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Inference in time series models using smoothed-clustered standard errors

JOURNAL OF econometrics 2021年第1期224卷 113-133页

作者： Rho, Seunghwa Vogelsang, Timothy J. Emory Univ Dept Quantitat Theory & Methods 201 Dowman Dr Atlanta GA 30322 USA Michigan State Univ Dept Econ 486 W Circle Dr110 Marshall Adams Hall E Lansing MI 48824 USA

This paper proposes a long run variance estimator for conducting inference in time series regression models that combines the nonparametric approach with a cluster approach. The basic idea is to divide the time periods into non-overlapping clusters. The long run variance estimator is constructed by first aggregating within clusters and then kernel smoothing across clusters or applying the nonparametric series method to the clusters with Type II discrete cosine transform. We develop an asymptotic theory for test statistics based on these "smoothed-clustered" long run variance estimators. We derive asymptotic results holding the number of clusters fixed and also treating the number of clusters as increasing with the sample size. For the kernel smoothing approach, these two asymptotic limits are different whereas for the cosine series approach, the two limits are the same. When clustering before kernel smoothing, we find that the "fixed-number-of-clusters" asymptotic approximation works well whether the number of clusters is small or large. finite sample simulations suggest that the naive i.i.d. bootstrap mimics the fixed-number-of-clusters critical values. The simulations also suggest that clustering before kernel smoothing can reduce over-rejections caused by strong serial correlation at a cost of power. When there is a natural way of clustering, clustering can reduce over-rejection problems and achieve small gains in power for the kernel approach. In contrast, the cosine series approach does not benefit from clustering. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Fixed-b asymptotics Equally weighted cosines Systematic missing data Heteroskedasticity autocorrelation robust inference

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The fixed-b limiting distribution and the ERP of HAR tests under nonstationarity

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JOURNAL OF econometrics 2024年第2期238卷

作者： Casini, Alessandro Univ Roma Tor Vergata Rome Italy Univ Roma Tor Vergata Dept Econ & Finance Via Columbia 2 I-00133 Rome Italy

We show that the limiting distribution of HAR test statistics under fixed -b asymptotics is not pivotal when the data are nonstationary (i.e., time-varying autocovariance structure). It takes the form of a complicated function of Gaussian processes and depends on the second moments of the relevant series (e.g., of the regressors and errors for the case of the linear regression model). Hence, fixed -b inference methods based on stationarity are not theoretically valid in general. The nuisance parameters entering the fixed -b limiting distribution can be consistently estimated under small -b asymptotics but only with nonparametric rate of convergence. We show that the error in rejection probability (ERP) is an order of magnitude larger than that under stationarity and can be also larger than that of HAR tests based on HAC estimators under conventional asymptotics. These theoretical results reconcile with recent finite-sample evidence showing that existing fixed -b HAR tests can perform poorly when the data are nonstationary. They can be conservative under the null hypothesis and have non-monotonic power under the alternative hypothesis irrespective of how large the sample size is. Based on the new nonstationary fixed -b distribution, we propose a feasible method that controls the null rejection rates well regardless of whether the data are stationary or not and of the strength of the serial dependence as verified for some representative data-generating processes in a simple location model.

关键词： asymptotic expansion Fixed-b HAC standard errors HAR inference Long-run variance Nonstationarity

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Estimating Conditional Average Treatment Effects with Heteroscedasticity by Model Averaging and Matching

arXiv

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arXiv 2023年

作者： Shi, Pengfei Zhang, Xinyu Zhong, Wei Paula and Gregory Chow Institute for Studies in Economics Xiamen University Fujian China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China MOE Key Lab of Econometrics WISE Department of Statistics and Data Science in SOE Xiamen University Fujian China

We propose a model averaging approach, combined with a partition and matching method to estimate the conditional average treatment effects under heteroskedastic error settings. The proposed approach has asymptotic optimality and consistency of weights and estimator. Numerical studies show that our method has good finite-sample performances. Copyright © 2023, The Authors. All rights reserved.

