The unit root hypothesis for aggregate output may not hold after all: new evidence from a panel stationarity test with multiple breaks.

• Author: Romero-Avila, Diego
• Position: Author abstract

1. Introduction

   Since the seminal work by Nelson and Plosser (1982), researchers have paid considerable attention to the presence of stochastic trends in macroeconomic variables. That work also changed the way macroeconomists think about secular trends and short-run fluctuations in business cycles. Since the existence of a unit root in output purports that shocks are permanent, short-run fluctuations cannot be explained by the traditional view as deviations around a deterministic trend that represents the secular component of the series. Instead, the trend function itself can fluctuate as a result of permanent shocks. King et al. (1991) found that supply factors are important in explaining economic fluctuations, but may not be the lone source of short-run fluctuations. Campbell and Mankiw (1987) stressed that demand shocks may also be the source of permanent shocks to output.

   The existence of a high degree of persistence in output has important implications in macroeconomics. For example, the Keynesian view, that most shocks to output are transitory and output fluctuations are temporary deviations from the secular trend, is inconsistent with a unit root in output. On the contrary, the real business cycle view conceives fluctuations as largely the result of real permanent shocks, essentially of a technological nature. This has important implications for economic policy since stabilization policies lose their effectiveness when variations of output are mainly permanent, thus running counter to the Keynesian view.

   Much of the empirical literature has focused on the nonstationarity properties of real U.S. gross national product (GNP). To cite a few studies, Perron and Phillips (1987), Schwert (1987), Campbell and Mankiw (1987), and Perron (1988) fail to reject the null hypothesis of a unit root in real U.S. GNP. These results have not gone unchallenged. Christiano and Eichenbaum (1990) and Rudebusch (1993) highlighted the low power of standard unit root tests of the augmented Dickey and Fuller (1979) type to distinguish between the trend stationary and unit root behavior in aggregate output.

   The development of cross-country data sets such as the long gross domestic product (GDP) series provided by Maddison (1989) and the Penn World Table (PWT) constructed by Summers and Heston (1990) has allowed researchers to provide international evidence on the unit root behavior in aggregate output. For instance, Wasserfallen (1986) found a unit root in GNP series for some Organization for Economic Co-operation and Development (OECD) countries over the postwar era. Kormendi and Meguire (1990) confirmed the existence of a unit root in output for twelve OECD countries over the period 1870-1985. (1) However, the seminal work of Perron (1989) uncovered the fact that nonstationarity may conceal the existence of stationarity with structural change, showing that standard unit root tests tend to misinterpret trend stationarity with a structural break as a unit root. By exogenously imposing a structural break in real U.S. GNP, Perron (1989) was able to strongly reject the unit root hypothesis. However, Zivot and Andrews (1992) provided slightly less evidence of a unit root in real U.S. GNP using a test that allowed for a structural break that was endogenously determined from the data.

   In an international context, Zelhorst and De Haan (1994, 1995) found evidence for OECD countries that over long-time periods, where the presence of structural change becomes more likely, the null of a unit root in output tends to be rejected in favor of regime-wise stationarity. Ben-David and Papell (1995) employed the Zivot and Andrews (1992) test to investigate the unit root behavior in output for 16 OECD countries over the period 1870-1989 and rejected the null of a unit root for one-third of the countries. Ben-David, Lumsdaine, and Papell (2003) revisited their previous work by employing the univariate unit root test developed by Lumsdaine and Papell (1997), which allows for two changes in level and slope. Their evidence points to the rejection of the unit root hypothesis for three-quarters of the countries.

