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on Econometrics |
| By: | Ruei-Chi Lee |
| Abstract: | Many real-world policies and business interventions require assessing short-term effects to inform timely decisions, even though most causal inference methods focus on long-term average treatment effects. In this paper, we introduce average treatment effect localization (ATEL), which captures localized, short-term policy impacts in panel data settings with a single treated unit and provides early indicators of policy impact. To accommodate both time-varying and nonlinear effects of observed and unobserved covariates, we propose a nonparametric model for untreated outcome, interpreted as a time-varying factor model via sieve approximation. Estimating the time-varying factor model is challenging due to the boundary bias and identification. Our estimation method based on diversified projection can effectively address these issues. We develop an asymptotic distribution theory to facilitate inference for the ATEL estimator. In an empirical application, we apply our proposed methodology to assess the impact of right-to-carry laws on violent crime rate. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.10617 |
| By: | Kirill O. Morozov |
| Abstract: | This paper develops a Poisson regression model with multivariate sample selection, in which the outcome is observed only when several potentially correlated selection conditions are satisfied. To the best of our knowledge, this is the first Poisson sample selection model that allows for an arbitrary number of selection equations. We derive the conditional mean of the observed outcome under joint normality of the outcome and selection errors and obtain a multivariate selection-correction term. We prove identification of the model parameters and show that, under suitable support and rank conditions, the outcome parameters can be identified without an exclusion restriction. We also propose two-step estimation procedures based on nonlinear least squares and Poisson pseudo-maximum likelihood. To the best of our knowledge, this paper is the first to apply PPML to a Poisson regression model with sample selection. The consistency of both estimators is established, and a robust two-step sandwich covariance matrix is proposed to account for the estimation error from the first-step selection model. In addition, factorial moments are used to recover the variance of the latent outcome error and the correlations between the outcome and selection errors. Monte Carlo simulations show that ignoring sample selection leads to persistent bias when the outcome and selection errors are correlated, while the proposed PPML estimator substantially reduces this bias and is more stable than nonlinear least squares, especially under moderate and strong selection dependence. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.21056 |
| By: | Huan Gong; Feiyu Jiang |
| Abstract: | Modern economic and financial data are increasingly organized as multiway arrays, with observations indexed simultaneously by geographic regions, industrial sectors, asset categories, and other economic characteristics. Representing such data as tensor-valued time series preserves their intrinsic multiway structure. Although substantial effort has been devoted to modeling the conditional mean of tensor-valued time series, comparatively less attention has been paid to their conditional covariance dynamics. The latter remains challenging because unrestricted multivariate covariance models involve many parameters and substantial computational cost. To address these challenges, we propose the Tensor-BEKK (T-BEKK) model, a tensor-structured BEKK specification that retains the positive definite covariance recursion for the vectorized process while imposing Kronecker structures on the intercept and the ARCH and GARCH coefficient matrices. The model reduces the parameter dimension and provides mode-specific interpretations of the covariance intercept, ARCH effects, and GARCH persistence. We establish stationarity, identification, and the asymptotic properties of the Gaussian quasi-maximum likelihood estimator. We further develop mode-specific restricted score tests tailored to the tensor structure, inference procedures for nonzero spillover intensities within each mode, and a portmanteau diagnostic test based on quadratic form residuals. For higher-dimensional settings, we also introduce the Tensor-Factor-BEKK (TF-BEKK) model. Under a first-step negligibility condition, its feasible second-step QMLE is asymptotically equivalent to the oracle QMLE based on the latent factors. Simulations and two empirical applications, covering currency futures and Chinese equity tensor portfolio allocation, illustrate the finite-sample behavior and empirical usefulness of the proposed methods. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.18157 |
| By: | Xuqing Lin; Xiaojun Song |
