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on Econometrics |
| By: | Supriya Tiwari; Pallavi Basu |
| Abstract: | Analysis of experimental data becomes challenging when the underlying population is connected by a network. Exposure mapping is a common tool in the literature for defining and estimating spillover effects. These mappings reduce the dimensionality of the estimand, thereby facilitating identifiability. It is assumed that this mapping is correctly specified, leaving the choice of the exposure mapping to the analyst. This makes estimators of the spillover effect, such as the Horvitz-Thompson estimator, vulnerable to bias from model misspecification. Although these estimators have been shown to be robust to certain forms of controlled misspecification, there has been relatively little methodological progress in empirically investigating appropriate exposure mappings. In this paper, we propose a novel design-based model specification framework for causal inference. Building on this, we develop a randomization-testing procedure to assess the correct specification of an exposure-mapping model in the presence of network interference. We provide theoretical guarantees for the asymptotic validity of the proposed testing procedure. We establish the favorable power properties of our method through an extensive simulation study and illustrate it in a field experiment investigating the effect of anti-conflict norms among adolescents. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.22890 |
| By: | Patrick Kline |
| Abstract: | Econometric models offer parsimonious but inexact approximations to data-generating processes. This paper studies the generalized method of moments (GMM) when exchangeable specification errors of order $n^{-1/2}$ contaminate the moment conditions. I develop estimators for the mean and variance of these specification errors, establishing their consistency in an asymptotic framework where the number of overidentifying restrictions grows with the sample size. These hyperparameter estimates are used to develop a feasible bias-corrected estimator of target parameters. I also propose an empirical Bayes estimator that weakly improves precision by subtracting a best linear predictor of the first-order estimation error from the bias-corrected estimator. Using a combinatorial central limit theorem, I establish asymptotic normality of both estimators and provide variance estimators that enable misspecification-aware frequentist inference. Simulation exercises indicate the procedures can meaningfully improve on standard two-stage least squares estimation when exclusion violations are present. Revisiting the influential study of Angrist and Krueger (1991), I consider an instrument set where exchangeable excludability violations are plausible. Repairing the two-stage least squares estimates of the returns to schooling moves them in the direction of ordinary least squares and reduces sensitivity to the specification of controls. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.23925 |
| By: | Lisa Leimenstoll; Melanie Schienle |
| Abstract: | Understanding the propagation of extreme events is important in many economic and environmental applications, yet most econometric methods for causal inference focus on average effects rather than tail behavior. This paper studies the identification of causal relations in extremes and derives resulting estimators and their asymptotic inference. As measure of causal dependence between extreme realizations of variables, we analyze the asymptotic behavior of the Causal Tail Coefficient (CTC) within a linear structural causal model with heavy-tailed regularly varying innovations. In contrast to the existing literature, we allow the variables in the system to exhibit heterogeneous tail indices and consider the presence of potentially heavy-tailed confounders. We derive theoretical results assessing the limiting behavior of the CTC under these conditions and show how differences in tail behavior can help to reach identification of the causal structure. Light-tailed confounders are asymptotically negligible, but sufficiently heavy-tailed confounders can induce extremal dependence patterns that are observationally indistinguishable from direct causal effects. When suitable proxy information is available, identification can be recovered using an adjusted Causal Tail Coefficient. Based on these results, we develop estimation and inference procedures for causal relations in extremes under general conditions. We establish asymptotic properties of the proposed estimators and derive tests for the causal direction and heavy-tailed confounding. Simulation evidence examines their finite-sample performance and provides guidance on their implementation. Applications to climate and financial extremes illustrate how the proposed methods can uncover causal relations that may remain undetected by approaches targeting average dependence. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.22957 |
| By: | Kyunghoon Ban; Zhengrun Chen; D\'esir\'e K\'edagni |
