1. Financial Frictions Under
Asymmetric Information and Costly
State Verification

2. General Idea
• Standard dsge 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.

3. Discussion of Financial Frictions
• Simple model to illustrate the basic costly state
verification (csv) model.
– Original analysis of Townsend (1978), Gale‐Helwig.
• Then: integrate 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
(2003,2009,2011).
• After fitting model to data, find that a new shock, ‘risk
shock’, appears to be important in business cycles.

4. 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.

5. Simple Model, cont’d
• Each entrepreneur has access to a project with
rate of return,
1  R 
k

• Here, is a unit mean, idiosyncratic shock
experienced by the individual entrepreneur after
the project has been started,

 0 dF  1

• The shock, , is privately observed by the
entrepreneur.
• F is lognormal cumulative distribution function.

6. Banks, Households, Entrepreneurs

 ~ F,  dF  1
0
entrepreneur
entrepreneur
entrepreneur
Households
Bank
entrepreneur
entrepreneur
Standard debt contract

7. • 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:
total assets net worth loans
  
A  N  B
• Entrepreneur who experiences sufficiently bad
≤ ̄
luck, , loses everything.

8. • Expected return to entrepreneur, over
opportunity cost of funds:
Expected payoff for
entrepreneur

  1Rk A−ZBdF
̄
N1R
For lower values of
 , entrepreneur opportunity cost of funds
receives nothing
‘limited liability’.

9. • Rewriting entrepreneur’s rate of return:
 
  1  R A − ZBdF
̄
k   1  R k A − 1  R k AdF
̄
̄

N1  R N1  R

   −  dF
̄ 1  Rk L

̄ 1R

̄ Z L−1
1R k  L
→ L→ Z
1R k 
• Entrepreneur’s return unbounded above
– Risk neutral entrepreneur would always want to
borrow an infinite amount (infinite leverage).

10. • 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.

11. ‘Indifference Curves’ of Entrepreneurs
• Think of the loan contract in terms of the loan
amount (or, leverage, (N+B)/N) and the cutoff, ̄

  1Rk A−ZBdF 
̄
   −  dF
̄ 1R k
L
N1R 
̄ 1R
Indifference curve, (leverage,  - bar) space
7
L A
 NB
6
5
N N
 - bar
4
3
2
1
Utility increasing
2 3 4 5 6 7
leverage

12. 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)

13. Banks, cont’d
• Monitoring cost for bankrupt entrepreneur
with   
̄ Bankruptcy cost parameter
1  R k A
• Bank zero profit condition
fraction of entrepreneurs with 
̄ quantity paid by each entrepreneur with 
̄

1 − F 
̄ ZB
quantity recovered by bank from each bankrupt entrepreneur

̄
 1 −   dF1  R k A
0
amount owed to households by bank
 1  RB

14. Banks, cont’d
• Simplifying zero profit condition:

̄
1 − F ZB  1 −   dF1  R k A  1  RB
̄
0

̄
1 − F 1 
̄ ̄ Rk A  1 −   dF1  R k A  1  RB
0

̄
1 − F   1 −  
̄ ̄ dF  1  R B/N
0 1  R k A/N
 1  Rk L − 1
1R L
• Expressed naturally in terms of , L
̄

15. Bank zero profit condition, in (leverage,  - bar) space
14
•Free entry of banks ensures zero profits
12
, L
̄
• zero profit curve represents a ‘menu’ of contracts, ,
10 that can be offered in equilibrium.
 - bar
8
•Only the upward‐sloped portion of the curve is relevant, because

̄
entrepreneurs would never select a high value of if a lower
6
one was available at the same leverage.
4
2
1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
leverage

16. Some Notation and Results
• Let
expected value of , conditional on 
̄

̄
G 
̄  0 dF , Γ   1 − F  G,
̄ ̄ ̄ ̄
• Results:
Leibniz’s rule

̄
G ′   d
̄  0 dF 
 F ′ 
̄ ̄
̄
d
Γ ′    1 − F − F ′    G  1 − F
̄ ̄ ̄ ̄ ̄ ̄

17. Moving Towards Equilibrium Contract
• Entrepreneurial utility:

   −  dF 1  R
̄
̄ 1  Rk L
 1 − G  − 1 − F 
̄ ̄ ̄ 1  Rk L
1R
share of entrepreneur return going to entrepreneur
 1 − Γ 
̄ 1  Rk L
1R

18. Moving Towards Equilibrium Contract, cn’t
• Bank profits:
share of entrepreneurial profits (net of monitoring costs) given to bank

̄
1 − F   1 −   dF
̄ ̄  1R L−1
0 1  Rk L
Γ  − G   1  Rk L − 1
̄ ̄
1R L
L 1
1R k
1− 1R
Γ  − G 
̄ ̄

19. Equilibrium Contract
• Entrepreneur selects the contract is optimal,
given the available menu of contracts.
• The solution to the entrepreneur problem is

̄
the that solves:
profits, per unit of leverage, earned by entrepreneur, given 
̄ leverage offered by bank, conditional on 
̄

   −  dF 11 R
k
log ̄  1
̄ R 1− 1R k
Γ  − G 
̄ ̄
1R
higher  drives leverage up (good!)
̄
higer  drives share of profits to entrepreneur down (bad!)
̄
 log 1  R − log 1 − 1  R Γ  − G 
k k
 log 1 − Γ 
̄ ̄ ̄
1R 1R

