Testing for spurious regression in a panel data model with the individual number and time length growing

This article shows a test for the spurious regression problem in a panel data model with a growing individual number and time series length. In the estimation, tapers are used and the integrated order for the remainder disturbance is extended to a real number; at the same time, the spurious regression problem can be detected without prior knowledge. Through Monte Carlo experiments, we examine the consistent estimators by various sizes of time length and individual number, in which the remainder disturbance is assumed to be either stationary or non-stationary. In addition, the asymptotic normality properties are discussed with a quasi log-likelihood function. From the power tests we can see that the estimators are quite successful and powerful.     

Estimation in a semiparametric panel data model with nonstationarity

In this paper, we consider a partially linear panel data model with nonstationarity and certain cross-sectional dependence. Accounting for the explosive feature of the nonstationary time series, we particularly employ Hermite orthogonal functions in this study. Under a general spatial error dependence structure, we then establish some consistent closed-form estimates for both the unknown parameters and the unknown functions for the cases where N and T go jointly to infinity. Rates of convergence and asymptotic normalities are established for the proposed estimators. Both the finite sample performance and the empirical applications show that the proposed estimation methods work well.     

Fixed T dynamic panel data estimators with multifactor errors

This article analyzes a growing group of fixed T dynamic panel data estimators with a multifactor error structure. We use a unified notational approach to describe these estimators and discuss their properties in terms of deviations from an underlying set of basic assumptions. Furthermore, we consider the extendability of these estimators to practical situations that may frequently arise, such as their ability to accommodate unbalanced panels and common observed factors. Using a large-scale simulation exercise, we consider scenarios that remain largely unexplored in the literature, albeit being of great empirical relevance. In particular, we examine (i) the effect of the presence of weakly exogenous covariates, (ii) the effect of changing the magnitude of the correlation between the factor loadings of the dependent variable and those of the covariates, (iii) the impact of the number of moment conditions on bias and size for GMM estimators, and finally (iv) the effect of sample size. We apply each of these estimators to a crime application using a panel data set of local government authorities in New South Wales, Australia; we find that the results bear substantially different policy implications relative to those potentially derived from standard dynamic panel GMM estimators. Thus, our study may serve as a useful guide to practitioners who wish to allow for multiplicative sources of unobserved heterogeneity in their model.     

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.     

Estimation and identification of change points in panel models with nonstationary or stationary regressors and error term

This article studies the estimation of change point in panel models. We extend Bai (2010 Bai, J. (2010). Common breaks in means and variances for panel data. Journal of Econometrics 157:78–92.[Crossref], [Web of Science ®] , [Google Scholar]) and Feng et al. (2009 Feng, Q., Kao, C., Lazarová, S. (2009). Estimation and Identification of Change Points in Panel Models, Working paper, Syracuse University. [Google Scholar]) to the case of stationary or nonstationary regressors and error term, and whether the change point is present or not. We prove consistency and derive the asymptotic distributions of the Ordinary Least Squares (OLS) and First Difference (FD) estimators. We find that the FD estimator is robust for all cases considered.     

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.     

Estimation of dynamic panel data models with both individual and time-specific effects

This paper proposes a generalized least squares and a generalized method of moment estimators for dynamic panel data models with both individual-specific and time-specific effects. We also demonstrate that the common estimators ignoring the presence of time-specific effects are inconsistent when N→∞$N\to \infty$ but T is finite if the time-specific effects are indeed present. Monte Carlo studies are also conducted to investigate the finite sample properties of various estimators. It is found that the generalized least squares estimator has the smallest bias and root mean square error, and also has nominal size close to the empirical size. It is also found that even when there is no presence of time-specific effects, there is hardly any efficiency loss of the generalized least squares estimator assuming its presence compared to the generalized least squares estimator allowing only the presence of individual-specific effects.     

