A residual-based test for autocorrelation in quantile regression models

Quantile regression (QR) models have been increasingly employed in many applied areas in economics. At the early stage, applications in the QR literature have usually used cross-sectional data, but the recent development has seen an increase in the use of QR in both time-series and panel data sets. However, testing for possible autocorrelation, especially in the context of time-series models, has received little attention. As a rule of thumb, one might attempt to apply the usual Breusch–Godfrey LM test to the residuals of a baseline QR. In this paper, we demonstrate analytically and by Monte Carlo simulations that such an application of the LM test can result in potentially large size distortions, especially in either low or high quantiles. We then propose a correct test (named the QF test) for autocorrelation in QR models, which does not suffer from size distortion. Monte Carlo simulations demonstrate that the proposed test performs fairly well in finite samples, across either different quantiles or different underlying error distributions.     

A weighted symmetric cointegration test

Weighted symmetric estimation is employed to develop a new test for cointegration. Using Monte Carlo simulation, the resulting test is shown to possess greater power than alternative existing tests.     

Likelihood-based panel cointegration test in the presence of a linear time trend and cross-sectional dependence

This article proposes a new likelihood-based panel cointegration rank test which extends the test of Örsal and Droge (2014 Örsal, D. D. K., Droge, B. (2014). Panel cointegration testing in the presence of a time trend. Computational Statistics and Data Analysis 76:377–390.[Crossref], [Web of Science ®] , [Google Scholar]) (henceforth panel SL test) to dependent panels. The dependence is modelled by unobserved common factors which affect the variables in each cross-section through heterogeneous loadings. The data are defactored following the panel analysis of nonstationarity in idiosyncratic and common components (PANIC) approach of Bai and Ng (2004 Bai, J., Ng, S. (2004). A PANIC attack on unit roots and cointegration. Econometrica 72(4):1127–1177.[Crossref], [Web of Science ®] , [Google Scholar]) and the cointegrating rank of the defactored data is then tested by the panel SL test. A Monte Carlo study demonstrates that the proposed testing procedure has reasonable size and power properties in finite samples.     

A test for fractional cointegration using the sieve bootstrap

The concept of fractional cointegration (Cheung and Lai in J Bus Econ Stat 11:103–112, 1993) has been introduced to generalize traditional cointegration (Engle and Granger in Econometrica 55:251–276, 1987) to the long memory framework. In this work we propose a test for fractional cointegration with the sieve bootstrap and compare by simulations the performance of our proposal with other semiparametric methods existing in literature: the three steps technique of Marinucci and Robinson (J Econom 105:225–247, 2001) and the procedure to determine the fractional cointegration rank of Robinson and Yajima (J Econom 106:217–241, 2002).     

Unbalanced panel data: A survey

This paper surveys the econometrics literature on unbalanced panels. This includes panels with randomly and non-randomly missing observations. In addition, we survey panels with special features including pseudo panels, rotating panels and censored panels.     

The accuracy of normal approximation in a heterogeneous panel data unit root test

Tests for unit roots in panel data have become very popular. Two attractive features of panel data unit root tests are the increased power compared to time-series tests, and the often well-behaved limiting distributions of the tests. In this paper we apply Monte Carlo simulations to investigate how well the normal approximation works for a heterogeneous panel data unit root test when there are only a few cross sections in the sample. We find that the normal approximation, which should be valid for large numbers of cross-sectional units, works well, at conventional significance levels, even when the number of cross sections is as small as two. This finding is valuable for the applied researcher since critical values will be easy to obtain and p-values will be readily available.     

Testing for panel cointegration in an error-correction framework with an application to the Fisher hypothesis

In this article, three innovative panel error-correction model (PECM) tests are proposed. These tests are based on the multivariate versions of the Wald (W), likelihood ratio (LR), and Lagrange multiplier (LM) tests. Using Monte Carlo simulations, the size and power of the tests are investigated when the error terms exhibit both cross-sectional dependence and independence. We find that the LM test is the best option when the error terms follow independent white-noise processes. However, in the more empirically relevant case of cross-sectional dependence, we conclude that the W test is the optimal choice. In contrast to previous studies, our method is general and does not rely on the strict assumption that a common factor causes the cross-sectional dependency. In an empirical application, our method is also demonstrated in terms of the Fisher effect—a hypothesis about the existence of which there is still no clear consensus. Based on our sample of the five Nordic countries we utilize our powerful test and discover evidence which, in contrast to most previous research, confirms the Fisher effect.     

LIML in the static linear panel data model

We consider the static linear panel data model with a single regressor. For this model, we derive the LIML estimator. We study the asymptotic behavior of this estimator under many-instruments asymptotics, by showing its consistency, deriving its asymptotic variance, and by presenting an estimator of the asymptotic variance that is consistent under many-instruments asymptotics. We briefly indicate the extension to the static panel data model with multiple regressors.     

Misspecified heterogeneity in panel data models

In this paper we analyse systematically through Monte Carlo simulations the consequences of misspecified heterogeneity on the most popular linear panel data models. We also illustrate our findings, through the estimation of a well known investment demand model.     

A nonparametric time-varying coefficient model for panel count data

In this research, we describe a nonparametric time-varying coefficient model for the analysis of panel count data. We extend the traditional panel count data models by incorporating B-splines estimates of time-varying coefficients. We show that the proposed model can be implemented using a nonparametric maximum pseudo-likelihood method. We further examine the theoretical properties of the estimators of model parameters. The operational characteristics of the proposed method are evaluated through a simulation study. For illustration, we analyse data from a study of childhood wheezing, and describe the time-varying effect of an inflammatory marker on the risk of wheezing.     

