We investigate both the rational explosive inflation paths studied by McCallum (2001), and the classification of fiscal and monetary policies proposed by Leeper (1991), for stability under least squares (LS) learning of the rational expectations equilibria (REE). Our first result is that the explosive fiscalist REE is not locally stable under LS learning. In contrast, in Leeper's setting, there are policy regimes for which the fiscalist solution, in which fiscal variables affect the price level, can be a locally stable outcome under LS learning. However, for other policy regimes the monetarist solution is, instead, the locally stable REE.