Testing for unit roots in heterogeneous panels

A number of panel unit root tests that allow for cross section dependence have been proposed in the literature, notably by Bai and Ng (2002), Moon and Perron (2003), and Phillips and Sul (2002) who use orthogonalization type procedures to asymptotically eliminate the cross dependence of the series before standard panel unit root tests are applied to the transformed series. In this paper we propose a simple alternative test where the standard DF (or ADF) regressions are augmented with the cross section averages of lagged levels and first-differences of the individual series. A truncated version of the CADF statistics is also considered. New asymptotic results are obtained both for the individual CADF statistics, and their simple averages. It is shown that the CADF_i statistics are asymptotically similar and do not depend on the factor loadings under joint asymptotics where N (cross section dimension) and T (time series dimension) tends to infinity, such that N/T tends to k, where k is a fixed finite non-zero constant. But they are asymptotically correlated due to their dependence on the common factor. Despite this it is shown that the limit distribution of the average CADF statistic exists and its critical values are tabulated. The small sample properties of the proposed tests are investigated by Monte Carlo experiments, for a variety of models. It is shown that the cross sectionally augmented panel unit root tests have satisfactory size and power even for relatively small values of N and T. This is particularly true of cross sectionally augmented and truncated versions of the simple average t-test of Im, Pesaran and Shin, and Choi's inverse normal combination test.

A Simple Panel Unit Root Test in the Presence of Cross Section Dependence

A number of panel unit root tests that allow for cross section dependence have been proposed in the literature that use orthogonalization type procedures to asymptotically eliminate the cross dependence of the series before standard panel unit root tests are applied to the transformed series. In this paper we propose a simple alternative where the standard ADF regressions are augmented with the cross section averages of lagged levels and first-differences of the individual series. New asymptotic results are obtained both for the individual CADF statistics, and their simple averages. It is shown that the individual CADF statistics are asymptotically similar and do not depend on the factor loadings. The limit distribution of the average CADF statistic is shown to exist and its critical values are tabulated. Small sample properties of the proposed test are investigated by Monte Carlo experiments. The proposed test is applied to a panel of 17 OECD real exchange rate series as well as to log real earnings of households in the PSID data.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/jae.951

A simple panel unit root test in the presence of cross-section dependence

Automatic forecasts of large numbers of univariate time series are often needed in business and other contexts. We describe two automatic forecasting algorithms that have been implemented in the forecast package for R. The first is based on innovations state space models that underly exponential smoothing methods. The second is a step-wise algorithm for forecasting with ARIMA models. The algorithms are applicable to both seasonal and non-seasonal data, and are compared and illustrated using four real time series. We also briefly describe some of the other functionality available in the forecast package.

/pdf/automatic-time-series-forecasting-the-forecast-package-for-r-5aiye6l7ao.pdf

Automatic Time Series Forecasting: The forecast Package for R

This paper proposes a residual-based Lagrange multiplier (LM) test for a null that the individual observed series are stationary around a deterministic level or around a deterministic trend against the alternative of a unit root in panel data. The tests which are asymptotically similar under the null, belong to the locally best invariant (LBI) test statistics. The asymptotic distributions of the statistics are derived under the null and are shown to be normally distributed. Finite sample sizes and powers are considered in a Monte Carlo experiment. The empirical sizes of the tests are close to the true size even in small samples. The testing procedure is easy to apply, including, to panel data models with fixed effects, individual deterministic trends and heterogeneous errors across cross-sections. It is also shown how to apply the tests to the more general case of serially correlated disturbance terms.

Testing for Stationarity in Heterogeneous Panel Data

Testing The Null Hypothesis Of Stationarity Against The Alternative Of A Unit Root In Panel Data With Serially Correlated Errors

This article extends the results obtained by Caudill, Ford, and Cropper in estimating and testing stochastic frontier cost functions in the presence of heteroscedastic inefficiency using cross-section data. It suggests the estimation of the model under the assumption of heteroscedasticity in both random terms. This avoids any possible misspecification bias and the use of incorrect tests. The same data as used by Caudill et al. supports the new specification. Moreover, we find that firm-specific inefficiency measures are extremely sensitive to the proposed correction for heteroscedasticity.

https://www.jstor.org/stable/info/1392293

Estimation of a Doubly Heteroscedastic Stochastic Frontier Cost Function

A Simple Panel Stationarity Test in the Presence of serial correlation and a common factor

This paper expands the tests of Hadri (2000, Econometrics Journal 3, 148–161) for the null of stationarity against the alternative of a unit root in panel data to the case where the time dimension of the panel is finite. This improves the finite sample properties of the tests for micro and macro panels. More importantly, the derivation of the tests for finite T as opposed to joint asymptotic where N and T→∞ simultaneously avoids the imposition of the rate condition N/T→ 0 and hence makes the test valid for any (T, N) combination. The asymptotic distributions of the tests are derived under the null and are shown to be normally distributed. Their moments for T fixed are derived analytically using Ghazal's (1994, Statistics and Probability letters 20, 313–319)1 lemma 1. Finite sample size and power are considered in a Monte Carlo experiment. The proposed tests have empirical sizes that are very close to the nominal 5% level. The Monte Carlo results clearly show that the power of the test statistics increases substantially with N, T and ω (ω being the number of unit root processes under the alternative). The results indicate that the assumption that T is asymptotic rather than fixed leads to tests that are substantially oversized particularly for relatively short panels with large N.

https://www.jstor.org/stable/pdfplus/23114967.pdf

Kaddour Hadri

Papers

Testing for Stationarity in Heterogeneous Panel Data

Testing The Null Hypothesis Of Stationarity Against The Alternative Of A Unit Root In Panel Data With Serially Correlated Errors

Estimation of a Doubly Heteroscedastic Stochastic Frontier Cost Function

A Simple Panel Stationarity Test in the Presence of serial correlation and a common factor

Testing for stationarity in heterogeneous panel data where the time dimension is finite