Information Frictions in Securitization Markets: Investor ...
Notes on Financial Frictions Under Asymmetric Information and Costly State Verification
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Transcript of Notes on Financial Frictions Under Asymmetric Information and Costly State Verification
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Notes on Financial Frictions Under Asymmetric Information and Costly
State Verification
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Incorporating Financial Frictions into a Business Cycle Model
• General idea:– Standard model assumes borrowers and lenders
are the same people..no conflict of interest
– Financial friction models suppose borrowers and lenders are different people, with conflicting interests
– Financial frictions: features of the relationship between borrowers and lenders adopted to mitigate conflict of interest.
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Discussion of Financial Frictions
• Simple model to illustrate the basic costly state verification (csv) model. – Original analysis of Townsend (1978), Bernanke-
Gertler.
• Integrating the csv model into a full-blown dsge model.– Follows the lead of Bernanke, Gertler and Gilchrist
(1999).– Empirical analysis of Christiano, Motto and Rostagno
(2003,2009).
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Simple Model• There are entrepreneurs with all different levels of
wealth, N. – Entrepreneur have different levels of wealth because they
experienced different idiosyncratic shocks in the past.
• For each value of N, there are many entrepreneurs.
• In what follows, we will consider the interaction between entrepreneurs with a specific amount of N with competitive banks.
• Later, will consider the whole population of entrepreneurs, with every possible level of N.
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Simple Model, cont’d• Each entrepreneur has access to a project with
rate of return,
• Here, is a unit mean, idiosyncratic shock experienced by the individual entrepreneur after the project has been started,
• The shock, , is privately observed by the entrepreneur.
• F is lognormal cumulative distribution function.
0
dF 1
1 Rk
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Banks, Households, Entrepreneurs
HouseholdsBank
entrepreneur
entrepreneurentrepreneur
entrepreneur
entrepreneur
Standard debt contract
~ F , 0
dF 1
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• Entrepreneur receives a contract from a bank, which specifies a rate of interest, Z, and a loan amount, B.– If entrepreneur cannot make the interest
payments, the bank pays a monitoring cost and takes everything.
• Total assets acquired by the entrepreneur:
• Entrepreneur who experiences sufficiently bad luck, , loses everything.
total assetsA
net worthN
loansB
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• Cutoff,
• Cutoff higher with:– higher leverage, L– higher
gross rate of return experience by entrepreneur with ‘luck’,
1 Rk total assetsA
interest and principle owed by the entrepreneurZB
1 Rk A ZB
Z1 Rk
BNAN
Z1 Rk
leverage LAN
1AN
Z1 Rk
L 1L
Z/1 Rk
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• Cutoff,
• Cutoff higher with:– higher leverage, L– higher
gross rate of return experience by entrepreneur with ‘luck’,
1 Rk total assetsA
interest and principle owed by the entrepreneurZB
1 Rk A ZB
Z1 Rk
BNAN
Z1 Rk
leverage LAN
1AN
Z1 Rk
L 1L
Z/1 Rk
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• Cutoff,
• Cutoff higher with:– higher leverage, L– higher
gross rate of return experience by entrepreneur with ‘luck’,
1 Rk total assetsA
interest and principle owed by the entrepreneurZB
1 Rk A ZB
Z1 Rk
BNAN
Z1 Rk
leverage LAN
1AN
Z1 Rk
L 1L
Z/1 Rk
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• Cutoff,
• Cutoff higher with:– higher leverage, L– higher
gross rate of return experience by entrepreneur with ‘luck’,
1 Rk total assetsA
interest and principle owed by the entrepreneurZB
1 Rk A ZB
Z1 Rk
BNAN
Z1 Rk
leverage LAN
1AN
Z1 Rk
L 1L
Z/1 Rk
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• Cutoff,
• Cutoff higher with:– higher leverage, L– higher
gross rate of return experience by entrepreneur with ‘luck’,
1 Rk total assetsA
interest and principle owed by the entrepreneurZB
1 Rk A ZB
Z1 Rk
BNAN
Z1 Rk
leverage LAN
1AN
Z1 Rk
L 1L
Z/1 Rk
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• Cutoff,
• Cutoff higher with:– higher leverage, L– higher
gross rate of return experience by entrepreneur with ‘luck’,
1 Rk total assetsA
interest and principle owed by the entrepreneurZB
1 Rk A ZB
Z1 Rk
BNAN
Z1 Rk
leverage LAN
1AN
Z1 Rk
L 1L
Z/1 Rk
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• Cutoff,
• Cutoff higher with:– higher leverage, L– higher
gross rate of return experience by entrepreneur with ‘luck’,
1 Rk total assetsA
interest and principle owed by the entrepreneurZB
1 Rk A ZB
Z1 Rk
BNAN
Z1 Rk
leverage LAN
1AN
Z1 Rk
L 1L
Z/1 Rk
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• Expected return to entrepreneur, over opportunity cost of funds:
Expected payoff for entrepreneur
opportunity cost of fundsFor lower values of , entrepreneur receives nothing‘limited liability’.
