International Business Cycle Models

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1 Inernaional Buine Cycle Model Sewon Hur January 19, 2015 Overview In hi lecure, we will cover variou inernaional buine cycle model Endowmen model wih complee marke and nancial auarky Cole and Obfeld 1991 One good producion model wih complee marke and non-coningen bond Baxer and Crucini 1995 Two good producion model wih complee marke Backu, Kehoe, and Kydland 1994 Two good producion model wih nancial auarky Heahcoe and Perri 2002 One good producion model wih endogenou incomplee marke Kehoe and Perri Heahcoe and Perri 2002 Conider a wo counry, wo good, real buine cycle model Backu, Kehoe, and Kydland Counrie pecialize in producion of one inermediae good each. Final good are bundle of boh inermediae good, and are ued for conumpion and invemen. There i home bia in producion of nal good, and he ubiuabiliy beween domeic and foreign inermediae good i given by. The law of one price hold. I-rm in he home counry produce good a, while hoe in he foreign counry produce good b. Boh good are ued in producion of nal good f-rm, which i ued for conumpion and invemen. 1

2 Graphical Repreenaion BKK 1994 HOME Producion Inermediae Good a FOREIGN Producion Inermediae Good b a b Producion Final Good F a b Producion Final Good F Conumpion, Invemen Conumpion, Invemen 1.1 Houehold Open Macro Par 5: Seup Equilibrium FOC Seady Sae Calibraion Soluion Reul 200 Preference of repreenaive houehold π β U c, 1 n =0 where U c, 1 n = 1 [ c µ 1 n 1 µ] 1 γ. 1 γ Houehold upply labor and ren capial o compeiive inermediae goodproducing rm i-rm. The law of moion of capial i given by 1.2 Inermediae good k +1 = 1 δk + x. I -rm' aic maximizaion problem i given by max k,n F z, k, n w n r k.. k, n 0. Each counry pecialize in producion of a ingle good i-rm: a + a = F z, k, n z k α n 1 α b + b = F z, k, n z k α n 1 α 2

3 1.3 Final good F -rm' aic maximizaion problem i given by max k,n Reource conrain f -rm: G a, b q a a q b b.. a, b 0. c + x = Ga, b c + x = G a, b [ω 1 a 1 [ω 2 a 1 ] + ω 2 b ω 1 b 1 ] 1 wih ω 1 > ω 2 repreening home bia 1.4 Budge conrain Complee marke BKK 1994 c + x + q a +1 Q, +1 B, +1 = q a r k + w n + q a B 1, Bond economy c + x + q a Q B = q a r k + w n + q a B 1 Financial auarky Heahcoe and Perri 2002 c + x = q a r k + w n 1.5 Variable of inere Real exchange rae e P c P c = q a q a = q b q b law of one price Term of rade p q b = G b q a G a f-rm opimaliy Ne expor nominal nx = q a a q b b 3

4 1.6 Equilibrium Condiion From houehold opimizaion U c U n = q a w U c = +1 βu c +1 [ q a +1 r +1 1 δ ] Complee marke +1 π Q, +1 Q, +1 U c, +1 U c Bond economy = π +1 β U c, +1 q a, +1 U c q a = π +1 β U c, +1 qa, +1 Uc qa = U c, +1 e, +1 U c e Financial auarky Q = π +1 U c, +1 q a, +1 β U c q a From i-rm opimizaion From f-rm opimizaion Noe for linearizaion ˆx = x x x log1 + ˆx ˆx c + x = y w = F n r = F k q a = G a q b = G b 4

5 fx, y f x, ȳ + x xf x x, ȳ + y ȳf y x, ȳ Le denoe he eady ae hare of locally produced inermediae good in nal good producion. Noe ha = ā ā + b = ā ā + ā = qā Ḡ From marke clearing condiion for inermediae good, a + a = F z, k, n b + b = F z, k, n a ā + a ā ā + ā = F z, k, n F z, k, n F z, k, = ŷ n b b + b b b + b = F z, k, n F z, k, n F z, k, n = ŷ a ā ā ā ā + ā + a ā ā ā ā + ā = â + 1 â = ŷ 1 b b b b b + b b b + b b b = 1 ˆb + ˆb + b = ŷ 2 Uing he f -rm FOC G a = q a G b = q b 1 1 ω 1a 1 G 1 = q a ω 2b 1 G 1 = q b 5

6 log log a ā b b 1 1 Ḡ G G Ḡ 1 1 = log = log qa q a qb q b Ĝ â = ˆq a 3 Ĝ ˆb = ˆq b 4 Uing producion of f -rm Ga, b G a, b [ω 1 a 1 [ω 2 a 1 ] + ω 2 b ω 1 b 1 ] 1 Ga, b Gā, b Gā, b Ga, b Gā, b + a āg a ā, b + b bg b ā, b = a āg aā, b + b bg b ā, b Gā, b Ĝ = â ā b + ˆb ḠḠa ḠḠb Ĝ = âā qa Ḡ + ˆb b q b Ḡ Ĝ = â + ˆb1 5 Ĝ = â 1 + ˆb 6 The real exchange rae and erm of rade can be wrien a e = q a q a = q b q b p = q b q a = q b q a 6

