On learnability of E–stable equilibria

While under recursive least squares learning the dynamics of the economy converges to rational expectations equilibria (REE) which are E–stable, some recent examples propose that E–stability is not a sufficient condition for learnability. In this paper, we provide some further evidence on the conditions under which E–stability of a particular equilibrium might fail to imply its stochastic gradient (SG) or generalized SG learnability. We also claim that the requirement on the speed of convergence of the learning process imposed by [4] also implies that E–stable equilibria are likely to be GSG learnable. We show this in a simple â€New Keneysian†model of optimal monetary policy design in which the stability of REE under SG learning. In this case, the paper gives the conditions which are necessary for reversal of learnability