Papers

This paper studies difference-in-differences with staggered adoption and a continuous, time-invariant dose. Each cohort-time comparison contains two margins. The level margin is the average treatment effect at realized doses. Under level parallel trends it equals the level contrast between the treated cohort and not-yet-treated controls. The response margin is the within-cohort slope of the outcome change on dose. It uses no controls, and its causal interpretation requires a response parallel trends assumption and a restriction on selection on gains. We show that the continuous-dose OLS coefficient in each cohort-time comparison is a convex combination of the response index and the level contrast per unit of mean dose, with a mixing weight that depends on the not-yet-treated share. We provide estimators of both margins, joint inference across cohort-time comparisons and event-time aggregates, and a covariate-adjusted extension. In an application to hydraulic fracturing, the level leads reject a joint zero restriction, whereas the response-index leads do not. The continuous-dose OLS coefficient draws primarily on the level margin. We report the level and response margin separately.

Should researchers adjust for covariates in randomized experiments, and if so, how? The literature offers three distinct prescriptions: do not adjust because randomization guarantees unbiasedness; adjust for outcome-prognostic covariates to improve precision; or adjust for covariates imbalanced between treatment arms. These competing prescriptions create confusion and uncertainty. We develop a unified framework for decision and practice. Given available information, we show that the optimal correction is what we call ex-post bias. The only relevant criterion for adjustment is prognosticity for ex-post bias; neither raw covariate imbalance nor outcome prognosticity is sufficient by itself. We also show that correcting imbalance and improving precision are two sides of the same decision problem. We develop two estimation approaches, one of which recovers familiar adjustment estimators and provides a new theoretical justification for them. Simulations compare alternative covariate-selection and adjustment strategies. Overall, our framework provides a unified foundation for covariate adjustment in randomized experiments.

When social assistance is scarce, should it prioritize households in greatest need or those expected to benefit most? Using panel data from the China Household Finance Survey, we distinguish allocation principles by combining predicted policy gains with entry into China's Minimum Living Standard Guarantee (Dibao). We estimate heterogeneous predicted gains in consumption and education and then recover the conditional priorities revealed by recipient selection. Predicted gains explain little of allocation: a Shapley decomposition attributes 96.9% of the improvement in allocation fit to household priorities and 3.1% to predicted gains. Lower income, lower education of the household head, and elderly presence consistently predict higher priority across supported outcome-value specifications. Holding local program capacity fixed and removing household-priority differences while retaining the full model's estimated outcome values, the resulting ranking overlaps with recipients by only 10.9%, implying 89.1% recipient churn. These findings show that Dibao allocation is more closely aligned with household circumstances associated with poverty and vulnerability than with policy gains predictable from the outcomes and information observed in our data, underscoring the distinction between distributional and impact targeting in social assistance.

Spatial treatments are interventions assigned to locations potentially distinct from those of the responding units. We study their optimal design under a general model in which a unit's response diminishes with distance to a treated site. Our estimand of interest is an “uncontaminated” effect equal to the average impact of a single intervention site over all hypothetical sites. We propose a novel design based on a Matérn point process which separates treatments by a distance of at least $r$. A larger choice of $r$ reduces bias by separating interventions but increases variance by reducing their numerosity. We choose $r$ to maximize the rate of convergence of a Horvitz-Thompson estimator and prove that this is minimax rate-optimal. We provide weak conditions under which the estimator is asymptotically normal and propose a variance estimator.

