Testing for unit roots, and the related issue of measuring shock persi
stence, has attracted considerable econometric interest. The issue of
the size of the random walk component raised by Cochrane (1988), has b
een extended by Cogley (1990), Jaeger (1990), Leung (1992), and latter
ly Mayadunne, Evans and Inder (1995). In this paper we add to the deba
te by considering the effects of structural change on spectral-based m
easures of persistence illustrating potential problems via three macro
economic data examples. We find that significant structural breaks exi
st in the majority of the series investigated and that measured persis
tence differs markedly across distinct periods.