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148 CHAPTER 5. INTERNATIONAL REAL BUSINESS CYCLESIt follows that the solution for the capital stock isˆk t+1 = ω 1ˆkt −"ρω 2 − ρ#[b 3 ρ + b 4 ]Ât. (5.26)To recover ŷ t , note that the Þrst-order expansion of the productionfunction gives y t = f(A, k) +f A Â t + f k kˆk t ,wheref A =1, andf k =(αy)/k. Rearrangement gives ŷ t = Ât + ˆk t .Torecoverî t , subtractthe steady state value γk = i +(1− δ)k from (5.8) and rearrange to getî t =(k/i)[γˆk t+1 −(1−δ)ˆk t ]. Finally, get ĉ t =ŷ t −î t from the adding-upconstraint (5.9). The log levels of the variables can be recovered byln(Y t ) = ŷ t +ln(X t )+ln(y),ln(C t ) = ĉ t +ln(X t )+ln(c),ln(I t ) = î t +ln(X t )+ln(i),ln(X t ) = ln(X 0 )+t ln(γ).Simulating the ModelWe’ll use the calibrated model to generate 96 time-series observationscorresponding to the number of observations in the data. From thesepseudo-observations, recover the implied log-levels and pass them throughthe Hodrick-Prescott Þlter. The steady state values arey =1.717, k =5.147, c =1.201, i/k =0.10.Plots of the Þltered log income, consumption, and investment observationsare given in Figure 5.3 and the associated descriptive statistics aregiven in Table 5.2. The autoregressive coefficient and the error varianceof the technology shock were selected to match the volatility of outputexactly. From the Þgure, you can see that both consumption and investmentexhibit high co-movements with output, and all three seriesdisplay persistence. However from Table 5.2 the implied investmentseries is seen to be more volatile than output but is less volatile thanthat found in the data. Consumption implied by the model is morevolatile than output, which is counterfactual.
5.2. CALIBRATING A TWO-COUNTRY MODEL 1490.050-0.05GDP (broken)Consumption-0.1-0.15Investment-0.273 75 77 79 81 83 85 87 89 91 93 95Figure 5.3: Hodrick-Prescott Þltered cyclical observations from themodel. Investment has been shifted down by 0.10 for visual clarity.This coarse overview of the one sector real business cycle modelshows that there are some aspects of the data that the model does notexplain. This is not surprising. Perhaps it is more surprising is howwell it actually does in generating ‘realistic’ time series dynamics of thedata. In any event, this perfect markets—no nominal rigidities Arrow-Debreu model serves as a useful benchmark against which reÞnementscan be judged.5.2 Calibrating a Two-Country ModelWe now add a second country. This two-country model is a specialcase of Backus et. al. [5]. Each county produces the same good so wewill not be able to study terms of trade or real exchange rate issues.The presence of country-speciÞc idiosyncratic shocks give an incentiveto individuals in the two countries to trade as a means to insure each
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To Shirley, Laurie, and Leslii
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CONTENTSvii11 Balance of Payments C
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2 CHAPTER 1. SOME INSTITUTIONAL BAC
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80 CHAPTER 3. THE MONETARY MODEL3.1
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198CHAPTER 6. FOREIGN EXCHANGE MARK
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208 CHAPTER 7. THE REAL EXCHANGE RA
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230 CHAPTER 8. THE MUNDELL-FLEMING
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264CHAPTER 9. THE NEW INTERNATIONAL
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308 CHAPTER 10. TARGET-ZONE MODELSa
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324 CHAPTER 10. TARGET-ZONE MODELS
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326 CHAPTER 10. TARGET-ZONE MODELS
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328 CHAPTER 11. BALANCE OF PAYMENTS
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358 AUTHOR INDEXFama, E.F., 161, 16
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Subject IndexAAbsorption, 16, 230AI
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362 SUBJECT INDEXEfficient capital
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364 SUBJECT INDEXMethod of undeterm
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366 SUBJECT INDEXRisk neutrality, 9
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368 SUBJECT INDEXImpulse response a
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