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on Econometrics |
| By: | Hugo Freeman; Dennis Kristensen |
| Abstract: | We develop a general estimation and inference procedure for the common parameters in linear panel data regression models with nonparametric two-way specification of unobserved heterogeneity. The procedure takes as input any first-step estimators of the nonparametric regression function and the fixed effects and relies on two key ingredients: First, we develop moment conditions for the common parameters that are Neyman orthogonal with respect to the nonparametric regression function. Second, we employ a novel adjustment of the nonparametric regression estimator so the estimated fixed effects do not generate incidental parameter biases. Together, these ensure that the resulting estimator of the common parameters is root-NT -- asymptotically normally distributed under weak conditions on the estimators of fixed effects and regression function. Next, we propose a novel two-step estimator of the nonparametric regression function and the fixed effects and verify that this particular estimator satisfies the conditions of our general theory. A numerical study shows that the proposed estimators perform well in finite samples. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.06491 |
| By: | Krumme, Anna (FernUniversität in Hagen); Westphal, Matthias (FernUniversität Hagen) |
| Abstract: | Building on the testable implications for IV validity underlying local average treatment effect (LATE) estimation, we (i) propose a simple testing procedure that may accommodate high-dimensional covariates and (ii) demonstrate that it can also detect biases arising from misspecified IV regression models. While recent research has highlighted the importance of a correct covariate specification, existing IV validity tests are not designed to capture this source of bias. Simulation studies strongly suggest that the test performs well at detecting violations of conditional independence, violations of the exclusion restriction, and biases arising from covariate misspecification. |
| Keywords: | testing instrument validity, local average treatment effects, covariate misspecification |
| JEL: | C12 C21 C26 C52 |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:iza:izadps:dp18573 |
| By: | Julius Owusu; Monika Avila M\'arquez |
| Abstract: | Empirical researchers routinely invoke the no-interference or \textit{individualistic treatment response} (ITR) assumption to identify causal effects in observational studies, despite concerns that interference across units may arise in many economic settings. This paper studies the causal content of standard ITR-based identification formulas when arbitrary interference is present. We show that, under restrictions on dependence between treatment assignments across units, conventional ITR-based identification formulas -- including those underlying selection-on-observables, instrumental variables, regression discontinuity designs, and difference-in-differences -- identify well-defined causal objects: types of \textit{average direct effects} (ADEs). These results do not require knowledge of the interference structure or specification of exposure mappings. We also propose a sensitivity analysis framework that quantifies the robustness of statistical inference to violations of treatment-assignment independence under arbitrary interference. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.22532 |
| By: | Aleksey Kolokolov; Shifan Yu |
| Abstract: | We develop a continuous-time penalized regression framework for the estimation of time-varying coefficients and variable selection when both the response and covariates are It\^o semimartingales with jumps. The coefficient paths are approximated by spline basis expansions and estimated via least squares from truncated high-frequency increments. In a finite-dimensional setting, we establish consistency and derive a feasible asymptotic distribution for the integrated coefficient estimator under infill asymptotics. We then extend the framework to high-dimensional settings in which the number of candidate covariates diverges, and show that a group-wise penalized estimator with a truncated $\ell_1$-penalty attains the oracle property, which delivers both consistent model selection and coefficient estimation. An empirical application to a large panel of more than two hundred high-frequency factors documents sparse factor structure across a large cross-section of stocks and industry portfolios. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.23023 |
| By: | Andre Lucas (Vrije Universiteit Amsterdam); Yicong Lin (Vrije Universiteit Amsterdam) |
| Abstract: | This paper proposes a quasi-likelihood ratio (QLR) test for the null of constant parameters against the alternative of score-driven parameter dynamics. Score-driven models have been widely used in the literature to capture time variation in parameters across a diverse range of both continuous and discrete, univariate and multivariate time series models, with or without random regressors. A formal testing procedure, however, is lacking thus far. Our QLR test addresses two key challenges: (i) parameters may lie on the boundary of the parameter space, and (ii) nuisance parameters are not identified under the null. The test statistic’s non-standard asymptotic distribution takes a simple form that only depends on the specified parameter space and is invariant to the specific formulation of the score-driven model and its degree of nonlinearity. Consequently, the asymptotic distribution applies to a wide range of score-driven models and can easily be simulated to conduct inference. We illustrate the new test using several models from the score-driven literature and show that the limiting distribution provides an adequate approximation for inference in finite samples. |