1 Rk A ZBdF
N1 R
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• Rewriting entrepreneur’s rate of return:
• Entrepreneur’s return unbounded above– Risk neutral entrepreneur would always want to
borrow an infinite amount (infinite leverage).
1 Rk A ZBdF
N1 R
1 Rk A 1 Rk AdF
N1 R
dF 1 Rk
1 R L
Z1 Rk
L 1L L
Z1 Rk
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• Rewriting entrepreneur’s rate of return:
• Entrepreneur’s return unbounded above– Risk neutral entrepreneur would always want to
borrow an infinite amount (infinite leverage).
1 Rk A ZBdF
N1 R
1 Rk A 1 Rk AdF
N1 R
dF 1 Rk
1 R L
Z1 Rk
L 1L L
Z1 Rk
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• Rewriting entrepreneur’s rate of return:
• Entrepreneur’s return unbounded above– Risk neutral entrepreneur would always want to
borrow an infinite amount (infinite leverage).
1 Rk A ZBdF
N1 R
1 Rk A 1 Rk AdF
N1 R
dF 1 Rk
1 R L
Z1 Rk
L 1L L
Z1 Rk
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• Rewriting entrepreneur’s rate of return:
• Entrepreneur’s return unbounded above– Risk neutral entrepreneur would always want to
borrow an infinite amount (infinite leverage).
1 Rk A ZBdF
N1 R
1 Rk A 1 Rk AdF
N1 R
dF 1 Rk
1 R L
Z1 Rk
L 1L L
Z1 Rk Gets smaller with L
Larger with L
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• Rewriting entrepreneur’s rate of return:
• Entrepreneur’s return unbounded above– Risk neutral entrepreneur would always want to
borrow an infinite amount (infinite leverage).
1 Rk A ZBdF
N1 R
1 Rk A 1 Rk AdF
N1 R
dF 1 Rk
1 R L
Z1 Rk
L 1L L
Z1 Rk
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1.5 2 2.5 3 3.5 4 4.5 5 5.5
1
1.2
1.4
1.6
1.8
2
2.2
leverage
Exp
ect
ed
re
turn
fo
r e
ntr
ep
ren
eur
Expected entrepreneurial return, over opportunity cost, N(1+R)
In our baseline parameterization, risk spread = 1.0063,return is monotonically increasingin leverage
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1.5 2 2.5 3 3.5 4 4.5 5 5.5
1
1.2
1.4
1.6
1.8
2
2.2
leverage
Exp
ect
ed
re
turn
fo
r e
ntr
ep
ren
eur
Expected entrepreneurial return, over opportunity cost, N(1+R)
Z/(1+R) = 1.0063Z/(1+R) = 1.5
Baseline parameters
More leverage locally reduces expected returnwith high risk spread.
High leverage always preferredeventually linearly increasing
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• If given a fixed interest rate, entrepreneur with risk neutral preferences would borrow an unbounded amount.
• In equilibrium, bank can’t lend an infinite amount.
• This is why a loan contract must specify both an interest rate, Z, and a loan amount, B.
• Need to represent preferences of entrepreneurs over Z and B.– Problem, possibility of local decrease in utility with
more leverage makes entrepreneur indifference curves ‘strange’ ..
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1.5 2 2.5 3 3.5
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4
Z/(
1+
R),
ris
k sp
rea
d
Leverage (i.e., Assets/Net Worth)
Entrepreneurial indifference curves
Indifference Curves Over Z and B Problematic
Utility increasing
Downward-sloping indifference curves reflect local fall in net worth with rise in leverage whenrisk premium is high.
