Quadrini (MRG Presentation)

8/19/2019 Quadrini (MRG Presentation)

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Financial Frictions in Macroeconomic Fluctuations

Vincenzo Quadrini(presented by Chi-Wa Yuen)

June 10, 2013


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1 Introduction

Role of …nancial frictions in business cycles (and crises) as

– impulse—source of ‡uctuations?

– propagation mechanism—ampli…cation of shocks?

Financial cycles—empirical regularity about …nancial variables (both prices and

quantities) and their relations with other macro variables over the business cycle?

Salient features of models with …nancial-market frictions

– missing/incomplete markets—departures from Arrow-Debreu and Modigliani-

Miller worlds—due to

asymmetric information;


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limited enforcement;

– heterogeneity in preferences/endowments/technologies between two groups of

agents that would end up being suppliers and demanders of loanable funds in

terms of preferences.


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2 Baseline model w/o …nancial frictions

2 periods: t = 0; 1:

2 agents: worker (w) vs. entrepreneur (e) ; di¤ering in

– preferences: "wh > 0 = "eh and

w > e (?);

– endowments: worker owns B vs. entrepreneur owns K ;

– technologies

yw0 = 0 vs. ye0 = A0K

he0

1;

yw1 = A1G

kw0;1

vs. ye1 = A1ke0;1; with G

0 (k) 1 for k 1 0 and

A1 > 1 ;

k j0;1 =

ji j0 + (1 ) k

j1;0; j = w;e; with

w = 0; e = () ;kw

1;0

= 0 < K = ke

1;0

; and = 0:


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Complete, perfectly competitive markets for labor(t = 0) ; capital (t = 1) ; bonds

(t = 0) ; and goods (t = 0; 1) :


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2.1 The worker

Worker’s problem

maxnhw0 ;c

w0 ;c

w1 ;k

w0;1;b

w0;1

oE 02640B@cw0

hw0

22

1CA + cw1

375

s:t:8>><>>:

cw

0 + q

0kw

0;1 + p

0bw

0;1 w

0hw

0 + B;

cw1 A1G

kw0;1

+ bw0;1;

cwt cmin ' 0; t = 0; 1;

given fw0; p0; q0; B; A1; g :


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Utility-maximizing conditions

w0 w0 = 1 =

w1

w1 ; (F OC (c

wt ))

hw0 = w0 w0; (F OC

hw0

)

w0 q0 = w1 A1G

0

kw0;1

; (F OC

kw0;1

)

w

0 p

0 = w

1 ; (F OC bw

0;1)

wt (cwt cmin) = 0; t = 0; 1: (CSC (c

wt ))


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Assume A1 > 1; then cw1 > cmin

CS C (cw1 )=) w1 = 0F OC (cw1 )=) w1 = 1: The

above conditions can be simpli…ed to

hw0 = (1 + w0 ) w0; (F OC

hw0

)

(1 + w0 ) q0 = A1G0

kw0;1

; (F OC

kw0;1

)

(1 + w0 ) p0 = ; (F OC bw0;1)

w0 (cw0 cmin) = 0: (CSC

cw0

)


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2.2 The entrepreneur

Entrepreneur’s problem

maxnhe0;c

e0;c

e1;k

e0;1;b

e0;1

oE 0 (ce0 + ce1)

s:t:

8>>>>>>>>>><>>>>>>>>>>:

ce0 + q0ke0;1 + p0b

e0;1 N0 +

ei N;

N0 e0 + q0K B; where e0 A0K

he01

w0he0;ei (q0 1) i

0; where i

0 arg max

hq0E () i

e0 i

e0

i;

ce1 A1ke0;1 + b

e0;1;

cet cmin ' 0; t = 0; 1;ie0 0;

given fw0; p0; q0; B ; K ; A0; A1; ; ; ()g :


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Utility-maximizing conditions

e0 e0 = 1 =

e1

e1; (F OC (c

et ))

w0 = (1 ) A0

K

he0

!; (F OC

he0

)

e0 [q0E () 1] + ei = 0; (F OC

ie0

)

e0q0 = e1A1; (F OC

ke0;1

)

e0 p0 = e1; (F OC

be0;1

)

et (cet cmin) = 0; t = 0; 1; (CSC (c

et ))

ei ie0 = 0: (CSC

ie0

)