| Keywords: | parameter constancy, score-driven models, quasi-likelihood ratio test, parameters on the boundary, nonidentification |
| JEL: | C10 C12 C32 |
| Date: | 2025–10–24 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20250063 |
| By: | Haoyuan Xu; Wei Miao; Geert Dhaene; Jad Beyhum |
| Abstract: | The maximum likelihood estimator in nonlinear panel data models with interactive fixed effects is biased. Several bias correction methods, such as analytical and jackknife approaches, have been proposed to enable valid inference. This paper shows that the parametric bootstrap also enables valid inference in such models. In particular, we show that the parametric bootstrap replicates the asymptotic distribution of the maximum likelihood estimator. Therefore, it yields asymptotically unbiased estimates and confidence sets with asymptotically correct coverage. We also propose a transformation-based bootstrap confidence interval that delivers improved finite-sample performance. Simulation results support the theoretical findings. Finally, we apply the proposed method to examine technological and product market spillover effects on firms' innovation behavior. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.26826 |
| By: | Byunghoon Kang |
| Abstract: | This paper develops efficient GMM estimation when the moment conditions are misspecified. We observe that the influence function of the standard GMM estimator under misspecification depends on both the original moment conditions and their Jacobian, motivating a new class of estimators based on augmented moment conditions with recentering. The standard GMM estimator is a special case within this class, and generally suboptimal. By optimally weighting the augmented system, we obtain a misspecification-efficient (ME) estimator with the smallest asymptotic variance for the same GMM pseudo-true value. In linear models, the asymptotic variance of ME estimator reduces to the textbook efficient-GMM variance formula $(G'W^{*}G)^{-1}$, where $W^{*}$ is the inverse of the variance of residualized moments after projection on the Jacobian $G$. We consider a feasible double-recentered bootstrap estimator, which can be considered as a misspecification-robust and efficient version of Hall and Horowitz (1996) recentered bootstrap GMM estimator, and also consider a split-sample ME estimator. Finally, we establish uniform local asymptotic minimax bounds over a class of weighting matrices. We illustrate the proposed methods in simulation and empirical examples. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.04961 |
| By: | Markku Lanne; Jani Luoto; Adam Rybarczyk |
| Abstract: | We propose a new approach to inference in tightly identified and large-scale structural vector autoregressions based on a reparameterization that enables imposing identifying inequality restrictions through continuously differentiable mappings. Permitted inequality restrictions include shape and ranking restrictions as well as bounds on economically relevant elasticities, and the approach is also able to accommodate zero restrictions in a straightforward manner. We implement a Hamiltonian Monte Carlo algorithm and show how the posterior density can be rapidly evaluated under the reparameterization, thus facilitating inference in high-dimensional settings. Two empirical applications demonstrate that our approach tends to result in lower serial dependence in Markov chains, larger effective sample sizes and reduced computation time relative to existing methods. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.22445 |
| By: | Sukhbir Kaur; Sukhbir Singh; Kanchan Jain; Pooja Soni |
| Abstract: | In this paper, a Mixed Data Sampling (MIDAS) model is studied when both low and high frequency variables are contaminated with measurement error. It is shown that the profile likelihood estimator becomes inconsistent in the presence of measurement error. Using the corrected score approach along with profile likelihood approach, a consistent estimator for parameters of MIDAS Measurement Error model is proposed. Small and large sample properties of the estimator are examined by performing a monte carlo simulation study and considering the effect of sample size, number of lags and profiling parameter. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.23469 |
| By: | Samuele Centorrino; Fr\'ed\'erique F\`eve; Jean-Pierre Florens |
| Abstract: | We develop a nonparametric approach to identify and estimate consumer preferences and unobserved heterogeneity under nonlinear price schedules. Leveraging variation across multiple price schedules, we show that both the utility function and the distribution of preference types can be nonparametrically identified. The quantile function of unobserved types becomes solution of a functional equation, and we derive conditions ensuring identification. We propose an iterative approach for estimation, in which the regularization bias decays exponentially in the number of iterations while the variance grows only polynomially, yielding a near-parametric convergence rate. We propose a valid bootstrap procedure for finite-sample inference and extend the framework to accommodate potential endogeneity of prices and additional observed heterogeneity. Monte Carlo simulations and an empirical application to data from a European mail carrier demonstrate how we can recover the utility functions and preference distributions in finite samples. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.25507 |