| Abstract: | Many structural and dynamic economic models imply that key parameters are identified by conditional quantile restrictions. Building on the exponential-weighting approach of Bierens (1990) and recent advances in penalized maximum statistics for conditional moment restrictions (Chen et al., 2025), we develop a unified inference framework for such parameters. We propose an adaptive $\ell_1$-penalized supremum statistic that transforms the conditional restriction into a continuum of unconditional moment conditions and aggregates evidence across quantile indices. The penalty regularizes the maximization over the weighting direction. Under the stated uniformity conditions, the known-parameter adaptive selector has no lower maximin local power than the unpenalized test and yields a strict maximin local-power gain whenever some positive candidate penalty has a strictly larger population maximin criterion than the zero penalty. We extend the theory to settings with pre-estimated nuisance parameters, characterizing the additional terms induced by the plug-in step in the limiting process. We derive an analytically corrected variance estimator that accounts for plug-in estimation uncertainty and establish the validity of a Gaussian multiplier bootstrap under the null and sequences of local alternatives. Monte Carlo simulations show that the proposed CvM-KS aggregation scheme has rejection rates relatively close to nominal size under pre-estimation in the linear design and approaches the nominal level in nonlinear designs as the sample size grows. The reported power comparisons between the adaptive and unpenalized procedures are design-specific, with higher empirical rejection frequencies for the adaptive procedure along some directions. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.23303 |
| By: | Paritosh Shankarrao Junare |
| Abstract: | Two frequent approaches for identifying structural VARs are external instruments, which carry economic content but are often weak, and non-Gaussianity of the shocks which provides statistical identification but carries no economic meaning. We combine the two strategies in a single generalized method of moments framework that stacks proxy exclusion restrictions with higher-order moment conditions of the structural shocks. This hybrid approach point-identifies the target shocks while also identifying the non-target shocks up to sign and ordering. Under suitable rank conditions, the higher-order moments anchor the identification uniformly over the instrument strength. Consequently, under local-to-zero proxy relevance, estimators of the dynamic causal effects remain consistent, and standard asymptotic inference remains valid. Moreover, the Anderson-Rubin confidence sets are substantially narrower than their instrument-only counterparts. The hybrid estimator is also more efficient than either source of identification used in isolation: at any fixed proxy relevance, even a weak instrument increases efficiency of the estimator through its covariance with the non-Gaussian moment block. Under local deviations from proxy exogeneity, we provide asymptotic bias bounds and show that stronger non-Gaussianity of the shocks compresses the bias. Finally, the over-identified structure yields two mutually orthogonal specification tests, for proxy exogeneity and validity of higher-order moment conditions. We derive their limiting distributions and provide a bootstrap procedure for finite-sample critical values. Monte Carlo simulations and two applications with identification of oil news-shock and a Euro-area MP shock demonstrate the potential of our framework. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.14398 |
| By: | Hua Jin; Rui Sun; Tian Xie |
| Abstract: | The random-coefficient demand model of Berry, Levinsohn, and Pakes (1995) is commonly estimated by the generalized method of moments (GMM), using an unconditional moment restriction with a fixed set of instruments. Identification of the model, however, rests on a conditional moment restriction. The two are not equivalent: the unconditional restriction may admit additional parameter values. We construct a counterexample in which the model is identified by the conditional restriction yet standard GMM is not, even with the optimal instrument. Building directly on the identifying restriction, we propose a two-step estimator, following Ai and Chen (2003), that first estimates the relevant conditional expectations nonparametrically and then selects the structural parameters by a conditional-variance-weighted minimum-distance criterion; standard GMM is recovered as the special case of a linear projection onto finitely many instruments. We establish root-T asymptotic normality for the proposed estimator, and we develop the theory for both kernel and series implementations of the first stage. The two implementations share a common limiting distribution, attaining the semiparametric efficiency bound. Simulation evidence illustrates the consequences of the identification gap and demonstrates that the proposed estimator outperforms standard GMM in finite samples. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.15736 |
| By: | Hong, Y.; Lin, Z.; Linton, O. B.; Newey, W. K.; Sun, J. |
| Abstract: | We propose affine-equivariant adjusted-range self-normalization for joint inference on time-series parameters. The method uses the projected ranges of a centered influence path to normalize estimation error, yielding pivotal limiting inference without estimating the long-run covariance matrix. The resulting statistic is invariant to nonsingular linear reparameterizations, and its inversion yields affine-equivariant confidence regions. In the univariate case, the proposed method reduces exactly to adjusted-range self-normalization. We derive scalar reference distributions and accommodate proportional variance accumulation through appropriate path centering. Simulations show power gains over quadratic self-normalization and quantify size distortions under persistent dependence. An application to U.S. fiscal multipliers illustrates joint inference across horizons and its sensitivity to concentrated identifying variation. |