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Assume A1 > 1; then ce1 > cmin

CS C (ce1)=) e1 = 0F OC (ce1)=) e1 = 1: We can

simplify F OC

ie0; ke0;1; b

e0;1

to

q0E () 5 1; (= if ie0 > 0) (F OC

ie0

)

(1 + e0) q0 = A1; (F OC

ke0;1

)

(1 + e0) p0 = : (F OC be0;1)


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2.3 Combining worker’s and entrepreneur’s F OCs

hw01 + w0

= w0 = (1 ) A0

K

he0

!

; (F OC (h0))

A1G0

kw0;1

1 + w0

= q0 = A11 + e0

; (F OC

k0;1

)

1 + w0= p0 =

1 + e0; (F OC

b0;1

)

F OC b0;1 =) w0 = e0 = 0:

Given -symmetry, F OC

k0;1

=) G0

kw0;1

= 1 =) kw0;1 = 0:

The asset prices are thus given by p0 = 1+

0

and q0 = A11+

0

; so that q0 p0

= A1:


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In equilibrium, hw0 = he0 = h0: F O C (h0) then implies

h0 = h(1 ) A0K (1 + 0)i1

1+ ;

w0 =

24(1 ) A0

K

1 + 0

!351

1+

:


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2.4 Market clearing

Labor: hs

0 hw

0 = he

0 hd

0

Capital: ks1 ie0 + K = k

w0;1 + k

e0;1 k

d1 (assuming zero rate of depreciation)

Bonds: bw0;1 + b

e0;1 = 0;

Final/intermediate goods

– yd0 cw0 + c

e0 + i

e0 = A0K

he01

ys0;

– yd1 cw1 + c

e1 = A1G

kw0;1

+ A1k

e0;1 y

s1:


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2.5 Business cycle implications

2.5.1 Case (i) : Reproducible capital [E () = 1]

The assumption A1 > 1 implies the following

– ie0 > 0F OC (ie0)=) q0 = 1 (given

ei = 0)

F OC

ke0;1;be0;1

=) p0 =

1A1

or r0;1 =

A1 1;

– cw0 = 0 = ce0 =) 0

F OC (b0;1)= A1 1 > 0:

Given 1 + 0 = A1; we have

– h0 =h

(1 ) A0K (A1)

i 11+ =)

@ ln(h0)@ ln(A0)

= 11+ = @ ln(h0)@ ln(A1)

;

– w0 = (1 ) A0 K A1

1

1+=)

@ ln(w0)@ ln(A0)

= 11+ & @ ln(w0)@ ln(A1)

= 1+;


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– @ ln(w0h0)

@ ln(A0) = 21+ &

@ ln(w0)@ ln(A1)

= 11+:

Macro e¤ects of a change in current productivity (4A0) and expected future productivity (4A1)

– y0 = A0K h10 =)

@ ln(y0)@ ln(A0)

= 21+ & @ ln(y0)@ ln(A1)

= 11+;

– i0 = y0 (given c0 = 0);

– kw0;1 = 0; given F OC

kw0;1; ke0;1

;

– ke0;1 = i0 + K = k1 =) @ ln(k1)@ ln(A0)

=

21+

i0k1

&

@ ln(k1)@ ln(A1)

=

11+

i0k1

;

– y1 = A1 (1 + k1) =) @ ln(y1)@ ln(A0)

=

21+

i01+k1

&

@ ln(y1)@ ln(A1)

= 1+

11+

i01+k1

;

– c1 = y1;

– q0 = 1;


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– p0 = 1=A1;

– bw0;1 = w0h0+B

p0

= be0;1 > 0; i.e., entrepreneur borrows from worker.

