Papers

In fixed-effect regressions with many groups, fixed effects can absorb most identifying variation, leaving a handful of observations to carry what remains. When variation is this concentrated, conventional $t$-tests can reject a true null more than half the time, and any fixed critical value is either invalid or so conservative it has essentially no power. This paper builds an exact test from the design alone. A nuisance-annihilating contrast is a linear combination of the treatment and fixed-effect dummies that eliminates the fixed effects without touching the outcome; sign-flipping these contrasts is then an exact symmetry of the null distribution at every sample size, under arbitrary heteroskedasticity. In two-way designs — worker-firm, firm-time — these contrasts are exactly the cycles of the bipartite mobility graph, so the movement that identifies the treatment effect is what makes exact inference possible. Exactness costs power: relative to an oracle test, a chosen set of cycles has an observable capture ratio $\kap\in[0,1]$ and standard-error premium $\kap^{-1/2}$, and a packing algorithm resolves the capture-granularity trade-off. In the Grunfeld investment regression (single-observation score concentration $73.9\%$), 32 cycle contrasts capture $\kap=0.627$ of the identifying variation, giving an exact $95\%$ confidence interval of $[0.150,\,0.450]$.

We develop a hierarchical Bayesian panel quantile regression model in which unit-specific coefficient paths are smoothed across quantiles by Gaussian processes, while a common time effect absorbs aggregate shocks. Componentwise-monotone Bernstein polynomials, perturbed by unit-specific deviations, deliver soft noncrossing, and we provide identification conditions together with a bound on the crossing probability. Applying the model to 33 countries over 1979–2023, we find that global temperature shocks generate a systemic, non-diversifiable downside risk to output growth. This risk is concentrated in the lower tail and disproportionately affects emerging markets. Finally, we apply our framework to risk analysis and show that the model reduces out-of-sample tail-risk forecast loss by roughly one-third relative to country-specific quantile regressions.

Estimating the dynamic effects of economic shocks in short and very short samples is impeded by a lack of degrees of freedom. We offer a solution based on a Bayesian hierarchical framework for estimating local projection (LP) impulse response functions across a panel of related time series. The framework explicitly accommodates unbalanced panels in which some series are substantially shorter than others, allowing the short series to borrow information from longer ones at horizons where the short series carry little or no own data. Since series might exhibit heterogeneous dynamics, we develop a sparse finite mixture pool that clusters units by similarity of their impulse response profiles. We show in simulations that our approach substantially improves LP estimation accuracy relative to the standard approach if the time series are short while producing similar LPs for longer time series. Using a US price dataset, augmented with survey responses, we find that supply-chain and oil shocks trigger heterogeneous reactions of different price measures, with headline price indices responding more sharply than their core counterparts and goods prices changing more than services prices.

Formula One outcomes reflect the joint contributions of drivers and constructors, but these contributions are unobserved and vary over time. We propose a Bayesian state-space model that disentangles dynamic driver and constructor abilities using two observed outcomes: fastest qualifying lap times and race rankings. Both outcomes depend jointly on latent driver and constructor states that evolve at the Grand Prix level, while the race equation additionally accounts for starting-grid position. The decomposition is supported by constraints that center the driver and constructor abilities at zero, together with variation in driver-constructor assignments over time. Bayesian inference is performed using the No-U-Turn sampler under weakly informative priors that treat driver and constructor abilities symmetrically. Applying the model to the Formula One hybrid era from 2014 to 2021, we find substantial heterogeneity in both driver and constructor abilities. Driver abilities are generally more stable over time, whereas constructor abilities exhibit greater variation and, for many driver–constructor combinations, contribute more strongly to observed performance.

Credit stress testing requires impulse responses of portfolio default probabilities, not only macro-financial drivers. We derive closed-form generalized impulse responses for the mean, quantiles (PD-at-Risk), and expected shortfall in a modular framework combining a Bayesian VAR, a Gaussian satellite, and the Merton-Vasicek model underlying Basel IRB regulation. Results extend to any probit-Gaussian mapping of a latent factor. Nonlinearity makes responses depend on conditional means and variances; plug-in evaluations understate projected default probability levels by 6-8% and miss tail quantiles. For U.S. geopolitical risk shocks, 99%-quantile responses exceed mean responses by 50%, and peak responses vary 4.6-fold across the credit cycle.