   More recently, researchers have turned to a panel methodology with the aim of increasing statistical power in testing for a unit root in output. Fleissig and Strauss (1999) employed the panel unit root tests by Levin, Lin, and Chu (2002); Im, Pesaran, and Shin (2003); Maddala and Wu (1999); and the seemingly unrelated procedure developed by Abuaf and Jorion (1990) to analyze the unit root behavior in output for 15 OECD countries over the period 1900-1987. (2) They reported overwhelming evidence that OECD output is trend stationary even after controlling for cross-correlation through bootstrap methods. Along similar lines, Rapach (2002) extended the analysis of the nonstationarity properties of OECD output data using four different data sets of real GDP and real GDP per capita. As opposed to Fleissig and Strauss (1999), he provided overwhelming evidence of a unit root in aggregate output using the tests by Levin, Lin, and Chu (2002); Im, Pesaran, and Shin (2003); Abuaf and Jorion (1990); and the less restrictive seemingly unrelated approach by Taylor and Sarno (1998). The reason for the discordant results from these studies using apparently similar panel unit root tests may be the misspecification of the trend function governing the time series behavior in the output series. Rapach (2002), indeed, found it surprising that panel unit root tests fail to reject the unit root hypothesis for output series, but not for other variables, such as inflation rates, unemployment rates, and nominal interest rates. He called for future research to examine the robustness of his results along two dimensions. First, he suggested including structural breaks so as to avoid misinterpretation of trend stationarity with breaks as difference stationarity. Second, he suggested employing a panel stationarity test of the KPSS-type (Kwiatkowski et al. 1992), which takes stationarity as the null hypothesis.

   We respond to this call by revisiting the work of Rapach (2002) and employing the panel stationarity test with multiple breaks recently developed by Carrion-i-Silvestre, del Barrio-Castro, and Lopez-Bazo (2005). The use of this test will allow us to shed some light on whether aggregate output in the OECD is characterized by a stochastic trend, for which shocks have a persistent effect in each period, or is regime-wise stationary, for which much of the time shocks have only a temporary effect, but occasionally, some infrequent changes occur that have a permanent effect on output.

   The main contributions of this paper are the following. First, I apply the panel stationarity test of Carrion-i-Silvestre, del Barrio-Castro, and Lopez-Bazo (2005), which assumes a highly flexible trend function by incorporating an unknown number of changes in level and slope. This test is, thus, more general than the one developed by Im, Lee, and Tieslau (2005), which only allows for a maximum of two changes in level, but not in the slope coefficient. This can be very restrictive for output series that are clearly upward-trending and have been subject to several infrequent shocks of great magnitude such as the World Wars, the Great Depression, and the oil shocks of the seventies. (3) Second, as noted by Bai and Ng (2004), for many economic applications, it is more natural to take stationarity as the null hypothesis rather than nonstationarity. By doing so, one can be more confident of the presence of a unit root in output, because the null will only be rejected when there is strong evidence against it. Third, our test that takes stationarity as the null will complement the work by Hegwood and Papell (2005), who applied a homogeneous panel unit root test allowing for one shift in level and slope, and found evidence of trend stationarity with one structural break for OECD countries. Similar results were provided for OECD countries by Strazicich, Lee, and Day (2004) using the Lagrange multiplier (LM) unit root test with two mean shifts. Thus, our work can act as confirmatory analysis of the unit root hypothesis for real GDP. Fourth, as opposed to previous studies, I will carry out a formal analysis of the prevalence of cross-sectional dependence in our panels of OECD countries by deploying the recent test for cross-dependence developed by Pesaran (2004). Finally, as a further departure from previous studies, which use panel unit root tests that assume a restrictive form of cross-correlation through cross-section de-meaning, I will allow for more general forms of cross-sectional dependence. For that purpose, I simulate the bootstrap distribution of the panel stationarity test with multiple breaks to allow for any kind of cross-sectional correlation following the approach by Maddala and Wu (1999). The allowance for general forms of cross-sectional dependence is crucial for panel unit root testing, since it has been widely recognized in the literature that panel unit root and stationarity tests that do not explicitly allow for cross-sectional dependence across individuals show large size distortions (see O'Connell 1998; Maddala and Wu 1999; Strauss and Yigit 2003; Banerjee, Marcellino, and Osbat 2005).

   The remainder of the paper is structured as follows. Section 2 describes the data and the panel stationarity tests employed in this paper. Section 3 presents the results of the analysis of the time series properties in OECD output for the four data sets analyzed in Rapach (2002), and section 4 concludes the paper.

2. Data and Methodology

   Data Description

   We now briefly present the data sources of the four data sets of OECD output series used in the analysis: (4)

   * Annual real GDP data spanning the period 1956-1996 (International Financial Statistics, International Monetary Fund [IMF]). This data set is composed of 13 countries: Australia, Canada, Denmark, France, Ireland, Japan...