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6.5. THE ‘PESO PROBLEM’ 187In ‘peso problem’ analyses, agents may have imperfect knowledgeabout some aspects of the underlying economic environment. Likeapplied econometricians, rational agents have observed an insufficientnumber of data points from which to exactly determine the true structureof the economic environment. Systematic forecast errors can ariseas a small sample problem.A Simple ‘Peso-Problem’ Example.The ‘peso problem’ was originally studied by Krasker [87] who observeda persistent interest differential in favor of Mexico even thoughthe nominal exchange rate was Þxed by the central bank. By coveredinterest arbitrage, there would also be a persistent forward premium,since if i is the US interest rate and i ∗ is the Mexican interest rate,i t − i ∗ t = f t − s t < 0. If the Þx ismaintainedatt +1,wehavearealizationof f t s 0 and a probability 1 − p that the s 0 pegwill be maintained. The process governing the exchange rate iss t+1 =(s1 with probability ps 0 with probability 1 − p . (6.31)The 1-period ahead rationally expected future spot rate isE t (s t+1 ) = ps 1 +(1− p)s 0 . As long as the peg is maintained andp>0, we will observe the sequence of systematic, serially correlated,but rational forecast errorss 0 − E t (s t+1 )=p(s 0 − s 1 ) < 0. (6.32)If the forward exchange rate is the market’s expected future spot rate,we have a rational explanation for the forward premium bias. Although ⇐(119)the forecast errors are serially correlated, they are not useful in predictingthe future depreciation.