Restricted Structural Change and the Unit Root Hypothesis

I. INTRODUCTION An important issue in economics involves the long-run response of macroeconomic and financial aggregates to shocks and disturbances. In a classic paper, Nelson and Plosser (1982) argued that, contrary to the traditional view, current shocks have permanent effects on the long-run level of macroeconomic time series. Using statistical techniques developed by Dickey and Fuller (1979), they found evidence in favor of unit roots for 13 out of 14 long-term annual macro series, the only exception being the unemployment rate. They conclude that these series behave more like a random walk than like transitory deviations from a steadily growing trend. (1) Nelson and Plosser's findings of a unit root have been called into question on a number of grounds. Rudebusch (1992, 1993) demonstrates that unit root tests have low power against estimated trend stationary alternatives. Moreover, he shows that if trend stationary models are correct, difference stationary models do not yield good approximations to the medium-term dynamic response. Perron (1989) questions the ability of unit root tests to distinguish unit root from stationary processes that contain segmented or shifted trends. Incorporating an exogenous break point and specifying 1929 as the break date, he found evidence of broken trend stationarity for 10 out of the 13 series. Perron's analysis was disputed by several papers, most notably Christiano (1992), Banerjee, Lumsdaine, and Stock (1992), and Zivot and Andrews (1992). These authors argued that it is inappropriate to specify the break date as known as it is not reasonable to believe that the choice has been made independently of the data. (2) They suggest that an appropriate procedure is to select the break date endogenously. In particular, Zivot and Andrews (1992), using a data-dependent algorithm to determine the break point and finite-sample critical values, reject the unit root null at the 5% significance level for only 3 out of 13 Nelson-Plosser series real gross national product (GNP), nominal GNP, and industrial production. (3) Once this is done there is again little evidence against the unit root hypothesis. Allowing for two endogenous breaks, Lumsdaine and Papell (1997) reexamined the unit root hypothesis for the Nelson-Plosser data. Using finite-sample critical values, they rejected the unit root null for five series, the three series found by Zivot and Andrews plus per capita real GNP and employment, therefore finding more evidence against unit roots than Zivot and Andrews. These studies reject the unit root hypothesis in favor of broken trend stationarity for macroeconomic aggregates but not for prices or financial variables. This seems to confirm not only the common practice of macroeconomists to model movements in real GNP as stationary fluctuations around a linear deterministic trend (Blanchard 1981; Kydland and Prescott 1980) but also previous analyses, which had advanced the unit root hypothesis for the velocity of money (Gould and Nelson 1974) and stock prices (Samuelson 1973). Results of the previous studies show that for many of the aggregate time series, the estimated breaks coincide with World Wars or the Great Depression. Standard macroeconomic theory, however, argues that while these events have long-lasting transitory effects, they do not have permanent effects on aggregate variables. The decline in output associated with the Great Depression has generally been interpreted as a temporary response to a significant reduction in the money stock (Friedman and Schwartz 1963) and the substantial increase in output that occurred during World War II is described as the result of the huge temporary increase in government purchases caused by the war (Barro 1981). Murray and Nelson (2000), studying long-term real gross domestic product (GDP) data, argued that the fluctuations of 1930-1946 seem to have had a temporary effect on the level of output and lead to rejections of the unit root hypothesis when it is true. …