Summary This paper develops panel data tests for the null hypothesis of no error correction in a model with common stochastic trends. The asymptotic distributions of the new test statistics are derived and simulation results are provided to suggest that they perform well in small samples. Copyright © 2015 John Wiley & Sons, Ltd.

Panel unit-root and no-cointegration tests that rely on cross-sectional independence of the panel unit experience severe size distortions when this assumption is violated, as has, for example, been shown by Banerjee, -91] via Monte Carlo simulations. Several studies have recently addressed this issue for panel unitroot tests using a common factor structure to model the cross-sectional dependence, but not much work has been done yet for panel nocointegration tests. This paper proposes a model for panel no-cointegration using an unobserved common factor structure, following the study by Bai panel unit roots. We distinguish two important cases: (i) the case when the non-stationarity in the data is driven by a reduced number of common stochastic trends, and (ii) the case where we have common and idiosyncratic stochastic trends present in the data. We discuss the homogeneity restrictions on the cointegrating vectors resulting from the presence of common factor cointegration. Furthermore, we study the asymptotic behaviour of some existing *Previous versions of this paper were presented at ]. Under the data-generating processes (DGP) used, the test statistics are no longer asymptotically normal, and convergence occurs at rate T rather than ffiffiffiffi N p T as for independent panels. We then examine the possibilities of testing for various forms of no-cointegration by extracting the common factors and individual components from the observed data directly and then testing for no-cointegration using residual-based panel tests applied to the defactored data.

In this paper we derive permanent‐transitory decompositions of non‐stationary multiple times series generated by (r)nite order Gaussian VAR(p) models with both cointegration and serial correlation common features. We extend existing analyses to the two classes of reduced rank structures discussed in Hecq, Palm and Urbain (1998). Using the corresponding state space representation of cointegrated VAR models in vector error correction form we show how decomposition can be obtained even in the case where the number of common feature and cointegration vectors are not equal to the number of variables. As empirical analysis of US business fluctuations shows the practical relevance of the approach we propose.

In this paper we propose an autoregressive wild bootstrap method to construct confidence bands around a smooth deterministic trend. The bootstrap method is easy to implement and does not require any adjustments in the presence of missing data, which makes it particularly suitable for climatological applications. We establish the asymptotic validity of the bootstrap method for both pointwise and simultaneous confidence bands under general conditions, allowing for general patterns of missing data, serial dependence and heteroskedasticity. The finite sample properties of the method are studied in a simulation study. We use the method to study the evolution of trends in daily measurements of atmospheric ethane obtained from a weather station in the Swiss Alps, where the method can easily deal with the many missing observations due to adverse weather conditions. JEL classifications: C14, C22.bootstrap samples with a smaller value for . Additionally, it provides a convenient framework for studying the theoretical properties of our method. Specifically, we need → ∞ as n → ∞, such that γ → 1. This is analogous to the block (and dependent wild) bootstrap, where the block size must increase to capture more dependence when the sample size increases. Assumption 7 postulates the formal conditions that needs to satisfy, which imply that γ → 1, but not too fast.Assumption 7. The bootstrap parameter = (n) satisfies → ∞ and / √ nh → 0 as n → ∞.Note that we propose to use a different bandwidthh in Step 1 of the algorithm. This is a common feature in the literature on bootstrap method for nonparametric regression, where by either selecting a larger (oversmoothing) or smaller bandwidth (undersmoothing) than used for the estimator, one can account for the asymptotic bias that is present in the local polynomial estimation, see Hall and Horowitz (2013, Section 1.4) for an extensive literature review. While undersmoothing, such as used in the related paper by Neumann and Polzehl (1998), aims at making the bias asymptotically negligible, oversmoothing aims at producing a consistent estimator of the (non-negligible) bias.Both have advantages and disadvantages, see the extensive discussion in Hall and Horowitz (2013).We follow Bühlmann (1998), also see Härdle and Marron (1991), and consider a solution based on oversmoothing, which we find to work well in practice. After presenting our theoretical results in Section 4, Remark 8 provides an intuition of why oversmoothing allows to consistently estimate the asymptotic bias. 1 We now state the formal conditions thath must satisfy in Assumption 8; one is that h/h → 0 as n → ∞, which ensures the oversmoothing. Assumption 8. The oversmoothing bandwidthh =h(n) satisfies max h , h/h, nh 5h4 → 0 and max h 4 , 1/nh → 0 as n → ∞. Remark 4. There are a number of ways to choose the AWB parameter γ in practice. Using the relation γ = θ 1/ , one can fix θ and choose as a deterministic function of the sample size. Smeekes and Urbain (2014) found in their simulation study that θ = 0.01 paired with = 1.75n ...