Language models increasingly perform empirical analyses end to end, yet existing evaluations assess the written explanation or whether generated code executes, not whether the executed workflow recovers the intended causal estimand. We introduce CausalVerify, an execution-grounded benchmark for end-to-end causal analysis that follows a model from research-context interpretation to estimand recovery. It scores this workflow at four distinct layers: method recognition, design specification, executable implementation, and estimand recovery. It combines 259 real-paper contexts, 100 fixed-seed synthetic scenarios with executable reference estimates, and 23 paper-twin pairs in which a model commits to a design before seeing the data and its executed analysis is scored against a canonical estimator on the same realised dataset. Execution is not correctness. Among 426 model-written workflows that run without error, 15.5% fail verification, and a keyword score of the effect direction stated in the text is a poor proxy for recovery. In a 23-pair, nine-model paired study, replacing a model's committed design with the reference design and its execution conventions raises joint recovery of the point estimate and standard error from 15.0% to 51.5%; yet 48.5% of eligible seeds still fail under the reference design. The direction replicates on six pairs built afterwards under a frozen construction protocol, although on the two newest pairs the gain is confined to models from the family that built the references. Design specification is consequential but not sufficient: a plausible method and runnable code do not guarantee recovery, and even supplying the reference design and its conventions leaves substantial downstream failure. CausalVerify evaluates the executed workflow rather than its surface plausibility, and every reported number is recomputed from frozen artifacts by a single script.

Heavy-tailed and skewed outcomes are common in the randomized experiments and observational studies used to estimate heterogeneous treatment effects, yet the mean-squared-error criterion that guides splitting in honest causal trees is sensitive to the extreme values they generate. Building on the causal forest framework (Athey and Imbens, 2016; Wager and Athey, 2018), we introduce the Median Squared Deviation (MSD) criterion, which replaces the leafwise difference in means in the honest splitting objective with the Hodges–Lehmann location estimator while leaving honest leaf estimation and forest inference unchanged. Two further median-based rules, the Median Absolute Deviation (MAD) and the Least Median of Squares (LMS), serve as robust baselines. We evaluate the criteria in a simulation study covering precision, bias, and confidence interval coverage. MSD restricts its robustness to split selection and lowers the error of conditional average treatment effect estimates under heavy-tailed and skewed outcomes. Further, we re-visit two empirical applications: the first analyzes the electoral effects of a Mexican conditional cash transfer program on precinct-level observations, while the second application studies antiretroviral treatments in HIV-positive adults.

A/B tests are standard in firm decision making. In the standard pipeline, experimental data is converted to a deployment decision by applying a t-test of the difference in means (the lift) and deploying the treatment if lift is positive and statistically significant. This common workflow answers the wrong question. We argue that firms need a decision rule for economic payoffs in the future deployment environment, not a test of equality in the experimental sample. We develop an ambiguity-averse decision framework in which each arm is evaluated by its ambiguity-penalized value over distributions close to the experimental outcome distribution. The resulting rule has a simple closed form thanks to the Donsker-Varadhan representation and it requires only the outcome data from a standard A/B test plus one interpretable parameter governing trust in the experiment. Our rule is thus no more difficult to implement than a t-test. A mean-variance approximation shows how the rule penalizes variability, while a connection to utility maximization shows it to be a certainty equivalent. We are able to perform a real-world evaluation of our proposed rule in the context of digital marketing using an archive of 552 advertising experiments from an anonymous US-based online platform. The proposed rule substantially reduces regret relative to conventional hypothesis testing. The results show that economically conservative, distribution-aware deployment rules can outperform statistical-significance rules in digital experimentation.

We develop a filter for time series, defined at each time $t$ as the minimizer of a discounted convex combination of observed and expected losses. The filter can be estimated by simulation to an arbitrary level of accuracy in $O(1)$ flops at each time point $t$ and can be run for all values $t=1,...,T$ in parallel. These methods are applied to robustly compute a preaveraged price process from the more than 1.5 million trades made on a single financial asset in a single day where the noise's variance is infinite. It yields a flat "volatility signature" plot, down to the 1 second level, so the microstructure noise no longer biases the volatility estimate. This is not true when linear methods are employed.