| Abstract: | We study difference-in-differences (DiD) designs in which a binary treatment changes an endogenous time-varying (continuous, discrete, or mixed) mediator that in turn affects an outcome. Under our model assumptions, we show that the usual DiD estimand mixes the average direct effect on the treated, the average indirect effect, and a trend bias term. A two-way fixed effects (TWFE) regression that controls for the mediator does not recover the average direct treatment effect on the treated. We show that a DiD estimand conditional on the observed mediator path identifies the conditional average direct effect for treated units at that path, and that averaging over the treated path distribution identifies the average direct effect even when unconditional parallel trends fails. A stable average mediator effect assumption helps recover the average mediator and indirect effects. The framework extends to multivariate mediators, nonlinear DiD, and multiple treatment periods settings. Existing doubly robust estimators can be used to conduct inference. Revisiting the effects of railroad access on agricultural land values, the specification yields a positive direct component not mediated by measured market access, while the corresponding indirect component is small and imprecise. A TWFE benchmark with the same sample and baseline geographic covariates gives a small, imprecise direct coefficient, whereas the original-control TWFE coefficient reverses sign. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.18375 |
| By: | Margherita Comola; Camila Comunello; Abhimanyu Gupta |
| Abstract: | Cross-unit dependence is pervasive in empirical applications and complicates econometric inference, especially when spillovers operate in nonlinear ways. We propose a novel nonparametric test for cross-unit spillovers that may operate through peers' attributes, peers' outcomes, or both. The test is straightforward to implement, as it requires only estimation under the null hypothesis of no cross-unit spillovers, and is shown to have a convenient asymptotic standard normal distribution. It is also versatile, accommodating data generated by a wide range of interaction structures. We present four empirical illustrations showing that the proposed test can yield substantively different conclusions about the presence of cross-unit spillovers than existing approaches. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.00136 |
| By: | Justus Holman (Vrije Universiteit Amsterdam); Yicong Lin (Vrije Universiteit Amsterdam); Andre Lucas (Vrije Universiteit Amsterdam); Anne Opschoor (Vrije Universiteit Amsterdam) |
| Abstract: | We introduce the Dynamic Spectral Rotation (DSR) model, allowing for dynamics in both eigenvalues and eigenvectors of time-varying conditional covariance matrices. The construction preserves orthonormality of the entire eigenvector matrix at every point in time. We study the model’s asymptotic properties and establish unique identification of all static parameters governing the joint dynamics of eigenvalues and eigenvectors. Notably, the parameters that determine the dynamic rotation angles remain uniquely identified under mild conditions even when the rotation angles are allowed to evolve over ranges far beyond intervals of length π. In an empirical application to US equity returns, we show that allowing the leading eigendirection of the covariance matrix to vary over time significantly improves the predicted portfolio covariance structure compared to a model in which all eigendirections are held fixed. |
| JEL: | C32 C53 C58 |
| Date: | 2026–08–28 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20260060 |
| By: | Justus Holman (Vrije Universiteit Amsterdam); Andre Lucas (Vrije Universiteit Amsterdam); Anne Opschoor (Vrije Universiteit Amsterdam) |
| Abstract: | We propose a new model for realized covariance matrix dynamics using a composite of univariate time series models for its realized eigenvalues, linked by a copula function. The dynamics of each eigenvalue are based on a conditional F distribution, thus allowing for fat-tailedness and outliers in the realized covariance matrices. Given its composition from univariate elements, the static parameters of the new model can be estimated efficiently by maximum likelihood. In an empirical application, we show that the new model outperforms relevant recent benchmarks in an extensive portfolio (Conditional) Volatility-at-Risk (VolaR) application. |
| JEL: | C22 C32 C58 |
| Date: | 2026–08–28 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20260061 |
| By: | Simon He{\ss}; Patrick W. Schmidt |
| Abstract: | Pairwise randomization can yield substantial efficiency gains in experiments. Yet methodological guidance cautions against pairwise randomization, especially in settings with attrition, partly because common practices for estimation (i.e., pair fixed effects) imply discarding data from incomplete pairs thus exacerbating data loss from attrition. This practice of dropping incomplete pairs reduces statistical power of tests as well as precision of estimates, in paired experiments, compared to designs with less finely stratified treatment assignment. We argue that this concern is misplaced if attrition is independent of treatment status and potential outcomes, and that these issues follow from an inefficient use of the data that remains post-attrition. First, we show how, by using a specific permutation test, it is possible to use all observed units for inference (complete pairs and incomplete pairs where one unit attrits) while still exploiting the pairwise randomization design structure. The test procedure we suggest provides exact size control under the sharp null. Second, we study an optimally weighted estimator that efficiently combines within-pair and across-pair comparisons. Finally, we show that combining these two insights yields a test procedure that dominates the two commonly used inference methods (a paired $t$-test and the two-sample $t$-test) in power, for any level of attrition. Usefully for applied researchers, we show that the efficient procedure can be implemented via a weighted fixed effects regression, straightforward in standard software. In sum, our results provide researchers with practical tools for conducting experiments with pairwise randomization without sacrificing observations or statistical power when facing independent attrition. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.18973 |
