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on Econometrics |
| By: | Nicholas L. Brown; Qiushi Bu |
| Abstract: | We study difference-in-differences (DID) estimation of average treatment effects on the treated when the researcher is uncertain about which pre-treatment periods satisfy the parallel trends assumption. Roth (2022) shows that pre-trend testing can induce bias, complementing the statistical literature on post-selection inference. We propose the model averaged difference-in-differences (MADID) estimator, a weighted average of the candidate $2\times2$ DID estimators. The weights are normalized exponential functions of the candidate residual sums of squares, so implementation requires no specification test. We derive MADID's asymptotic properties under conditions that make invalid comparisons detectably more variable than at least one valid comparison. Under these conditions, MADID is consistent when the parallel trends assumption holds for at least one pre-treatment period. Although its joint limiting distribution across post-treatment periods is generally non-Gaussian, inference can be conducted by subsampling or simulation. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.05705 |
| By: | Alain Hecq; Ivan Ricardo; Ines Wilms |
| Abstract: | Matrix autoregressive (MAR) models offer a parsimonious framework for modeling matrix-valued time series, yet tools for estimation and inference for their impulse response functions are lacking. We develop asymptotic and bootstrap-based inference for impulse responses of stable MAR($p$) models. We derive the joint asymptotic distribution of the coefficient and covariance estimators, which permits closed-form delta-method standard errors. To address finite-sample bias, we propose ProBAB-MAR, a bias-corrected bootstrap that projects the corrected coefficients back onto the Kronecker parameter space, and prove that it attains asymptotically correct coverage. Monte Carlo simulations show that delta-method intervals undercover in small samples, while ProBAB-MAR achieves near-nominal coverage with intervals considerably narrower than those from an unrestricted VAR. An application to euro area inflation illustrates how shocks transmit across countries and inflation categories. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.05405 |
| By: | Shiyao Huang; Xiaojun Song |
| Abstract: | This paper develops novel smooth tests for structural changes in the innovation copula of multivariate dynamic models. We characterize deviations from copula constancy through a collection of generalized Fourier coefficients and test their joint significance. Under the null hypothesis, estimation of the dynamic parameters and the unknown marginals has no first-order estimation effect on the proposed statistics. Consequently, the feasible tests based on estimated residuals are asymptotically equivalent to their infeasible counterparts based on the unobserved innovations, yielding a desirable oracle property. Our proposed tests are asymptotically $\chi^2$-distributed and possess nontrivial power against local alternatives that approach the null at the parametric rate. To enhance the practicability of our methods, we further develop a data-driven procedure that automatically selects the truncation orders of the basis expansions. Unlike existing methods based on empirical copula processes or kernel smoothing, our tests require neither computationally intensive bootstrap procedures nor bandwidth selection. Extensive simulations demonstrate the satisfactory empirical size and power of our proposed tests. In particular, the data-driven test delivers substantial power gains under sparse alternatives, while remaining competitive under dense alternatives. Applications to exchange rates and stock returns further illustrate the practical usefulness of the proposed methods. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.09351 |
| By: | Keita Sunada; Yukitoshi Matsushita; Taisuke Otsu |
| Abstract: | Quadratic-form test statistics are widely used in econometrics, and their performance depends on accurate variance estimation. Conventional plug-in estimators are consistent under the null hypothesis, but under alternatives the drift in the residuals inflates them and the test loses power. We develop a general framework for variance estimation in such statistics, replacing one of the two squared-residual factors by an auxiliary linear combination of the residuals (``cross-fitting'') chosen to annihilate the drift. We characterize the conditional bias of each estimator exactly. The drift enters the plug-in estimator squared, multiplied by quantities bounded away from zero, so its bias is positive whenever the drift is non-degenerate. It reaches the cross-fit estimator only through the part that survives the cross-fitting, and then only through off-diagonal entries of a residual-maker matrix. From this calculation we obtain conditions under which the cross-fit estimator remains consistent under alternatives while the plug-in estimator does not. At a common critical value the cross-fit test therefore rejects whenever the plug-in test does, and against distant alternatives the plug-in statistic converges to a finite limit, small when few observations carry the departure: its power can tend to zero where the cross-fit test's tends to one. We verify the conditions under primitive assumptions in nonparametric specification testing, overidentification testing, and testing many linear restrictions, and illustrate the procedure on the Oregon Health Insurance Experiment. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.06119 |