关键词： Monte Carlo methods

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What time use surveys can (and cannot) tell us about labor supply

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JOURNAL OF APPLIED econometrics 2021年第7期36卷 917-937页

作者： Chou, Cheng Shi, Ruoyao Univ Leicester Sch Business Leicester Leics England UC Riverside Dept Econ Riverside CA USA

The American Time Use Survey (ATUS) accurately measures hours worked on a single day. We propose several estimators of elasticities of weekly labor supply in a linear regression model, despite certain impossibility results due to the time specific feature of the ATUS. We recommend the impute estimator, a simple modification of the standard two stage least squares estimator, that imputes the dependent variable using daily subsamples, based on our careful investigation of asymptotic and finite sample properties of the estimators under the potential outcome framework. We apply the impute estimator to the ATUS and find substantially different elasticity estimates from the Current Population Survey, especially for married women.

关键词： labor supply time use surveys impute estimator relative asymptotic efficiency survey methods

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The uniform validity of impulse response inference in autoregressions

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JOURNAL OF econometrics 2020年第2期215卷 450-472页

作者： Inoue, Atsushi Kilian, Lutz Vanderbilt Univ Dept Econ Nashville TN 37235 USA Fed Reserve Bank Dallas Res Dept 2200 N Pearl St Dallas TX 75201 USA CEPR London England

Existing proofs of the asymptotic validity of conventional methods of impulse response inference based on higher-order autoregressions are pointwise only. In this paper, we establish the uniform asymptotic validity of conventional asymptotic and bootstrap inference about individual impulse responses and vectors of impulse responses when the horizon is fixed with respect to the sample size. For inference about vectors of impulse responses based on Wald test statistics to be uniformly valid, lag-augmented autoregressions are required, whereas inference about individual impulse responses is uniformly valid under weak conditions even without lag augmentation. We introduce a new rank condition that ensures the uniform validity of inference on impulse responses and show that this condition holds under weak conditions. Simulations show that the highest finite-sample accuracy is achieved when bootstrapping the lag-augmented autoregression using the bias adjustments of Kilian (1999). The conventional bootstrap percentile interval for impulse responses based on this approach remains accurate even at long horizons. We provide a formal asymptotic justification for this result. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Impulse response Autoregression Lag augmentation asymptotic normality Bootstrap Uniform inference

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Extensions to IVX methods of inference for return predictability

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JOURNAL OF econometrics 2023年第2期237卷

作者： Demetrescu, Matei Georgiev, Iliyan Rodrigues, Paulo M. M. Taylor, A. M. Robert TU Dortmund Univ Dept Stat Dortmund Germany Univ Bologna Dept Econ Bologna Italy CSIC Inst Anal Econ Bellaterra Spain Banco Portugal NOVA Sch Business & Econ Lisbon Portugal NOVA Sch Business & Econ Carcavelos Portugal Univ Essex Essex Business Sch Colchester England Banco Portugal Econ & Res Dept Ave Almirante Reis 716th Floor P-1150012 Lisbon Portugal

The contribution of this paper is threefold. First, we demonstrate that, provided either a suitable bootstrap implementation is employed or heteroskedasticity-consistent stan-dard errors are used, the IVX-based predictability tests of Kostakis et al. (2015) retain asymptotically valid inference under the null hypothesis under considerably weaker as-sumptions on the innovations than are required by Kostakis et al. (2015). Second, under the same assumptions, we develop asymptotically valid bootstrap implementations of the IVX tests. Monte Carlo simulations show that the bootstrap tests deliver considerably more accurate finite sample inference than the asymptotic implementations of the tests under certain problematic parameter constellations, most notably for one-sided testing, and where multiple predictors are included. Third, we show how sub-sample implementations of the IVX approach can be used to develop asymptotically valid one-sided and two-sided tests for the presence of temporary windows of predictability. (c) 2022 Published by Elsevier B.V. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).