| By: | Bia, Michela (LISER and University of Luxembourg); Menta, Giorgia (LISER); Huber, Martin (University of Fribourg); D'Ambrosio, Conchita (University of Luxembourg) |
| Abstract: | When multiple instruments are available, conventional instrumental variable estimators aggregate across heterogeneous margins of compliance, often yielding effects without a clear economic interpretation. This issue worsens when some instruments violate the exclusion restriction, as in settings using genetic variants. We propose a clustering-based plurality framework for instrumental variable estimation that addresses both instrument heterogeneity and invalid instruments. Rather than imposing a single causal parameter, our method groups instruments by similarity in the first stage and applies a plurality rule on subgroups with similar reduced-form relationships to identify locally valid subsets. This produces a set of margin-specific local average treatment effects instead of a single pooled estimate. We extend plurality-based identification to settings with non-mutually exclusive instruments, such as Mendelian Randomization designs. We illustrate the method in a two-sample Mendelian Randomization study of the effect of education on smoking. Results confirm a negative causal effect while revealing substantial heterogeneity across instrument-defined margins, masked by pooled IV approaches. |
| Keywords: | causal inference, LATE, heterogeneous treatments, instrumental variables, Mendelian Randomization |
| JEL: | C31 C36 I10 |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:iza:izadps:dp18595 |
| By: | Ertian Chen; Hiroyuki Kasahara; Katsumi Shimotsu |
| Abstract: | Estimating dynamic discrete choice models with unobserved heterogeneity is computationally costly because it requires repeatedly solving fixed-point equations for all unobserved types. We develop the EM-NPL(q) framework that combines the Expectation-Maximization (EM) algorithm with an inner fixed-point solver truncated to q iterations. For the workhorse class of linear-in-parameters models, we establish a truncation-invariance result: for any q$\geq$1, EM-NPL(q) is numerically identical to the EM-NPL estimator that solves the inner fixed-point problem to convergence. Therefore, the choice of q affects computation but not statistical properties. We also establish consistency, asymptotic normality of our estimator, and local convergence of the EM-NPL(q) algorithm. In Monte Carlo simulations, EM-NPL(q) reduces runtime by at least 20% and can be 3--5 times faster. In an application to cola demand, we show that ignoring unobserved heterogeneity understates long-run own-price elasticities by up to 60%, short-run elasticities by up to 85%, and compensating variation from a soda tax by up to 90%. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.26205 |
| By: | Zizhong Yan; Jingrong Li; Yi Zhang |
| Abstract: | Estimating network formation models with degree heterogeneity raises two problems in empirical networks. First, agents that send no links, receive no links, or link to all remaining agents can make the fixed-effects MLE fail to exist. Trimming these agents changes the estimation sample and induces selection bias. Second, the incidental-parameter problem biases common parameters and average partial effects. We resolve both issues through a penalized likelihood approach. Our leading specification is a directed network model with reciprocity, nesting the standard undirected and non-reciprocal directed models. The penalty guarantees finite-sample existence and yields bias corrections for coefficients and partial effects. We establish asymptotic results without imposing compactness on the fixed-effects. Allowing the fixed effects to diverge at a logarithmic rate, our asymptotic framework accommodates the degree sparsity ubiquitous in large empirical networks. A global trade application demonstrates that our estimator avoids selection bias and recovers robust parameters where conventional methods fail. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.00771 |
| By: | Timothy Christensen; Silvia Goncalves; Benoit Perron |
| Abstract: | AI/ML methods are increasingly used in economics to generate binary variables (or labels) via classification algorithms. When these generated variables are included as covariates in regressions, even small misclassification errors can induce large biases in OLS estimators and invalidate standard inference. We study whether the bootstrap can correct this bias and deliver valid inference. We first show that a seemingly natural fixed-label bootstrap, which generates data using estimated labels but relies on a corrupted version in estimation, is generally invalid unless a strong independence condition between the latent true labels and other covariates holds. We then propose a coupled-label bootstrap that jointly resamples the true and imputed labels, and show it is valid without this condition. Two finite-sample adjustments further improve coverage: a variance correction for uncertainty in estimated misclassification rates and a Hessian rotation for near-singular designs. We illustrate the methods in simulations and apply them to investigate the relationship between wages and remote work status. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.23770 |
