Can perpetual learning explain the forward-premium puzzle?

Abstract

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 perpetual learning is potentially able to explain the forward premium puzzle.JEL classifications: D83, D84, F31, G12, G15

Learning, the Forward Premium Puzzle, and Market Efficiency

“…Although these 27 For a more analytical exposition on how learning dynamics leads to opposite movements in the forward premium and exchange rate changes, see Chakraborty (2004).…”

“…The idea is that the regression incorporates an omitted variable bias because the error term in the regression equation and Lewis (1993). Interested readers may also refer to Oh and Pippenger(1994), Mark and Wu(1998), Mark (2001) and Chakraborty (2004).…”

Learning and Macroeconomics

“…Chakraborty and Evans (2008) focus on the forward-premium puzzle. Letting s t be the log of the price of foreign currency and F t the log of the forward rate at t for foreign currency at t + 1, under RE and risk neutrality we have α = 0 and β = 1 in the forward-premium regression s t+1 − s t = α + β(F t − s t ) + u t+1 .…”

Do Emerging Market Currencies Lure the Forward Premium Bias to its Doom?

“…The first well known equation tying the future spot rate to the forward one is called "naïve regression" or "Levels regression", it was widely studied by Cornell (1977), Beljer & Khan (1980), Frankel (1981, Fama (1984), Barnhart and Szakmary (1991), McCallum (1994), Hai et al (1997), Roll & Yan (2000), Chakraborty & Haynes (2008), Chakraborty & Evans (2008), Thornton (2007), and so on……”