| By: | Jieun Lee |
| Abstract: | Spatial autoregressive inference is typically conditional on the spatial weights matrix, W, even though the underlying interaction structure is often unknown and empirical conclusions can be sensitive to its specification. This paper develops double/debiased machine learning inference for low-dimensional SAR parameters when the spatial interaction operator is learned flexibly from potentially endogenous characteristics. Within a maintained admissible support, interaction strength is generated by an unknown function of geographic and socioeconomic characteristics, making inference robust to functional form specification of the weights within that support. Endogeneity in the characteristics generating W is addressed through a nonlinear control function based on locally relevant first-stage residual information. Because the learned operator enters both the spatial lag and spatially transformed instruments, treating the estimated W as known generally leaves a first-order generated-W effect. I construct an operator-orthogonal SAR-IV/GMM score that removes this leading sensitivity and combine it with buffered spatial cross-fitting that separates evaluation-score footprints from nuisance-training observations. Under near epoch dependence on a spatially mixing innovation field and target-relevant nuisance rate and regularity conditions, the estimator is asymptotically linear and root-n normal. Monte Carlo simulations show improved finite-sample inference relative to nonorthogonal alternatives when the interaction function is misspecified, weight generating characteristics are endogenous, and observations are spatially dependent. In a U.S. application, diabetes estimates vary with the choice of W, showing the sensitivity of SAR inference to the interaction structure. Even for the same learned W, results differ across inferential methods, highlighting the importance of inference when W is learned. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.22706 |
| By: | Zequn Jin; Gaoqian Xu; Zixin Yang; Zhengyu Zhang |
| Abstract: | This paper studies quantile treatment and spillover effects in network experiments. Average spillover effects reveal how treating a unit's neighbors affects its outcome on average, but mask the heterogeneity of these effects across the outcome distribution. We define structural quantile effects that compare outcome quantiles between exposure states, characterizing how own treatment and exposure to treated neighbors affect different parts of the outcome distribution. Building on \citet{leung2020treatment}, we first establish the weak convergence of the estimated quantile-effect process under conditions requiring the stabilization of the degree distribution and the network-dependent covariance structure. Our main contribution is to propose uniform confidence bands (UCBs) based on Gaussian approximations conditional on the realized network, avoiding these stabilization requirements. The proposed method is evaluated through extensive simulation studies and an empirical application to a randomized savings-account experiment in Nepal \citep{prina2015banking}. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.22286 |
| By: | Yicong Lin (Vrije Universiteit Amsterdam) |
| Abstract: | We develop confidence sets for the date of a single mean break in functional data when the break may be too weak to be consistently detected. Under each maintained null, segmentwise demeaning removes the unknown mean and break functions, so valid inference does not require consistent detection of the break. We select among invariant tests by maximizing their weighted average local power over alternative break dates and directions. In infinite dimensions, the resulting covariance perturbation can render the null and alternative measures mutually singular, causing the usual likelihood-based derivation of a test that maximizes weighted average power to break down. We characterize the weights under which likelihood-based comparison remains valid and show that covariance-squared weighting yields a simple locally best invariant statistic. Under mild conditions, we establish the asymptotic validity of the procedure and characterize its local power under weak breaks. Simulations show that the resulting confidence sets achieve accurate empirical coverage, whereas a competing interval designed for consistently detectable breaks exhibits severe undercoverage when the break magnitude is small. |
| Keywords: | confidence set, functional data, infinite dimensional inference, locally best invariant test, weak mean break |
| JEL: | C12 |
| Date: | 2026–08–11 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20260055 |
| By: | Guilherme Vianna |
| Abstract: | 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. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.02943 |
