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 show that replacing rational expectations by discounted least-squares (or "perpetual") learning generates a negative bias that becomes strongest when the fundamentals are strongly persistent, i.e. close to a random walk. Perpetual learning can explain the forward-premium puzzle while simultaneously replicating other features of the data, including positive serial correlation of the forward premium and disappearance of the anomaly in other forms of the test.