Estimating the first stage of an instrumental variables (IV) model with the least absolute shrinkage and selection operator (LASSO) requires choosing a dictionary of technical instruments and a penalty level. First-order asymptotic theory offers no guidance on these choices, as any consistent implementation yields a structural parameter estimator with the same limiting distribution. In finite samples, however, these choices can have a substantial impact on the resulting structural parameter estimate. Working in a model with a single endogenous regressor and homoskedastic Gaussian errors, we use first- and second-order Stein identities to derive the approximate mean squared error (AMSE) of the instrumental-variables LASSO (IV-LASSO) estimator, which can be consistently estimated and used to rank a prespecified list of dictionary-penalty candidates. The AMSE reveals a bias-variance trade-off: more complex first-stage fits better approximate the conditional mean of the endogenous variable but are also more correlated with the structural errors, with complexity measured by the degrees of freedom of the LASSO fit. The weight on this bias rises with the endogeneity of the regressor, a quantity that neither plug-in nor cross-validation penalty rules take into account. Despite the AMSE being derived in a Gaussian model, penalty selection by minimizing the feasible AMSE criterion delivers up to a one-third lower mean squared error compared to cross-validation and plug-in penalty rules in Gaussian and non-Gaussian simulation designs calibrated to the data of Gilchrist and Sands (2016).

Sign restrictions on the slopes of supply and demand curves are often used to identify historical decompositions in structural vector autoregressions. I show that the identifying power of these restrictions depends on both reduced-form parameters and realised forecast errors. Consequently, unlike many other structural objects, the strength of identification cannot be assessed from reduced-form parameters alone. Empirically, identified sets for historical decompositions of US inflation are typically largely uninformative, both in aggregate and in most expenditure categories. Existing inflation decompositions are therefore sensitive to auxiliary assumptions used to select among observationally equivalent models.

We develop an expected shortfall factor model (ESFM) to estimate and price common variation in the severity of lower-tail losses in large panels of asset returns. Mean factor models describe common variation in average returns, while quantile factor models describe common movements in tail thresholds. ESFM instead captures common variation in the average severity of losses below those thresholds. The model combines observed risk exposures with latent common factors. We estimate ESFM using an orthogonalized two-step procedure under which first-stage quantile estimation error has no first-order effect on the ES coefficient estimates. We establish nonasymptotic error bounds for the ES coefficients, a finite-sample Gaussian approximation, and consistent selection of the number of latent factors. Applied to a large panel of equities, ESFM uncovers common factors that react sharply to market stress and contain information not captured by mean and quantile factors. Average returns increase across portfolios sorted on ESFM exposure; high-minus-low portfolios earn annualized returns of 8.0%–11.7% and Fama–French five-factor alphas of 10.3%–15.0%. These spreads remain positive and statistically significant after conditioning separately and jointly on mean- and quantile-factor exposures. Tail-by-tail spanning tests show that ESFM factors retain significant alphas after controlling for standard traded factors and the corresponding mean and quantile factors. Adding ESFM to these benchmark factor sets increases the maximum attainable Sharpe ratio. These findings identify common loss severity as a distinct and priced dimension of downside risk.

Heterogeneous-agent New Keynesian (HANK) models characterize how entire cross-sectional distributions respond to structural shocks. Traditional representative-agent models are routinely disciplined by impulse responses from aggregate vector autoregressions (VARs). HANK models have no comparable established empirical benchmark because they make predictions not only about aggregates, but also about distributions of micro-level data. We propose a Bayesian benchmark that jointly models macroeconomic aggregates and several marginal distributions from repeated cross sections, including distributions observed in different surveys. Our approach can use both standard structural VAR identification approaches on macroeconomic aggregates and identification restrictions imposed on micro-level data. The model delivers a joint posterior of the distributional effects of shocks, without the need for household panel data or a separate first-stage density estimate.

This paper develops fixed-smoothing (fixed-b, fixed-K) inference methods for time-series quantile regression that are robust to heteroskedasticity and autocorrelation. Our approach is uniformly valid over quantile levels and accounts for dependence both over time and across quantiles. It enables the construction of uniform confidence bands, Wald, and Sup-t tests for joint hypotheses, and tests of shape restrictions, providing a unified framework for assessing heterogeneity in quantile effects. A key challenge is that, under weak dependence, uniform inference for quantile regression processes is generally non-pivotal because the limiting distributions depend on the long-run covariance structure across quantiles. To address this issue, we develop two complementary approaches. The uniform-in-$\tau$ method estimates the covariance structure and simulates the non-pivotal limiting distribution. For certain tests involving a finite collection of quantile levels, the stack-Wald method delivers pivotal fixed-smoothing inference. We establish the asymptotic validity of both approaches. Simulation results show that the proposed methods substantially improve size control relative to existing HAC-based procedures while maintaining good power. An application to predictive quantile regressions for stock returns reveals substantial heterogeneity in predictive effects across both quantiles and forecast horizons.

