Academic journal article Journal of Money, Credit & Banking

A Multicountry Characterization of the Nonstationarity of Aggregate Output

Academic journal article Journal of Money, Credit & Banking

A Multicountry Characterization of the Nonstationarity of Aggregate Output

Article excerpt

A Multicountry Characterization of the Nonstationarity of Aggregate Output

WHETHER THE UNIVARIATE TIME SERIES REPRESENTATION of real GNP contains a unit root or a deterministic linear trend has been much debated of late. The straightforward application of Box-Jenkins identification techniques strongly suggests the presence of a unit root, in that the autocorrelations of the first differences of the log of annual real GNP are all smaller than two (asymptotic) standard errors after the second lag or so, and the Q(k) statistic for low-order ARIMA models is small for large k. The tests derived by Dickey and Fuller concur in this conclusion. (1) The classic reference is Nelson and Plosser (1982), who find that a unit root dominates a linear trend in nearly every long U.S. macroeconomic series they examine. Schwert (1987) reached similar conclusions. Using varying methods, Harvey (1985), Rose (1986), Stock and Watson (1986), and Campbell and Mankiw (1987) report similar results for quarterly U.S. GNP. (2)

In a paper that focuses on the "long" U.S. GNP data, Cochrane (1988) reached a contrary conclusion. He found that less than 20 percent of the variance of the growth rate of the log of annual real per capita U.S. GNP (henceforth simply GNP) over the period 1869-1986 could be attributed to the presence of a unit root. (3) Cochrane contended that previous evidence in favor of a unit root in GNP is misleading, because nonrandomness in the high-order autocorrelations was overlooked. Although small, these autocorrelations are mostly negative, which is consistent with overdifferencing. He concluded that a statitonary AR(2) model about a linear trend fits the data better in-sample than did parsimonious unit root models.

The question of whether or not GNP contains a unit root arises frequently in macroeconomics. (4) For example, Mankiw and Shapiro (1985) show that when income has a unit root, findings that consumption is "too sensitive" to innovations in income (for example, Flavin 1981) may be an artifact of assuming trend stationarity. In fact, using differenced specifications, Deaton (1986), Campbell and Deaton (1987), and West (1988a) (all for the United States) and Kormendi and LaHaye (1987) (for a panel of thirty countries) found that consumption appears to be undersensitive to income. A properly specified consumption function is also needed to analyze aspects of fiscal policy such as the substitutability between public and private consumption, the possibility of Ricardian equivalence and the effects of transfer payments on savings. (5) whether or not income and money have unit roots is also important when estimating the demand for money and the effects of monetary policy under rational expectations. (6) Finally, recent theories of endogenous growth by P. Romer (1986), Lucas (1988), and King and Rebelo (1986) have implications for the nonstationarity of aggregate output.

Because the literature to date yields conflicting results for U.S. GNP, particularly for the long data, we examine the data from many countries, using the longest time series possible. In this paper, we draw on Cochrane (1988), Campbell and Mankiw (1987), and Cressie (1987) to develop the scaled variogram, R(k). We compute R(k) for the century-long data on annual real output for twelve countries, and for thirty-two countries over the postwar era. Campbell and Mankiw (1989) also compare results computed from the postwar quarterly time series for seven countries, and find results similar to our own. (7)

In section I, we briefly discuss the scaled variogram and its stimulated sampling distribution. In section 2, we estimate the scaled variograms for the century-long series from twelve countries and the postwar series from thirty-two countries. In section 3, we present a new simulation method for determining whether these series are more properly characterized as parsimonious trend stationary (TS) or difference stationary (DS) processes. …

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