| Keywords: | Self-Normalized Inference, Long-Run Covariance, Affine Equivariance, Influence Functions, Local Projections |
| JEL: | C12 C13 C22 C32 |
| Date: | 2026–09–08 |
| URL: | https://d.repec.org/n?u=RePEc:cam:camdae:2678 |
| By: | Anish Agarwal; Munther Dahleh; Devavrat Shah; Dennis Shen |
| Abstract: | We develop a causal framework for matrix completion under missing not at random (MNAR) data. Drawing on synthetic controls from the econometric panel data literature, our approach relaxes two assumptions common in MNAR matrix completion: positivity and independence of observation indicators. Unlike traditional panel data models, which often require prescribed block-sparse geometries, our framework accommodates flexible, heterogeneous observation patterns through target-specific local information structures. We propose synthetic nearest neighbors (SNN), a local synthetic-controls-inspired estimator, and establish finite-sample entrywise error bounds and consistency for mean recovery under suitable conditions. We further derive asymptotic normality under heteroskedastic noise and develop feasible entrywise inference. To estimate entry-specific noise variances, we apply the same local principle to squared outcomes, obtaining consistency under bounded noise and asymptotic unbiasedness under general subgaussian noise. Simulation studies corroborate the theoretical findings across a range of missingness designs and observation patterns. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.13586 |
| By: | Zhentong Lu; Myung Hwan Seo; Youngki Shin; Qichen Zhang |
| Abstract: | We develop a stochastic nested fixed point (SNFP) estimator for random coefficients logit demand models that updates model parameters using stochastic gradients and performs demand inversion one market at a time. Relative to the conventional nested fixed point (NFP) estimator, SNFP substantially reduces memory requirements and computational cost, making estimation feasible in very large datasets. We establish the large-$T$ (number of markets) asymptotic properties of the estimator under regularity conditions. We also characterize the effect of sharing one block of simulation draws across markets and show how to correct for it. Monte Carlo simulations show that the SNFP estimator achieves statistical accuracy comparable to the NFP estimator, and in our benchmark a single online pass estimates a model with 100 million markets in about 5.5 hours. An empirical application using scanner data further demonstrates the practical advantages of SNFP for large-scale demand estimation. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.23998 |
| By: | Danil Fedchenko |
| Abstract: | This paper studies the practice of combining multiple outcomes into a summary index to estimate a causal effect. For common estimators and index constructions, the estimate equals a weighted sum of the estimated effects on the components, with weights that are implicit and rarely reported. The paper derives the weights and shows that, for inverse-covariance-weighted indices, they can be negative and unrestricted in magnitude, so the index effect can have the opposite sign to every component effect. The paper proposes two procedures for valid inference on the index effect: a variance estimator that accounts for the data-dependent weights, and a shifted t-test that requires no such correction. Conventional t-tests of the null of no effect remain valid. Contrary to common claims, summary indices do not generally improve power. Three published studies illustrate the results. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.21393 |
| By: | Shakeeb Khan (Boston College); Elie Tamer (Harvard University) |
| Abstract: | This paper studies identification in linear quantile panel models with unrestricted individual heterogeneity when the number of time periods is fixed and small. We impose quantile strict exogeneity, whereby the conditional quantile restriction holds given the individual’s complete regressor history and latent individual effect, but otherwise allow the disturbances to be arbitrarily dependent over time. We show that the common slope coefficient can be partially identified from the requirement that the residuals in all periods be compatible with a common latent individual effect. We characterize the sharp identified set as the set of coefficients for which there exists a latent coupling satisfying the period-specific quantile restrictions. This characterization yields observable crossing inequalities that provide computationally convenient outer bounds and an observable dual representation that is sharp. When the regressors and outcomes have finite support, the sharp identified set can be computed exactly using finite-dimensional linear programs, without discretizing the latent individual effect; for continuously distributed regressors, we develop nested dual-sieve procedures that converge to the sharp set. We further characterize how identification depends on directional variation in the regressor paths, showing that additional periods need not generate identification unless they provide sufficiently rich variation relative to the support of the composite residual. Under a finite-width composite-residual condition, we obtain explicit bounds on the identified set and give conditions under which even a two-period model is point identified. Finally, we consider a quantile-varying factor-loading extension in which the latent individual effect is common across quantiles, and show how cross-quantile restrictions can identify economically meaningful relative loadings. |