We extend the clustered connectedness framework of Buchwalter, Diebold and Yilmaz (2026) in two complementary directions that improve the robustness and interpretability of cross-cluster connectedness. First, we develop a diagnostic for residual ordering sensitivity by characterizing the distribution of cluster-level net connectedness across all admissible identification orderings and, in particular, by pairing first- and last-position orderings while holding fixed the relative ordering of all other clusters. Second, we introduce a dedicated cluster of control variables to absorb variation associated with observed common macro-financial factors while preserving the computational scalability of the clustered framework. The control cluster is fixed first, and bank innovations are residualized with respect to it before the remaining bank clusters are permuted and orthogonalized as usual, leaving the number of admissible bank-cluster identification strategies unchanged. Under the maintained recursive assumption that control-cluster innovations are contemporaneously exogenous to bank-cluster innovations, the remaining cross-cluster connectedness among the bank clusters can be interpreted as bank-to-bank transmission net of those observed common-factor shocks. We apply the methodology to seventy-one global banks grouped into seven regional clusters over 2003–2024. The treatment of common macro-financial factors materially affects both system-wide cross-group connectedness and cluster-level net positions. Placing the controls in a dedicated first cluster also substantially reduces paired first-versus-last ordering sensitivity across all seven bank clusters, with especially large reductions for the United States and the European clusters.

We develop a Dynamic Spatial Panel Bayesian Additive Regression Trees model with Horseshoe shrinkage (DSP-BART-HS) for high-dimensional spatio-temporal panel data. We jointly evaluate the model against a comprehensive suite of structural spatial econometrics, non-parametric machine learning methods, and small-area estimators across nine data-generating scenarios spanning 200 replicates each, including irregular spatial topologies, dense policy effects, and non-linear individual-level interactions. DSP-BART-HS is the best or statistically indistinguishable from the best estimator in every scenario. Conventional region-time-aggregate comparators suffer severe performance degradation – trailing by a factor of three or more – whenever individual-level non-linearity drives outcome variance, a limitation this framework's tree-ensemble design directly addresses. The model also maintains strong predictive accuracy under a zero-training-region spatial holdout via its spatial diffusion mechanism. We demonstrate practical utility across two U.S. county-level panel applications – intergenerational economic mobility and geographic income inequality – under genuine unseen-region, random, and temporal holdouts, with results validated through repeated-split uncertainty quantification and paired significance testing against every comparator. One clear limitation emerges: under temporal extrapolation specifically, a lighter per-region autoregressive specification (MTS-CAR-X) achieves a robust, and consistent advantage. DSP-BART-HS nonetheless establishes strong predictive performance, automated variable selection, and flexible inference for hierarchical spatio-temporal panel data.

This paper studies the effects of p-hacking on the bias of published estimates when papers with statistically significant results are selectively published. We show that fast p-hacking—actions that lead to large changes in p-values—always exacerbates the bias from selective publication. On the other hand, slow p-hacking—actions that lead to small changes in p-values—exacerbates bias when selection is weak, but mitigates it when selection is strong. In a model featuring both types of p-hacking, we show that a normality assumption identifies the true distribution of effects as well as the counterfactual mean that would obtain under selective publication without p-hacking. Applying the model to meta-analyses on the effects of behavioral nudges and development aid, we find suggestive evidence that both mitigation and exacerbation can arise in practice.