We comment on the optimally-transported generalized method of moments (OTGMM) estimator proposed by Schennach & Starck (2026a) and give counterexamples to Theorems 2-6 under their stated assumptions. First, the assumptions used in the small-error analysis are insufficient for consistency in Theorem 2 and asymptotic normality in Theorem 3. Next, we consider the large-error analysis, in which Theorem 4 states that the OTGMM estimator is equivalent to a GMM estimator with modified moments. We show that in a scalar model, Theorem 4 selects a value that differs from the unique OTGMM minimizer and violates the OTGMM sample moment restriction. In an overidentified model satisfying the assumptions used in Theorems 5 and 6, the first component of the Lagrange multiplier has different probability limits under the OTGMM estimator and the GMM estimator with modified moments. Under misspecification, the population value selected by OTGMM depends on the transport metric and on which variables may be adjusted. We give a sufficient condition under which solutions of the modified moment equations also solve the original constrained problem at a given parameter value, and separate conditions for consistency and asymptotic normality of the OTGMM estimator. We also show that Assumption 16 does not imply the matrix bound used in the supplemental proofs and replace Assumption 16 with a matrix condition that yields the bound.

Objectives: While causal analysis of travel behavior is an emerging field, estimating heterogeneity in mode choice through causal modeling remains unexplored. This study demonstrates the application of a novel causal method, causal forest, to quantify the heterogeneity in travel mode choice shifts caused by the COVID-19 pandemic. Methods: We applied causal forests, a non-parametric causal machine learning method, to 802,935 trip records from the 2017 and 2022 waves of the National Household Travel Survey. The 2017 wave serves as the pre-pandemic control group, while the 2022 wave represents the treatment condition. Within the potential outcomes framework, we estimate average treatment effects (ATE), heterogeneous treatment effects (HTE), and conditional average treatment effects (CATE) across diverse socio-demographic groups and trip characteristics. Findings: Our results reveal an estimated ATE of a 1.86 percentage point (pp) increase in car-mode share, contrasted with decreases of 0.38 pp and 1.57 pp in public transit and walking, respectively. The largest increases in car use appeared for short-distance trips (one mile or less), households with annual incomes exceeding USD 200,000, and female travelers. Novelty: This is one of the first applications of causal forests to travel mode choice, and the first to use causal machine learning to estimate the pandemic's causal effect on mode choice analysis. Practical Applications: This study discusses methodological advantages, inherent assumptions, and limitations of causal forests within the context of transportation planning. This methodology is applied to COVID-19 travel data to illustrate how causal heterogeneity analysis can offer a deeper understanding of changes in mode choice. These insights are valuable for planners and policymakers in making policies related to mode shifts under an intervention.

The set of $n\times n$ correlation matrices, known as the elliptope, has volume decaying at the super-exponential rate $\exp\{-\tfrac14 n^2\log n\}$. We characterize where this vanishing volume concentrates. A uniform draw is entrywise close to the identity yet globally far from it and nearly singular. Its maximum absolute correlation is of order $\sqrt{\log n/n}$, its Frobenius distance is asymptotic to $\sqrt n$, its empirical spectral distribution converges to the Marchenko-Pastur law with ratio one, and its smallest eigenvalue has the exact $\operatorname{Beta}(1,d)$ distribution, where $d=n(n-1)/2$, and is therefore of order $n^{-2}$. Distinct off-diagonal entries are exactly pairwise independent under every $\operatorname{LKJ}(\eta)$ law, which yields a Chen-Stein proof of the extreme-correlation point-process limit for the whole LKJ family and an $O(n^{-1})$ total-variation bound for finite-dimensional exceedance counts relative to Poisson laws with their exact finite-$n$ means. Finally, for a bounded, centered i.i.d. off-diagonal perturbation of any correlation matrix, the nearest-correlation projection removes a fraction of the squared perturbation that tends to one and recovers the original matrix in average squared error per entry.

