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/papers/gkn.pdf

Simulated minimum distance estimation of dynamic models with errors-in-variables

The coronavirus is a global event of historical proportions and just a few months changed the time series properties of the data in ways that make many pre-covid forecasting models inadequate. It also creates a new problem for estimation of economic factors and dynamic causal effects because the variations around the outbreak can be interpreted as outliers, as shifts to the distribution of existing shocks, or as addition of new shocks. I take the latter view and use covid indicators as controls to 'de-covid' the data prior to estimation. I find that economic uncertainty remains high at the end of 2020 even though real economic activity has recovered and covid uncertainty has receded. Dynamic responses of variables to shocks in a VAR similar in magnitude and shape to the ones identified before 2020 can be recovered by directly or indirectly modeling covid and treating it as exogenous. These responses to economic shocks are distinctly different from those to a covid shock which are much larger but shorter lived. Disentangling the two types of shocks can be important in macroeconomic modeling post-covid.

Modeling Macroeconomic Variations After COVID-19

The coronavirus is a global event of historical proportions and just a few months changed the time series properties of the data in ways that make many pre-covid forecasting models inadequate. It also creates a new problem for estimation of economic factors and dynamic causal effects because the variations around the outbreak can be interpreted as outliers, as shifts to the distribution of existing shocks, or as addition of new shocks. I take the latter view and use covid indicators as controls to 'de-covid' the data prior to estimation. I find that economic uncertainty remains high at the end of 2020 even though real economic activity has recovered and covid uncertainty has receded. Dynamic responses of variables to shocks in a VAR similar in magnitude and shape to the ones identified before 2020 can be recovered by directly or indirectly modeling covid and treating it as exogenous. These responses to economic shocks are distinctly different from those to a covid shock, and distinguishing between the two types of shocks can be important in macroeconomic modeling post-covid.

/pdf/modeling-macroeconomic-variations-after-covid-19-3e2i2ff9g6.pdf

Modeling Macroeconomic Variations after Covid-19

In a recent paper, Engel, C. (1999) presents monte-carlo evidence to suggest that unit root tests cannot detect a non-stationary component in the real exchange rate even when this component accounts for almost half of its longhorizon forecast error variance. This hidden non-stationary component led to the conclusion that long run purchasing power parity might not hold afterall. In this note, we first point out some conceptual difficulties with the statistic being used to measure the size of the non-stationary component, and then argue that it bears no systematic relationship with rejection rates in unit root tests. The problems stem from near observational equivalence of the simulated model in not one, but two dimensions. We then discuss the steps a practitioner can take to minimize Type I error in cases when the non-stationary component is hard to detect. Real exchange rate data for 19 countries are examined and estimates are obtained for the duration of the real exchange rate shocks.

PPP May not Hold Afterall: A Further Investigation

Uncertainty about the future rises in recessions. But is uncertainty a source of business cycle fluctuations or an endogenous response to them, and does the type of uncertainty matter? Answer: we find that sharply higher uncertainty about real economic activity in recessions is fully an endogenous response to other shocks that cause business cycle fluctuations, while uncertainty about financial markets is a likely source of the fluctuations. Financial market uncertainty has quantitatively large negative consequences for several measures of real activity including employment, production, and orders. Such are the main conclusions drawn from estimation of three-variable structural vector autoregressions. To establish causal effects, we propose an iterative projection IV (IPIV) approach to construct external instruments that are valid under credible interpretations of the structural shocks.

Serena Ng

Papers

Simulated minimum distance estimation of dynamic models with errors-in-variables

Modeling Macroeconomic Variations After COVID-19

Modeling Macroeconomic Variations after Covid-19

PPP May not Hold Afterall: A Further Investigation

Uncertainty and Business Cycles: Exogenous Impulse or Endogenous Response?