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d 1 d 1
n ; n ;
x E x E
Q 0 z db1 0 z W 0,( 0,d 0,1
( (,W z 0 z 0 z 0 z z z z z z z z z z z z z z z z z z 0 Date 0 Date 1 Date 2 Borrowing Crisis Repayment Investment Consumption Date 0 Budget Constraint: d 0,f + w 0 = k n + k t T-Production: k t R t k t N- Production: Time-to-build k (INTACT) n R n k n Prob = ρ (DISTRESSED) Need additional investment of r n k n + n θ n k n θ n k n T-goods Figure 1: Time Line = R n (θ n ) k n
0 0 0 0 M 0 0 0 0 0 0 z z z z z z z M 0 0
d( dd,d1 dn d( dd d1 dn
0 0 0 4 0 4 0 0 t 0 t 0 0 0 0 0 0 d; 0 dx z 0 d; dx
(,W 0 z (,W 0 0 z pz>z à pz>z U à 0 0 0 z z (,W 7 0 0 0 z z (,W z z z z z z z z z X 0 0 0 z z z (,W (,W 0 0 0 z z
de z z 0 0 z z z 0 0 z z z z z z d,w 0 0 0 (,W 0 0 0 (,W d,w d,q p z,q d,w,q d,q 0 0 K z wz D> z à X p 0 0 0 (,W K zwz D>z U à z z d,w Q d,q U X z (,W d,w d,q d,w Q d,q U de
d,w d,q d,q? d,q U 7? d,q 0 0 pz>z à d,q? d,q U 0 0 0 (,W? d,q U >z,> 0,Q (,W ;\t,4i X (,W 0 0 0 z>z U à z 0 ( (,W d,q d,q d,q d,q d,q d,q z 0 z z z z z 0 0 0 z z (,W z 0 (,W z d,w d,q d,q ;\t,4i ;\t,4i 7
z Æ z à z z z Æ z à z d,w z 0 0 0 (,W z z d,q z d,w Æz à d,w d,q? d,q U d,q 0 0 0 (,W d,q 0 0 0 (,W d,q d,q z
d L = n e L = n e L = 1 L = 1 θ n = 1 Panel (a) : Excess Supply θ n = 1 Panel (b) : Supply Shortage Figure 2: Equilibrium and the International Collateral Constraint d,q 0 0 0 (,W d,q z 0 0 0 (,W z 0 0 0 (,W z 0 0 0 (,W z d
W W 0 Æz à dm 0 d 1( L= n e L = 1 1 / λ t Figure 3: Interest Rates and International Collateral dm 0 d z 0 0 0 1(
z 0 0 0 (,W z z z 0 0 0 (,W z 0 0 0 (,W z Æz z z d ' 0 0 0 (,W z Ã
z z z z z z 0 z X 0 0 0 z z z z (,W I X p z 0 0 K zwz D>z à (,W d,w d,q I X 0 0 0 (,W É zp K z wz D> z U à z z d,w Q d,q U z d,w Q d,q U I z z z ÉzÆz 0 0 0 (,W z z U à z 0 0 0 (,W z z z
z z L = n e L = n e L = 1 L = 1 θ n = 1 Panel (a) : Regions I and II θ n = 1 Panel (b) : Regions III and IV Figure 4: Equilibrium when λ n < 1 d,q z z z z
z Q z z z z 1d 11 z 1d 11 Æz à z 0
Æz à Æz à 1n z z Q W z Q W z Æz 1n Ã
Q W z Q W z z 0 (,W z 0 (,W z 1; 1 1 db1 Q 0 z 1 z 1;
1 0 0 z z (,W z t z t 0 z z 0 0 (,W z z 4 z 4 0 0 0 (,W z z z 4 z ÉzÆz U 4 Ãw4D 4 z z 4 0 0 0 (,W 4 z z z 4 z 4 4 0 0 0 (,W 4 4 z 4 0 z z 4 z z 0 0 4 z z (,W 1 0 0 z z z (,W z 4 4 0 0 0 (,W z zz z 4 4 4 z
4 Æ z Ãw4D 4 Æz Ãw4D 1 0 0 z z z (,W 4 W 4 Q 4 0 0 0 (,W 4 Q zz z 4 4 z 1 1 É 1 É 1 4 Q 1x z z 4 z 4 0 0 0 (,W 1x
1 1 É 4 Q Æz Ãw4D 4 4 Q Æ z Ãw4D 4 1E z 1 1E Æz 4 Ãw4D Æz Ãw4D 4 Q z z z 1
z 0 (,W z z z 0 (,W 1 É z, 0,; (,W ;\t,4i d 1 1 É 1 É 0 0 wpz'æzdz Ãw4D (,W 4 Q 4 W 4 0 0 0 (,W 1 É 0 0 pzz à t (,W z (,W 0 0 0 z z z U à z 0 ( (,W z ÉÉ 0 É (,W z É 0 É (,W É z z z 1M (,W 0 z 0 0 z z z (,W 0 z 0 0 z z z 0 0 0 (,W 1M 4 W 4 Q z
