Can Perpetual Learning Explain the Forward Premium Puzzle?

Under rational expectations and risk neutrality the linear projection of exchange rate change on the forward premium has a unit coefficient. However, empirical estimates of this coefficient are significantly less than one (and often negative). We investigate whether replacing rational expectations by discounted least squares (or "perpetual") learning can explain the result. We calculate the asymptotic bias under perpetual learning and show that there is a negative bias that becomes strongest when the fundamentals are strongly persistent, i.e. close to a random walk. Simulations confirm that adaptive learning is potentially able to explain the forward premium puzzle.