7 log ē e log p p = log = log q a q a q a qa q b q b q a q a Now combine 4-6 and 7 o obain ê = ˆq a ˆq a = ˆq b ˆq b 7 ˆp = ˆq b ˆq a = ˆq b ˆq a 8 1 ˆb â ˆb â = ˆq a 9 = ˆq b = ê + ˆq b Similarly, ˆb â = ˆq a = ˆq a ê 1 ˆb â = ˆq b 10 Hence Combining 9 and 10 give Finally combine and 8 o obain 1 ˆq a = ê + ˆq b 11 1 ˆq b = ê ˆq a 12 ˆq a = 1 2 1ê 13 ˆq b = 1 2 1ê 14 ˆp = ˆq b ˆq a = ê + ˆq b ˆq a = 1 2 1ê 15 Noe ha ince < 1, he variance of he real exchange rae i alway le han he variance of he erm of rade. The oppoie i rue in he daa. relaed o he exchange rae diconnec puzzle: real exchange rae highly volaile in he daa, no in he model 7

8 1.7 Repone o produciviy hock In repone o a one percen increae o home produciviy, home foreign counry work more le and inve more le. In nancial auarky, invemen repond le. Figure 1: Produciviy, Oupu, and Invemen The produciviy increae and higher home labor upply lead o a fall in he price of good a. Thi increae he erm of rade a deerioraion for he home counry. Expor of good a increae, and in he cae of complee marke and bond rading, impor of good b alo increae ince he home counry wihe o inve more. The increae in invemen i higher han he increae in foreign conumpion, leading o a rade deci. In nancial auarky, invemen repond le becaue he home counry canno run a rade deci o nance more invemen. 8

9 Figure 2: Conumpion and Trade 1.8 Buine cycle aiic Thi cla of model generae counercylical ne expor, a in he daa. Thi i in conra o, for example, a wo-counry, one good pure exchange economy in which opimal rik haring implie ha an increae in home endowmen would lead o a maller increae in home conumpion and hu procyclical ne expor. In BKK, rik haring implie ha a poiive home produciviy hock lead o an increae decreae in home foreign invemen and oupu, and an increae in conumpion in boh counrie. However domeic invemen increae more han foreign conumpion, leading o a rade deci. make hay where he un hine. 9

10 % d dev % d dev % d dev % d dev of y Table 2: Model reul Benchmark parameer Economy Y c x N ex im nx Ir U.S. Daa A Volailiie Complee marke % d dev % d dev % d dev Bond economy % d dev of y Financial auarky Economy Y c x N ex im nx Ir y U.S. = GDP, Daa c = conumpion, x = 1.67 invemen, 0.81 n = employmen ex = a 2 = expor, im = b 1 = impor Complee nx = a 2 -pb 1 / marke y 1 = raio of ne expor 1.21 o GDP 0.53 all a 2.74 curren 0.31 price ir Bond = b 1 / economy a 1 = raio of real impor 1.21 o real domeic 0.52 non 2.73 expored 0.32 oupu Financial auarky 1.18 B Correlaion wih oupu y = GDP, c = conumpion, x = invemen, n = employmen ex = a 2 = expor, im = b 1 = impor correlaion beween nx = a Economy 2 -pb 1 / y 1 = raio of ne c,y expor x,y o GDP n,y all a curren price ex,y im,y nx,y p,y rx,y ir = b U.S. 1 / a Daa 1 = raio of real impor o real domeic non expored oupu B Correlaion wih oupu Complee marke Bond economy correlaion beween Financial auarky Economy c,y x,y n,y ex,y im,y nx,y p,y rx,y P U.S. = erm Daa of rade rx = real exchange rae Complee marke C Bond Cro economy counry correlaion and inernaional 0.97 relaive 0.59 price 0.86 volailiy Financial Compared auarky o he 0.92 complee 0.99 marke 0.99 and bond 1.00 economy, 0.15 he 0.00 nancial 0.65 auarky 0.65 model beer generae poiive correlaion inernaional beween correlaion in invemen % d dev and P = erm labor. Economy of rade Thi i becaue y 1,y 2 he channel C 1,c 2 highlighed x 1,x 2 N 1,nabove 2 i mued. p Rx Daa rx = real exchange rae C Cro counry correlaion and inernaional relaive price volailiy Complee marke Bond economy correlaion beween % d dev Financial auarky Economy y 1,y 2 C 1,c 2 x 1,x 2 N 1,n 2 p Rx Daa The daa aiic in able for panel A and B are calculaed from US ime erie for he period Complee The marke daa aiic 0.18 for panel C 0.65 refer o he correlaion of US erie wih erie for 0.78 an aggregae 0.55 of he Bond re economy of he world for he 0.17 period ee he daa appendix for deail. All 0.84 erie have 0.59 been logged Financial excep auarky ne expor 0.24 and Hodrick-Preco 0.85 filered 0.35 wih a 0.14 moohing parameer of The 1.18 aiic from he model are he average of 100 imulaion each 104 period long. Sandard error are available upon reque. The daa aiic in able for panel A and B are calculaed from US ime erie for he period The daa aiic for panel C refer o he correlaion of US erie wih erie for an aggregae of he re of he world for he period ee he daa appendix for deail. All erie have been logged excep ne expor and Hodrick-Preco filered wih a moohing parameer of The aiic from he model are he average of 100 imulaion each 104 period long. Sandard error are available upon reque. 2 Kehoe and Perri Model One good producion model wih endogenou incomplee marke. Planner' objecive: max [ λ 1 =0 β π U c1, l 1 + λ 2 β π U c2, l 2 ] =0 Reource conrain: i=1,2 [ ci + k i ] = i=1,2 [ F ki 1, A i l i + 1 δ k i 1 ] Enforcemen conrain: r= r β r π r U c i r, l i r V i ki 1, 10