| By: | Haonan Miao |
| Abstract: | We prove the validity of using subsampling method for inference under a two-way clustered panel in which the time effects are serially correlated. Subsamples should be drawn without replacement from randomly partitioned individual index set and consecutive blocks of time effects. We present two subsampling inference methods: estimating the quantiles directly and constructing the confidence interval by first estimating the asymptotic variance. The quantile method is very adaptive, allowing for non-Gaussian limit which invalidates all existing methods in two-way clustering with serial correlation. Although the variance method only works under Gaussian limit, it comes with a data-driven bandwidth selection algorithm and a bias-correction under suitable estimators. Monte Carlo simulations demonstrate our methods exhibiting the desired coverage level in the finite sample except when the serial correlation is extremely strong. This paper is the first one that allows for inference on non-Gaussian asymptotics under two-way clustering with serial correlation. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.27215 |
| By: | Yamato Igarashi |
| Abstract: | This paper develops a difference-in-differences (DiD) estimation method that selects the optimal length of pre-trends by minimizing the mean squared error (MSE). Conventional DiD regression models, such as the two-way fixed effects model or the event study model, may suffer from accuracy and validity concerns. If the sample size is small, the estimator may have a larger variance. Also, pre-tests often lack power to detect violations of the parallel trends assumption as Roth (2022) highlights. By focusing on the bias and variance tradeoff, the proposed method derives the MSE-optimal estimator from the optimal length of pre-trends. Simulation results and an empirical application demonstrate the practical applicability of the proposed method. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.05056 |
| By: | Ulrich Hounyo; Jiahao Lin |
| Abstract: | This paper develops bootstrap procedures for inference in linear regression models with two-way clustered data. We characterize the estimator's asymptotic behavior in five mutually exclusive and exhaustive regimes: three Gaussian and two non-Gaussian. We establish four impossibility results: heterogeneous score components preclude uniform consistency; uniform consistency also fails in one non-Gaussian (infeasible) regime; the infeasible regime is not uniformly distinguishable from a feasible one; and uniform validity over all feasible regimes rules out uniform conservativeness over the infeasible regime. To address the feasible regimes, we propose a data-driven regime classifier and a projection-based wild bootstrap procedure. The procedure delivers uniformly valid inference across the four feasible regimes while allowing serial dependence along the second clustering dimension and spatial dependence along the first. This combination of regime adaptivity and flexible dependence is new to the two-way clustering literature. Monte Carlo simulations confirm the accuracy and flexibility of the proposed methods in settings with complex clustering structures. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.00709 |
| By: | Murilo Cardoso; Bruno Ferman; Marcelo Fernandes |
| Abstract: | This paper studies the interactive fixed effects (IFE) estimator in a panel-data setting with heterogeneous treatment effects. We show that, if the treatment-effect heterogeneity admits a linear factor structure, the IFE estimator could fail to recover the average treatment effect on the treated units. The problem arises because the interactive fixed effects absorb the heterogeneity in the treatment effect, creating a \textit{bad-control} problem. With time-invariant factors or unit-invariant loadings in the treatment effect heterogeneity, identification may further break down due to multicollinearity. These problems are not present in alternative estimation methods that exclude treated units in post-treatment periods from the factor estimation. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.27187 |
| By: | Yuehao Bai; Kirill Ponomarev; Andres Santos; Azeem M. Shaikh; Max Tabord-Meehan; Alexander Torgovitsky |
| Abstract: | This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system of equations, including the slope coefficients, to be unknown. For this reason, we describe the linear system as having unknown (as opposed to known) coefficients. This hypothesis testing problem arises naturally when constructing confidence sets for possibly partially identified parameters in the analysis of nonparametric instrumental variables models, treatment effect models, and random coefficient models, among other settings. To rule out certain instances in which the testing problem is impossible, in the sense that the power of any test will be bounded by its size, we begin our analysis by characterizing the closure of the null hypothesis with respect to the total variation distance. We then use this characterization to develop novel testing procedures based on sample-splitting. We establish the validity of our testing procedures under weak and interpretable conditions on the linear system. An important feature of these conditions is that they permit the dimensionality of the problem to grow rapidly with the sample size. A further attractive property of our tests is that they do not require simulation to compute suitable critical values. We illustrate the practical relevance of our theoretical results in a simulation study. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.24904 |