| By: | Lennart Empting; Saskia \"Ozt\"urk; Simone Maxand; Konstantin Wagner |
| Abstract: | We develop inference for heterogeneous panel vector autoregressive (VAR) models and their structural impulse response functions, where the error terms are dependent in the cross-sectional and time dimensions (two-way dependence). For proxy-identified structural VARs, we first adapt mean-group estimation and construct a closed-form pooled identification. Considering the reduced-form VAR dynamics, residual covariances, and structural parameters, we derive a joint central limit theorem under joint limits in the cross-sectional and time dimensions. We then propose a recursive-design panel moving-block bootstrap that resamples the estimated error terms in (i) the temporal, (ii) the cross-sectional, or (iii) both dimensions jointly, and prove consistency of the joint panel-block scheme under two-way dependence. Simulations show coverage close to the nominal level for the joint scheme but severe undercoverage for cross-sectional resampling. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.11898 |
| By: | Oriol González-Casasús |
| Abstract: | The grouped fixed-effects (GFE) approach of Bonhomme and Manresa (2015) has become an increasingly popular tool in applied economics for modeling latent heterogeneity in panel data, yet its implementation raises two recurring concerns: how many groups to select, and whether groups are sufficiently distinct to be meaningfully recovered. It is shown here that both concerns may be largely immaterial for inference on common parameters. First, the GFE estimator remains asymptotically equivalent to the oracle that knows the true groups even when the number of groups is overspecified, provided the additional groups fit idiosyncratic noise rather than latent structure in the covariates. Second, oracle equivalence continues to hold under weak group separation provided the cross-section does not grow too fast relative to the time dimension, at a rate that depends on the degree of separation. Simulations confirm that the robustness properties emerge quickly in finite samples, and identify the situations in which they fail. The paper concludes with updated guidance for applied researchers, revisiting the income-democracy debate as an illustration. Overall, the findings reframe GFE as a more reliable and user-friendly tool for applied work than previously recognized. |
| Keywords: | fixed-effects, information criteria, latent grouped heterogeneity, misspecification, robust econometrics, weak separation |
| JEL: | C23 C38 C13 C52 |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:bge:wpaper:1599 |
| By: | Yihong Liu |
| Abstract: | A common empirical strategy in triple-differences (DDD) is to include either covariate trends or covariate levels to a three-way fixed effects (3WFE) regression. This strategy is typically motivated by the conditional parallel gaps assumption which assumes that deviations from parallel trends are similar among units with comparable observed covariates. We formally study both 3WFE specifications and show that, in general, neither consistently estimates the average treatment effect on the treated (ATT). Our diagnosis has two parts. First, we show that the OLS estimands of both specifications fail to satisfy the covariate balancing condition that is sufficient for them to equal the ATT. Second, we characterize the additional assumptions for each OLS estimand to equal the ATT. To address these limitations, we propose a matched triple-differences framework that accommodates a general class of matching procedures, including nearest-neighbor matching and kernel matching. Within this framework, we construct a class of consistent matching estimators, establish their asymptotic normality, and provide a consistent variance estimator that accounts for the variability introduced by the matching step. Our empirical application shows that the proposed matched triple-differences estimator can yield estimates and qualitative conclusions that differ from those obtained using the 3WFE regression. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.04223 |