This paper considers estimation of factor-augmented panel data regression models. One of the most popular approaches towards this end is the common correlated effects (CCE) estimator of Pesaran (Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica, 2006Econometrica, , 74, 967-1012Econometrica, , 2006. For the pooled version of this estimator to be consistent, either the number of observables must be larger than the number of unobserved common factors, or the factor loadings must be distributed independently of each other. This is a problem in the typical application involving only a small number of regressors and/or correlated loadings. The current paper proposes a simple extension to the CCE procedure by which both requirements can be relaxed. The CCE approach is based on taking the cross-section average of the observables as an estimator of the common factors. The idea put forth in the current paper is to consider not only the average but also other cross-section combinations. Asymptotic properties of the resulting combination-augmented CCE (C 3 E) estimator are provided and tested in small samples using both simulated and real data. which can be estimated consistently using least squares (LS). If, however, x i is correlated with F, then consistency will be Our very good friend and co-author Jean-Pierre Urbain passed away shortly after the submission of the first version of this paper. 268 SUPPORTING INFORMATIONAdditional supporting information may be found online in the Supporting Information section at the end of the article.How to cite this article: Karabiyik H, Urbain J-P, Westerlund J. CCE estimation of factor-augmented regression models with more factors than observables. J Appl Econ. 2019;34:268-284. https://doi.

Ethane is the most abundant non-methane hydrocarbon in the Earth’s atmosphere and an important precursor of tropospheric ozone through various chemical pathways. Ethane is also an indirect greenhouse gas (global warming potential), influencing the atmospheric lifetime of methane through the consumption of the hydroxyl radical (OH). Understanding the development of trends and identifying trend reversals in atmospheric ethane is therefore crucial. Our dataset consists of four series of daily ethane columns. As with many other decadal time series, our data are characterized by autocorrelation, heteroskedasticity, and seasonal effects. Additionally, missing observations due to instrument failure or unfavorable measurement conditions are common in such series. The goal of this paper is therefore to analyze trends in atmospheric ethane with statistical tools that correctly address these data features. We present selected methods designed for the analysis of time trends and trend reversals. We consider bootstrap inference on broken linear trends and smoothly varying nonlinear trends. In particular, for the broken trend model, we propose a bootstrap method for inference on the break location and the corresponding changes in slope. For the smooth trend model, we construct simultaneous confidence bands around the nonparametrically estimated trend. Our autoregressive wild bootstrap approach, combined with a seasonal filter, is able to handle all issues mentioned above (we provide R code for all proposed methods on https://www.stephansmeekes.nl/code.).

In this article, we investigate the validity of the univariate autoregressive sieve bootstrap applied to time series panels characterized by general forms of cross‐sectional dependence, including but not restricted to cointegration. Using the final equations approach we show that while it is possible to write such a panel as a collection of infinite order autoregressive equations, the innovations of these equations are not vector white noise. This causes the univariate autoregressive sieve bootstrap to be invalid in such panels. We illustrate this result with a small numerical example using a simple DGP for which the sieve bootstrap is invalid, and show that the extent of the invalidity depends on the value of specific parameters. We also show that Monte Carlo simulations in small samples can be misleading about the validity of the univariate autoregressive sieve bootstrap. The results in this article serve as a warning about the practical use of the autoregressive sieve bootstrap in panels where cross‐sectional dependence of general form may be present.

This article makes an analytical study of the effects of the presence of both common and idiosyncratic stochastic trends on the pooled least squares estimator. The results suggest that the usual result of asymptotic normality depends critically on the absence of the common stochastic trend.