| By: | Max Cytrynbaum |
| Abstract: | We study how fast experimental designs can approach the semiparametric efficiency bound in finite samples, as measured by the excess variance of unadjusted treatment effect estimation. We prove an impossibility theorem: under weak conditions, no design can approach the variance bound uniformly over smooth outcome models unless covariate dimension $d \ll \log n$. Even in experiments with thousands of units, this permits only a handful of covariates. Motivated by this, we propose new designs based on discrepancy minimization that instead attempt to control imbalances over restricted-complexity nonparametric function classes. Such designs achieve fast rates to their corresponding restricted efficiency targets, permitting $d \ll n$ covariates in an additive nonparametric specification. They can also be combined with matching to protect against unmodeled outcome variation. In simulations calibrated to 12 published experiments, our designs reduce variance relative to matched pairs randomization in every empirical setting. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.18057 |
| By: | Junting Duan; Markus Pelger |
| Abstract: | Empirical researchers increasingly use large language models (LLMs) to extract structured features, such as sentiment scores, classifications, and expectations, from unstructured data and treat these generated features as observed covariates in downstream estimation. This practice can invalidate inference when systematic, input-dependent errors in generated features, such as hallucination and look-ahead bias, distort the downstream moment conditions. Even after correction, generated features remain noisy proxies whose error profiles differ across models and prompts. We introduce AI-Powered Inference (AI-PI), a method-of-moments framework for valid and efficient inference that combines three components: a moment-specific bias correction based on a small human-labeled calibration set; adaptive weights that optimally combine multiple model-prompt pairs; and an optimal calibration-set design that concentrates costly human labels where the generated features are least reliable. We establish consistency and asymptotic normality of the AI-PI estimator, allowing for data-adaptive labeling designs, cross-fitted LLM-pipeline tuning, and overidentified GMM. Simulations confirm substantial gains over naive LLM regressions and over debiasing without optimal weighting or labeling design. In an application to news-based sentiment and stock returns, AI-PI produces stable conclusions where naive analyses vary substantially across LLM and prompt choices, with a confidence interval roughly half as long as using the human-labeled data alone. |
| JEL: | C10 C13 C50 C55 C80 G12 |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:35481 |
| By: | Grigory Franguridi; Arie Kapteyn |
| Abstract: | In panels with sample selection (that may occur due to attrition, nonresponse, etc.), the assumption of selection on observables (missing at random, MAR) is commonly imposed despite often being implausible. However, this assumption becomes testable when a refreshment sample is available. We develop a statistical test of MAR based on a distance between two estimated distributions: one obtained using the standard inverse probability weighting (IPW) that is valid under MAR and the other obtained using an alternative weighting that is valid under a weaker assumption of additive nonignorability of Hirano et al. (2001). This test implicitly compares the distribution of the IPW-weighted sample in the attrition period with the distribution of the refreshment sample, which coincide if the MAR assumption holds. We establish that, when the input distributions are parametric, our test statistic converges to the generalized chi-squared distribution under the null of MAR. This limit distribution can be estimated using the recursive formulas derived by Franguridi et al. (2026). We illustrate the performance of our test in Monte Carlo simulations. Finally, we apply our test to an empirical example using a subsample of the Understanding America Study (UAS) dataset. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.23508 |
| By: | Stanis{\l}aw M. S. Halkiewicz |
| Abstract: | In saturated fixed-effects regressions, Gaussian inference depends not on total identifying variation but on its concentration, measured by the self-normalized leverage $\lambda_n$ of the residualized treatment. When finitely many score weights remain persistent, the $t$-statistic converges to a convolution of raw errors and a Gaussian component. At full concentration, its null distribution varies across symmetric error laws with equal variance, so no fixed critical value is uniformly valid. We instead construct nuisance-annihilating contrasts from the design alone. These eliminate the fixed effects identically and yield finite-sample exact sign-flip inference under symmetric, arbitrarily heteroskedastic errors, with no homogeneity assumptions or restrictions on the fixed-effect dimension. In two-way designs, admissible contrasts form the cycle space of the observation multigraph. Their efficiency is summarized by an observable capture ratio $\kappa$, which equals Pitman efficiency. The resulting design problem involves a capture--granularity trade-off: coarse supports maximize capture but reduce the number of randomization signs. Cycle packing provides sufficiently granular supports. On matched employer--employee data, a structure-exploiting algorithm achieves $\kappa \approx 0.51$, compared with $0.26$ for naive packing. In the Grunfeld investment regression, realized score concentration is $0.739$, corresponding to $N_{\mathrm{eff}}^{\mathrm{score}}=1.80$, while $32$ valid supports attain $\kappa=0.627$. The resulting exact $95%$ confidence interval is $[0.150, 0.450]$. A worker--firm application demonstrates scalability to large networks. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.04839 |