Detecting and identifying interventions with the Whittle spectral approach in a long memory panel data model

This article provides a procedure for the detection and identification of outliers in the spectral domain where the Whittle maximum likelihood estimator of the panel data model proposed by Chen [W.D. Chen, Testing for spurious regression in a panel data model with the individual number and time length growing, J. Appl. Stat. 33(88) (2006b), pp. 759–772] is implemented. We extend the approach of Chang and co-workers [I. Chang, G.C. Tiao, and C. Chen, Estimation of time series parameters in the presence of outliers, Technometrics 30 (2) (1988), pp. 193–204] to the spectral domain and through the Whittle approach we can quickly detect and identify the type of outliers. A fixed effects panel data model is used, in which the remainder disturbance is assumed to be a fractional autoregressive integrated moving-average (ARFIMA) process and the likelihood ratio criterion is obtained directly through the modified inverse Fourier transform. This saves much time, especially when the estimated model implements a huge data-set.

Through Monte Carlo experiments, the consistency of the estimator is examined by growing the individual number N and time length T, in which the long memory remainder disturbances are contaminated with two types of outliers: additive outlier and innovation outlier. From the power tests, we see that the estimators are quite successful and powerful.

In the empirical study, we apply the model on Taiwan's computer motherboard industry. Weekly data from 1 January 2000 to 31 October 2006 of nine familiar companies are used. The proposed model has a smaller mean square error and shows more distinctive aggressive properties than the raw data model does.     

Testing for parameter constancy in the time series direction in panel data models

We propose tests for parameter constancy in the time series direction in panel data models. We construct a locally best invariant test based on Tanaka [Time series analysis: nonstationary and noninvertible distribution theory. New York: Wiley; 1996] and an asymptotically point optimal test based on Elliott and Müller [Efficient tests for general persistent time variation in regression coefficients. Rev Econ Stud. 2006;73:907–940]. We derive the limiting distributions of the test statistics as T→∞ while N is fixed, and calculate the critical values by applying numerical integration and response surface regression. Simulation results show that the proposed tests perform well if we apply them appropriately.     

A Monte Carlo comparison of GMM and QMLE estimators for short dynamic panel data models with spatial errors

We suggest a generalized spatial system GMM (SGMM) estimation for short dynamic panel data models with spatial errors and fixed effects when n is large and T is fixed (usually small). Monte Carlo studies are conducted to evaluate the finite sample properties with the quasi-maximum likelihood estimation (QMLE). The results show that, QMLE, with a proper approximation for initial observation, performs better than SGMM in general cases. However, it performs poorly when spatial dependence is large. QMLE and SGMM perform better for different parameters when there is unknown heteroscedasticity in the disturbances and the data are highly persistent. Both estimates are not sensitive to the treatment of initial values. Estimation of the spatial autoregressive parameter is generally biased when either the data are highly persistent or spatial dependence is large. Choices of spatial weights matrices and the sign of spatial dependence do affect the performance of the estimates, especially in the case of the heteroscedastic disturbance. We also give empirical guidelines for the model.     

A small sample estimator for a polynomial regression with errors in the variables

An adjusted least squares estimator, introduced by Cheng and Schneeweiss for consistently estimating a polynomial regression of any degree with errors in the variables, is modified such that it shows good results in small samples without losing its asymptotic properties for large samples. Simulation studies corroborate the theoretical findings.     

Structural breaks in panel data: Large number of panels and short length time series

The detection of (structural) breaks or the so called change point problem has drawn increasing attention from the theoretical, applied economic and financial fields. Much of the existing research concentrates on the detection of change points and asymptotic properties of their estimators in panels when N, the number of panels, as well as T, the number of observations in each panel are large. In this paper we pursue a different approach, i.e., we consider the asymptotic properties when N→∞ while keeping T fixed. This situation is typically related to large (firm-level) data containing financial information about an immense number of firms/stocks across a limited number of years/quarters/months. We propose a general approach for testing for break(s) in this setup. In particular, we obtain the asymptotic behavior of test statistics. We also propose a wild bootstrap procedure that could be used to generate the critical values of the test statistics. The theoretical approach is supplemented by numerous simulations and by an empirical illustration. We demonstrate that the testing procedure works well in the framework of the four factors CAPM model. In particular, we estimate the breaks in the monthly returns of US mutual funds during the period January 2006 to February 2010 which covers the subprime crises.     