p K zwz Dz à (,W 0 0 0 >z,> 0,Q (,W ;\t,4i d 1 1 1 0 0 pz>z à t (,W z 1 0 0 wp z'æ z D> z Ãw4D (,W 4 W 4 Q 4 0 0 0 (,W 4 Éz z> z Q Ãw4DU 4 (,W 0 0 0 z > z z U à z 0 ( (,W z 0 (,W z 4 Q z 0 (,W z I 0 I I (,W I (,W (,W I z z I 0 0 1 1 É z 4 Q 4 Q I z 0 (,W z I I 0 I (,W I
1 t ' 0 0 0 (,W t z É t 0 p00; (,W 'z. t I n( ρk n / z B ρk n / z B L = n e C B ρk n / z G ρk n / z G L = 1 A ρk n θ n = 1 Figure 5: Excess and Costly Volatility I I 1 n( 0 (,W z
z nd n1 nd 7 X z n1
z 0 nn,n; K (,W K z 0 K (,W z 0 K (,W 7 0 0 0 0 z z z (,W X 0 0 0 0 z z z z (,W z z nn n;
K d,q K d,q ; K d,q K d,q K K d,q K d,q nx ;? K d,q wd,q K d,q wd 0 yz à K (,W K d,w K d,q ; K d,q K K d,q K d,q K d,q K d,w K d,w 0 K (,W K d,q K d,q ; K d,q K d,q 0 K d,q nx
L = n e L = n e L = 1 L = 1 θ n = 1 Panel (a) : Regions (i) and (ii) θ n = 1 Panel (b) : Regions (iii) and (iv) Figure 6: Equilibrium with Banks
ne n L = n e C B L = 1 A θ n = 1 Figure 7: Multiple Equilibria with Banks ne n
nm,n z nm n
;( ;(
;d ;1 ;n ;d ;1 ;n
;; ;x ;E ;; ;x ;E
; ;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 z,x 0,X d 1 z,7 0,7 d 1 z,x z,7 0,X 0,7
z,x z 0,X 0 z,7 0,7 z 0 z,x 0,X d 1 z,7 0,7 d 1 z 0 d 1 z,x 0,X d 1 z,7 0,7 d 1 z 0 d 1 z z z z z 0 0 0 z z z z z 4 z 0 0 0 4 z z (,W z 4 4 0 0 0 (,W >z,> 0,Q (,W ;\t,4i z 0 d 1 t z z z 0 t 0 0 (,W z z 4 z z z z 4 4 0 0 0 4 z z (,W z 4 É4 0 p 0 0 ; (,W ' (,W 0 p 0 0 K zwz Dz z U Ã z z z 0 ( (,W
z z, 0,; (,W ;\t,4i d 1 1 É 1 É 0 0 wpz'æzdz Ãw4D (,W 4 Q 4 W 4 0 0 0 (,W 1 É 0 0 p z z à t (,W z (,W Kp 0 0 0 z wz D z z U à z 0 ( (,W z,x 0,X d 1 z,7 0,7 d 1 z, 0,; (,W, z,7, 0,7, z,x, 0,X 0,X 0,X 0 z,x z,x z t z z z 0 t 0 0 (,W z z 4 z z z z 4 4 0 0 0 4 z z (,W z 4 É4 0 p00; (,W ' (,W Kp 0 0 0 z wz D z z U à z z z 0 ( (,W z 0 (,W z,x 0,X d 1 z,7 0,7 d 1, z,7, 0,7, z,x, 0,X 0,X 0,X 0 z,x z,x z z,x 0,X d 1 z,7 0,7 d 1 0 0,X 0,X 0 z z,x z,x z B z,x 0,X d 1 0
0 0 z,7 0,7 z,x 0,X z,7 0,7 d 1 d 1 d 1 z z 0 z z B 0 d z d 1 d 1 0 z B d É 1 1 B ;\t,4i d 1 1 z 0 ( (,W t d 1 1 4 d 1 1 z z z t d 1 1 4 d 1 1 0 0 0 t d 1 1 4 d 1 1 (,W (,W (,W z 0 (,W É t d É 1 1 4 d É 1 1 z z z É t d É 1 1 4 d É 1 1 0 0 0 É t d É 1 1 4 d É 1 1 (,W (,W (,W
É z 0 (,W É 4 d 1 4 Q z z z z 4 É 4 d 1 4 0 Q 4 0 0 0 É 4 d 1 4 (,W Q (,W 4 Q I (,W (,W z I z 0 I 0 (,W 0 0 0 z z >z,> 0,Q (,W ;\t,4i d 1 1 1 0 0 p z> z t à t (,W z 1 0 0 wpz'æzd>z 4 Ãw4D (,W 4 W 4 Q 4 z> z Q Ãw4DU 4 (,W 0 0 0 z> z z U à z 0 ( (,W 4 0 0 0 4 (,W 0
z, 0,; (,W ;\t,4i d 1 É 1 1 É 0 0 pz>z Ãw4D 4 (,W 4 Q 4 W 1 É 0 0 p z z à t (,W t z (,W 0 0 0 z Kp z w z D z U à z 0 ( (,W 4 0 0 0 4 (,W 1 É 4 1 K d,q K ; K d,q K d,q 0 K (,W ; K d,q K d,q 0 K (,W d,q ; d,q 0 0 0 (,W 0 ; d,q 0 0 0 (,W 0 d,q z d,q z d,w z d,q z d,w
K d,q K d,q d,q d,q K d,q K d,q d,q d,q 0 0 0 K (,W (,W K d,q d,q 0 0 0 K (,W (,W K d,q d,q K z z 0 0 0 (,W K (,W ; z z 0 0 0 (,W K (,W ; z z ; z 0 0 0 (,W 0 K z z 0 0 0 (,W 0 K z z