| By: | Yann Bramoull\'e; Sebastiaan Maes |
| Abstract: | In many practical applications, only noisy proxies for the true regressors are available, which is commonly believed to induce an attenuation bias. In the linear-in-means model, however, estimated peer effects might be inflated, potentially leading to false positives. This paper shows that the asymptotic bias depends on the interplay between individual characteristics and network links and demonstrates how the network structure can facilitate identification without the need for additional external information. Based on these identification results, we present consistent GMM and 2SLS estimators that are easily implementable. Our results are illustrated by means of a Monte Carlo simulation. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.00336 |
| By: | Niko Hauzenberger; Michael Pfarrhofer |
| Abstract: | We develop fast methods for conditional forecasting and structural scenario analysis with high-dimensional Bayesian vector autoregressions (VARs). Our general framework features a factor structure on the reduced-form errors, which enables fast and order-invariant equation-by-equation estimation; suitably identified factors admit a structural interpretation. The scenarios are defined through separate distributional restrictions on observables, structural shocks and idiosyncratic components. The computational cost of our proposed algorithm is cubic only in the number of restrictions, while the dimension of the forecasted system enters linearly. In our application with $33$ macroeconomic and financial variables and ten set-identified structural shocks for the US, we compute counterfactual predictions for oil price scenarios in the context of the 2026 closure of the Strait of Hormuz. The same oil price path is consistent with outcomes ranging from a mostly benign episode to pronounced stagflation, depending on which structural and idiosyncratic shocks are allowed to deliver it. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.29215 |
| By: | Savi Virolainen |
| Abstract: | 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. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.03486 |
| By: | Michael P. Keane; Timothy Neal; Patrick Vu |
| Abstract: | In instrumental-variable (IV) studies, researchers often evaluate multiple candidate instruments and selectively report the specification with the most favorable first- or second-stage statistics. We show that this form of instrument selection (“instrument-hacking”) induces median bias in IV estimators toward the OLS estimand, undermining the rationale for using IV. When all candidate instruments have the same true strength, median bias increases monotonically with the number of available instruments. More generally, when candidate instruments differ in true strength, monotonicity need not hold because increasing the number of instruments can lead researchers to select genuinely stronger instruments. Nonetheless, in simulations calibrated to the empirical distribution of instrument strengths in the IV literature, median bias increases monotonically with the number of available instruments. Furthermore, it is substantial in magnitude, even when only a few instruments are available. |
| JEL: | C26 |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:35633 |
| By: | Masahiro Tanaka |
| Abstract: | Moment restrictions provide a flexible basis for quasi-Bayesian inference when a full likelihood is unavailable, but the weighting matrix in a quadratic moment criterion determines both the relative importance of the moments and the information scale of posterior updating. We propose curvature-calibrated quasi-Bayesian updating, which uses the inverse of the covariance (or long-run covariance) of the moment conditions evaluated at a self-consistent quasi-posterior center. The resulting fixed-point procedure alternates between covariance estimation and simulation from a fixed-weight quasi-posterior, thereby avoiding parameter-dependent weighting during each simulation run. Under a Bernstein-von Mises condition for the fixed-weight quasi-posterior at the efficient population weight, we show that the calibration map is locally contractive, that its fixed point is consistent at the standard parametric rate, and that the Gaussian approximation continues to hold under the calibrated data-dependent weight, with covariance given by the inverse Godambe information matrix. Under a uniform fourth-moment condition, the scaled quasi-posterior covariance converges to the same matrix, so quasi-posterior and repeated-sampling uncertainty agree to first order. Simulations show improved covariance calibration and interval coverage after a few updates. An application to longitudinal binary-response data illustrates the method with within-subject dependence and overidentified residual moments. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.19634 |