Measuring the intergenerational transmission of lifetime economic status is complicated by researchers often only observing snapshots of income at specific ages. Consequently, standard practice estimates intergenerational mobility using income averages, introducing life-cycle bias that compromises reliability and comparability across studies, time, and place. I develop a missing data framework that exploits available income data and observable characteristics to eliminate life-cycle bias. This method combines nonparametric identification with Neyman-orthogonal moments to construct debiased machine learning estimators for intergenerational income mobility measures under plausible missing-at-random and testable independence assumptions. I apply this framework to estimate the intergenerational elasticity for the U.S. using the Panel Study of Income Dynamics across birth cohorts from 1954 to 1977 with rolling 10-year windows. While existing approaches estimate values between 0.41 and 0.54, the proposed method yields substantially higher estimates ranging from 0.6 to 0.7, averaging 0.64. These results align closely with recent evidence using long time averages over mid-career periods, reinforcing high U.S. intergenerational persistence.

This paper analyzes the implementation of blockchain-based integrity mechanisms in Greek Fiscal Electronic Mechanisms (FEMs) and the central tax information system eSEND. The study examines the cryptographic architecture of fiscal devices, including Electronic Cash Registers, Fiscal Printers, Fiscal Signing Machines, and FEMAS devices, which implement double or triple hash-chain structures to ensure transaction immutability. The transmission protocol between fiscal devices and the central database is also evaluated with respect to encryption, sequential validation, and blockchain verification. In contrast, the architecture of Electronic Invoicing Provider Services and the myDATA central platform is analyzed, highlighting the absence of blockchain-based integrity guarantees. The comparison demonstrates that hardware-based fiscal mechanisms provide stronger guarantees for transaction completeness and tamper resistance than purely software-based invoicing infrastructures. The findings highlight architectural weaknesses in the current e-invoicing framework and propose improvements for ensuring transaction integrity in digital tax ecosystems.

When natural disasters strike, individuals, communities, and even entire countries can suffer. Researchers have studied the impacts of disasters on various factors of interest, from mental health, to poverty, to economic activity. However, the impact of disasters on the nonprofit sector is understudied despite the nonprofit sector's perhaps surprising role in local or national economies as well as its role in disaster response and recovery. Thus, we study the effect of natural disaster damage on different county-level nonprofit outcomes using a panel dataset spanning 1991 to 2021 and causal inference methods tailored to panel data. Contrary to prior work, which found small but positive associations between disaster damage and nonprofit revenue or assets, we find no evidence of a causal effect.

We give an exact randomization-based confidence set for the average treatment effect (ATE) in matched-pair studies with a binary outcome, requiring neither monotonicity nor any distributional assumption beyond the within-pair coin flip. At its core is an analytic solution to the worst-case allocation of attributable effects: two binomial-symmetry lemmas identify the pattern hardest to reject as a single boundary corner, so testing null hypotheses needs no integer program and no numerical search. Inverting the test via binary search yields a prediction set for the attributable effect in O(log S) Binomial tail calculations; the Bonferroni proposition of Rigdon and Hudgens (2015) produces the ATE confidence set at the same computational cost. The same corner extends without further machinery to a sensitivity analysis for matched observational studies under Rosenbaum's $\Gamma$-model. A simple formula for the design sensitivity illuminates when an observational study can hope to provide evidence for an effect.

In the presence of interference, where the treatment assigned to one unit can affect the outcomes of others, many causal estimands depend on the treatment-assignment policy under which the experiment is conducted. This policy dependence creates a fundamental challenge for off-policy estimation, where the goal is to estimate causal quantities under a hypothetical intervention policy different from the one used to collect data. We study this problem of off-policy estimation of causal effects for heterogeneous Bernoulli policies. By representing exposure-weighted potential outcomes in the biased Fourier basis of the experimental design, we construct, for any prespecified Fourier subspace encoding the assumed interference structure, the unique minimum-$L^2$ weight that transports every function in that subspace. Global and local inverse-probability weights, linear-interference weights, and no-interference weights are special cases. The weight variance is a structured chi-square distance between the experiment and target policies. When the assumed interference structure is misspecified, the introduced bias couples the omitted outcome spectrum with the corresponding policy-shift coefficients, yielding a sharp robustness bound and a bias-variance trade-off. A Fourier-neighborhood-overlap condition gives consistency under structured interference, and we state a Doob-martingale central limit theorem for off-policy estimators. As the variance is not identified, we derive identifiable bounds and associated conservative estimators of the variance. Simulations illustrate these theoretical results for the design and analysis of experiments under network interference and design mismatch.

