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144 CHAPTER 5. INTERNATIONAL REAL BUSINESS CYCLESy/k =(γ/β + δ − 1)/α. Now divide the production function (5.7) by kand re-arrange to get k =(y/k) 1/(α−1) =[(γ/β + δ − 1)/α] 1/(α−1) .Nowthat we know k, we can get y. From the accumulation equation (5.8),we have i/k = γ + δ − 1, and in turn, c/k = y/k − i/k. Again, given k,we can solve for c. To summarize, in the steady state we havey/k = (γ/β + δ − 1)/α, (5.14)i/k = γ + δ − 1, (5.15)c/k = y/k − i/k, (5.16)k = (y/k) 1/(α−1) . (5.17)Calibrating the ModelEach time period corresponds to a quarter. We set α = 0.33,β = 0.99, δ =0.10, γ =1.0038. 2 The transient technology shockevolves according to the Þrst-order autoregressionwhere ρ =0.93, and ² tiid∼ N(0, 0.010224 2 ).A t =(1− ρ)+ρA t−1 + ² t , (5.18)Approximate Solution Near the Steady State.Many methods have been applied to solve real business cycle models.One option for solving the model is to take a Þrst—order Taylor expansionof the nonlinear Þrst—order condition (5.13) in the neighborhoodaround the steady state. 3 . This yields the second—order stochasticdifference equation in k t − ka 0 +a 1 (k t+2 −k)+a 2 (k t+1 −k)+a 3 (k t −k)+a 4 (A t+1 −1)+a 5 (A t −1) = 0,(5.19)2 This is the depreciation rate used by Backus et. al. [5]. Cooley andPrescott [33] recommend δ =0.048. γ is the value used by Cooley and Prescottand King et. al..3 This is the method of King, Plosser, and Rebelo [83]