This paper considers difference-in-differences identification strategies when the parallel trends assumption holds after conditioning on covariates that may themselves be affected by the treatment (often referred to as "bad controls"). We show that common approaches such as simply dropping bad controls are often ill-advised and develop two alternative approaches that allow bad controls to function as genuine controls despite being affected by treatment. First, we derive explicit conditions that rationalize conditioning only on pre-treatment values of the bad control, leading naturally to the Callaway and Sant'Anna (2021) estimator with pre-treatment values as covariates. Second, under a covariate unconfoundedness condition, we develop imputation and double/debiased machine learning estimators that recover the average treatment effect on the treated. We extend these results to staggered treatment adoption, provide pre-tests for the identifying assumptions, and apply the methods to study the effects of job displacement on earnings.

Empirical work often removes fixed effects, latent factors, or high-dimensional controls before estimating structural relationships. These transformations reduce confounding but may also remove identifying variation. We study linear panel IV after one equation-compatible nuisance projection under two-way dependence. The projected Jacobian determines which structural directions remain visible; the projected-score law determines their precision; and, on Gaussian fixed-rank strata, they combine in a Projected Information Matrix. We derive weak-identification limits with dimension-specific information accumulation, feasible factor-transfer conditions, identification-robust tests, bootstrap procedures for non-Gaussian interaction limits, and inference for the projected spectrum, rank, subspaces, and information matrix. Simulations show that a raw first-stage statistic above 500 can support the wrong sign while projected diagnostics reveal weak valid information. In an international monetary application, common projection substantially attenuates apparent foreign-output persistence, while Gaussian-reference Anderson–Rubin sets remain unbounded. Identification should therefore be assessed after nuisance removal.

This paper develops an econometric framework for analysing smooth structural change in cointegrated systems following a known intervention time. We consider a vector error-correction model in which the cointegration rank and the pre-intervention cointegrating structure are identified from a stable pre-intervention subsample. After the intervention, both the adjustment coefficients and the cointegrating vectors are allowed to evolve smoothly as functions of rescaled time, which are estimated using kernel-weighted local reduced-rank methods. The analysis is formulated directly in a cointegrated VAR/VECM system, which preserves the treatment of long-run relations and short-run error-correction dynamics. By working with the decomposition $\Pi(\delta)=\alpha(\delta)\beta(\delta)'$, the method separates changes in the equilibrium relation from those in the speed of adjustment. We also provide two tests for the parameter consistency and the post-intervention parameter smoothness respectively. An empirical application to energy market, foreign-exchange, and gold-market index around the 24 February 2022 Russia's invasion of Ukraine illustrates how the proposed approach distinguishes between a discrete regime shift and smooth post-intervention evolution. The results suggest that cointegrating relation among the price of Brent crude oil, the spot exchange rate (USD/EUR), and the Credit Suisse NASDAQ Gold Price Index has smoothly changed after the outbreak of war, instead of a constant long-run conintegration system in the pre-intervention period.

We develop a fully nonlinear structural vector autoregressive framework in which the contemporaneous structural mapping may be nonlinear and non-additive. Identification is achieved by exploiting variation in the conditional distributions of the mutually independent structural shocks induced by an observed exogenous variable. Specifically, a general contrastive learning framework that makes use of this variation together with the assumed exponential-family structure is employed to recover the shocks. Existing independent innovation analysis results identify such shocks only up to arbitrary componentwise invertible transformations, which is generally insufficient for structural econometric analysis. We strengthen this result by imposing a structured exponential-family specification for the conditional shock distributions. With the imposed sufficient statistics, the remaining ambiguity is reduced to a one-parameter transformed-scale map for each shock. We then show that, under a logistic specification used for the natural parameters, the identification is further strengthened up to permutation and componentwise sign changes. Once the shocks have been recovered, the fully nonlinear structural vector autoregression can be estimated using feed-forward neural networks, motivated by their universal approximation capabilities. The empirical application studies asymmetries in the responses of U.S. industrial production to the real oil price shock. We find modest asymmetries with respect to the sign of the shock and state of the economy. The accompanying R package iiasvar implements the introduced methods.