We establish the consistency and asymptotic normality of a two-step estimator of conditional expectiles in the context of conditional scale models. We first estimate the conditional variance parameters by quasi-maximum likelihood and then compute the unconditional expectile of the innovations using the empirical distribution of the standardized residuals. We show how replacing true innovations with standardized residuals affects the asymptotic variances of both conditional and unconditional expectile estimators. Finally, our empirical analysis reveals that conditional expectiles assess tail risk in cryptomarkets in a more robust manner than traditional quantile-based risk measures, such as value at risk and expected shortfall.

To study a scalar parameter, a researcher may consider multiple research designs. Based on the evidence across designs, the researcher may wish to formulate a headline estimate of the parameter. I examine how to choose this headline when it is unclear which design is most appropriate for studying the parameter. I model this setting by assuming that (i) exactly one of the designs is valid for the parameter and (ii) the researcher has ambiguity about which design is valid, represented by a class of priors over the candidate designs. To account for ambiguity, I propose reporting the headline estimate that minimizes the worst-case posterior risk over the class of priors. In three applications, I show cases where accounting for ambiguity materially affects the quantitative conclusion and cases where an existing headline is already close to optimal.

Inference in linear regression commonly treats OLS residuals as proxies for unobserved errors. This approximation can fail when the regression projection is nonlocal relative to the error-dependence structure. Residualization then shifts covariance information across observations and clusters, while conventional heteroskedasticity-consistent (HC) and cluster-robust variance estimators (CRVE) retain only diagonal or within-cluster residual moments and may therefore understate sampling uncertainty. This paper develops a projection-geometry framework for robust variance estimation. The variance of the OLS estimator is represented exactly as a Riesz functional of latent covariance blocks, and observable residual moments are linked to the target through a linear operator determined by the full regression projection. This formulation reduces variance estimation to a linear inverse problem. I propose a Riesz variance estimator that combines within- and cross-cluster residual moments. Conventional HC and CRVE emerge as restricted approximations whose validity depends on negligible projection spillovers. The estimator remains well defined when cluster-specific leverage matrices are singular and is computed by an iterative algorithm that avoids explicit matrix inversion. Simulations show substantial undercoverage by conventional methods under projection spillovers, whereas the proposed estimator restores near-nominal coverage. In an application to colonial governor promotions, the correction changes the significance of four of five reported coefficients.

Policies with a common objective and implementation date may differ in details or context. We distinguish the aggregate average treatment effect on the treated (ATT) from sub-aggregate ATTs defined by implementation cohort, jurisdiction, period, or policy type. UN-DID and DID-INT, two DiD estimators that construct jurisdiction-by-time effects, estimate these ATTs under parallel-trends conditions matched to the aggregation. In CPS placebo-law simulations, randomization inference is generally well-sized, though some jurisdiction-specific tests are conservative. The jackknife can be undefined for sub-aggregate ATTs; when defined, it over-rejects with few treated or comparison jurisdictions. Estimands and inference methods should match the policy question and implementation setting.

Market efficiency relies fundamentally on stable liquidity. Consequently, forecasting liquidity dynamics is a priority for both investors and regulators. We introduce a new tail-risk metric, Illiquidity-at-Risk (IlliQaR), designed to quantify the magnitude of extreme liquidity dry-ups. Relying upon the realized Amihud (a precise illiquidity measurement derived from high-frequency data as the ratio of realized volatility to trading volume) we assess the predictive power of various linear and non-linear econometric models, with a specific focus on the impact of discontinuous jump components. Accounting for these jumps is essential for achieving accurate probability coverage and better IlliQaR predictions during periods of systemic stress, where standard continuous models systematically underestimate the severity of liquidity evaporation. Our empirical analysis, encompassing the S&P 500 index and a cross-section of 25 large U.S. equities, demonstrates that incorporating jumps significantly improves forecasts of illiquidity. Our results suggest that individual stock IlliQaR violations often cluster during periods of S&P 500 liquidity stress. This indicates that Illiquidity at Risk is not just a localized concern but a systemic one, where the main index acts as a leading indicator for extreme dry-ups in individual stock liquidity.

