The question of whether aggregate output is best described as a trend-stationary (TS) or as a difference-stationary (DS, or unit root) process continues to generate a substantial volume of research a dozen years after it was first raised by Nelson and Plosser (1982), including a recent paper by Rudebusch (1993). Rudebusch argues that "Based on the usual unit root tests, little can be said about the relative likelihood of the specific DS and TS models of real GNP." Rudebusch concludes by emphasizing "the importance of measuring the confidence intervals for estimates of persistence without conditioning on the TS or DS model." ; This paper provides a strong theoretical result on distinguishing TS and DS models, and gives confidence intervals for the GNP impulse response function that do not require such distinction. Theoretically, the paper shows that, in the absence of a priori specification restrictions, the classes of unit root and stationary processes are nearly observationally equivalent: no finite data sample can provide information on the TS/DS issue. The paper then shows how the principle of parsimony for time series model specification masks near observational equivalence and implicitly rules out plausible shapes for the univariate impulse response function. Finally, the paper provides confidence intervals for the GNP impulse response function using two methods that nest parsimonious TS and DS models.