Recursive nonlinear impulse responses require an estimated innovation law whenever the impact shock is normalized by innovation ranks and future innovations are integrated out. The closest semiparametric recursive construction in the literature estimates the relevant innovation quantile functions smoothly and discusses a direct empirical-residual implementation without developing its complete first-order inference theory. We tackle this gap in a finite-dimensional nonlinear structural autoregression with unrestricted continuous marginal innovation distributions and a fixed normal-rank shock. Our estimator replaces each innovation quantile function with the empirical quantile of generated structural residuals and iterates the same structural transition. For any fixed collection of responses, we establish a joint \sqrt{T} asymptotic linear representation with four components: direct transition estimation, the effect of transition estimation on residual order statistics, ordinary innovation-quantile estimation, and the shifted impact quantile. After projection through the recursion, the quantile terms admit a residual-rank-and-spacing representation, yielding feasible inference without innovation-density estimation or quantile smoothing. We then characterize the propagated bias from smoothing, establish validity of a full recursive residual bootstrap, and derive the additional covariance contribution from a finite number of simulated paths, providing bandwidth-free inference for the empirical-residual version of the same normal-rank response used in the smooth recursive construction.

Prediction-based methods, including Large Language Models (LLMs) and other machine learning techniques, are often used to construct measures of political phenomena that are difficult to quantify directly, such as policy positions in manifestos or emotions expressed on social media. In many applications, these prediction-generated measures are used as explanatory variables in regression models, even though they are measured with error. This leads to biased estimates. In this paper, we propose a simple solution to these biases: instrumental variables constructed from multiple measures created on independent splits of the original data. This approach is theoretically valid, easy to implement, and does not require new data. Through simulations, we show that this approach recovers estimates close to the true values, even in relatively small samples, while the standard approach can produce substantial bias in practice. We illustrate the method by revisiting two applications: whether gendered speech affects legislative outcomes in the German Parliament, and whether political risk influences poverty alleviation programs in China.

We present a simple Gaussian approximation to the finite-sample distribution of the classical ridge regression estimator. Our approximation captures the fact that, in finite samples, the ridge regression estimator trades off bias and variance to reduce estimation and prediction error. Our approximation is based on nonstandard asymptotics where $i)$ we let the estimator's regularization parameter grow proportionally to the sample size; and $ii)$ we treat the population regression coefficients as local to the reference vector that defines the estimator's direction of shrinkage. In contrast to other asymptotic approximations in the literature, we allow for general forms of heteroskedasticity and autocorrelation in the data generating process (at the cost of considering a low-dimensional model where the number of covariates is not allowed to grow with the sample size). We use our simple Gaussian approximation to propose two new strategies to select the regularization parameter for the ridge regression estimator. The suggested strategies select the regularization parameter to minimize either average or worst-case excess prediction risk, where risk is computed using our suggested Gaussian approximation.

Agentic AI is gaining acceptance in asset management, but governance has not kept pace: 88% of surveyed finance professionals report no operational governance framework for agentic AI, and only 24 of 75 large U.S. money managers disclosing AI use in Form ADV filings report a formal governance policy. We argue this gap is architectural: governance built for static validation does not survive continuously retrained agentic policies. We propose a four-layer framework (Policy, Engineering, Composition, Systemic) grounded in two distinct kinds of evidence, kept explicitly separate: two calibrated synthetic illustrations (a regret-covariance drift monitor; a crowding simulation showing joint drawdown risk rising from 39.2% to 79.3%), and three real, documented cases (a deployed LLM-embedding trading strategy, a \$45 billion discretionary fund's forced-deleveraging blowup, and a tribunal ruling holding an airline liable for its chatbot). The synthetic examples demonstrate computability from observable data; the cases demonstrate that the failure modes are not hypothetical. We provide a 90-day implementation sequence spanning trading and payments/customer-facing systems.

Modern economic panel data sets are often high-dimensional: they contain information on a wide variety of control variables whose number may even exceed the sample size. Nevertheless, the literature on econometric methods for high-dimensional panels is quite limited. In this paper, we study high-dimensional panel models with interactive fixed effects where the regression function has an additive structure, i.e., each covariate enters the model via an unknown nonlinear component function. We develop estimation methodology and theory in this additive framework which substantially extends previous work on the high-dimensional linear case by Ruecker et al. (2025). In the theoretical part of the paper, we derive the convergence rate of our estimator for both the small-T and the large-T panel case. The theory is complemented by comprehensive Monte Carlo experiments and an empirical application.