Are real GDP levels trend, difference, or regime-wise trend stationary? Evidence from panel data tests incorporating structural change.

• Author: Hegwood, Natalie

1. Introduction

   The evidence, presented by Nelson and Plosser (1982), that the unit root hypothesis cannot be rejected for most long-term U.S. macroeconomic time series ran contrary to many economic theories that relied on the idea of cyclical fluctuations around stable long-run trends, and it set off an explosion of research. Real GDP, real exchange rates, and real interest rates are among the many variables for which the unit root question has been investigated.

   A common criticism of unit root tests, notably the Augmented-Dickey-Fuller (ADF) test, is that they have low power against persistent, but stationary, alternatives with normally available time spans of data. One response to this criticism has been the development of panel unit root tests, such as those of Levin, Lin, and Chu (2002); Ira, Pesaran, and Shin (2003); and Maddala and Wu (1999), that exploit the cross section as well as the time series dimension of the data in order to increase power. These tests have been successful in finding evidence of stationarity that cannot be found by univariate methods, particularly for real exchange rates. (l)

   In a recent article, Rapach (2002) examined four international data sets of real GDP and real GDP per capita, which he divided into a variety of panels. He tested the panels using a variety of panel unit root tests and is rarely able to reject the unit root for his many combinations of panel, test, and lag length. He concludes that "the results overwhelmingly indicate that international real GDP and real GDP per capita levels are nonstationary" (p. 473). These results are important because, since the panel unit root tests employed have good power for the time series and cross-section dimension of the data, they show that previous failures to reject the unit root hypothesis for international real GDP were not caused by the low power of ADF tests.

   The central point of this article is that Rapach's results that the unit root null cannot be rejected against a level stationary alternative do not constitute evidence that international real GDP and real GDP per capita levels can be characterized by unit roots. Using panel methods, we show that there is strong evidence that the unit root null can be rejected against an alternative hypothesis of stationarity with one or two structural changes in either the slope or in both the intercept and the slope of the international real GDP series. Our research was inspired by the last paragraph of Rapach's paper, in which he suggests that, with univariate methods, the unit root null can be rejected more frequently once structural breaks are allowed in deterministic trends for long-horizon, as in Ben-David and Papell (1995), but not postwar, as in Cheung and Chinn (1996), international real GDP series.

   In order to focus on issues involving structural change, we start by using the same data analyzed by Rapach: annual real GDP from 1956 to 1996 for 13 countries, annual real GDP per capita from 1950 to 1992 for 21 countries, and annual real GDP per capita from 1900 to 1987 for 15 countries. (2) While this process is useful for providing a benchmark for our results, it obviously does not allow us to utilize all available data. Therefore, we also estimate panels for which the data is extended to 2003, providing a common end point.

   For the long-horizon annual real GDP per capita data set, we want to incorporate potential structural change in the level of the series from events such as World War I, World War II, and the Great Depression, as well as possible changes in growth rates. Since the level of GDP cannot change instantaneously, but rather is necessarily spread out over time, we estimate Innovational Outlier (IO) models, for which the effects of the structural change can occur slowly and that allow for a one-time change in both the intercept and the slope of the series. For the two postwar data sets, in which no events of comparable magnitude have occurred, the potential structural change is in growth rates, such as may have occurred during the growth slowdown of the 1970s, but not in levels. Since growth rates can change quickly, we estimate Additive Outlier (AO) models, for which the effects of the structural change occur instantaneously and that allow for a one-time change in only the slope of the series.

   We first conduct panel unit root tests that do not allow for structural change. For each panel, we simulate critical values under the unit root null that reflect the exact number of observations as well as the serial correlation and the contemporaneous correlation present in the actual data. The unit root null cannot be rejected (at the 10% significance level) in favor of the trend stationary alternative for any of the six panels. This both confirms Rapach's results and demonstrates that they are unchanged by the inclusion of additional data.

   We proceed to develop panel unit root tests that incorporate a one-time structural change. Murray and Papell (2000) construct an AO panel unit root test that allows a single common structural break in nontrending data, which they apply to panels of OECD annual unemployment rates. We extend their technique to trending data and develop AO models that allow for a slope change and IO models that allow for both an intercept and a slope change.

   For Rapach's original data, the results of the panel unit root tests in the presence of a onetime structural change are extremely strong. The unit root null can be rejected at the 1% significance level using an AO model for panels with postwar annual real GDP and real GDP per capita data and at the 5% significance level using an IO model for the panel with long-horizon annual real GDP per capita data. The breaks occur in the early 1970s for the postwar data and at the start of World War II for the long-horizon data. A different picture emerges when the data is extended through 2003. While the unit root null is still rejected at the 1% level for the panel with postwar annual real GDP per capita data and at the 10% significance level for the panel with long-horizon annual real GDP per capita data, it is not rejected (at the 10% level) for the panel with postwar annual real GDP data.

   We conjecture that with the additional data the effects of the growth slowdown of the 1970s might be counteracted by the resumption of higher growth in the 1980s and 1990s, and we therefore construct panel unit root tests that incorporate two structural changes. Using these tests, we reject the unit root null at the 1% level in favor of broken trend stationarity for all three panels. For the two postwar panels, the first break is in the early 1970s and the second is in the mid-1980s or early 1990s, while for the long-horizon data the first break is at the start of World War II and the second is in the mid-1960s. We conclude that real GDP levels are better described as regime-wise trend stationary, with two structural changes in either the slope or in both the intercept and the slope, than as either trend stationary...