| By: | Christian Alemán; Christopher Busch; Raül Santaeulàlia-Llopis; Tetyana Surovtseva |
| Abstract: | We introduce a unified double selection framework accommodating group-specific additive and multiplicative shifters of an unobserved common time trend (CTT). Under double selection, the CTT does not manifest as a parallel trend; the resulting non-constant selection bias is a linear combination nesting standard difference-in-differences (DiD) in levels and logs. Opposing shifters can yield patterns structurally impossible under standard DiDs, such as a ranking reversal of the groups over time. We establish that in the presence of double selection bias treatment effects are non-parametrically identified by the change of the ratio of within-group outcome changes over time. The double selection structure induces a stable linear relationship in the outcome-on-outcome space, grounding a simple two-step estimator operating in levels. Revisiting Card (1992), double selection uncovers valid counterfactuals where standard DiD fails. |
| Keywords: | double Selection, difference-in-differences, causal inference, nonparametric identification |
| JEL: | C14 C21 J38 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_13035 |
| By: | A. Colin Cameron; Douglas L. Miller |
| Abstract: | Many regression analyses use observations that are correlated within uncorrelated clusters and/or are correlated in distance or other spatial measure. Such data are often positively correlated. This reduces the information content of an additional observation compared to the default of independent observations. Consequently, failure to adjust standard errors for such correlation leads to confidence intervals that are too narrow, and to hypothesis tests that over reject. In this paper we first provide a general framework. We then focus on inference when observations are correlated within cluster and uncorrelated across clusters. We detail cluster-robust inference methods, particularly methods that provide improved finite-sample performance when there is not a large number of clusters. Such adjustments are often necessary. A companion paper, Cameron and Miller (2026), presents inference when correlation is spatially dampening in the distance between observations. The two papers are intended to provide a guide to empirical researchers. |
| JEL: | C12 C21 C23 |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:35800 |
| By: | David Broska; Michael Howes |
| Abstract: | Data collection is often costly or logistically demanding, limiting both the questions researchers can pursue and how precisely they can answer them. Prediction-powered inference (PPI) can reduce the amount of data needed for precise parameter estimation by combining labeled data with machine learning predictions. However, ignoring dependence within clusters can produce confidence intervals that cover the true parameter less often than their nominal rate. We introduce Cluster-Robust PPI++, which provides standard errors in closed form and asymptotically valid confidence intervals under arbitrary dependence within independent clusters, requiring no bootstrap or resampling. Our central contribution is to accommodate partially labeled clusters, a common empirical setting in which clusters contain both labeled and unlabeled units. As units are dependent within clusters, partially labeled clusters violate the independence assumption of PPI++. We also show how precision increases depend on the labeling design, and derive a cluster-aware power tuning rule that minimizes asymptotic variance. In an application to television news, standard PPI++ confidence intervals have coverage below 60%, whereas Cluster-Robust PPI++ can achieve nominal 95% coverage. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.09601 |
| By: | A. Colin Cameron; Douglas L. Miller |
| Abstract: | This article presents inference for regression with data that are correlated across some measure of distance; most often geographic distance. Failure to appropriately adjust standard errors can lead to confidence intervals that are too narrow, and hypothesis tests that over-reject. If spatial correlation exists within region but not across regions then one can use cluster-robust inference methods presented in the companion paper, Cameron and Miller (2026). In this paper we focus on methods when spatial correlation is dampening in distance. Then the standard inference method is the spatial HAC of Conley (1999). This method does not work well when spatial persistence is high, and alternative inference methods are needed. Additionally it is important that regression models control for any spatial trends to avoid finding spurious correlation. |
| JEL: | C12 C21 C23 |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:35801 |
| By: | Martin Schumann |
