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11.1. A FIRST-GENERATION MODEL 329Flood—Garber Deterministic CrisesThe model is based on the deterministic, continuous-time monetarymodel of a small open economy of Chapter 10.2. All variables exceptfor the interest rate are expressed as logarithms–m(t) is the domesticmoney supply, p(t) the price level, i(t) the nominal interest rate, d(t)domestic credit, and r(t) the home-currency value of foreign exchangereserves. From the log-linearization of the central bank’s balance sheetidentity, the log money supply can be decomposed asm(t) =γd(t)+(1− γ)r(t). (11.1)Domestic income is assumed to be Þxed. We normalize units suchthat y(t) =y = 0. The money market equilibrium condition ism(t) − p(t) =−αi(t). (11.2)The model is completed by invoking purchasing-power parity and uncoveredinterest paritys(t) = p(t), (11.3)i(t) = E t [ ús(t)] = ús(t), (11.4)where we have set the exogenous log foreign price level and the exogenousforeign interest rate both to zero p ∗ = i ∗ = 0. Combine (11.2)—(11.4) to obtain the differential equation, ⇐(219)m(t) − s(t) =−α ús(t) (11.5)The authorities establish a Þxedexchangerateregimeatt =0bypegging the exchange rate at its t = 0 equilibrium value, ¯s = m(0).During the time that the Þx isineffect, ús(t) = 0. By (11.5), theauthorities must maintain a Þxed money supply at m(t) =¯s to defendthe exchange rate.Suppose that the domestic credit component grows at the rated(t) ú =µ. The government may do this because it lacks an adequatetax base and money creation is the only way to pay for governmentspending. But keeping the money supply Þxed in the face of expandingdomestic credit means reserves must decline at the rateúr(t) =−γ d(t)1 − γ ú = −µγ1 − γ . (11.6)