Dynamics of Firms and Trade in General Equilibrium. Robert Dekle, Hyeok Jeong and Nobuhiro Kiyotaki USC, KDI School and Princeton

Transcription

1 Dynamics of Firms and Trade in General Equilibrium Rober Dekle, Hyeok Jeong and Nobuhiro Kiyoaki USC, KDI School and Princeon

2 real exchange rae.5 2 Figure. Aggregae Exchange Rae Disconnec in Japan year real exchange rae aggregae impor aggregae expor.

3 Firm level Kaigin daa ( rm h = ; 2; :::; 352; 52 four-digi level indusries, = ) [Dekle-Jeong-Ryoo(2)] ln Q F h = h + ln + r ln r + f ln p F + Y ln Y :77 :6 :35 :4 :74 :7 :9 :6 + Z ln Z + z ln z h + s ln s F h + u h :9 :65 :68 :4 :6 :3 : real exchange rae, r : real ineres rae, p F : foreign price, Y : world real income, Z : TFP, z h : indusry produciviy, s h : rm h s indusry expor share, excluding h. R 2 wihin :45; beween :; overall :3; # of observaions 5445

4 Small Open Economy wihou Governmen A coninuum of home rm h 2 H : Firm h produces I h number of di ereniaed producs for home and expor marke q H hi = a hi Z l H hi L l F hi L C A L C A m H hi L m F hi C A L ; for i = ; 2; ::; I h L qhi F C = a hi Z A 7 5 ; for i = ; 2; ::I h L L Home oupu for home and expor markes are produced as Q H = Q F = 2 Z Z 6 4 h2h h2h I h X i= I h X i= q H hi q F hi 3 7 C A dh C A dh

5 A new enran who pays a sunk cos E a dae draws an opporuniy of producing b 2 f; 2g number of new producs from dae +, where b = 8 >< >: 2; wih probabiliy (wp:) ; wp: The produciviy of each new produc is independenly disribued as a hi = 8 >< >: 2 [; a]; wp: F (a) = ( a ) ; wp: Assume ( + ) < ; > and >

6 A rm mus pay he xed mainenance cos for each produc in order o produce and mainain is produciviy. The mainained produc has he same produciviy in he nex period (a hi+ = a hi ) wih probabiliy ; and receives a new produciviy draw according o he same disribuion as a new enran wih probabiliy : Each rm can produce many producs. Each produc muliplies and dies like "amoeba." Home nal goods marke Q H = C + E N E + N N E is measure of enering rms, N is measure of di ereniaed producs mainained. No governmen secor.

7 The represenaive household supplies labor L ; consumes nal goods C and holds home and foreign real bonds D H and D H o maximize is expeced uiliy U = E X = subjec o he budge consrain L += ln C + = + H ln D H C + E N E + N + D H + D H = w L L + + R D H + R D H C A H : uiliy (liquidiy) shock o foreign bond holding

8 = wihou gov- Foreigners do no hold home bond! D H ernmen Foreign bond holding of home household where M H D H = R D H + p F Q F M H is oal impor Foreign aggregae demand for home expors are given by where Y Q F = (p F ) ' Y is an exogenous foreign demand parameer.

9 Compeiive Equilibrium Price of di ereniaed goods is a mark-up over he uni cos of composie inpu p H hi = w a hi Z p F hi = w = a hi Z w = (w L ) L Aggregae producion of he composie inpu X = L L L C A M H L L C A L

10 We conjecure ha in equilibrium, all rms choose o pay he xed mainenance cos wih posiive produciviy N + = ( + ) N + N E () Price index of home nal oupu for home marke = p H = a Z 2 Z 6 4 h2h I h X i= p H hi a df (a) = C A dh = A - w an Z (2)

11 Only producs wih higher han a produciviy is expored. a = ( + ) az N ' Y (-)+(+-)(-') (3) = p F Q F 82 >< 6 4 >: (-) +- az N (+-)(-') ( ' Y ) (-) 9 >= >; (-)+(+-)(-') (4) ' is small relaive o! aggregae expor is no very sensiive o he real exchange rae Low producive producs drop like " ies" wih an adverse shock, while expor of high producive producs is no very sensiive! Disconnec beween aggregae and rm-level responses

12 Equilibrium Dynamics The inpu composie marke equilibrium is X = L ( C ) w L+ ( L)(+ ) C A L (5) = X H a N (6) The value funcion of he average produc V = + ( + )E ( ;+ V + ) (7) where ;+ = C =C +. The average pro per produc = w X 7 a 5 (8) ( )N E = E ( ;+ V + ) : free enry (9) 3

13 The nal goods marke clearing implies C + E N E + N = an Z X H () Ne foreign asses evolve as D H = R D H + p F Q F ( L ) w X () Home demand for foreign bond is D H = H C R E ( ;+ + ) (2) ( 2) deermine w ; a ; X ; X H ; C ; ; V ;,N E,p F Q F, N + and D H as a funcion of he sae variables N ; D H ; Z, H,Y and R.

14 Solving for he Model Equilibrium A "shrunk" model: Shor-run dynamics of real exchange rae is dominaed by he liquidiy shock! Regard he real exchange rae as exogenous in he shor-run. From he free enry condiion, E 2 = E 6 4 ( + )E 8 >< >: C C an C C + +Z + 3 C7 A 5 (3) X + (-)N + - a + C A - 39 >= 7 5 >;

15 From labor marke clearing X = L ( C ) an Z A ( L)(+ ) L + C A L (4) The goods marke clearing condiion is C + N + E [N + ( + )N ] (5) 8 = an < Z X : a = N ; (a ; X ; C ; N + ) solve (3,3,4,5) as a funcion of N ; Z, Y and :

16 Impulse Response Funcions. Impulse response funcions from one uni of produciviy innovaion: 2 x.2 c n.2 z

17 2. Impulse response funcions from one uni of real exchange rae innovaion: x c n.2 xr

18 3. Impulse response funcions from one uni of foreign demand innovaion: 6 x c n.2 Ysar

19 4. Impulse response funcions from one uni of governmen purchases innovaion:.5 x c n.2 G