| By: | Marko Mlikota |
| Abstract: | I consider an AR($p$) process that is observed every $q$ periods, either as a snapshot (stock variable) or as a sum over the sampling interval (flow variable). Under fairly mild assumptions, I derive the identified set for general lag lengths $p \in \mathbb{N}$ and sampling frequencies $q \in \mathbb{N}$, I bound its cardinality, and I provide a recipe to compute all candidate points and determine their membership in the identified set. My analysis supports the following conjecture: (i) the error term-variance is point-identified, (ii) under temporal aggregation, the autoregressive parameters are point-identified, and (iii) under discrete sampling they are point-identified for odd sampling frequencies and identified up to alternating sign for even sampling frequencies. I prove this conjecture in some settings and verify it numerically more broadly. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.13224 |
| By: | Jushan Bai; Jesse Chieh Chen |
| Abstract: | We study a dynamic spatial panel model with observed regressors, interactive effects, and contemporaneous and lagged dependence in a large-$N$, fixed-$T$ framework. The spatial model constitutes an $N$-dimensional simultaneous-equations system. In this $N$-equation view, the interactive effects introduce $N$ unit-specific loading vectors. Estimating them individually when $T$ is fixed creates the type of incidental-parameters problem underlying Nickell bias. We use the $N$-equation view to account for spatial simultaneity through the spatial Jacobian. Crucially, however, we view the same model as a $T$-equation system with $N$ observations. Together with a spatially enriched random-loadings (SERL) specification, this $T$-equation view yields a quasi-likelihood without unit-specific incidental parameters. We propose a computationally tractable block-coordinate algorithm. Simulations show small estimation errors and generally near-nominal coverage probabilities. Applying the method to U.S. county female labor-force participation, we find substantial dynamic and spatial dependence and an important role for education in explaining the rise in female labor-force participation. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.22499 |
| By: | Brent R. Hickman; John A. List; Ian Muir; Gregory K. Sun |
| Abstract: | We study identification and optimal policy design in a broad class of principal-agent models. We show that the most common empirical framework within the literature is equivalent to an unstructured potential-outcomes model augmented with three specific assumptions: the Law of Demand (LoD), or treatment-effect monotonicity; extrapolative model structure (EMS), which rules out lumpy agent responses to price changes; and rank invariance (RI), which restricts unobserved heterogeneity (UH) to be one-dimensional. This decomposition isolates the identifying content of each assumption and clarifies its economic role. The LoD and MS are empirically testable using exogenous price variation; RI, on the other hand, is a strong assumption ruling out many economically plausible behaviors, and also not empirically testable. We derive sharp bounds on counterfactual outcomes when RI is relaxed. The conventional 1-dimensional model delivers an upper bound on planner objectives, while the lower bound, which allows for arbitrary multi-dimensional UH, has an adversarial interpretation for policy design. We estimate empirical bounds and apply them to nonlinear pricing of rideshare services. The resulting robust pricing policy fully insures against worst-case latent selection while preserving most of the profit and consumer-surplus gains predicted by the conventional model. Our framework provides a tractable approach to robust policy design in adverse-selection settings including Mirrleesian taxation, regulation, labor supply, and procurement. |
| JEL: | B4 C14 C51 C52 C93 D04 J2 L1 L5 |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:35547 |
| By: | Pranjal Rawat; John Rust |
| Abstract: | This article surveys two deeply connected literatures that approach the same fundamental problem from different disciplinary traditions: dynamic discrete choice (DDC) in structural econometrics and inverse reinforcement learning (IRL) in machine learning. Both seek to infer the preferences of decision makers from observed sequential behavior, assuming that individuals act to maximize an expected reward function within a dynamic, uncertain environment formalized as a Markov decision process (MDP). Despite independent origins, the two fields have converged on similar mathematical formulations. We show that the (soft Q-learning) framework now prevalent in IRL is closely related to DDC models under additive extreme value preference shocks, yielding the same softmax (multinomial logit) choice probabilities and smooth Bellman equations that underpin structural estimation in economics. We compare the estimation and computational methods developed in each field. DDC has emphasized maximum likelihood estimation, conditional choice probability estimators, and policy iteration methods. IRL has developed scalable alternatives, including maximum entropy methods, adversarial approaches, and model-free temporal difference estimators that extend to high-dimensional state spaces using deep neural networks. Model-free IRL estimators that combine temporal difference learning with classical two-step methods from econometrics represent a promising direction for bridging the two literatures. Both fields confront shared foundational challenges: the identification problem, whereby multiple reward functions can rationalize the same observed behavior, and the curse of dimensionality in solving the underlying MDP. We believe that cross-fertilization offers substantial opportunities for methodological progress in both fields. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.24362 |
