economy in this century is that growth will converge to 2.5%/year or less: population growth is expected to slow or halt by 2100; and as more countries approach the technological frontier, economic growth should slow as well. To test that view, this paper models gross world product (GWP) observed since 10,000 BCE or earlier, in order to estimate a base distribution for changes in the growth rate as a function of the GWP level. For econometric rigor, it casts a GWP series as a sample path in a stochastic diffusion whose specification is novel yet rooted in neoclassical growth theory. After estimation, most observations fall between the 40th and 60th percentiles of predicted distributions. The fit implies that GWP explosion is all but inevitable, in a median year of 2047. The friction between inside and outside views highlights two insights. First, accelerating growth is more easily explained by theory than is constant growth. Second, the world system may be less stable than traditional growth theory and the growth record of the last two centuries suggest.

This paper introduces the concept of Engineering Economy as a new paradigm for understanding and managing macroeconomic policy in middle-income countries seeking to escape the middle-income trap. Drawing on Turkiye's post-2001 economic trajectory and South Korea's successful transition from a low-income to a high-income economy, the study argues that conventional frameworks whether the Washington Consensus's market liberalization prescriptions or the institutionalist critique alone are insufficient. Instead, it proposes treating the economy as a dynamic control system requiring continuous calibration rather than static equilibrium. The paper develops a road-surface metaphor (highway, side-road, off-road) to characterize different global economic regimes and presents eleven interconnected policy pillars spanning venture capital formation, regulatory sandboxes, technology-focused industrial policy, and human capital development. By synthesizing insights from endogenous growth theory (Romer), institutional economics (Acemoglu), the catching-up literature (Lee), cybernetic systems theory (Wiener), and Schumpeterian creative destruction, the framework reconceptualizes macroeconomic instruments through control-engineering analogies: interest rates as energy gradients, fiscal policy as energy flow, exchange rates as balance motors, and regulation as adaptive suspension. The analysis demonstrates that Turkiye's structural challenge is not merely institutional weakness but a systemic absence of R&D demand from its dominant enterprise structures, creating a vicious cycle that conventional reforms cannot break. Seven specific opportunity windows arising from US-China technological rivalry are identified, and a phased implementation roadmap is proposed.

Noise traders can be dispensed with entirely. Partial revelation of information through prices arises under any non-exponential expected utility preference, including CRRA, without noise traders, random endowments, supply shocks, hedging motives, or behavioral biases. The model contains zero exogenous noise. The mechanism is a mismatch between the space in which market clearing aggregates signals and the Bayesian sufficient statistic. CARA demand is linear in log-odds, so prices aggregate in log-odds space and reveal the statistic exactly. Every other preference aggregates differently; the resulting Jensen gap makes revelation partial. I prove that CARA is the unique fully revealing preference class, characterize the rational expectations equilibrium via a contour integration fixed point, and verify that partial revelation survives learning from prices. The Grossman-Stiglitz paradox is resolved: information acquisition has positive value within the rational class. Numerical solution of the rational expectations fixed point at K = 3 confirms partial revelation, positive trade volume, and positive value of information across the full range of CRRA risk aversion, vanishing only in the CARA limit.

Communication is secret if a message is independent of the state; however, the receiver's subsequent action may still reveal that she has acted on hidden information. This paper studies when secret communication can also provide plausible deniability: under single-crossing preferences, every action induced by the sender's message must be rationalizable using the receiver's baseline information alone. We characterize joint information structures that satisfy both secrecy and plausible deniability. We show that plausible deniability restricts communication exactly when the baseline message is directional -- meaning its likelihood is monotone in the state. Combining this restriction with secrecy, we show that, for directional messages, frontier communication reveals at most whether the state lies above or below a cutoff. Finally, we identify conditions under which a greatest feasible communication structure exists and can be constructed explicitly in a simple way.

A series of papers has introduced the Heuristic Rating Estimation method, which evaluates a set of alternatives based on pairwise comparisons and the weights of reference alternatives. We formulate the conditions under which the HRE method can be applied correctly. The research considers both arithmetic and geometric algorithms for complete and incomplete pairwise comparison methods. The illustrative examples show that the estimations of inconsistency in the arithmetic variant are optimal.

