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158 CHAPTER 5. INTERNATIONAL REAL BUSINESS CYCLESand investment rates areĩ t = γ˜k t+1 − (1 − δ)˜k t , (5.58)ĩ ∗ t = γ˜k ∗ t+1 − (1 − δ)˜k ∗ t . (5.59)Let world consumption be ˜c w t =˜c t +˜c ∗ t =ỹ t +ỹ ∗ t − (ĩ t + ĩ ∗ t ). By theoptimal risk-sharing rule (5.39) ˜c ∗ t =[(1− ω)/ω]˜c t,whichcanbeusedto determine˜c t = ω˜c w t . (5.60)It follows that ˜c ∗ t =˜c w t − ˜c t . The log-level of consumption is recoveredbyln(C t )=ln(X t )+ln(˜c t + c).Log levels of the other variables can be obtained in an analogous manner.Simulating the Two-Country ModelThe steady state values arey = y ∗ =1.53, k = k ∗ =3.66, i = i ∗ =0.42, c = c ∗ =1.11.The model is used to generate 96 time-series observations. Descriptivestatistics calculated using the Hodrick—Prescott Þltered cyclical parts ofthe log-levels of the simulated observations and are displayed in Table5.4 and Figure 5.4 shows the simulated current account balance.The simple model of this chapter makes many realistic predictions.It produces time-series that are persistent and that display coarse comovementsthat are broadly consistent with the data. But there arealso several features of the model that are inconsistent with the data.First, consumption in the two-country model is smoother than output.Second, domestic and foreign consumption are perfectly correlated dueto the perfect risk-sharing whereas the correlation in the data is muchlower than 1. A related point is that home and foreign output arepredicted to display a lower degree of co-movement than home andforeign consumption which also is not borne out in the data.