| By: | Stanis{\l}aw M. S. Halkiewicz |
| Abstract: | Fixed-effect saturation alone is not weak identification: in the baseline model, fixed-effect--residualized OLS is unbiased and conventional inference is asymptotically exact for every residual treatment variance $\tau^2=nQ_K>0$. Classical measurement error in the treatment restores it, and we derive Stock--Yogo-style critical values for $\tau^2$. Under the local drift $\sigma_\nu^2 = c^2/n$, attenuation produces a non-central limit whose non-centrality $\eta$ decreases in $\tau^2$ and, under a treatment-balance condition, depends on the fixed-effect dimension $\rho$ only through an overall $\sqrt{1-\rho}$ scaling, leaving the within reliability $\rho$-free. Inverting the leading quadratic size distortion gives a closed-form threshold; the breakdown reliability has a fixed-point form in the reported $t$-statistic alone. The diagnostic needs only a lower bound on reliability, where bias correction needs a point estimate. We separate a descriptive \emph{point pass} from a \emph{formal certificate}, evaluated at an upper confidence bound and carrying false-certification probability at most $\gamma$. A cluster-level score CLT and Arellano-variance consistency under a checkable projection-compatibility condition yield $\eta_{CR}=\eta/\sqrt{\psi}$. Simulations confirm the threshold; in a saturated democracy--growth panel, aggregate V-Dem polyarchy is certified at $\gamma=0.05$ while its judicial-constraints sub-index is flagged under i.i.d.\ and clustered errors. The diagnostic covers classical error in a continuous regressor, \emph{not} binary-treatment misclassification. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.06053 |
| By: | Andrew C. Eggers; Zikai Li |
| Abstract: | Social scientists rely on hypothesis testing to support their research conclusions, but the standard tests are designed for testing one hypothesis rather than adjudicating between rival possibilities. We develop a new framework, "classification testing", as an alternative. Instead of selecting one hypothesis to test, a researcher conducting a classification test decides what qualitative distinctions ("classes") are most substantively relevant; the test either assigns the estimand to a class with error control similar to that of a conventional hypothesis test, or declares the result inconclusive. We argue that classification testing is superior to current practice not just when the objective is to adjudicate between rival possibilities but also when there is one research hypothesis to be tested, because classification testing exposes that hypothesis to refutation. We illustrate the framework by applying it to a well-known media experiment and offer an R package to aid in implementation. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.23315 |
| By: | Frederik Bjerg Krabbe |
| Abstract: | In this paper, we study causal non-causal state space models to model time series characterised by a local explosive increase followed by a sharp decrease such as stock prices. To motivate the use of causal non-causal state space models, we show that the causal non-causal convolution autoregressive model introduced by Gourieroux and Zakoian (2017) can be consistent with the rational expectations stock price model. As in a causal state space model, a central question is how to perform state and parameter inference in the causal non-causal state space model, which we discuss in the paper. We also study the causal non-causal convolution autoregressive model in more detail, providing some new results for the model. To illustrate the usefulness of causal non-causal state space models, we use the causal non-causal convolution autoregressive model to estimate the size of the dot-com bubble in both real time and a posteriori with the stable non-causal autoregressive model considered also by Gourieroux and Zakoian (2017) as a benchmark. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.28115 |
| By: | Michael Dueker; Inés Kishkill; Martín Sola |
| Abstract: | We study the extraction of a common European business cycle from quarterly GDP growth when countries need not provide equally informative signals about the contemporaneous common regime. We show that the usual signal-extraction argument for enlarging a cross section can fail when country-specific regime behavior is imperfectly aligned: additional observations may then weaken rather than strengthen common-state identification. Motivated by this result, we develop a Markov-switching Seemingly Unrelated Regressions (MS–SUR) model with an endogenous positive-definite crosssectional weighting structure. The model distinguishes the informational influence of each economy in identifying the common regime from the strength of its cross-sectional commonality. A separate Markov process governs the innovation covariance matrix, allowing changes in the volatility environment to be separated from the weighting mechanism. Empirically, alternative treatments of the cross section generate materially different common-cycle signals, with the largest differences arising during periods of pronounced cross-country heterogeneity. The endogenous specification assigns approximately 95 percent of the posterior informational weight to Germany and the Netherlands, while the estimated commonality loadings produce a substantially different cross-country ranking. These results show that common-regime inference depends not only on the amount of cross-sectional information available, but also on which observations are most informative about the latent state. |