In a network with ramp-limited generators and inaccurate net-demand forecasts, practical rolling-window dispatch can drive locational marginal prices (LMPs) below generators' bid-in offers. In such cases, out-of-market (OOM) settlements are used to compensate generators and maintain dispatch-following incentives, but OOM can have negative consequences, including nontransparent real-time price signals, discriminatory compensation, and incentives for untruthful bidding. This paper presents an optimal uniform pricing rule that minimizes demand payments, eliminates OOM make-whole payments, preserves LMP-based congestion charges, and ensures revenue adequacy. We derive the proposed pricing rule in closed form and relate it to existing pricing schemes. Numerical comparisons demonstrate favorable generator profits and reduced price volatility. However, higher generator profits are accompanied by increased demand payments, reflecting the in-market, uniform allocation of ramping costs while preserving the LMP-based congestion charges widely used in real-time market settlements. The numerical results also show that, under LMP with OOM settlement, a price-taking generator has an incentive to inflate its offer, whereas this incentive is absent under the proposed pricing rule within the tested bid range.

We propose the first manipulation test designed for boundary discontinuity designs (BDDs) with general boundary shapes. A BDD is a multidimensional extension of the regression discontinuity design (RDD) in which treatment assignment is determined by whether the multidimensional running variable crosses a lower-dimensional boundary set. The test avoids multivariate density estimation and builds on the observation that, in the absence of manipulation, observations near the boundary should be approximately evenly split between treatment and control within arbitrary groups defined by their projections onto the boundary. We test this implication using a collection of binomial balance tests on observations near the boundary, with groups formed by k-means clustering. We establish the asymptotic validity of the test under suitable regularity conditions. We also evaluate finite-sample performance through Monte Carlo simulations and illustrate the test in three empirical applications.

Foundation models promise accurate forecasts with little or no task-specific training, but whether they can replace models designed specifically for electricity price forecasting remains unclear. We compare nine variants from five foundation model families, evaluated in zero-shot mode, with two state-of-the-art electricity price forecasting benchmarks in Germany, Poland, and Spain over 2021-2025. Their performance is assessed in terms of point and probabilistic forecasting accuracy, as well as economic value in battery energy storage arbitrage. Only the TabPFN models consistently and significantly outperform the benchmarks across all three markets and all statistical measures. However, this statistical dominance does not translate directly into economic dominance: TabPFN performs best under unlimited bids and riskier quantile-based strategies, whereas the Distributional Deep Neural Network benchmark is more profitable when risk tolerance is lower. Thus, foundation models cannot universally replace market-specific models, and their value depends on both model architecture and the decision problem.

We study identification and estimation of moments of random coefficients in short linear panels, allowing the number of heterogeneous coefficients to exceed the number of equations observed for each unit. Under moment homogeneity, different regressor histories impose restrictions on the same moment vector. We give necessary and sufficient conditions for these restrictions to identify moments of a given order, stated in terms of the row spaces generated by the regressor support. The results show that moments may be identified even when the coefficients cannot be recovered for any individual, and, for two full-row-rank histories, give the exact loss of independent restrictions caused by overlap of their row spaces. When the support condition fails, we establish nonidentification in the maintained model and characterize the sharp identified set implied by these conditional moments. At second order, the identified set is determined by positive-semidefinite covariance restrictions and is also sharp relative to the full joint distribution of outcomes and regressors. Under the support condition, weighted minimum-distance estimators are root-$N$ asymptotically normal; under conditional nondegeneracy, oracle generalized-inverse weighting attains the Chamberlain (1987) efficiency bound for the maintained conditional-moment model.