Trend-stationarity, difference-stationarity, or neither: further diagnostic tests with an application to
U.S. Real GNP, 1875–1993
Paul Newbold
a,
, Stephen Leybourne
a
, Mark E. Wohar
b
a
Department of Economics, University of Nottingham, Nottingham NG7 2RD, UK
b
Distinguished Enron Professor, Department of Economics, University of Nebraska at Omaha, Omaha, NE 68182, USA
Received 4 May 1999; received in revised form 24 July 2000; accepted 28 July 2000
Abstract
Recent studies have found evidence suggesting that US Real GNP is trend-stationary over a long period of time. This paper presents an analysis of US real GNP over the period 1875–1993 and finds
that neither simple trend-stationary nor difference-stationary specifications are adequate. We find very strong evidence against a common fixed trend-stationary representation in the periods 1875–1929 and
1950 –1993. If a choice between difference-stationarity and trend-stationarity must be made, we prefer the former, as it implies less stringent assumptions. Our analysis provides a new diagnostic testing
procedure that practitioners can employ when faced with conflicting results concerning trend-station- ary versus difference-stationary specifications. © 2001 Elsevier Science Inc. All rights reserved.
JEL classification: C22; C51
Keywords: Unit root; Trend-stationary; Difference-stationary
1. Introduction
Prior to the publication of the Nelson and Plosser 1982 paper it was common to model real GNP as transitory deviations about a deterministic trend. With the publication of the
Nelson-Plosser paper, the tide changed, and US real GNP henceforth RGNP was deemed
Corresponding author. Tel.: 1011-44-115-951-5392; fax: 1011-44-115-951-4159. E-mail addresses:
paul.newboldnottingham.ac.uk P. Newbold. Journal of Economics and Business 53 2001 85–102
0148-619501 – see front matter © 2001 Elsevier Science Inc. All rights reserved. PII: S 0 1 4 8 - 6 1 9 5 0 0 0 0 0 3 5 - 7
to contain a nonstationary stochastic trend random walk and hence, it was argued, should be modeled as a first difference stationary DS process. Empirical studies by Stock and
Watson 1986, Perron and Phillips 1987, Campbell and Mankiw 1987, Evans 1989 and most recently, Murray and Nelson 2000, have failed to reject the null of a unit root in
RGNP supporting a DS model for post-World War II quarterly RGNP.
Other studies, using longer spans of data on RGNP, have argued against the apparent stochastic trend or DS nature of RGNP, in favor of a trend stationary TS process. For
example, using Dickey-Fuller tests,
1
Diebold and Senhadji 1996 and Cheung and Chinn 1997, analyzing US RGNP beginning in the 1870s, found very strong evidence against unit
autoregressive roots, and, by implication, in favor of TS.
2
Diebold and Senhadji 1996 suggested that, in part, this outcome could be attributed to the additional power resulting
from a larger sample, and also that the Nelson-Plosser findings were driven by the special circumstances in an important subperiod of their series.
As there is still considerable debate about the time series nature of RGNP, it seems appropriate to ask how robust are these results to various factors, including sample period
and testing techniques. The purpose of this paper is to critically examine the conflicting results concerning the data generating process for RGNP over the period 1875–1993, a
period chosen so as to make our results comparable with previous studies. In particular, this paper provides a new diagnostic testing procedure that practitioners can employ when faced
with conflicting results concerning TS vs. DS specifications. Specifically, we first utilize a moving Dickey-Fuller parametric bootstrap test, based on standard deviations, to test the
adequacy of a TS specification versus a DS specification. Second, we combine this test with multistep ahead forecasts and ratios of mean squared errors to provide guidance in choosing
between alternative specifications.
As a preview of our findings, we conclude that over the very long time period analyzed, RGNP is neither DS nor TS. We are not surprised by this conclusion. Stationarity of any sort
over a period of 119 years, including a vast array of shocks, strikes us as a priori implausible. For the full period 1875–1993 we find that neither simple TS nor DS specifications are
adequate. The aberrant behavior of the time series over the period 1930 –1949, is a strong factor in reaching this conclusion, as the data generating regime operating during these 20
years is very different from the data generating process operating before or subsequent to this period. We argue that it is not reasonable to believe that the same data generating regime
operated in 1930 –1949 as elsewhere, as this period in history witnessed major changes. When we discount the experience of the years 1930 –1949 we find very strong evidence
against a common fixed TS representation in the periods 1875–1929 and 1950 –1993. However, with respect to the post-World War II years, we do not find strong evidence against
a DS process. We thus favor the adoption of the DS model for RGNP for the periods 1875–1929 and 1950 –1993. The remainder of this paper is organized as follows: Section 2
provides a discussion of the difficulties involved in discerning between a TS and DS process. Section 3 provides empirical evidence and the application of new econometric techniques to
the time series properties of RGNP over the period 1875–1993, while section 4 presents results for subsamples 1875–1929 and 1950 –1993. Section 5 concludes the paper, with some
suggestions for applied times series analysis.
86 P. Newbold et al. Journal of Economics and Business 53 2001 85–102
2. Uncertainty about the unit root hypothesis
