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188CHAPTER 6. FOREIGN EXCHANGE MARKET EFFICIENCY(120)⇒Lewis’s ‘Peso-Problem’ with Bayesian LearningLewis [93] studies an exchange rate pricing model in the presence ofthe peso-problem. The stochastic process governing the fundamentalsundergo a shift, but economic agents are initially unsure as whethera shift has actually occurred. Such a regime shift may be associatedwith changes in the economic, policy, or political environment. Oneexample of such a phenomenon occurred in 1979 when the Federal Reserveswitched its policy from targeting interest rates to one of targetingmonetary aggregates. In hindsight, we now know that the Fed actuallydid change its operating procedures, but at the time, one may not havebeen completely sure. Even when policy makers announce a change,there is always the possibility that they are not being truthful.Lewis works with the monetary model of exchange rate determination.The switch in the stochastic process that governs the fundamentalsoccurs unexpectedly. Agents update their prior probabilities aboutthe underlying process as Bayesians and learn about the regime shiftbut this learning takes time. The resulting rational forecast errors aresystematic and serially correlated during the learning period.As in chapter 3, we let the fundamentals be f t = m t −m ∗ t −φ(y t −yt ∗ ),where m is money and y is real income and φ is the income elasticity ofmoney demand. 9 For convenience, the basic difference equation (3.9)that characterizes the model is reproduced heres t = γf t + ψE t (s t+1 ), (6.33)where γ =1/(1 + λ), and ψ = λγ, andλ is the income elasticity ofmoney demand. The process that governs the fundamentals are knownby foreign exchange market participants and evolves according to arandom walk with drift term δ 0f t = δ 0 + f t−1 + v t , (6.34)where v tiid∼ N(0, σ 2 v).We will obtain the no-bubbles solution using the method of undeterminedcoefficients (MUC). To MUC around this problem, begin with(6.33). From the Þrst term we see that s t depends on f t . s t also depends9 Note: f denotes the fundamentals here, not the forward exchange rate.