| Keywords: | panel data, quantile regression, fixed effects, partial identification, sharp identified set, duality, linear programming |
| JEL: | C14 C23 C61 |
| Date: | 2026–08–31 |
| URL: | https://d.repec.org/n?u=RePEc:boc:bocoec:1116 |
| By: | Lennard Ma{\ss}mann; Jens Klenke |
| Abstract: | Discovering interpretable subgroups whose complier effects deviate from the average is a central goal of instrumental variable analysis under imperfect compliance, yet existing tree-based methods degrade when most covariates are irrelevant to the effect. We propose Shrinkage Bayesian Causal Forest with Instrumental Variable (SBCF-IV) for discovering and estimating subgroups with heterogeneous Complier Average Causal Effects (CACE) in sparse high-dimensional settings. SBCF-IV places a sparsity-inducing Dirichlet prior on the splitting probabilities of the Bayesian Additive Regression Trees that estimate the conditional intention-to-treat and the complier share, concentrating posterior mass on the few covariates that moderate the complier effect and thereby regularizing effect estimation. The posterior split frequencies additionally enter a downstream CART as variable-level costs that steer the partition toward relevant moderators, providing an interpretable division of the covariate space. Monte Carlo experiments show that, as the share of irrelevant covariates grows, SBCF-IV recovers the true partition more reliably than its non-sparse predecessor BCF-IV at the tree and unit level, and retains nominal coverage where BCF-IV's intervals deteriorate. We apply the method to the Oregon Health Insurance Experiment and the 401(k) eligibility data. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.18903 |
| By: | Pengfei Tian; Jizhou Liu; Lei Shi; Peng Ding |
| Abstract: | We study randomized experiments involving two interacting populations, such as buyers and sellers in a marketplace. In the two-sided experiments we consider, we randomize the two populations separately and independently. For a pair consisting of one member from each population, the two assignments jointly determine one of four exposure conditions. Under a local interference assumption, we consider a broad class of linear estimands, including total, interaction, and buyer- and seller-side spillover effects. Our first main result establishes that researchers can estimate these effects using ordinary least squares and conduct asymptotically valid design-based inference using the conventional two-way cluster-robust variance estimator, clustered at the buyers' and sellers' levels. Our second main result develops a sharper variance estimator for a single linear estimand that better preserves dependence within the buyer and seller dimensions and is asymptotically less conservative than the two-way clustered estimator and existing alternatives. Our third main result establishes the theory for covariate adjustment and recommends a two-way analysis-of-variance-type covariate representation to ensure efficiency gains. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.22761 |
| By: | Juejue Wang; Pedro H. C. Sant'Anna; Victor Chernozhukov; Carlos Cinelli |
| Abstract: | We study the omitted variable bias (OVB) problem in canonical difference-in-differences (DiD) designs when unobserved confounding induces departures from the parallel trends assumption. Our results provide a novel characterization of the OVB formula for the average treatment effect on the treated (ATT), which is of independent interest. We show how the ATT bias is mainly governed by the strength of confounding in the treatment assignment mechanism and provide alternative ways of quantifying this strength, such as (i) changes in the average odds of treatment among the treated, (ii) confounding imbalance between treated and control units, or (iii) variation explained in treatment odds among the untreated. Building on these results, we offer sensitivity statistics for routine reporting, describing the minimum strength of confounding required to overturn the conclusions of a DiD study, as well as formal bounds on the strength of confounders based on comparisons to observed covariates or pre-trends. Finally, we provide flexible and efficient statistical inference methods for the bounds on ATT, which can leverage modern machine learning algorithms for estimation. We demonstrate the utility of our approach in an empirical example that estimates the effects of minimum wage on teen employment. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.19386 |
| By: | Eduardo Fonseca Mendes |
| Abstract: | We provide sufficient conditions for the consistency of penalized least squares procedures that select the order (dimension) of a regression model from a sequence of nested classes, allowing for dependent, martingale-difference errors. The main contribution is to relax the classical identifiability requirement: parameters indexing classes larger than the true order need not be identified, provided the additional, excess directions admit a linear approximation to the truth in a neighbourhood of the true parameter. This relaxation lets the number of candidate models grow with the sample size, removing the usual need for a fixed upper bound. We verify the resulting high-level conditions for two classes of nonlinear regression models used in applied work: multiple-regime smooth transition regression and mixture-of-experts models with generic generalized linear model experts. Under a BIC-type penalty, the resulting order selection rule is consistent in either model class whenever the number of candidate models grows slower than the logarithm of the sample size. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.23220 |