| Keywords: | EuropeanBusiness Cycle, Markov switching, Endogenous weighting, Bayesian estimation. |
| JEL: | C11 C32 E32 |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:udt:wpecon:2026_05 |
| By: | Joshua C. C. Chan |
| Abstract: | Rejection sampling requires a proposal that dominates the target by a known constant, generally unavailable for non-Gaussian state space models. We construct such a proposal for the latent state path, yielding independent exact smoothing draws and an unbiased likelihood estimator whose relative variance is at most $1/p-1$ per draw at acceptance probability $p$. The method covers scalar states with affine Gaussian dynamics and log-concave observation densities, including multivariate observations. Transition twisting makes the log target-to-proposal ratio separable, and tangent-line twists make each term nonpositive, producing an attained, sharp dominating constant. With a companding node placement, the accumulated envelope error is $O(T/G^2)$ for a sample of length $T$ with $G$ nodes per date, so $G\propto\sqrt{T}$ keeps acceptance bounded away from zero; for stochastic volatility, the required conditions hold almost surely. A simpler mode-centered grid shows the same scaling empirically. At $T=2{, }000$, acceptance is $75\%$, versus roughly $10^{-16}$ for the Gaussian envelope. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.21619 |
| By: | Vahid Moghani (Erasmus University Rotterdam) |
| Abstract: | Mover-design event studies are a leading approach to separating place effects from sorting. The coefficient is often interpreted as the share of cross-sectional variation in location means due to places. I show the coefficient depends on how movers connect locations: two economies can be identical in place effects, sorting, and location means, yet deliver different mover coefficients. Only under directional isotropy, a testable condition, does the coefficient permit a cross-sectional reading: it averages the variance share of place effects and the share that equalizing them removes. An illustration in Dutch employer–employee wage data rejects the condition. |
| Keywords: | mover design, place effects, two-way fixed effects |
| JEL: | C23 C52 J31 |
| Date: | 2026–08–11 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20260056 |
| By: | Amadeo Grob; Maurizio Daniele; Johanna Ziegel |
| Abstract: | Traditional statistical tests are poorly suited for the sequential evaluation of probabilistic forecast calibration. We address this limitation in macroeconomic forecasting by applying a new sequential testing method based on e-values. The e-value-based methodology enables anytime-valid inference. It allows practitioners to test against calibration continuously without invalidating statistical guarantees. To illustrate the framework's practical value, we apply it to probabilistic inflation forecasts for the United States, the Euro Area, and Switzerland. Our analysis shows that the sequential approach gives detailed insights into the timing and nature of forecast misspecification. We find these diagnostics are particularly insightful during major structural breaks. During these events, we find evidence against calibration that static, full-sample tests often miss. Therefore, this work shows that e-value-based tests are a practical method for the evaluation of forecast calibration in empirical macroeconomics. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.23064 |
| By: | Melissa Dell; Ashesh Rambachan |
| Abstract: | Artificial intelligence (AI) is transforming measurement in economics. AI models convert unstructured data, such as text and images, into structured variables at low cost, making previously prohibitive measurement feasible at scale. This shifts the bottleneck from finding any scalable measure of a phenomenon to choosing among many plausible ones, which may support different empirical conclusions. This review provides guidance for navigating that shift. We describe three stages at which AI enters the measurement pipeline---discovery, construct definition, and observation---and what each demands of researchers. We argue that credible inference with AI-generated variables requires appropriately designed validation: anchoring measurement to explicit criteria, rather than informal claims that a proxy is reasonable. We then examine how validation samples support valid inference even when AI predictions are arbitrarily biased, and what can be done when a random validation sample is unavailable. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.23524 |
| By: | Haofeng Liao; Xing Wang |
| Abstract: | 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. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.03773 |
| By: | Honny, Emmanuel; Chung, Chanjin |
| Keywords: | Research Methods/ Statistical Methods |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ags:aaea26:404723 |