Unit Root Hypothesis
Economists debate whether various economic statistics, especially output, have a unit root or are trend stationary. A unit root process with drift is given in the first-order case by
where c is a constant term referred to as the "drift" term, and is white noise. Any non-zero value of the noise term, occurring for only one period, will permanently affect the value of as shown in the graph, so deviations from the line are non-stationary; there is no reversion to any trend line. In contrast, a trend stationary process is given by
where k is the slope of the trend and is noise (white noise in the simplest case; more generally, noise following its own stationary autoregressive process). Here any transient noise will not alter the long-run tendency for to be on the trend line, as also shown in the graph. This process is said to be trend stationary because deviations from the trend line are stationary.
The issue is particularly popular in the literature on business cycles. Research on the subject began with Nelson and Plosser whose paper on GNP and other output aggregates failed to reject the unit root hypothesis for these series. Since then, a debate—entwined with technical disputes on statistical methods—has ensued. Some economists argue that GDP has a unit root or structural break, implying that economic downturns result in permanently lower GDP levels in the long run. Other economists argue that GDP is trend-stationary: That is, when GDP dips below trend during a downturn it later returns to the level implied by the trend so that there is no permanent decrease in output. While the literature on the unit root hypothesis may consist of arcane debate on statistical methods, the hypothesis carries significant practical implications for economic forecasts and policies.
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