关键词： Predictive regression IVX estimation (Un)conditional heteroskedasticity Subsample tests Unknown regressor persistence Endogeneity Residual wild bootstrap

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Mean group instrumental variable estimation of time-varying large heterogeneous panels with endogenous regressors

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econometrics and Statistics 2023年

作者： Bai, Yu Marcellino, Massimiliano Kapetanios, George Department of Econometrics and Business Statistics Monash University 900 Dandenong Rd Caulfield East 3145 VIC Australia Bocconi University IGIER CEPR Baffi Carefin and BIDSA King's College London

The large heterogeneous panel data models are extended to the setting where the heterogenous coefficients are changing over time and the regressors are endogenous. Kernel-based non-parametric time-varying parameter instrumental variable mean group (TVP-IV-MG) estimator is proposed for the time-varying cross-sectional mean coefficients. The uniform consistency is shown and the pointwise asymptotic normality of the proposed estimator is derived. A data-driven bandwidth selection procedure is also proposed. The finite sample performance of the proposed estimator is investigated through a Monte Carlo study and an empirical application on multi-country Phillips curve with time-varying parameters. © 2023 EcoSta econometrics and Statistics

关键词： Large heterogeneous panels Mean Group estimator Non-Parametric methods Time-varying parameters

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Inference on finite-population treatment effects under limited overlap

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econometrics JOURNAL 2020年第1期23卷 32-47页

作者： Hong, Han Leung, Michael P. Li, Jessie Stanford Univ Dept Econ 579 Serra Mall Stanford CA 94305 USA Univ Southern Calif Dept Econ 3620 S Vermont Ave Los Angeles CA 90089 USA Univ Calif Santa Cruz Dept Econ 1156 High St Santa Cruz CA 95064 USA

This paper studies inference on finite-population average and local average treatment effects under limited overlap, meaning that some strata have a small proportion of treated or untreated units. We model limited overlap in an asymptotic framework, sending the propensity score to zero (or one) with the sample size. We derive the asymptotic distribution of analogue estimators of the treatment effects under two common randomization schemes: conditionally independent and stratified block randomization. Under either scheme, the limit distribution is the same and conventional standard error formulas remain asymptotically valid, but the rate of convergence is slower the faster the propensity score degenerates. The practical import of these results is two-fold. When overlap is limited, standard methods can perform poorly in smaller samples, as asymptotic approximations are inadequate owing to the slower rate of convergence. However, in larger samples, standard methods can work quite well even when the propensity score is small.

关键词： treatment effects overlap instrumental variables stratified randomization propensity score

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Robust causality test of infinite variance processes

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JOURNAL OF econometrics 2020年第1期216卷 235-245页

作者： Akashi, Fumiya Taniguchi, Masanobu Monti, Anna Clara Univ Tokyo Grad Sch Econ Tokyo Japan Waseda Univ Res Inst Sci & Engn Tokyo Japan Univ Sannio Dept Law Econ Management & Quantitat Methods Benevento Italy

This paper develops a robust causality test for time series with infinite variance innovation processes. First, we introduce a measure of dependence for vector nonparametric linear processes, and derive the asymptotic distribution of the test statistic by Taniguchi et al. (1996) in the infinite variance case. Second, we construct a weighted version of the generalized empirical likelihood (GEL) test statistic, called the self-weighted GEL statistic in the time domain. The limiting distribution of the self-weighted GEL test statistic is shown to be the usual chi-squared one regardless of whether the model has finite variance or not. Some simulation experiments illustrate satisfactory finite sample performances of the proposed test. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Granger causality Nonparametric hypothesis testing Generalized empirical likelihood Self-weighting

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Semiparametric Single-Index Estimation for Average Treatment Effects

arXiv

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arXiv 2022年

作者： Huang, Difang Gao, Jiti Oka, Tatsushi Academy of Mathematics and Systems Science Chinese Academy of Sciences China Department of Econometrics and Business Statistics Monash University Australia Keio University Japan

We propose a semiparametric method to estimate the average treatment effect under the assumption of unconfoundedness given observational data. Our estimation method alleviates misspecification issues of the propensity score function by estimating the single-index link function involved through Hermite polynomials. Our approach is computationally tractable and allows for moderately large dimension covariates. We provide the large sample properties of the estimator and show its validity. Also, the average treatment effect estimator achieves the parametric rate and asymptotic normality. Our extensive Monte Carlo study shows that the proposed estimator is valid in finite samples. Applying our method to maternal smoking and infant health, we find that conventional estimates of smoking’s impact on birth weight may be biased due to propensity score misspecification, and our analysis of job training programs reveals earnings effects that are more precisely estimated than in prior work. These applications demonstrate how addressing model misspecification can substantively affect our understanding of key policy-relevant treatment effects. © 2022, CC BY.

关键词： Monte Carlo methods

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