- The Great Depression and Output Persistence:A Reply to Papell and Prodan
business cycle, unit root, Great Depression
In a letter to this journal, Papell and Prodan (2004a), hereafter PP, conduct unit root tests for annual U.S. real GDP, 1870-1998, that allow for off-setting level shifts in the trend, following Papell and Prodan (2004b). PP report p-values of about 0.01 from a parametric bootstrap of their regression equation under homoskedasticity, but 0.05 if the bootstrap is instead based on the unobserved components representation of Murray and Nelson (2002) (hereafter MN), which was designed to incorporate into the null the heteroskedastic turmoil of the Great Depression and WWII. PP reach two conclusions: First, contrary to MN, the evidence favors the alternative hypothesis of a trend stationarity for long-run U.S. GDP with off-setting level shifts during the Depression-WWII period. Since this structural change is restricted to be transitory, an implication of their model is that there were no permanent shocks to GDP from 1870 to 1998. Second, PP conclude that rejection of the unit root in favor of trend-stationarity with offsetting level breaks is not subject to the MN critique that heteroskedasticity matters.
We consider PP's second point first. It seems to us that there is a very great difference between a p-value of 0.01 (under homoskedasticity) and 0.05 (under heteroskedasticity) as measures of the strength of the evidence against the unit root hypothesis. Though many economists may regard 0.05 as sufficient for rejection, some may care whether the probability of a type 1 error is 1 in 100 or 1 in 20. In that sense, the MN critique does matter. [End Page 429]
Turning to PP's rejection of the unit root, we note that it is based on the empirical distribution of their test statistic in MN's parametric model of real GDP that incorporates the unit root as well as other assumptions: the trend is a random walk, the Great Depression-WWII turmoil is a stationary AR(2) that switches on or off according to a Markov process, there is no other business cycle component, and shocks to the trend and Great Depression-WWII components are normal, homoskedastic, and orthogonal. The p-value of 0.05 reported by PP may reflect actual trend stationarity in the economy, or it may be the result of the violation of one or more of these other maintained assumptions. Since the MN data-generating process is driven by the higher volatility of the period through WWII, and noting that the PP break dummies switch in 1929 and 1940, we think it is relevant to consider the evidence from the more homogeneous post-war period. Figure 1 plots the p-value for the ADF test statistic1 as a function of the beginning year of the sample. Since the last break in PP occurs in 1940, we compute unit root statistics with data beginning in 1941. For starting dates from 1941 through 1944, p-values are essentially zero, but jump abruptly as the data from WWII is deleted, settling in around 0.50 by the early 1950s. Thus, post-war data contains no evidence at all against the unit root null. This could be because stationarity is so gradual that it does not become evident even over half a century (the low power of unit roots tests against local trend-stationary alternatives is widely recognized), or it could be that the lower p-values for the longer time series reflect failure to model adequately the extreme heterogeneity of the data over the entire 1870-1998 period.
Next we consider the economic implications of the trend stationary hypothesis. Fitting the PP trend function with restricted structural change, we obtain the stationary deviations from trend plotted in Figure 2. This implied cycle contains a number of features which call into question its credibility as a measure of the cyclical component of economic activity. Consider the following points:
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