A test of the missing data mechanism for repeated measures data

The occurrence of missing data is an often unavoidable consequence of repeated measures studies. Fortunately, multivariate general linear models such as growth curve models and linear mixed models with random effects have been well developed to analyze incomplete normally-distributed repeated measures data. Most statistical methods have assumed that the missing data occur at random. This assumption may include two types of missing data mechanism: missing completely at random (MCAR) and missing at random (MAR) in the sense of Rubin (1976). In this paper, we develop a test procedure for distinguishing these two types of missing data mechanism for incomplete normally-distributed repeated measures data. The proposed test is similar in spiril to the test of Park and Davis (1992). We derive the test for incomplete normally-distribrlted repeated measures data using linear mixed models. while Park and Davis (1992) cleirved thr test for incomplete repeatctl categorical data in the framework of Grizzle Starmer. and Koch (1969). Thr proposed procedure can be applied easily to any other multivariate general linear model which allow for missing data. The test is illustrated using the hip-replacernent patient.data from Crowder and Hand (1990).     

A combined SR-CUSUM procedure for detecting common changes in panel data

Abstract

A procedure based on the sum of N Shiryayev–Roberts processes is proposed to detect common changes in panel data and shown to perform better for small portions of changed panels. The change-point for each panel is estimated by using the CUSUM process calculated in parallel. The changed panels are isolated by using the scores formed by the post-change parameter estimations and the common change point is then estimated from the isolated changed panels. A real example is used for illustration. An adaptive detection procedures is also proposed when the unknown post-change parameters are estimated adaptively in each panel.     

On the usability of the fluctuation test statistic to identify multiple cointegration break points

The fluctuation test suggested by Hansen and Johansen [Some tests for parameter constancy in cointegrated VAR models, Econometrics J. 2 (1999), pp. 306–333] intends to distinguish between the presence of zero and one break in cointegration relations. In this article, we provide evidence by Monte Carlo simulations that it also serves as a graphical device to detect even multiple break locations. It suffices to consider a simplified and easy-to-implement version of the original fluctuation test. Its break detection performance depends on the sign of change in cointegration parameters and the break height. The sign issue can be approached successfully by a backward application of the test statistic. If breaks are observable, the break locations are detected at the true location on average. We apply the graphical procedure to assess the cointegration of bond yields of Spain, Italy and Portugal with German yields for the period 1995–2013 which is surprisingly supported by the trace test. However, the recursive cointegration approach shows that a stable relationship with German yields is only present for sub-periods between the introduction of the Euro and the global financial crisis which is in line with expectations. The statistical robustness of these results is supported by a forward and backward application of the cointegration breakdown test by Andrews and Kim [Tests for cointegration breakdown over a short time period, J. Bus. Econom. Stat. 24 (2006), pp. 379–394].     

A new test of discordancy in cylindrical data

ABSTRACT

Cylindrical data are bivariate data from the combination of circular and linear variables. However, up to now no work has been done on the detection of outlier in cylindrical data. We introduce a definition of outlier for cylindrical data and present a new test of discordancy to detect outlier in this type of data, based on the k-nearest neighbor’s distance. Cut-off points of the new test statistic based on the Johnson-Wehrly distribution are calculated and its performance is examined using simulation. A practical example is presented using wind speed and wind direction data obtained from the Malaysian Meteorological Department.     

Benefits and limitations of panel data

Observations for a number of cross-sectional units over time have become increasingly available. The new data sources enable econometricians to construct and test more complicated behavioral models than a single cross sectional or time series data set would allow. The availability of new data sources, however, also raises new issues. In this paper we review some basic econo- metric methods that have been used to analyze such data sets. We also indicate areas of research where panel data may be useful.     

Benefits and limitations of panel data

Observations for a number of cross-sectional units over time have become increasingly available. The new data sources enable econometricians to construct and test more complicated behavioral models than a single cross sectional or time series data set would allow. The availability of new data sources, however, also raises new issues. In this paper we review some basic econo- metric methods that have been used to analyze such data sets. We also indicate areas of research where panel data may be useful.     

Statistical inference in dynamic panel data models

Anderson and his collaborators have made seminal contributions to inference with instrumental variables and to dynamic panel data models. We review these contributions and the extensive economic and statistical literature that these contributions spawned. We describe our recent work in these two areas, presenting new approaches to (a) making valid inferences in the presence of weak instruments and (b) instrument and model selection for dynamic panel data models. Both approaches use empirical likelihood and resampling. For inference in the presence of weak instruments, our approach uses model averaging to achieve asymptotic efficiency with strong instruments but maintain valid inferences with weak instruments. For instrument and model selection, our approach aims at choosing valid instruments that are strong enough to be useful.     

Response predictions in regressions on panel data

In this paper we consider the problem of obtaining best linear unbiased estimators of individual response coefficients in a Random Coefficient Linear Regression (RCR} Model, comparing alternative estimators for these response vectors through a simulation study. We also provide an empirical example that illustrates the estimation procedure proposed here.     

Approximate estimation in nonlinear panel data models

This paper is concerned with the estimation of a general class of nonlinear panel data models in which the conditional distribution of the dependent variable and the distribution of the heterogeneity factors are arbitrary. In general, exact analytical results for this problem do not exist. Here, Laplace and small-sigma appriximations for the marginal likelihood are presented. The computation of the MLE from both approximations is straightforward. It is shown that the accuracy of the Laplace approximation depends on both the sample size and the variance of the individual effects, whereas the accuracy of the small-sigma approximation is 0(1) with respect to the sample size. The results are applied to count, duration and probit panel data models. The accuracy of the approximations is evaluated through a Monte Carlo simulation experiment. The approximations are also applied in an analysis of youth unemployment in Australia.