| By: | Blagov, Boris; Krause, Clara |
| Abstract: | This paper introduces a mixed-frequency Gaussian state-space framework that embeds forecast reconciliation into Bayesian VAR modeling for hierarchical macroeconomic data. Using precision-based sampling to generate high-frequency latent estimates, we construct a consistent proxy for the forecast-error covariance matrix, enabling optimal reconciliation with short datasets. We prove the symptotic convergence of this estimator and show that forecast reconciliation can be formally derived as a special case of conditional forecasting, allowing straightforward implementation with standard state-space algorithms. We derive reconciled impulse response functions that ensure bottom-level structural responses aggregate exactly to the top-level impulse response. Applying the framework to UK and German regional economic data, we demonstrate improvements in the forecast accuracy alongside structurally consistent impulse responses. |
| Abstract: | In diesem Beitrag wird ein Modell vorgestellt, das die Prognoseabstimmung in die bayessche VAR-Modellierung für hierarchische makroökonomische Daten mit fehlenden Daten integriert. Durch den Einsatz präzisionsbasierter Sampling-Verfahren zur Erzeugung hochfrequenter latenter Schätzwerte konstruieren wir einen konsistenten Proxy für die Kovarianzmatrix der Prognosefehler, was eine optimale Abstimmung auch bei kurzen Datensätzen ermöglicht. Wir beweisen die asymptotische Konvergenz dieses Schätzers und zeigen, dass sich die Prognoseabstimmung formal als Sonderfall der bedingten Prognose ableiten lässt, was eine unkomplizierte Implementierung mit Standard-Zustandsraumalgorithmen ermöglicht. Wir leiten abgestimmte Impulsantwortfunktionen ab, die gewährleisten, dass sich die strukturellen Antworten der untersten Ebene exakt zur Impulsantwort der obersten Ebene summieren. Durch die Anwendung des Modells auf regionale Wirtschaftsdaten aus Großbritannien und Deutschland zeigen wir Verbesserungen der Prognosegenauigkeit bei gleichzeitig strukturell konsistenten Impulsantworten. |
| Keywords: | forecast reconciliation, regional forecasts, mixed-frequency, hierarchical impulse responses |
| JEL: | C32 C53 R11 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:rwirep:343573 |
| By: | Ma, Tianyi; Verchand, Kabir A.; Berrett, Thomas B.; Wang, Tengyao; Samworth, Richard J. |
| Abstract: | We study the effects of missingness on the estimation of population pa rameters. Moving beyond restrictive missing completely at random (MCAR) assumptions, we first formulate a missing data analogue of Huber’s arbi trary ϵ-contamination model. For mean estimation with respect to squared Euclidean error loss, we show that the minimax quantiles decompose as a sum of the corresponding minimax quantiles under a heterogeneous, MCAR assumption, and a robust error term, depending on ϵ, that reflects the addi tional error incurred by departure from MCAR. We next introduce natural classes of realisable ϵ-contamination models, where an MCAR version of a base distribution P is contaminated by an ar bitrary missing not at random (MNAR) version of P. These classes are rich enough to capture various notions of biased sampling and sensitivity condi tions, yet we show that they enjoy improved minimax performance relative to our earlier arbitrary contamination classes for both parametric and nonpara metric classes of base distributions. For instance, with a univariate Gaussian base distribution, consistent mean estimation over realisable ϵ-contamination classes is possible even when ϵ and the proportion of missingness converge (slowly) to 1. We extend our results to the setting of departures from miss ing at random (MAR) in normal linear regression with a realisable missing response, and also demonstrate that our methods can be made adaptive to the case of unknown ϵ |
| Keywords: | missing data;Huber contamination model;missing not at random;robust estimation |
| JEL: | C1 |
| Date: | 2026–08–31 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:138134 |
| By: | Fangzhou Yu |
| Abstract: | This paper studies difference-in-differences with staggered adoption and a continuous, time-invariant dose. Each cohort-time comparison contains two margins. The level margin is the average treatment effect at realized doses. Under level parallel trends it equals the level contrast between the treated cohort and not-yet-treated controls. The response margin is the within-cohort slope of the outcome change on dose. It uses no controls, and its causal interpretation requires a response parallel trends assumption and a restriction on selection on gains. We show that the continuous-dose OLS coefficient in each cohort-time comparison is a convex combination of the response index and the level contrast per unit of mean dose, with a mixing weight that depends on the not-yet-treated share. We provide estimators of both margins, joint inference across cohort-time comparisons and event-time aggregates, and a covariate-adjusted extension. In an application to hydraulic fracturing, the level leads reject a joint zero restriction, whereas the response-index leads do not. The continuous-dose OLS coefficient draws primarily on the level margin. We report the level and response margin separately. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.09488 |
