International macroe.. - Free

5.2. CALIBRATING A TWO-COUNTRY MODEL 151Table 5.3: Open-Economy MeasurementsStd. AutocorrelationsDev. 1 2 3 4 6ex t 0.01 0.61 0.50 0.40 0.40 0.12yt ∗ 0.014 0.84 0.62 0.36 0.15 -0.15c ∗ t 0.010 0.68 0.47 0.30 0.04 -0.15i ∗ t 0.030 0.89 0.75 0.57 0.40 0.07Cross correlations at lag k6 4 1 0 -1 -4 6y t ex t−k 0.43 0.42 0.41 0.41 0.37 0.03 0.32y t yt−k ∗ 0.28 0.22 0.21 0.36 0.43 0.36 0.22c t c ∗ t−k 0.26 0.39 0.28 0.25 0.05 0.15 0.26Notes: ex t is US net exports divided by GDP. Foreign country aggregates data fromFrance, Germany, Italy, and the UK. All variables are real per capita from 1973.1to 1996.4 and have been passed through the Hodrick—Prescott Þlter with λ = 1600.the same capital shares and Cobb-Douglas form of the production function,and identical utility. Let the social planner attach a weight of ω tothe domestic agent and a weight of 1 − ω to the foreign agent. In termsof efficiency units, the social planner’s problem is now to maximizesubject to,E t ∞ Xj=0β j [ωU(c t+j )+(1− ω)U(c ∗ t+j )], (5.27)y t = f(A t ,k t )=A t kt α , (5.28)yt ∗ = f(A ∗ t ,kt ∗ )=A ∗ t kt ∗α , (5.29)γk t+1 = i t +(1− δ)k t , (5.30)γkt+1 ∗ = i ∗ t +(1− δ)k∗ t , (5.31)y t + yt ∗ = c t + c ∗ t +(i t + i ∗ t ). (5.32)In the market economy interpretation, we can view ω to indicate thesize of the home country in the world economy. (5.28) and (5.29) are the