Increase in A0=)h0"=) y0 "=) i0 " (given c0 = 0) =) k1

= ke0;1

"=) y1 " :

Increase in A1 =) h0 "=) y0 "=) i0 " (given c0 = 0) =) k1

= ke0;1"=)

y1 " :


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2.5.2 Case (ii) : Fixed capital [E () = 0]

F OC ie0 =) ie0 = 0– ke0;1 = K; given k

w0;1 = 0;

– cw0 + ce0 = y0 > 0

CSC (c0)=) 0 = 0;

– F OC

k0;1

=) q0 = A1 > 1 =) both agents are indi¤erent betweencurrent and future consumption, so that bw0;1 = b

e0;1 becomes indeterminate.

Given 0 = 0; we have

– h0 =h

(1 ) A0K i 1

1+ = w0 =) @ ln(x0)@ ln(A0) = 11+ & @ ln(x

0)@ ln(A1)

= 0; x =

h;w:

Macro e¤ects of a change in current productivity (4A0) and expected future

productivity (4A1

)


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– y0 = A0K h10 =)

@ ln(y0)@ ln(A0)

= 21+ & @ ln(y0)@ ln(A1)

= 0;

– c0 = y0 (given i0 = 0);

– kw0;1 = 0; given F OC

kw0;1; ke0;1

;

– ke0;1 = K = k1 =) @ ln(k1)@ ln(A0)

= 0 = @ ln(k1)@ ln(A1)

;

– y1 = A1 (1 + k1) =) @ ln(y1)@ ln(A0) = 0 & @ ln(y1)@ ln(A1) = 1;

– q0 = A1 > 1;

– p0 = :

Increase in A0=)h0"=) y0 "=) c0 " (given i0 = 0) =) no e¤ects on k1 and y1:

Increase in A1 =) y1 " (given k1 = K ), but no e¤ects on h0; y0; c0; and

i0 (= 0) :


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3 Friction #1: Costly state veri…cation (under asym-

metric information) à la Bernanke-Gertler

Assume frictions in the production of new capital goods. The productivity para-

meter is freely observable by the entrepreneur, but can only be observed by other

agents by incurring a veri…cation cost per unit investment ie0: () is common

knowledge, though.

Suppose E () = 1: This guarantees capital accumulation in equilibrium.

The entrepreneur …nances her investment i

e

0 partly by using her internal funds N

0(net worth before the production of new capital goods) and partly by borrowing

external funds

ie0 N0

at the interest rate rk0;1 (denominated in new capital).


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Default if ie0 <

1 + rk0;1

ie0 N0

or if

< 1 + rk0;1 i

e0 N0

ie0! = (N

0(); ie

0(+); rk

0;1(+)

):

In case of default, the lender would pay the cost ie0 to observe the true value of

and then con…scates the entrepreneur’s residual assets ( ) ie0:

Zero-pro…t condition for (intra-period loan made by) the lender:

q0n

E


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represented by the RHS of the period-0 budget constraint, viz., N0 + ei —should

now be written as

N = N (N0; q0; ) maxn

0; q0n

i0 h

1 + rk0;1 (N0; i0; q0)i

(i0 N0)oo

; where

i0 = i0 (N0; q0) arg max E

nie0

h1 + rk0;1 (N0; i

0; q0)

i(ie0 N0)

o:


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Two possible equilibria: i

0 N

0 (internal …nance only) vs. i

0 > N

0 (external

…nance is necessary).

Focus on the latter case, esp. when N0 < i0 (N0; q0) < A0K

h10 ; so that

c0 > 0 and 0 = 0:

In this case, q0 = A1 > 1:

Labor employment h0 =h

(1 ) A0K

i1

1+

= w0 =)

@ ln(x0)

@ ln(A0) =

1

1+ &@ ln(x0)@ ln(A1)

= 0; x = h; w:

Output y0 = A0K h10 =)

@ ln(y0)@ ln(A0)

= 21+ & @ ln(y0)@ ln(A1)

= 0:


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3.1.1 Increase in A0

A0 "

=)h0"

=) y0 "=)

e

0 "=)N

0 "=) i0 "=) k1 "=) y1 " :

For e¤ects to be bigger than in baseline model, we require N0 e0 + q0K B

">

y0 "; which in turn requires B > q0K —unlikely to hold empirically.