| By: | Parush Arora (Ashoka University) |
| Abstract: | Applied instrumental variables (IV) practice reports a first-stage F, now often the conditional F of Sanderson and Windmeijer (2016), and reads a large value as a license to interpret the second stage. We show that no first-stage diagnostic can deliver that license. With a scalar instrument, a scalar treatment, and covariates entered linearly, the 2SLS estimand splits into a signal that a saturated specification would target and a contamination, the covariance between curvature in the instrument propensity and a level function of the covariates. The same nuisance sits in both terms, so it biases the estimand and inflates the reported strength at once. When the instrument is nearly collinear with the covariates the signal vanishes and the strength is manufactured. When the strength is honest the curvature still biases the estimand through the outcome, where no first-stage number reaches it. We prove that no functional of the joint distribution of instrument, treatment, and covariates can detect this second bias, and we build a directed test from reduced-form regressions, a corrected estimator, and a reportable contamination share. Two applications show both failures. A husband’s insurance instrument (Olson, 1998) has a conditional F above 36, 000, yet correcting a linear income control more than doubles the estimate. The instrument of Nunn and Wantchekon (2011) loses most of its first stage once geography enters flexibly. |
| Date: | 2026–09–18 |
| URL: | https://d.repec.org/n?u=RePEc:ash:wpaper:170 |
| By: | Bastien Buchwalter; Francis X. Diebold; Kamil Yilmaz |
| Abstract: | Identification in vector autoregressions involves two distinct choices: how extensively to orthogonalize shocks and whether orthogonality is imposed sequentially or simultaneously. Generalized identification imposes no orthogonality; Sims (1980} imposes full orthogonality sequentially; Francis et al. (2026) impose full orthogonality simultaneously; and Buchwalter et al. (2026a) provide clustered partial orthogonalization sequentially. We fill the remaining case by developing simultaneous clustered orthogonalization (SCO). SCO preserves contemporaneous dependence within economically meaningful clusters while imposing orthogonality across clusters jointly, thereby eliminating dependence on cluster ordering. We formulate the associated correlation-maximizing identification problem and show that, in correlation space, it reduces to a quadratic matrix equation. This yields a closed-form solution, and we prove that the associated identification matrix is the unique global maximizer. SCO is order- and scale-invariant and nests generalized identification and full simultaneous orthogonalization as special cases, yielding a flexible family of structural decompositions indexed by the number and composition of clusters. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.12280 |
| By: | Antonio Mosca; Piero Mazzarisi |
| Abstract: | Likelihood-based network models are often fitted under links' independence and low-order constraints, while empirical networks frequently exhibit systematic higher-order structures such as triangles and wedges, characterizing the observed clustering patterns. Real-world core-periphery networks such as the interbank market or the air transportation system represent key examples, with cores displaying complex and nonlinear features. We formalize Penalized Likelihood with Structural Discrepancies (PLSD) as an inference-level correction that trades likelihood fit for agreement with targeted motifs. PLSD augments the negative log-likelihood with a penalty on standardized wedge and triangle discrepancies, yielding a controlled distortion of the likelihood surface that can be interpreted through a linear response analysis. A calibration approach for the unique tuning hyperparameter is introduced to turn off the penalization term when the model is correctly specified, thereby recovering maximum-likelihood estimation in that case. We then introduce a mixed-constraint maximum-entropy core-periphery Exponential Random Graph Model (ERGM), derive unconditional semi-closed motif formulas under Pareto-distributed core fitness, and interpret sparse-regime scaling through a big-jump mechanism for heavy-tailed distributions. We finally corroborate the PLSD inference methodology both with Monte Carlo simulations of a toy stochastic block model and by applying the novel core-periphery ERGM to weekly eMID interbank networks (2009-2015) and monthly US air traffic networks (1991-2000). We show that PLSD describes cores that are not only dense but also higher-order-rich and captures the observed heterogeneous degree distributions and the overexpression of wedges and triangles, at a link-level cost proportional to the model misspecification. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.15796 |
| By: | Won-Ki Seo; Kyungsik Nam |
