Do Interest Rates Follow Unit-Root Processes?
Evidence from Cross-Maturity Treasury Bill Yields
West Virginia University
Department of Finance, The Chinese University of Hong Kong, Shatin, NT, Hong Kong
Abstract. It is widely reported in the literature that interest rates follow integrated processes. Many empirical
studies have, in fact, taken this result as a maintained hypothesis. This article demonstrates that the failure to
reject the hypothesis that interest rates contain a unit root may be due to the severe power problem of standard
test procedures in small samples. We analyze a panel of cross-maturity Treasury-bill yield series by employing a
panel-based test. This test exploits cross-maturity variations of the data to improve estimation efficiency and is
more powerful than standard tests for unit roots. The critical values of the test statistics are computed by Monte
Carlo simulations tailored to our samples. It is found that the null hypothesis that each yield series contains a
unit root can be decisively rejected. Our findings cast some doubt on previous studies that rely on the nonsta-
tionarity assumption of interest rates.
Key words: Treasury bill yields, Unit roots, panel data
It is well documented that interest rates follow unit-root processes. Representative work in
this area include Engle and Granger (1987), Perron (1988), Rose (1988), and Stock and
Watson (1988). These studies apply standard augmented Dickey and Fuller (1979, 1981,
hereafter ADF) and/or Phillips and Perron (1988, hereafter PP) tests for unit roots and
report overwhelming evidence that interest rates contain a unit root, regardless of the
terms to maturity, data frequencies, or sample periods. The results are so strong that they
cannot be altered even when structural breaks in the deterministic trend function of inter-
est-rate processes are allowed.
The conclusion that interest rates are nonstationary has, in
fact, been taken as a maintained hypothesis in further empirical research.
Whether interest rates are stationary is an important issue on both theoretical and
empirical grounds. If interest rates are indeed unit-root processes, any shocks to inter-
est rates are permanent and will never be reversed even in the long run. Empirically,
there is a growing body of literature that investigates the cointegration implications of
the expectations hypothesis of the term structure of interest rates (see, for example,
Bradley and Lumpkin, 1992; Campbell and Shiller, 1987; Engle and Granger, 1987;
Engsted and Tanggaard, 1994; Hall, Anderson, and Granger, 1992; Shea, 1992; and
Stock and Watson, 1988). It is well known that the cointegration analysis techniques
require all the component time series to be integrated processes of the same order.
Therefore, if interest rates are in fact stationary, it will not be appropriate to apply these
Review of Quantitative Finance and Accounting, 8 (1997): 69–81
© 1997 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands.