- The Uncertain Unit Root in U.S. Real GDP:Evidence with Restricted and Unrestricted Structural Change
unit root, structural change, real GDP
The trend-stationary model, where business cycles were modeled as stationary fluctuations around a linear deterministic trend, was the canonical representation of aggregate output until the publication of Nelson and Plosser (1982), who argued in favor of a difference-stationary model where current shocks have a permanent effect on the long-run level of macroeconomic and financial aggregates. Using Augmented-Dickey-Fuller (ADF) tests, they could not reject the unit root null hypothesis against the trend stationary alternative for 13 out of 14 long-term annual U.S. macro series, including real GNP.
Nelson and Plosser's findings of a unit root in U.S. real GNP have been called into question on a number of grounds. Much research has focused on studying the performance of conventional unit root tests: Rudebusch (1993) proposes a bootstrap approach to evaluate the tests. Using postwar data, he demonstrates that unit root tests have low power against economically relevant trend-stationary alternatives. Diebold and Senhadji (1996), using long-span annual U.S. GNP data, argue that Rudebusch's procedure produces evidence that favors trend-stationarity.
Ben-David and Papell (1995) and Ben-David, Lumsdaine, and Papell (2003), using tests for a unit root against the alternative of broken trend-stationarity allowing [End Page 423] for, respectively, one and two endogenous break points, developed by Zivot and Andrews (1992) and Lumsdaine and Papell (1997), reject the unit root null in favor of broken trend-stationarity for long-term U.S. GDP. In all cases, the estimated breaks coincide with the Great Depression and/or World War II.
Murray and Nelson (2002) examine the performance of ADF tests in the context of models where the effects of the Great Depression are large, but transitory, based on a parametric bootstrap of a Markov switching model for real GDP from 1870-1994. They find that when a temporary component from 1930-1945 is added to an underlying unit root process, the unit root hypothesis is (incorrectly) rejected too often. Kilian and Ohanian (2002) examine the performance of Zivot and Andrews unit root tests when both the Great Depression and World War II produce transitory fluctuations. They also find that the unit root hypothesis is rejected too often.
While a single structural change is (by definition) permanent, multiple structural changes can, in principle, be consistent with transitory fluctuations. In this paper we use Lumsdaine and Papell (1997) tests for a unit root in the presence of unrestricted structural change (two endogenous breaks) and Papell and Prodan (2003) tests for a unit root in the presence of restricted structural change (two offsetting structural changes) to investigate long-term U.S. real GDP. The unit root null is rejected at the 1% level with both tests. Using the Murray and Nelson (2002) procedure to evaluate the rejections, we find that, in contrast with ADF tests, the unit root null is not rejected too often if the data generating process is a unit root with transitory fluctuations.
1. Unit Root Tests for Long-Term Real Gdp
ADF tests for a unit root, both with and without allowing for shifts in the deterministic trend at unknown dates, can be described as follows:
for t = 1,....,T, where DU1t and DU2t are indicator dummy variables for the intercept changes in the trend function, occurring at times TB1 and TB2. That is, DU1 = 1 (t > TB1) and DU2 = 1 (t > TB2).
We use the "general-to-specific" recursive t-statistic procedure suggested by Ng and Perron (1995) to choose the number of lags. We set the maximum value of k equal to 8, and use a critical value of 1.645 from the asymptotic normal distribution to assess significance of the last lag. The null hypothesis of a unit root is rejected in favor of trend stationarity if α is significantly different from zero. Equation (1) is estimated sequentially for each break year Tbi = k + 2, ..., T - 2, where i = 1, 2 and T is...