| Abstract: | Anthropogenic forcing components follow different long-run paths, while persistent temperature change can involve distributional changes beyond the mean. Scalar regressions aggregate these components and retain only mean temperature, obscuring how distinct forcing paths relate to persistent distributional change. We develop new testing, estimation, and inference methods for long-run relations between an integrated predictor vector and a density-valued response. These comprise a residual-based test of between-cointegration (whether predictor trends account for all stochastic trends in the response density), a fully modified least-squares estimator of predictor-specific functional responses, and simulation-based inference for interpretable projections. We apply the methods to densities of observed local temperature anomalies and anthropogenic effective radiative forcing divided into CO$_2$ and non-CO$_2$ portfolios. The test results are consistent with persistent movements in these portfolios statistically accounting for the persistent evolution of the anomaly distribution, with no additional stochastic trend detected in the residual. A joint test rejects the common-response restriction imposed by aggregating the two portfolios. The fitted CO$_2$ response mainly shifts mass toward warmer anomalies and increases central concentration, whereas the non-CO$_2$ response produces a smaller shift but greater dispersion and off-center reshaping. Positive fitted mean responses for both portfolios conceal these contrasts, demonstrating the information lost through scalar aggregation. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.16509 |
| By: | Xu, Yongdeng (Cardiff University, Cardiff, UK) |
| Abstract: | Realized measures are biased for the moments of returns. We propose a two-step approach to forecasting large correlation matrices: machine-learned forecasts of realized measures enter a dynamic conditional correlation model as drivers, and their weights are estimated by quasi-maximum likelihood on returns. The correlation recursion is run in a matrix-logarithm parametrization, so every forecast is a valid correlation matrix. For Dow Jones stocks, a learned volatility driver and this recursion improve on a dynamic conditional correlation model with realized drivers at horizons of one, five and 22 days. For S&P 500 stocks, the model fits monthly returns better than machine-learned projections of realized correlations, has no invalid forecast in any month, and trades less. The criterion that selects the weight on a realized driver matters as much as the model, and practitioners can obtain valid forecasts calibrated to returns with standard software. |
| Keywords: | DCC-GARCH-X; Realized measures; Covariance forecasting; Forecast evaluation; Positive definiteness; Log-correlation coordinates; Nonlinear shrinkage |
| JEL: | C32 C53 C58 G11 G17 |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:cdf:wpaper:2026/12 |
| By: | Mertens, Elmar; Clark, Todd E. |
| Abstract: | We develop a direct approach to incorporating survey density forecasts into model-based predictive distributions. Histogram forecasts from the U.S. Survey of Professional Forecasters (SPF) carry rich nonparametric information about expected outcomes, but existing methods rely on moment-based approximations that discard part of it. We instead tilt entropically to the histogram probabilities themselves, matching them exactly. After reformulating the single-histogram problem, we derive a new analytic characterization of the multiple-histogram case, solved by Iterative Proportional Fitting and applicable to simulated densities from essentially any model. Applying the method to real-time forecasts from a Bayesian VAR with time-varying volatility, we find that tilting to SPF histograms substantially improves accuracy relative to the model’s baseline forecasts, especially during the Great Recession and the COVID-19 pandemic. The gains extend beyond the variables the SPF targets, improving forecasts for other variables in the system as well. JEL Classification: C11, C53, E37 |
| Keywords: | Bayesian vector autoregression, iterative proportional fitting, predictive densities, relative entropy, survey expectations |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:ecb:ecbwps:20263284 |
| By: | Ali Moghaddasi Kelishomi (Loughborough University); Daniel Sgroi (University of Warwick) |
| Abstract: | Empirical comparisons of preferences often treat the dispersion parameter in a random utility model as noise around a correctly specified utility function. We show that this interpretation can fail: dispersion absorbs systematic behaviour that the fitted preference family cannot span. Using portfolio choices from four studies, we estimate disappointment-aversion random utility models and compare the dispersion parameter with revealed-preference diagnostics. A money-metric decomposition separates axiomatic inconsistency from the additional loss due to imposing DA-CRRA preferences. Both components in dependently predict dispersion, and model-relative misspecification remains strongly predictive among subjects who satisfy revealed-preference consistency. In our sharpest test, coefficients estimated on three studies predict dispersion in a held-out representative sample. A calibrated simulation illustrates the distinction. The dispersion parameter is therefore not a model-free measure of decision quality. It is jointly informative about choice inconsistency and preference-model fit, with implications for comparisons of recovered preferences and stochastic precision across people and environments |