11 Auarky problem: V i ki 1, = max β r π r U c i r, l i r r= r.. c i r + k i r F k i r 1, A i r l i r + 1 δ k i r 1 Soluion mehod exend Marce and Marimon Repone o produciviy hock In repone o a one percen increae o home produciviy, home counry work more and inve more. Wih complee marke, he foreign counry work le and inve le, while in he enforcemen economy he foreign counry alo inve more wih no change in employmen. If he planner hif invemen from foreign o home, hi would increae he value of defaul, he RHS of he enforcemen conrain. Inead he planner increae invemen in he foreign counry o increae he home value of aying in he conrac, he LHS of he enforcemen conrain. 11

12 Figure 3: Produciviy, Oupu, and Invemen LJXUHV,PSXOVH5HVSRQVHVWRD+RPH3URGXFWLYLW\6KRFN LJXUH3URGXFWLYLW\6KRFNV 2XWSXW ERUHLJQ&RXQWU\ +RPH&RXQWU\ RUHLJQ&RXQWU\ LJXUHV,PSXOVH5HVSRQVHVWRD+RPH3URGXFWLYLW\6KRFN 2XWSXW &RQVXPSWLRQ &RQVXPSWLRQ,QYHVWPHQW ERUHLJQ&RXQWU\ ERUHLJQ&RXQWU\ ERUHLJQ&RXQWU\ ERUHLJQ&RXQWU\,QYHVWPHQW &RPSOHWHPDUNHWV %RQG QIRUFHPHQW ERUHLJQ&RXQWU\ PSOR\PHQW ERUHLJQ&RXQWU\ &RPSOHWHPDUNHWV %RQG QIRUFHPHQW +RPH&RXQWU\1HW[SRUWV in he enforcemen economy. Becaue conumpion and invemen increae in RUHLJQ+RPH5DWLRRI0DUJLQDO8WLOLWLHV In he complee marke economy, rik haring lead foreign conumpion o rie along wih he rie in home conumpion. Rik haring i grealy inhibied 12 &RPSOHWHPDUNHWV %RQG QIRUFHPHQW

13 2XWSXW LJXUHV,PSXOVH5HVSRQVHVWRD+RPH3URGXFWLYLW\6KRFN he foreign counry wihou an increae in oupu, ne expor of he home counry become poiive in he enforcemen economy. PSOR\PHQW &RQVXPSWLRQ ERUHLJQ&RXQWU\ Figure 4: Conumpion and Trade +RPH&RXQWU\1HW[SRUWV,QYHVWPHQW ERUHLJQ&RXQWU\ ERUHLJQ&RXQWU\ RUHLJQ+RPH5DWLRRI0DUJLQDO8WLOLWLHV ERUHLJQ&RXQWU\ &RPSOHWHPDUNHWV %RQG QIRUFHPHQW &RPSOHWHPDUNHWV %RQG QIRUFHPHQW 2.3 Buine cycle aiic Alo included are aiic from Heahcoe and Perri 2002 complee marke and nancial auarky. The Enforcemen model perform well in maching cro counry correlaion, while geing he cyclicaliy of ne expor wrong. Noe ha all verion ge cro counry conumpion correlaion o be more higher han ha of oupu. he conumpion correlaion puzzle The enforcemen economy doe perform beer in ha regard. corr Daa CM Enforcemen CM adj co BKK 94 HP 02 y, y c, c x, x n, n nx, y y 13