| By: | Juan Juan Cai (Vrije Universiteit Amsterdam); Yicong Lin (Vrije Universiteit Amsterdam); Julia Schaumburg (Vrije Universiteit Amsterdam); Chenhui Wang (Vrije Universiteit Amsterdam) |
| Abstract: | We propose a nonparametric framework for estimating the extremal index that captures the persistence of extreme observations. The framework provides unified and simple procedures for verifying the well-known local dependence condition $D^{(d)}(u_n)$, which characterizes the extremal index yet is often assessed through heuristic checks, and for selecting $d$ (a key parameter for estimation) when the condition holds. Under a general ω-mixing condition, we establish the asymptotic normality of the proposed estimator and prove the consistency of both the tuning parameter selection and the verification procedure for the $D^{(d)}(u_n)$ condition. Simulation studies show improved performance relative to two commonly used methods in terms of empirical mean squared errors. We analyze summer apparent temperature data for nine European cities from 1940 to 2025. The results show strong evidence of persistence in extreme temperatures for all cities, with such extremes typically lasting at least two days. The probability of two-day extreme-temperature events is two to four times higher in the most recent three decades relative to 1940–1974. |
| Keywords: | Extremal index, extremal serial dependence, nonparametric, heatwaves |
| JEL: | C01 Q54 |
| Date: | 2026–01–09 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20260002 |
| By: | Chaoyi Chen; Elena Pesavento; Balazs Vonnak |
| Abstract: | Local projections (LP) and vector autoregressions (VAR) are the two standard tools for impulse response analysis, but they often display a finite-sample trade-off: LP is typically less biased but more volatile, while VAR is more precise but can be biased under misspecification. We propose an easy-to-implement estimator-averaging approach that combines LP and VAR at each horizon by minimizing the mean squared error of the impulse response itself, rather than in-sample fit. We derive closed-form oracle weights for this finite-sample risk problem, develop feasible AR-sieve-bootstrap procedures, and compare them against an Rsquare-based model-averaging benchmark. For a benchmark class of short-memory linear data generating processes in which LP and VAR are both consistent, we establish the consistency and limiting distribution of the feasible averaged estimator. Monte Carlo results show meaningful risk reductions relative to LP and VAR alone. In an empirical application revisiting Bauer and Swanson (2023), estimator averaging delivers stable and economically intuitive responses for yields, activity, prices, and credit spreads. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.05456 |
| By: | Davide Golinelli (Department of Economics and Management (DEM) and SEEDS, University of Ferrara); Andrea Musolesi (Department of Economics and Management (DEM) and SEEDS, University of Ferrara); Alexandra Soberon (Department of Economics, University of Cantabria; SANFI, University of Cantabria) |
| Abstract: | This paper studies the estimation of Engel curves for rural China using the dataset of Gong, van Soest and Zhang (2005), extending their partially linear specification in two directions. First, we replace the parametric first stage — which imposes linearity of the relationship between log disposable income and log total expenditure — with a nonparametric kernel regression, motivated by the pronounced threshold nonlinearity documented in their own data. Second, we replace the linear parametric control function correction with a nonparametric counterpart, following the semiparametric triangular system framework of Newey, Powell and Vella (1999), Su and Ullah (2008), and Delgado and Parmeter (2014). The resulting three-stage estimator is √N-consistent and asymptotically normal for the parametric component β, and converges at the standard kernel rate for the nonparametric component. Monte Carlo simulations confirm the finite-sample reliability of the proposed estimator across a range of sample sizes and endogeneity levels. We assess whether the gender-of-children effects on expenditure shares documented by Gong et al. (2005) are robust to these two relaxations. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:srt:wpaper:0926 |
| By: | Daniel de Abreu Pereira Uhr; Guilherme Valle Moura |
| Abstract: | This paper develops a doubly robust extension of local-projections difference-in-differences (LP-DiD) for staggered absorbing treatments. The resulting estimator, DRLPDID, preserves the LP-DiD local-stack ATT target and is consistent when either the local untreated-outcome regression or the local treatment-probability model is correctly specified. It also delivers influence-function-based inference for post-treatment summaries and multiplier-bootstrap bands for dynamic paths. In Monte Carlo designs with covariate-driven selection, DRLPDID matches regression-adjusted LP-DiD under outcome-model alignment and clearly outperforms the IPT-only variant under propensity-score misspecification. In the no-fault-divorce application, DRLPDID tracks robust staggered-adoption estimators and is less negative than unadjusted LP-DiD. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.27035 |
| By: | Jad Beyhum; Geert Dhaene; Cavit Pakel; Martin Weidner |