| Keywords: | Revealed Preference, Random Utility Models, Model Misspecification, Structural Noise, Choice Consistency JEL codes: D81, D11, D12, C91 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:wrk:warwec:1629 |
| By: | Thomas Leavitt |
| Abstract: | In the canonical Difference-in-Differences design, the control group's post-treatment change serves as an imputation of the treated group's counterfactual change in the same period, an imputation justified by parallel trends. However, differences in group composition can produce between-group differences in how outcomes would evolve over time, rendering this imputation vulnerable to confounding. An alternative imputation -- such as one based on the treated group's pre-treatment change -- avoids such between-group confounding but introduces the risk of confounding from within-group temporal shifts. Ideally, both imputations, each vulnerable to different sources of confounding, would have concordant values, thereby yielding the same causal conclusions. When the imputations are discordant, conclusions under parallel trends hinge more critically on that assumption since alternative imputations would point to different results. Yet in these scenarios, existing pretrends-based sensitivity analyses can show low sensitivity because they ignore post-treatment deviations from pretrends in the control group. This paper therefore proposes a discordance-based sensitivity model in which parallel pretrends are necessary but not sufficient for low sensitivity. I formally justify this model in terms of the expected distance between the ATT under parallel trends and under alternative assumptions, weighted by the joint plausibility of those assumptions. I then provide a decision-theoretic rationale for benchmarking violations of parallel trends using the worst-case discordance between the parallel trends imputation and alternative imputations. Finally, I apply both pretrends- and discordance-based sensitivity models to assess how a labor supply shock influenced electoral support for apartheid-era policies in South Africa, showing how the two approaches yield different results. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.19081 |
| By: | Mikkel Bennedsen; Kim Christensen; Peter Korsbakke Christensen; Jun Yu; Chen Zhang |
| Abstract: | This paper proposes discrete-time approximations to rough continuous-time models of realized variance (RV). The leading rough models can be viewed as autoregressive processes driven by fractional Gaussian noise. We show that the Wold representation of this noise concentrates its dependence at the first lag when the Hurst parameter is below one half. Augmenting the autoregressive (AR) and heterogeneous autoregressive (HAR) models with a first-order moving-average (MA(1)) component therefore approximates the roughness, and the MA coefficient maps almost linearly into the Hurst parameter. We refer to these extensions as the "rough" AR and "rough" HAR models. Estimating them on the log RV of ten ETFs, we find negative MA coefficients for every asset, and the implied Hurst parameters align closely with the estimates from the continuous-time models. In the HAR literature, the negative MA(1) component is a significant feature that has been largely overlooked. In out-of-sample comparisons, the "rough" models outperform their classical counterparts for nearly every asset and horizon, with the largest gains at short horizons, and their accuracy is comparable to that of the rough continuous-time models but much easier to estimate by standard off-the-shelf software. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.21587 |
| By: | Gabriel Nova; Stephane Hess; Sander Van Cranenburgh |
| Abstract: | Discrete choice model specification is a time-consuming task in which modellers often specify and estimate multiple models while balancing goodness-of-fit, parsimony, and behavioural plausibility. We present Delphos, a multitask reinforcement learning framework that learns transferable specification strategies across transport choice datasets. Delphos frames model specification as a sequential decision-making problem in which it applies a sequence of modelling actions and receives feedback from an estimation environment based on model performance and convergence. To transfer modelling decisions across datasets with different sets of variables, Delphos represents utility specifications as sets of modelling terms using a DeepSet-Q architecture, allowing a shared specification policy to learn across multiple datasets. Trained on nine transport choice datasets, Delphos consistently outperforms independently trained single-task agents, indicating that sharing modelling experience improves learning efficiency and helps identify promising sequences of modelling decisions with fewer unsuccessful estimation attempts. When applied without further training to the unseen Swissmetro and Decisions datasets, the same agent identifies competitive specifications in less than 20 minutes on a standard CPU. It achieves a higher log-likelihood per observation than the VNS metaheuristic on Swissmetro and performance comparable to a published MNL specification developed by expert modellers on Decisions. These findings show that accumulating and reusing modelling experience enables Delphos to function as an intelligent assistant for discrete choice model specification. It reduces manual trial-and-error while allowing modellers to retain control over model diagnosis, refinement, and final selection. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.18441 |