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5.1. CALIBRATING THE ONE-SECTOR GROWTH MODEL 141Table 5.1: Closed-Economy MeasurementsStd. AutocorrelationsDev. 1 2 3 4 6y t 0.022 0.86 0.66 0.46 0.27 0.02c t 0.013 0.85 0.72 0.57 0.38 0.14i t 0.056 0.89 0.73 0.56 0.40 0.08Cross correlation with y t−k at k6 4 1 0 -1 -4 -6c t 0.09 0.20 0.72 0.87 0.87 0.46 0.14i t 0.01 0.43 0.91 0.94 0.81 0.20 0.10Notes: All variables are logarithms of real per capita data for the US from 1973.1to 1996.4 and have been passed through the Hodrick—Prescott Þlter with λ = 1600.y t is gross domestic product less government spending, c t is consumption of nondurablesplusservices,andit is gross business Þxed investment. Source: InternationalFinancial Statistics.subject to Y t = A t Kt α (NX t) 1−α , (5.2)K t+1 = I t +(1− δ)K t , (5.3)Y t = C t + I t , (5.4)U(C) =ln(C). (5.5)The model allows for one normalization so you can set N =1.In the steady state, you will want the economy to evolve along abalanced growth path in which all quantities except for N grow at thesame gross rateγ = X t+1X t= Y t+1Y t= C t+1C t= I t+1I t= K t+1K t.The steady state is reasonably straightforward to obtain. However, ifcapital lasts more than one period, δ < 1, the dynamics of the modelmust be solved by approximation methods. We’ll Þrst solve for thesteady state and then take a linear approximation of the model aroundits steady state. The exogenous growth factor γ gives the model a