TY - JOUR
AU - Elliott,Graham
AU - Stock,James H.
TI - Inference in Time Series Regression When the Order of Integration of a Regressor is Unknown
JF - National Bureau of Economic Research Technical Working Paper Series
VL - No. 122
PY - 1992
Y2 - June 1992
DO - 10.3386/t0122
UR - http://www.nber.org/papers/t0122
L1 - http://www.nber.org/papers/t0122.pdf
N1 - Author contact info:
Graham Elliott
Department of Economics
UC, San Diego
9500 Gilman Drive
La Jolla, CA 92093
E-Mail: gelliott@weber.ucsd.edu
James H. Stock
Department of Economics
Harvard University
Littauer Center M26
Cambridge, MA 02138
Tel: 617/496-0502
Fax: 617/495-7730
E-Mail: James_Stock@harvard.edu
AB - It is well known that the distribution of statistics testing restrictions on the coefficients in time series regressions can depend on the order of integration of the regressors. In practice the order of integration is rarely blown. This paper examines two conventional approaches to this problem, finds them unsatisfactory, and proposes a new procedure. The two conventional approaches- simply to ignore unit root problems or to use unit root pretests to determine the critical values for second-stage inference - both often induce substantial size distortions. In the case of unit root pretests, this arises because type I and II pretest errors produce incorrect second-stage critical values and because, in many empirically plausible situations, the first stage test (the unit root test) and the second stage test (the exclusion restriction test) are dependent. Monte Carlo simulations reveal size distortions even if the regressor is stationary but has a large autoregressive root, a case that might arise for example in a regression of excess stock returns against the dividend yield. In the proposed alternative procedure, the second-stage test is conditional on a first-stage "unit root" statistic developed in Stock (1992); the second-stage critical values vary continuously with the value of the first-stage statistic. The procedure is shown to have the correct size asymptotically and to have good local asymptotic power against Granger-causality alternatives.
ER -