| Abstract: | We study the estimation of average effects in nonlinear panel data models with fixed effects when the time dimension $T$ is only moderately large. Our approach, called approximate operator inversion (AOI), offers a new perspective on bias correction. Instead of first estimating unit-specific fixed effects and then correcting the resulting plug-in bias, AOI approximately inverts the likelihood-induced mapping from the fixed-effect distribution to the outcome distribution. AOI can be interpreted as the limit of an infinitely iterated bias correction scheme, and this limit is available in closed form. We show that the bias of the AOI estimator has a rate double robustness property and converges to zero at an exponential rate in $T$ under regularity conditions. Our asymptotic theory requires $T \to \infty$, but the exponential convergence rate of the bias means that finite-sample performance is very good even for moderately large $T$. We establish asymptotic normality and provide feasible inference. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.05037 |
| By: | Joel M. David; Raffaella Giacomini; Xiyu Jiao; Weining Wang |
| Abstract: | State-dependent local projections (LPs) are widely used to estimate how responses to exogenous aggregate shocks vary as a function of observable state variables, yet their causal interpretation remains unclear. We show that this interpretation obtains under the sufficient condition that the conditional mean is linear in the aggregate shock at each horizon, and that this condition holds in a broad class of canonical micro-macro environments, including first-order perturbation solutions of heterogeneous-agent models and macro-finance models. Under this condition, LPs recover causal impulse responses without requiring specification of the full data-generating process. We further show that the causal interpretation of state-dependent LPs is robust to the choice of state variable. By contrast, commonly used linear interaction LPs generally fail to recover causal objects. We therefore develop a sieve-based nonparametric LP estimator that restores causal interpretation and delivers valid pointwise and uniform inference in micro-macro panels. Empirically, allowing for nonparametric state dependence materially changes both the pattern of heterogeneous firm investment responses and their aggregate implications for the transmission of monetary policy shocks. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.05404 |
| By: | Meng Hsuan Hsieh |
| Abstract: | Triple differences (DDD) is a workhorse quasi-experimental design in applied economics. But, under staggered adoption, its conventional three-way fixed-effects (3WFE) implementation inherits the forbidden-comparison and interpretation issues now well understood in the difference-in-differences literature. To resolve these issues, I introduce stacked DDD. I extend the stacked difference-in-differences approach to the DDD setting by creating self-contained stacks, each consisting of four cells over an event window: treated and clean comparison cohorts, each with treatment-eligible and treatment-ineligible units. Appending these stacks yields a unified dataset for estimating treatment effects without making forbidden comparisons. I prove that, at each post-treatment event-time, a linear regression with fully saturated fixed-effects applied to the stacked dataset identifies a strictly positive, cell-size-weighted average of stack-level conditional average treatment effects, with stack weights proportional to stack-level cell sizes. Building on this characterization, I outline alternative weighting schemes that recover distinct, transparent causal estimands with clear interpretations. Stacked DDD complements recent GMM and imputation-based frameworks by trading efficiency for regression-based transparency, pairwise (rather than global) parallel trends, and direct control over aggregation weights. I provide two empirical illustrations where stacked DDD yields substantially different quantitative conclusions compared to existing procedures. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.22982 |
| By: | Tomasz J. Kozubowski; Andrey Sarantsev; James A. Spiker |
| Abstract: | We consider a generalization of the variance-gamma (generalized asymmetric Laplace) distribution, defined as a normal mean - variance mixture with a gamma mixing distribution. While this model is typically studied in the univariate setting, we assume that the gamma mixing variable is observed alongside the primary variable, resulting in a bivariate framework. In this setting, maximum likelihood estimation becomes significantly simpler than in the standard univariate case, reducing to a form of classical linear regression. We derive explicit expressions for the resulting estimators. For certain parameter configurations, the estimators exhibit nonstandard convergence rates, exceeding the usual square-root rate. Finally, we illustrate the applicability of this model in financial contexts by analyzing stock index returns and associated volatility for several major indices. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.00196 |
| By: | Martin Bruns; Helmut Lütkepohl; James McNeil |
| Abstract: | Several recent studies consider a set of proxies to identify different monetary policy shocks for different regions in the world. We show that the way the proxies are used to identify the monetary policy shocks may lead to correlated shocks and dubious structural analysis and we demonstrate how to overcome the problem of correlated shocks. We illustrate that, if correlated shocks are used in applied studies, key statistics of interest such as impulse responses and forecast error variance decompositions can be severely distorted and we consider benchmark studies on monetary policy in the euro area (EA), the US and the UK to demonstrate the problems. |
| Keywords: | Structural vector autoregression, proxy VAR, GMM, correlated structural shocks |
| JEL: | C32 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:diw:diwwpp:dp2163 |
| By: | Isaiah Andrews; Ricky Li; Yucheng Shang |
| Abstract: | We study optimal estimation when the likelihood may be misspecified. Building on tools from the theory of decision-making under uncertainty, we analyze a class of axiomatically grounded optimality criteria which nests several existing misspecification-robust objectives. Within this class, we introduce the constrained multiplier criterion, which allows for flexible misspecification attitudes. We prove a local asymptotic minimax theorem for this criterion, extending a classical efficiency bound to a limit experiment which incorporates moment-constrained misspecification concerns. We characterize asymptotically optimal estimators as Bayes decision rules under a flat prior and an exponentially tilted likelihood that incorporates the moment constraints, and show that feasible plug-in analogs are asymptotically optimal. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.23176 |
| By: | Yuhao Deng; Haoyu Wei; Zhongzhe Ouyang |
| Abstract: | Causal mediation analysis is a powerful tool for disentangling the total effect of a treatment into its direct effect on the outcome and its indirect effect mediated through an intermediate variable. However, in observational studies, confounding between treatment and potential outcomes typically renders the total and natural effects non-identifiable. In this work, we advance mediation analysis within the difference-in-differences framework. Under a mediator-adjusted parallel trends assumption and additional conditions, we demonstrate that natural indirect, direct, and total effects are identifiable in the treated group. We further derive efficient influence functions for these estimands, enabling the construction of multiply robust and nonparametrically efficient estimators. We establish the asymptotic properties of these estimators. Applying our methodology to data from the Job Corps Study, we find that job training significantly increases both short-term and long-term earnings, after controlling for the indirect effect through the proportion of weeks employed. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.24049 |
| By: | Santiago Acerenza; Francisco Rosas |
| Abstract: | This paper studies sensitivity analysis of Stochastic Frontier Models. We elaborate relaxations of the baseline assumptions in the Stochastic Frontier Models and characterize the identified set under this relaxations. Furthermore, we derive the breakdown frontier for a relevant parameter of interest, the average inefficiency of a production unit. We show an application of the procedures on a well known dataset, and make the code available for the interested practitioner. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.26088 |
| By: | Sicco Kooiker (Vrije Universiteit Amsterdam); Janneke van Brummelen (Vrije Universiteit Amsterdam); Julia Schaumburg (Vrije Universiteit Amsterdam); Marcin Zamojski (Vrije Universiteit Amsterdam) |
| Abstract: | We propose a factor model with time-varying loadings for term structure modeling and forecasting. While maintaining the interpretation of the factors as level, slope, and curvature through explicit identification restrictions, we allow the loadings to take flexible shapes by specifying them as neural networks that evolve over time using a “self-driving†updating scheme based on past forecast errors, with gradient scaling to improve robustness. Using an empirically calibrated simulation study and an application to U.S. Treasury yields across 24 maturities, we show that flexible and dynamic factor loadings improve forecasting performance relative to standard benchmarks, including Nelson-Siegel models and the random walk. The gains are strongest at medium maturities and shorter forecast horizons, highlighting the importance of capturing curvature dynamics. In-sample results further illustrate how time-varying loadings provide insight into changes in yield curve shape beyond traditional parametric specifications. |
| Keywords: | time-varying neural networks, observation-driven dynamics, yield curve |
| JEL: | C38 C45 E43 |
| Date: | 2026–02–26 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20260007 |
| By: | Haiqiang Chen; Li Chen; Difang Huang; Yuexin Li; Zhengjun Zhang |
| Abstract: | We show that the leading bubble test suffers severe size distortion when fundamentals incorporate general-purpose technology adoption. Embedding a hump-shaped technology shock in the Campbell-Shiller present-value model, we prove that the fundamental price becomes locally explosive during adoption, contaminating the test's limit distribution with a non-centrality parameter proportional to the shock's peak. We propose a fundamental-versus-speculative decomposition that projects prices onto observable technology proxies and applies the test to the residual. Empirically, the decomposition eliminates evidence of speculation in the 2020-2025 AI rally while confirming a speculative peak confined to December 1999-March 2000 in the dot-com episode. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.25826 |