Mean-Squared errors of small area estimators under a multivariate linear model for repeated measures data

In this paper, we discuss the derivation of the first and second moments for the proposed small area estimators under a multivariate linear model for repeated measures data. The aim is to use these moments to estimate the mean-squared errors (MSE) for the predicted small area means as a measure of precision. At the first stage, we derive the MSE when the covariance matrices are known. At the second stage, a method based on parametric bootstrap is proposed for bias correction and for prediction error that reflects the uncertainty when the unknown covariance is replaced by its suitable estimator.     

An additive–multiplicative mean model for panel count data with dependent observation and dropout processes

This paper discusses regression analysis of panel count data with dependent observation and dropout processes. For the problem, a general mean model is presented that can allow both additive and multiplicative effects of covariates on the underlying point process. In addition, the proportional rates model and the accelerated failure time model are employed to describe possible covariate effects on the observation process and the dropout or follow‐up process, respectively. For estimation of regression parameters, some estimating equation‐based procedures are developed and the asymptotic properties of the proposed estimators are established. In addition, a resampling approach is proposed for estimating a covariance matrix of the proposed estimator and a model checking procedure is also provided. Results from an extensive simulation study indicate that the proposed methodology works well for practical situations, and it is applied to a motivating set of real data.     

Analyzing panel count data with a dependent observation process and a terminal event

Panel count data occur in many fields and a number of approaches have been developed. However, most of these approaches are for situations where there is no terminal event and the observation process is independent of the underlying recurrent event process unconditionally or conditional on the covariates. In this paper, we discuss a more general situation where the observation process is informative and there exists a terminal event which precludes further occurrence of the recurrent events of interest. For the analysis, a semiparametric transformation model is presented for the mean function of the underlying recurrent event process among survivors. To estimate the regression parameters, an estimating equation approach is proposed in which an inverse survival probability weighting technique is used. The asymptotic distribution of the proposed estimates is provided. Simulation studies are conducted and suggest that the proposed approach works well for practical situations. An illustrative example is provided. The Canadian Journal of Statistics 41: 174–191; 2013 © 2012 Statistical Society of Canada     

Hausman-type tests for individual and time effects in the panel regression model with incomplete data

By comparing estimators of the variance of idiosyncratic error at different robust levels, two Hausman-type test statistics are respectively constructed for the existence of individual and time effects in the panel regression model with incomplete data. The resultant test statistics have several desired properties. Firstly, they are robust to the presence of one effect when the other is tested. Secondly, they are immune to the non-normal distribution of the disturbances since the distributional conditions are not needed in the construction of the statistics. Thirdly, they have more robust performances than the main competitors in the literature when the covariates are correlated with the effects. Additionally, they are very simple and have no heavy computational burden. Joint tests for both of the two effects are also discussed. Monte Carlo evidence shows that the proposed tests have desired finite sample properties, and a real data analysis gives further support.     

Modeling the contemporaneous relationship in a continuous variable panel model

Continuous-variable panel models are widely used in social and business research to assess the relationships between variables over time given measurements at several waves on a single sample of individuals. Emphasis is often placed on estimating and testing the cross-effects which are the regression coefficients indicating the lagged effect of one variable on another. For the simple two-variable model we consider the problem of incorpomating the contemporaneous relationship between the variables into the model. Three extensions of the “independent regressions” model are considered. Their similarities and differences are examined. The use of the models is illustrated by examining data on the attitudes toward the criminal justice system and capital punishment for a panel of petit jurors.     

Bias and mean squared error of the slope estimator in a regression with not necessarily normal errors in both variables

The least squares estimation of the slope parameter of a simple linear regression is biased if the regressor variable is measured with random errors. This bias as well as the mean squared error is computed up to the order of 1/T without assuming normality for the error variable. They depend on the fourth moment of the error variable.