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Solution to Technical Problem Posed by Result in Previous Slide
• Think of the loan contract in terms of the loan amount (or, leverage, (N+B)/N) and the cutoff,
1 Rk A ZBdF
N1 R
dF 1 Rk
1 R L
2 3 4 5 6 7
1
2
3
4
5
6
7
-
ba
r
leverage
Indifference curve, (leverage, - bar) space
L AN N B
N
Utility increasing
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Solution to Technical Problem Posed by Result in Previous Slide
• Think of the loan contract in terms of the loan amount (or, leverage, (N+B)/N) and the cutoff,
1 Rk A ZBdF
N1 R
dF 1 Rk
1 R L
2 3 4 5 6 7
1
2
3
4
5
6
7
-
ba
r
leverage
Indifference curve, (leverage, - bar) space
L AN N B
N
Utility increasing
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Banks• Source of funds from households, at fixed
rate, R
• Bank borrows B units of currency, lends proceeds to entrepreneurs.
• Provides entrepreneurs with standard debt contract, (Z,B)
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Banks, cont’d• Monitoring cost for bankrupt entrepreneur
with
• Bank zero profit conditionfraction of entrepreneurs with
1 F
quantity paid by each entrepreneur with ZB
quantity recovered by bank from each bankrupt entrepreneur
1 0
dF 1 Rk A
amount owed to households by bank
1 RB
Bankruptcy cost parameter
1 Rk A
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Banks, cont’d• Monitoring cost for bankrupt entrepreneur
with
• Bank zero profit conditionfraction of entrepreneurs with
1 F
quantity paid by each entrepreneur with ZB
quantity recovered by bank from each bankrupt entrepreneur
1 0
dF 1 Rk A
amount owed to households by bank
1 RB
Bankruptcy cost parameter
1 Rk A
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Banks, cont’d• Simplifying zero profit condition:
• Expressed naturally in terms of
1 F ZB 1 0
dF 1 Rk A 1 RB
1 F 1 Rk A 1 0
dF 1 Rk A 1 RB
1 F 1 0
dF 1 R
1 RkB/NA/N
1 R1 Rk
L 1L
,L
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Banks, cont’d• Simplifying zero profit condition:
• Expressed naturally in terms of
1 F ZB 1 0
dF 1 Rk A 1 RB
1 F 1 Rk A 1 0
dF 1 Rk A 1 RB
1 F 1 0
dF 1 R
1 RkB/NA/N
1 R1 Rk
L 1L
,L
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1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
2
4
6
8
10
12
14
-
ba
r
leverage
Bank zero profit condition, in (leverage, - bar) space
•Free entry of banks ensures zero profits
• zero profit curve represents a ‘menu’ of contracts, , that can be offered in equilibrium.
•Only the upward-sloped portion of the curve is relevant, because entrepreneurs would never select a high value of if a lower one was available at the same leverage.
,L
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1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
2
4
6
8
10
12
14
-
ba
r
leverage
Bank zero profit condition, in (leverage, - bar) space
•Free entry of banks ensures zero profits
• zero profit curve represents a ‘menu’ of contracts, , that can be offered in equilibrium.
•Only the upward-sloped portion of the curve is relevant, because entrepreneurs would never select a high value of if a lower one was available at the same leverage.
,L
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1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
2
4
6
8
10
12
14
-
ba
r
leverage
Bank zero profit condition, in (leverage, - bar) space
•Free entry of banks ensures zero profits
• zero profit curve represents a ‘menu’ of contracts, , that can be offered in equilibrium.
•Only the upward-sloped portion of the curve is relevant, because entrepreneurs would never select a high value of if a lower one was available at the same leverage.
,L
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1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
2
4
6
8
10
12
14
-
ba
r
leverage
Bank zero profit condition, in (leverage, - bar) space
•Free entry of banks ensures zero profits
• zero profit curve represents a ‘menu’ of contracts, , that can be offered in equilibrium.
•Only the upward-sloped portion of the curve is relevant, because entrepreneurs would never select a high value of if a lower one was available at the same leverage.
,L
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Some Notation and Results• Let
• Results:
G
expected value of , conditional on
0
dF , 1 F G ,
G dd
0
dF
Leibniz’s rule F
1 F F G 1 F
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Moving Towards Equilibrium Contract• Entrepreneurial utility:
dF 1 Rk
1 R L
1 G 1 F 1 Rk1 R L
share of entrepreneur return going to entrepreneur
1 1 Rk1 R L
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Moving Towards Equilibrium Contract, cn’t
• Bank profits:
share of entrepreneurial profits (net of monitoring costs) given to bank
1 F 1 0
dF 1 R
1 RkL 1L
G 1 R1 Rk
L 1L
L 11 1 Rk
1 R G
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Equilibrium Contract• Entrepreneur selects the contract is optimal,
given the available menu of contracts.