| Abstract: | The Information Matrix (IM) test is a natural specification check for likelihood-based models, yet cross-sectional implementations are often badly sized, confound neglected heterogeneity with distributional misspecification, and require third derivatives. We develop the panel information matrix (PIM) test for models with fixed effects. Explicit fixed effects isolate functional-form misspecification from time-invariant unobserved heterogeneity. Although the profile maximum likelihood estimator inherits incidental-parameter bias of order $O(1/T)$, the leading bias of the profile PIM is of order $\sqrt{n}/T$, so it is asymptotically negligible whenever $n/T^2\to 0$, which includes the rectangular regime $n/T\to\mathrm{const}$, and stabilizes under parabolic asymptotics $n/T^2\to\rho\in(0, \infty)$. This robustness arises because the indicator fluctuates at rate $\sqrt{n}$ rather than $\sqrt{nT}$. The same rate argument makes third-derivative corrections asymptotically unnecessary, so the test uses only first- and second-order likelihood derivatives. Simulations confirm that asymptotic PIM critical values suffice in moderately long panels, even when Wald tests for $\theta$ are badly sized, while a parametric bootstrap largely removes size distortions when $\rho>0$. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.12350 |
| By: | Antoine A. Djogbenou |
| Abstract: | The paper develops a theory for selecting the rolling window when generating out-of-sample forecasts with factor-augmented regression (FAR) models in the presence of structural instabilities. It shows how to select a rolling window by minimizing the conditional mean squared forecast error (MSFE) while accounting for uncertainty in factor estimation. Because the conditional MSFE is unobserved and the factors are latent, this paper proposes a feasible version of the criterion and derives conditions under which the new method is asymptotically loss-efficient. A simulation experiment documents the procedure's performance. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.12025 |
| By: | Ulrich Hounyo; Jungbin Hwang |
| Abstract: | Random assignment can make ordinary least squares (OLS) inference insensitive to outcome dependence, yet iid resampling can still fail because assignment and resampling need not remove the same covariance terms. With binary treatment, the iid variance target differs from the sampling variance by exactly minus aggregate cross-unit covariance of treatment effects. Under a Gaussian first-order limit, positive covariance leads to over-rejection and negative covariance to under-rejection. Two designs can generate the same distribution for each observation but require variance corrections of opposite signs, so no marginal-only variance correction is first-order exact for both. For first-order Gaussian inference, only one covariance component---the covariance carried by the randomized-regressor score---must be recovered. Standard dependence estimators on that score restore validity under suitable ordered or grouped dependence conditions. In simulations with ordered data, fixed-bandwidth calibration reduces several large-bandwidth size distortions. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.04217 |
| By: | Rok Spruk |
| Abstract: | Synthetic control relies on pre-treatment fit to balance the unobserved factors that drive untreated outcomes. The argument fails when an observed common shock, such as a commodity price, moves with the latent factors before treatment and departs from them afterwards and pre-treatment fit then says almost nothing about the synthetic unit's exposure to the shock. I derive a period-specific bound that links the post-treatment bias of any weighting estimator to pre-treatment misfit through a leverage statistic, and show that the statistic decomposes exactly into a latent-factor component and the partial leverage of the observed shock. The decomposition yields a diagnostic for such silent factor that uses no post-treatment outcome of the treated unit. Balancing an observed exposure index removes the problem, but simplex weights can achieve balance only when the treated unit lies inside the donors' exposure hull. Outside the hull, every simplex-weighted estimator carries an exposure imbalance with an explicit lower bound. For that case I propose an exposure-augmented synthetic control that corrects the remaining imbalance with a cross-donor regression, characterise what the correction identifies and when it fails, and derive bias-aware confidence intervals with a breakdown value. Monte Carlo experiments, including designs in which the correction's assumptions fail, map its gains and its limits. Iran's 2012 sanctions coincided with the 2014 oil collapse, and Iran is more oil-dependent than any of its natural comparators. The 2012-15 output loss of about 12 percent survives every adjustment. The persistent loss that standard synthetic control reports after 2016 does not. Any adjustment for oil exposure removes it, and the long-run effect is not identified with these comparators. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.05535 |
