NBER Working Papers by George Evans

We study the properties of generalized stochastic gradient (GSG) learning in forward-looking models. We examine how the conditions for stability of standard stochastic gradient (SG) learning both differ from and are related to E-stability, which governs stability under least squares learning. SG algorithms are sensitive to units of measurement and we show that there is a transformation of variables for which E-stability governs SG stability. GSG algorithms with constant gain have a deeper justification in terms of parameter drift, robustness and risk sensitivity.

We construct a rational expectations model in which aggregate growth alternates between a low growth and a high growth state. When all agents expect growth to be slow, the returns on investment are low, and little investment takes place. This slows growth and confirms the prediction that the returns on investment will be low. But if agents expect fast growth, investment is high, returns are high, and growth is rapid. This expectational indeterminacy is induced by complementarity between different types of capital goods. In a growth cycle there are stochastic shifts between high and low growth states and agents take full account of these transitions. The rules that agents need to form rational expectations in this equilibrium are simple. The equilibrium with growth cycles is stable un...