Testing for unit roots in heterogeneous panels

Any series of observations ordered along a single dimension, such as time, may be thought of as a time series. The emphasis in time series analysis is on studying the dependence among observations at different points in time. What distinguishes time series analysis from general multivariate analysis is precisely the temporal order imposed on the observations. Many economic variables, such as GNP and its components, price indices, sales, and stock returns are observed over time. In addition to being interested in the contemporaneous relationships among such variables, we are often concerned with relationships between their current and past values, that is, relationships over time.

Time Series Analysis

The panel data unit root test suggested by Levin and Lin (LL) has been widely used in several applications, notably in papers on tests of the purchasing power parity hypothesis. This test is based on a very restrictive hypothesis which is rarely ever of interest in practice. The Im–Pesaran–Shin (IPS) test relaxes the restrictive assumption of the LL test. This paper argues that although the IPS test has been offered as a generalization of the LL test, it is best viewed as a test for summarizing the evidence from a number of independent tests of the sample hypothesis. This problem has a long statistical history going back to R. A. Fisher. This paper suggests the Fisher test as a panel data unit root test, compares it with the LL and IPS tests, and the Bonferroni bounds test which is valid for correlated tests. Overall, the evidence points to the Fisher test with bootstrap-based critical values as the preferred choice. We also suggest the use of the Fisher test for testing stationarity as the null and also in testing for cointegration in panel data.

/pdf/a-comparative-study-of-unit-root-tests-with-panel-data-and-a-3mrtl7499l.pdf

A Comparative Study of Unit Root Tests with Panel Data and a New Simple Test

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

http://www.columbia.edu/~sn2294/pub/red03.pdf

Intergenerational time transfers and childcare

Consumption is partly a social activity, yet most studies of consumer behavior treat households in isolation. We investigate familial relationships in consumption patterns using a sample of parents and their children from the Panel Study of Income Dynamics. We find a positive and statistically significant parent-specific effect on children's consumption even after controlling for the effect of parental income, and we find similar effects for sibling pairs. Child consumption responds negatively to large post-retirement shortfalls in consumption of the parents. This behavior holds up even after allowing for the possibility of smaller parent-to-child transfers made necessary by the parental consumption shortfalls. These results suggest that although income is an important source of the intergenerational correlation, parental choices and experiences also affect consumption behavior of the children.

Intergenerational Linkages in Consumption Behavior

Many unit root and cointegration tests require an estimate of the spectral density function at frequency zero at some process. Kernel estimators based on weighted sums of autocovariances constructed using estimated residuals from an AR(1) regression are commonly used. However, it is known that with substantially correlated errors, the OLS estimate of the AR(1) parameter is severely biased. in this paper, we first show that this least squares bias induces a significant increase in the bias and mean-squared error of kernel-based estimators.

/pdf/an-autoregressive-spectral-density-estimator-at-frequency-2i8erf3e6y.pdf

An Autoregressive Spectral Density Estimator at Frequency Zero for Nonstationarity Tests

This paper uses a decomposition of the data into common and idiosyncratic components to develop procedures that test if these components satisfy the null hypothesis of stationarity. The decomposition also allows us to construct pooled tests that satisfy the cross-section independence assumption. In simulations, tests on the components separately generally have better properties than tests on the observed series. However, the results are less than satisfactory, especially in comparison with similar procedures developed for unit root tests. The problem can be traced to the properties of the stationarity test, and is not due to the weakness of the common-idiosyncratic decomposition. We apply both panel stationarity and unit root tests to real exchange rates. We find evidence in support of a large stationary common factor. Rejections of PPP are likely due to nonstationarity of country-specific variations. INTRODUCTION A notable result of Rothenberg (2000) and Elliott, Rothenberg and Stock (1996), is that for data with sample sizes frequently encountered, the maximal achievable power of unit root tests is rather low. There is now a growing interest in using panel data to perform unit root and stationarity analysis. One of the major motivations for using panel data for hypothesis testing is the enhanced power relative to a single time series. But most of the panel tests in the literature assume cross-sectional independence, which is difficult to satisfy for macroeconomic data. As discussed in O'Connell (1998), panel unit root tests tend to be oversized, while stationarity tests have low power.

/pdf/a-new-look-at-panel-testing-of-stationarity-and-the-ppp-1ido55temh.pdf

A New Look at Panel Testing of Stationarity and the PPP Hypothesis

Many unit root tests have distorted sizes when the root of the error process is close to the unit circle. This paper analyses the properties of the Phillips-Perron tests and some of their variants in the problematic parameter space. We use local asymptotic analyses to explain why the Phillips-Perron tests suffer from severe size distortions regardless of the choice of the spectral density estimator but that the modified statistics show dramatic improvements in size when used in conjunction with a particular formulation an autoregressive spectral density estimator. We explain why kernel based spectral density estimators aggravate the size problem in the Phillips-Perron tests and yield no size improvement to the modified statistics. The local asymptotic power of the modified statistics are also evaluated. These modified statistics are recommended as being useful in empirical work since they are free of the size problems which have plagued many unit root tests, and they retain respectable power.

Serena Ng

Papers

Intergenerational time transfers and childcare

Intergenerational Linkages in Consumption Behavior

An Autoregressive Spectral Density Estimator at Frequency Zero for Nonstationarity Tests

A New Look at Panel Testing of Stationarity and the PPP Hypothesis

Useful Modifications to Some Unit Root Tests with Dependent Errors and Their Local Asymptotic Properties