| By: | Artem Kuriksha; Kenneth Hung |
| Abstract: | We present a methodology for analyzing node-level outcomes while experimenting with edge-level treatments in a population connected by an undirected graph. Under our design, nodes are randomly assigned to test or control, and each edge inherits the treatment of its endpoints, with conflicts resolved by randomization. We use each node's assigned status as an instrument for its treatment exposure. We show that the Wald estimator is consistent for the global average treatment effect (GATE), even when the edge weights used to construct the exposure are misspecified. We formalize the assumptions needed both in terms of the linearity of potential outcomes and the sparsity of the graph, and prove the asymptotic normality of the Wald estimator. The estimator is straightforward to implement, requiring no assignment simulations over the graph. Our Monte Carlo study demonstrates the strong performance of our approach in the context of a social platform. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.07363 |
| By: | Ying Jin |
| Abstract: | One-to-one matching without replacement is a classical approach to constructing comparable treated and control samples in the design of observational studies. It pairs each treated unit with a distinct control while minimizing a covariate distance objective. With continuous covariates, the matched pairs generally remain inexact, which contributes to bias in downstream analysis. Its key theoretical properties, such as the resulting imbalance between matched pairs and when it is negligible to support valid inference, remain unclear. In this paper, we analyze one-to-one matching based on $d$-dimensional, continuous covariates with a quadratic covariate-distance objective. First, we find that when $d\leq 3$, under standard conditions on the propensity score ensuring abundant control samples near each treated sample, the imbalance (difference between within-group averages) is root-$n$ negligible uniformly over the family of smooth functions with a common first- and second-order derivative bound. However, such balance is subject to a dimension restriction, as we construct examples in which the imbalance is root-$n$ non-negligible when $d=4$ and dominates root-$n$ rate when $d>4$. Second, we show that when $d\leq 3$, the matched design allows valid Wald-type and bootstrap inference for the average treatment effect on the treated, distributional treatment effects, and quantile treatment effects. Thus, the same outcome-blind matched design supports various downstream inferences without having to tailor the design to the targets. Finally, paired randomization inference based on the matched design is asymptotically valid in the super-population sense for $d\leq 3$ but can fail when $d=4$. We corroborate the theoretical results with numerical experiments. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.10873 |
| By: | Yu, Xuewen |
| Abstract: | Individual-level time series data, such as longitudinal survey data, are increasingly used for policy evaluation. To infer the impact of a policy given such data, we propose a hierarchical Bayesian structural time series (HBSTS) model that extends the existing Bayesian structural time series model. Hierarchical Bayesian structural time series can accommodate multiple observations per time point by adding an extra layer to capture individual-level variation. It also uses a regularized horseshoe prior with a signal-adaptive variable selection algorithm. These extensions provide a more flexible and realistic framework for policy evaluation, and make inference less sensitive to the prior specification of the expected model size (i.e. the expected number of covariates included in the model that are predictive of outcomes). In simulation studies, HBSTS demonstrated greater robustness to misspecification of the expected model size and was more powerful in detecting putative intervention effects compared with BSTS. We apply our model to the UK Household Longitudinal Study to investigate the impact of a UK immigration policy reform. Our findings indicated that the policy led to psychological distress among individuals from Black Caribbean backgrounds, which was also observed in an earlier Bayesian interrupted time series analysis, though derived by comparing them with people from White backgrounds. |
| Keywords: | Bayesian structural time series;causal inference;synthetic control method |
| JEL: | C1 |
| Date: | 2026–10–06 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:141174 |
| By: | Hong Kiat Tan; Isaac-Neil Zanoria; James Chen; Haoyang Lyu; Mihai Cucuringu |