Many environments assign several Elo ratings to the same agent: a chess player has classical, rapid, and blitz ratings; an online platform may rate by time control, mode, or format; an evaluator may rate performance across tasks or roles. This paper axiomatizes when such a vector of ratings can be reduced to a single scalar rating that is itself on the Elo scale. We impose three substantive conditions: same-scale normalization (a uniform profile keeps its rating), recursive consistency (aggregating in blocks gives the same answer as aggregating directly, provided each block carries the total weight of its members), and marginal Elo-strength consistency (for two equally weighted coordinates, the ratio of marginal contributions to the combined rating equals the ordinary Elo odds). The unique rating rule satisfying these conditions converts each component to its Elo strength, takes a weighted arithmetic mean of strengths, and converts back. We show how this rule differs from a random-format lottery and from rating-scale averaging, prove the axioms are independent, and illustrate the rule on combining classical, rapid, and blitz ratings.

The Spanish Price Revolution is usually treated as a classic case in which American bullion inflows expanded the money supply and generated inflation. This view captures the first phase of the episode but fails to explain why the same monetary expansion did not continue to produce proportional price growth after 1600. We develop a two-phase Money Phase Transition Theory (MPTT) model in which the classical monetary relation is recovered before a transition point, while a second-phase correction term modifies the money-price transmission coefficient after the transition. Using annual Spanish CPI and reconstructed money-supply data, we show that 1500-1600 was a high-transmission metallic inflationary phase: CPI increased approximately 3.35-fold while money supply increased approximately 3.73-fold. After 1600, money supply continued to rise, increasing approximately 1.82-fold during 1600-1650, while CPI rose only approximately 1.22-fold. A classical one-phase model fitted on 1500-1600, therefore, overpredicts post-1600 prices when extrapolated forward. The MPTT two-phase model with transition point tau=1600 estimates beta_1=0.949, gamma=-0.812, and beta_2=beta_1+gamma=0.137, indicating a sharp post-transition weakening of monetary transmission. An unrestricted break scan identifies a deeper BIC-minimizing break around 1636. These results suggest that the Spanish Price Revolution was not a single monotonic bullion-inflation process but the rise and exhaustion of high-transmission metallic money inflation.

This paper assesses whether NASA Black Marble nightlight intensity can serve as an early indicator of annual taxable income at the Italian municipal level, where official data are released with a 12--18 month lag. Using a panel of 7{,}631 municipalities over 2012--2021, we compare four recurrent neural network architectures (LSTM, BiLSTM, GRU, Transformer) against six benchmarks: simple persistence, panel fixed effects, autoregressive distributed lag, and two spatial econometric specifications (SAR, Spatial Durbin) on a queen-contiguity matrix. Models are trained on 2012--2019 and evaluated out-of-sample on 2020--2021 with a cross-sectional Diebold--Mariano test. A single-layer GRU achieves a median forecast error of 1.07 million euros across the cross-section of municipalities -- approximately $4\%$ of the median municipal IRPEF income of 29 million euros -- statistically dominating every benchmark (DM $>4$ against persistence, $>40$ against spatial linear models, all $p<0.001$). Spatial models recover statistically significant spatial autocorrelation ($ρ\approx 0.71$) and a meaningful nightlight spillover ($θ\approx 0.05$), but their forecasting gap with the GRU is virtually identical to that of spatially-naive linear specifications. We conclude that nightlights contain genuine predictive content for municipal income, but extracting it requires a model class flexible enough to capture cross-sectional heterogeneity and non-linearities that linear specifications, spatial or otherwise, cannot recover.

Empirical Bayes methods can improve inference on unobservable individual effects by borrowing strength across units. This paper proposes nonparametric empirical Bayes confidence intervals (NP-EBCIs) for unobservable individual effects in a normal means model. The oracle intervals are constructed from posterior quantiles under a point-identified, fully nonparametric prior; feasible intervals replace these quantiles with nonparametric estimates. The NP-EBCIs are asymptotically exact in the sense that both their conditional and marginal coverage probabilities converge to the nominal level. The flexibility of this nonparametric construction has an unavoidable statistical cost. We demonstrate that posterior quantiles, unlike posterior means, inherit the severe ill-posedness of nonparametric deconvolution: the minimax optimal estimation rate is logarithmic. This logarithmic rate is minimax optimal for errors in the conditional coverage probability, and the resulting errors in the marginal coverage probability also vanish at the same logarithmic rate. Despite these slow asymptotic rates, simulations show that the NP-EBCIs remain close to nominal coverage when the prior is non-Gaussian, and deliver substantial length reductions relative to intervals that treat each unit in isolation.