In their 1982 article, Nelson and Plosser provided evidence supporting the existence of an autoregressive unit root in a variety of macroeconomic time series. I re-examine their evidence using small-sample distributions for various unit root test statistics. These distributions are calculated from specific null and alternative models (including median-unbiased models that correct for OLS coefficient bias) estimated from the data. Contrary to earlier assertions, the null and alternative models of many macroeconomic series provide very different characterizations of persistence but cannot be distinguished with unit root tests.