| Abstract: | Finding which variables cause which others in multivariate time series, and at what lags, is central to science and policy, yet existing methods force a choice between flexible confounder adjustment, data-driven lag selection, and inference that controls the false discovery rate (FDR). ORACLE-VARX does all three in one pipeline. First, double/debiased machine learning (DML) removes nonlinear confounder effects from the outcomes and the lagged series. Second, adaptive causal lag estimation (ACLE) picks the lag order at each time step by sequential significance tests, tracking regime changes. Third, entry-wise $z$-tests with Benjamini--Hochberg correction select directed edges at a target FDR. We prove that in each rolling window, the debiased coefficients are asymptotically normal around a window-averaged target, so their $z$-tests are asymptotically valid. On a synthetic benchmark with time-varying structure and nonlinear confounding, ORACLE-VARX (LightGBM) tracks the true lag order best (RMSE $0.96$ vs $1.1$--$1.5$), has edge FDR $0.047$, close to PCMCI ($0.045$) and below VAR ($0.129$) and VAR-LiNGAM ($0.187$), and forecasts better than all three. On nine U.S. sector ETFs with macroeconomic confounders, it yields interpretable causal graphs whose lag order rises in high-volatility regimes. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.05618 |
| By: | Christophe Barrette; Philippe Goulet Coulombe; Tim Reinicke |
| Abstract: | What should a macroeconomically relevant climate index contain? The composition is inherently ambiguous, and aggregation choices affect structural inference. We introduce the Assemblage VAR, which jointly estimates nonnegative aggregation weights and VAR parameters by maximizing the system likelihood-gain criterion, effectively outsourcing aggregation to observed macroeconomic dynamics. Two variants operate in component-space and rank-space, reweighting named subcomponents or emphasizing regions of the cross-sectional distribution. Applied to disaggregated U.S. climate data from the Actuaries Climate Index and NOAA, VARs using the assembled climate measures yield contractionary impulse responses that are substantially larger than those estimated using fixed-weight benchmarks. Weights emphasize high-wind variables and distributional tails over slow-moving components such as sea level. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.10043 |
| By: | Orazio Attanasio; Lina Cardona-Sosa; Ziqian Liu |
| Abstract: | This paper considers the estimation of heterogeneous impacts within a Randomized Controlled Trial (RCT) in a situation where heterogeneous status is endogenous and is not fully observed in the control sample. We show how to use information in the treatment sample and a noisy signal on the heterogeneous status to estimate meaningful impacts under a minimal set of assumptions. We provide an application of this approach to a data set from Ghana, collected around a clustered RCT to evaluate the impacts of an early-years intervention, differentiating the impact between households that participate actively in the program from those who participate only passively, as recipients. We show that, for some outcomes, the properly estimated heterogeneous impacts differ substantially from those computed with a naive estimator. |
| JEL: | C10 C9 O15 |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:35872 |
| By: | Luisa Tibiletti; Simone Farinelli; Eric Dal Moro |
| Abstract: | Hierarchical copula models are widely used for aggregating market and credit risks across multi-level portfolio structures. Existing approaches often rely on Monte Carlo simulation, recursive sample reordering, or high-dimensional numerical procedures. This paper develops an analytical framework for hierarchical copula aggregation based on explicit finite-sum representations of aggregate loss distributions and tail-risk measures for two-level market-credit aggregation with Gaussian and mirrored Clayton copulas under empirical leaf-level marginals. We derive deterministic formulas for aggregate distribution functions, quantiles, expected tail losses, and market-credit tail contributions, together with a compatibility condition linking local hierarchical copulas and global leaf-level dependence structures. Estimation-error expressions for quantiles and expected tail losses are also obtained in finite-sum form. The paper further analyzes the qualitative asymptotic behavior of hierarchical aggregation under increasing tree depth. Gaussian hierarchies are argued to remain diversification-dominated, whereas mirrored Clayton hierarchies propagate upper-tail dependence recursively and may amplify extreme losses across aggregation levels. The resulting formulas provide a deterministic alternative to simulation-based aggregation methods and clarify how tail dependence propagates through hierarchical market-credit portfolios, with direct relevance for portfolio risk measurement and capital assessment. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.08799 |