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5.2. CALIBRATING A TWO-COUNTRY MODEL 155Now let a ‘tilde’ denote the deviation of a variable from its steady statevalue so that ˜k t = k t − k and write these equations out as0 = a 1˜kt+2 + a 2˜k∗ t+2 + a 3˜kt+1 + a 4˜k∗ t+1 + a 5˜kt + a 6˜k∗ t + a 7 Ã t+1+a 8 Ã ∗ t+1 + a 9Ãt + a 10 Ã ∗ t + a 11˜c ∗ t+1 + a 12˜c ∗ t + a 13, (5.45)0 = b 1˜kt+2 + b 2˜k∗ t+2 + b 3˜kt+1 + b 4˜k∗ t+1 + b 5˜kt + b 6˜k∗ t + b 7 Ã t+1+b 8 Ã ∗ t+1 + b 9Ãt + b 10 Ã ∗ t + b 11˜c ∗ t+1 + b 12˜c ∗ t + b 13, (5.46)0 = d 3˜kt+1 + d 4˜k∗ t+1 + d 5˜kt + d 6˜k∗ t + d 9 Ã t + d 10 Ã ∗ t+d 12˜c ∗ t + d 13 , (5.47)where the coefficients are given byj a j b j d j1 βQ 31 βQ 41 02 βQ 32 βQ 42 03 βQ 33 + Q 11 βQ 43 + Q 21 Q 714 βQ 34 + Q 12 βQ 44 + Q 22 Q 725 Q 13 Q 23 Q 736 Q 14 Q 24 Q 747 βQ 35 βQ 45 08 βQ 36 βQ 46 09 Q 15 Q 25 Q 7510 Q 16 Q 26 Q 7611 Q 37 Q 47 012 Q 17 Q 27 Q 7713 R 1 + βR 3 R 2 + βR 4 R 7Mimicking the algorithm developed for the one-country model andusing (5.47) to substitute out c ∗ t and c ∗ t+1 in (5.45) and (5.46) gives0 = ã 1˜kt+2 +ã 2˜k∗ t+2 +ã 3˜kt+1 +ã 4˜k∗ t+1 +ã 5˜kt +ã 6˜k∗ t +ã 7 Ã t+1+ã 8 Ã ∗ t+1 +ã 9 Ã t +ã 10 Ã ∗ t +ã 11 , (5.48)0 = ˜b 1˜kt+2 + ˜b 2˜k∗ t+2 + ˜b 3˜kt+1 + ˜b 4˜k∗ t+1 + ˜b 5˜kt + ˜b 6˜k∗ t + ˜b 7 Ã t+1+˜b 8 Ã ∗ t+1 + ˜b 9 Ã t + ˜b 10 Ã ∗ t + ˜b 11 . (5.49)