NONSENSE REGRESSIONS BETWEEN INTEGRATED PROCESSES OF DIFFERENT ORDERS
| DOI | http://doi.org/10.1111/j.1468-0084.1996.mp58003006.x |
| Date | 01 August 1996 |
| Author | Francesc Marmol |
| Published date | 01 August 1996 |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 58,3 (1996)
0305-9049
NONSENSE REGRESSIONS BETWEEN
INTEGRATED PROCESSES OF DIFFERENT
ORDERS
Francesc Marmol *
I. INTRODUCTION
In the last decade, the permanent nature of macroeconomic fluctuations
has become the center of intense theoretical and applied debate. Most
macroeconomic flows and stocks such as the output level or the employ-
ment rate evolve like 1(1) stochastic processes (e.g. Nelson and Plosser,
1982) while for instance, the price level appears to be an 1(2) stochastic
process (e.g. Juselius, 1993, 1994). It is unusual to find 1(3) or greater
economic series, but money stocks or price levels in hyperinflationary
economics such as interwar Germany or Hungary after World War II do
have this characteristic (Cagan, 1956). The nonstationarity of the macro-
economic time series induces, as a rule, (seemingly) significant correla-
tions when we run a linear regression between the levels of these time
series, independently of the theoretical meaning. This possibility was
suggested in a seminal paper by Granger and Newbold (1974) and is
known in the econometric literature as the nonsense or spurious regres-
sions problem. In 1986 Phillips developed an asymptotic theory for regres-
sions between very general - in the sense of allowing for
heterogeneously and weakly dependent distributed time series inde-
pendent 1(1) random processes showing that the distributions of the
conventional statistics are quite different from those derived under the
assumption of stationarity. He found that the distribution of the intercept
diverges, that both the regression and the R2 correlation coefficients have
non-degenerate distributions, that the distributions of the t-tests diverge
so that there are no asymptotically correct critical values for these
conventional significance tests and that the DurbinWatson test for auto-
correlation in the perturbations converges to zero. Marmol (1995a)
tI am very grateful to Stéphane Gregoir, Juan J. Dolado and Howard Petith for their
suggestions and comments. Financial support was provided by Beca de Formació de Doctors
i de Professorat Universitary en Determinades Arecs de Coneixement Deficitàries, General-
itat de Catalunya, Spain.
*Address for correspondence: Department of Economics, Universitat Autènoma de Barce-
lona, 08193, Bellaterra, Barcelona, Spain. E-mail: IEHIF@cc.uab.es. Fax: 5812012.
525
© Blackwell Publishers 1996. PuNished by Blackwell Publishers, 108 Cowley Road, Oxford 0X4 1JF,
UK & 238 Main Street, Cambridge, MA 02142, USA.
To continue reading
Request your trial