In other words, this kind of …nancial friction would likely dampen the impact of a

transitory productivity shock.


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A1 "=) y1 " & q0 "=) N0 " =) i0 "=) k1 "=) y1 " :

But q0 "=) rk0;1 "=) "; i.e., the cost of external …nancing as well as the

probability of default would increase in response to an anticipated productivity (or

“news”) shock, thus implying pro-cyclicality of interest-rate premia and bankruptcy

rates (which can be reverted by adding adjustment cost of investment).


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3.1.3 Quantitative performance

Financial accelerator models like this fail to amplify signi…cantly e¤ects of produc-

tivity shocks, but can do so for other types (e.g., monetary-policy) of shocks.

The model could generate greater persistence , though, because k1 "=) N1 "=)rk0;1#

=)

i1 "=) k2 "=) y2 " & N2 " =)rk

1;2#=) i2 "=) k3 "=) y3 " & N3 " =)rk

2;3#=)

:::


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4 Friction #2: Collateral constraint (under limited

enforcement) à la Kiyotaki-Moore

Assume frictions in the enforcement of loan contracts, given borrowers’s ability to

repudiate debt.

The following collateral constraint has to be added to the entrepreneur’s utility-

maximization problem

be0;1 q1ke0;1: ('0)

Suppose E () = 0; so the entrepreneur has no incentive to invest and the RHS of

her period-0 budget constraint simpli…es to N0:

F OC

he0; ce0; c

e1

same as before, but F OC

ke0;1; b

e0;1

have to be revised

(1 + e0) q0 = A1 + '0q1; (F OC ke0;1)


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(1 + e0) p0 = + '0: (F OC

be0;1

)

Combining F OC

k0;1

with F OC

b0;1

and noting that q1 = A1G0

kw0;1

;where kw0;1 = K k

e0;1; we get

'0 =h

1 G0

K ke0;1

i(1 ) G0 K ke0;1

()


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Focus on the case where collateral constraint is binding

'0 > 0 ()=) G0

K ke0;1

< 1

=) ke0;1 < K; so that kw0;1 > 0:

In this case, ce0 = 0 and e0 > 0:

But cw0 = y0 ce0 > 0; so that

w0 = 0

F OC

kw0;1

=) q0 = A1G

0

K ke0;1

:

When be0;1 = q1ke0;1 and c

e0 = 0; entrepreneur’s period-0 budget constraint implies

(q0 p0q1) ke0;1 = N0

e0 + q0K B;

where the term q0 p0q1 can be interpreted as the minimum down-payment

required to purchase each unit of new capital.


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Since q1 = A1G0

K ke0;1

F OC kw0;1;bw0;1= q0 p0

; we can rewrite the above condi-

tion as

ke0;1 =

11

!K B

e0

q0

!: ()


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Direct e¤ects: A0 "=) y

e

0 (= y0) "=)

e

0 "

()

=) k

e

0;1 " (but k

w

0;1 #) =) y

e

1 "(> yw1 #) and y1 "

Indirect (ampli…cation) e¤ects: A0 "=) ::: =) ke0;1 "=) q0 " = A1G

0

K ke0;ke

0;1" if B > e

0 (i.e., if the entrepreneur is highly leveraged).


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Direct e¤ects: A1 "=) y1 = A1G K ke0;1 + A1ke

0;1

"

Indirect (ampli…cation) e¤ects: A1 "=) q0 " = A1G0

K ke0;1

"

()=)

ke0;1 "=) q0 " ()=) ke0;1 "=) q0 "

()=) ke0;1 "=) ::: =) y1 " :

In other words, anticipated news could generate asset-price boom, but still no

impact e¤ects on current output.


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4.1.3 Quantitative performance

Ampli…cation e¤ects are weak.

Reasons

– direct e¤ects of frictions are on investment, with marginal e¤ects on capital and

labor (the factor inputs that produce output); V working capital model

– low volatility of asset prices, which determine the stringency of the (endogenous)

borrowing constraint.

– risk aversion(?)

Documents

Quadrini (MRG Presentation)