• The solution to the entrepreneur problem is the that solves:
log
profits, per unit of leverage, earned by entrepreneur, given
dF 1 Rk
1 R
leverage offered by bank, conditional on
11 1 Rk
1 R G
log
higer drives share of profits to entrepreneur down (bad!)
1 log 1 Rk1 R
higher drives leverage up (good!)
log 1 1 Rk1 R G
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0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
1.0128
1.013
1.0132
1.0134
1.0136
1.0138
utili
ty
- bar
entrepreneurial utility as a function of - bar only
1 2 3 4 5 6 7 8 9
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
utili
ty
- bar
Equilibrium Contracting Problem Not Globally Concave, But Has Unique Solution Characterized by First Order Condition
Close up of the objective, in neighborhood of optimum. Locally concave.
Non-concave part
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0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
1.0128
1.013
1.0132
1.0134
1.0136
1.0138
utili
ty
- bar
entrepreneurial utility as a function of - bar only
1 2 3 4 5 6 7 8 9
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
utili
ty
- bar
Equilibrium Contracting Problem Not Globally Concave, But Has Unique Solution Characterized by First Order Condition
Close up of the objective, in neighborhood of optimum
Non-concave part
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Computing the Equilibrium Contract• Solve first order optimality condition uniquely for the
cutoff, :
• Given the cutoff, solve for leverage:
• Given leverage and cutoff, solve for risk spread:
elasticity of entrepreneur’s expected return w.r.t.
1 F 1
elasticity of leverage w.r.t.
1 Rk1 R 1 F F
1 1 Rk1 R G
L 1
1 1 Rk1 R G
risk spread Z1 R 1 Rk
1 R LL 1
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Result• Leverage, L, and entrepreneurial rate of
interest, Z, not a function of net worth, N.
• Quantity of loans proportional to net worth:
• To compute L, Z/(1+R), must make assumptions about F and parameters.
L AN
N BN
1 BN
B L 1N
1 Rk1 R , , F
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The Distribution, F
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
dens
ity
Log normal density function, E = 1, = 0.82155
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Results for log-normal• Need: G
0
dF , F
Can get these from the pdf and the cdf of the standard normaldistribution.
These are available in most computational software, like MATLAB.
Also, they have simple analytic representations.
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Results for log-normal• Need: G
0
dF , F
0
dF
change of variables, x log 1
x 2
logexe
x Ex 2
2 x2 dx
E 1 requires Ex 12 x2
1 x 2
logexe
x 12 x2
2
2 x2 dx
combine powers of e and rearrange 1
x 2
loge
x 12 x2
2
2 x2 dx
change of variables, vx 1
2 x2
x 1
x 2
log 12 x2
x xexp
v22 xdv
prob v log 1
2 x2
x x cdf for standard normal
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Results for log-normal• Need: G
0
dF , F
0
dF
change of variables, x log 1
x 2
logexe
x Ex 2
2 x2 dx
E 1 requires Ex 12 x2
1 x 2
logexe
x 12 x2
2
2 x2 dx
combine powers of e and rearrange 1
x 2
loge
x 12 x2
2
2 x2 dx
change of variables, vx 1
2 x2
x 1
x 2
log 12 x2
x xexp
v22 xdv
prob v log 1
2 x2
x x cdf for standard normal
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Results for log-normal• Need: G
0
dF , F
0
dF
change of variables, x log 1
x 2
logexe
x Ex 2
2 x2 dx
E 1 requires Ex 12 x2
1 x 2
logexe
x 12 x2
2
2 x2 dx
combine powers of e and rearrange 1
x 2
loge
x 12 x2
2
2 x2 dx
change of variables, vx 1
2 x2
x 1
x 2
log 12 x2
x xexp
v22 xdv
prob v log 1
2 x2
x x cdf for standard normal
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Results for log-normal• Need: G
0
dF , F
0
dF
change of variables, x log 1
x 2
logexe
x Ex 2
2 x2 dx
E 1 requires Ex 12 x2
1 x 2
logexe
x 12 x2
2
2 x2 dx
combine powers of e and rearrange 1
x 2
loge
x 12 x2
2
2 x2 dx
change of variables, vx 1
2 x2
x 1
x 2
log 12 x2
x xexp
v22 xdv
prob v log 1
2 x2
x x cdf for standard normal
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Results for log-normal• Need: G
0
dF , F
0
dF
change of variables, x log 1
x 2
logexe
x Ex 2
2 x2 dx
E 1 requires Ex 12 x2
1 x 2
logexe
x 12 x2
2
2 x2 dx
combine powers of e and rearrange 1
x 2
loge
x 12 x2
2
2 x2 dx
change of variables, vx 1
2 x2
x 1
x 2
log 12 x2
x xexp
v22 xdv
prob v log 1
2 x2
x x cdf for standard normal
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Results for log-normal, cnt’d• The log-normal cumulative density:
• Differentiating (using Leibniz’s rule):
F 0
dF 1
x 2
loge
x 12 x2
2
2 x2 dx
F ; 1
12
exp
log 1
2 2
2
2
1 Standard Normal pdf
log 12 2
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‘Test’ of the Model• Obtain the following for each firm from a
micro dataset:
• Using definition of F, risk spread, first order condition associated with optimal contract and zero profit condition of banks, can compute:
• Test the model: do the results look sensible?
probability of default (from rating agency)
F ,
firm leverageL ,
interest rateZ
ex ante mean return on firm investment projectRk ,
ex ante idiosyncratic uncertainty ,
monitoring costs ,
cutoff productivity
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• Levin, Natalucci, Zakrajsek, ‘The Magnitude and Cyclical Behavior of Financial Market Frictions’, Finance and Economics Discussion Series, Federal Reserve Board, 2004-70.
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A jump in spreads occurred here, interpreted bythe model as a jump (in part) of bankruptcy costs.
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Changes in idiosyncratic volatility not very important
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400 1 Rk1 R 1
400 1 Rk1 R 1
High values consistent with highbankruptcy costs.
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0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
dens
ity
Impact on lognormal cdf of doubling standard deviation
Effect of Increase in Risk, • Keep
• But, double standard deviation of Normal underlying F.
0
dF 1
Doubled standard deviation
Increasing standard deviation raisesdensity in the tails.
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1.08 1.1 1.12 1.14 1.16 1.18
1
2
3
4
5
6
7
8
9
leverage, qK/N
risk
spre
ad (
AP
R)
Effect of a 5% jump in
Risk spread= 2.67Leverage = 1.12
Risk spread=2.52Leverage = 1.13
Risk spread = , Leverage = (B+N)/N 400 Z1 R 1
Entrepreneur Indifference curve
Zero profit curve
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Issues With the Model• Strictly speaking, applies only to ‘mom and pop grocery
stores’: entities run by entrepreneurs who are bank dependent for outside finance.– Not clear how to apply this to actual firms with access to equity
markets.
• Assume no long-run connections with banks.
• Entrepreneurial returns independent of scale.
• Overly simple representation of entrepreneurial utility function.
• Ignores alternative sources of risk spread (risk aversion, liquidity)
• Seems not to allow for bankruptcies in banks.
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Incorporating BGG Financial Friction into Neoclassical Model
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Model with Financial Frictions
Firms
household
Entrepreneurs
Labor market
Capital Producers
L
C I
K
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Model with Financial Frictions
Firms
household
Entrepreneurs
Labor market
banks
Capital Producers
Loans
K’
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Equations of the Model• Aggregate resource constraint:
• Households:
• Capital producers:
bought by households ct
bought by capital producersI t
monitoring costs of banks
0
t dF 1 R tk kt yt
t 0
tuct , ct bt 1 1 R t 1 bt wtl t
uc,t uc,t 11 R t , l t 1
kt 1 1 kt I t
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Equations, ctn’d• Entrepreneurs:
– First order condition associated with optimization problem.
– Zero profit condition of banks.
– Law of motion of aggregate net worth.Nt 1 time t earnings of entrepreneurs net of interest on previous period’s bank loans T t
1 T t,
~fraction of entrepreneurs that survive, 1 ~fraction of entrepreneurs born
T t~small transfer made to all entrepreneurs
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Conclusion• We’ve reviewed one interesting model of
financial frictions.
• Needs a lot more work!