20. Computing the Equilibrium Contract
• Solve first order optimality condition uniquely for the
̄
cutoff, :
elasticity of leverage w.r.t. 
̄
elasticity of entrepreneur’s expected return w.r.t. 
̄
1R k
1 − F
̄ 1 − F − F ′  
̄ ̄
 1R
1 − Γ 
̄ 1− 1R k
Γ  − G 
̄ ̄
1R
• Given the cutoff, solve for leverage:
L k
1
1− 1R Γ −G 
1R
̄ ̄
• Given leverage and cutoff, solve for risk spread:
1R k
risk spread ≡ Z
1R
 1R
 L−1
̄ L

21. Result
• Leverage, L, and entrepreneurial rate of
interest, Z, not a function of net worth, N.
• Quantity of loans proportional to net worth:
L  A  NB  1 B
N N N
B  L − 1N
• To compute L, Z/(1+R), must make
assumptions about F and parameters.
1  R k , , F
1R

22. The Distribution, F
Log normal density function, E = 1,  = 0.82155
0.9
0.8
0.7
0.6
density
0.5
0.4
0.3
0.2
0.1
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5


23. Results for log‐normal

̄
• Need: G 
̄  0 dF, F′ 
Can get these from the pdf and the cdf of the standard normal
distribution.
These are available in most computational software,
like MATLAB.
Also, they have simple analytic representations.

24. Results for log‐normal

̄
• Need: G 
̄  0 dF, F′ 
change of variables, xlog  −x−Ex  2

̄ log 
̄
 0 dF 
 1  − ex e 2 2
x dx
 x 2
E1 requires Ex− 1
2
x − x 1  2
2
2 log 
̄ 2 x

 1  − ex e 2 2x dx
 x 2
2
combine powers of e and rearrange − x− 1  2
x
log 
̄
  −
2
 1 e 2 2x dx
 x 2
x− 1  2
2 x log  1  2
̄
change of variables, v x 2 x
− x

 1  − x
exp
−v 2
2  x dv
 x 2
log  
̄ 1
2
x
 prob v  x
2
− x cdf for standard normal

25. Results for log‐normal, cnt’d
• The log‐normal cumulative density:
2
− x 1  2
x

̄ log 
̄
0  −
2
F 
̄ dF  1 e 2 2x dx
 x 2
• Differentiating (using Leibniz’s rule):
2
log  1  2
̄
− 2

F  ;   1 1 exp
̄ 2

̄ 2
1 Standard Normal pdf log  
̄ 1
2
 
2

̄

26. Figure : Impact on standard debt contract of a 5% jump in 
9
8
risk spread, 400(Z/R-1)
7
Entrepreneur
Indifference curve
6
5
4 Risk spread= 2.67
Leverage = 1.12 Zero profit curve
3
2
Risk spread=2.52
Leverage = 1.13
1
1.08 1.1 1.12 1.14 1.16 1.18
leverage, L = (B+N)/N

27. Put this Into DSGE Model

28. Standard Model ‘Marginal Efficiency of
Investment’
Firms
consumption  f,t
Investment goods
 0 Yjt
1 1
Yt   f,t
dj , 1 ≤  f,t  ,
Yjt   t K z t l jt  1−
jt
other   oil au t Kt  G t  Ct  I,t ≤ Yt .
t
̄ t
Supply labor Rent capital
Households
Backyard capital accumulation: ̄ ̄
Kt1  1 − Kt  G i,t , I t , I t−1 
Rk u t1 r k  1 − P k ′,t1
u c,t  E t  c,t u c,t1  t1
t1 Rk
t1  t1
P k ′,t

29. Standard Model
Firms
L
K
Labor
market C I
Market for
Physical
Capital
household

30. Financing
• In the standard model, already have borrowing by firms for
working capital.
– will now have banks intermediate this borrowing between
households and firms.
• In standard model, ‘putting capital to work’ is completely
straightforward and is done by households. They just rent
capital into a homogeneous capital market.
• Now: ‘putting capital to work’ involves a special kind of
creativity that only some households – entrepreneurs – have.
– Entrepreneurs finance the acquisition of capital in part by
themselves, and in part by borrowing from regular ‘households’.
– Conflict of interest, because there is asymmetric information
about the payoff from capital.
– Standard sharing contract between entrepreneur and household
not feasible.

31. Financial Frictions with Physical K
Firms
L
K
Labor
market C I
Capital
Producers Entrepreneurs
Entrepreneurs
sell their K
to capital producers
household

32. Financial Frictions with Physical K
Firms
Labor
market
Capital K’
Producers Entrepreneurs
Loans
household banks

33. Accounts for nearly 50% of GDP
Banks, Households, Entrepreneurs
~F,  t , E  1
entrepreneur
entrepreneur
entrepreneur
Households
Bank
entrepreneur
entrepreneur
Standard debt contract

34. • Net worth of an entrepreneur who goes to
the bank to receive a loan in period t:
value of capital after production earnings from capital after utilization costs
nt  ̄
P k ′,t 1 − Kt  ̄
r k Kt
t −B t−1 Z t−1
t
An entrepreneur who bought capital in t-1 experienced an idiosyncratic shock, .
This log-normal shock has mean unity across all entrepreneurs,  ~ F,  t  .
An entrepreneur’s shock can only be observed by lender by paying a monitoring
cost.
Under standard debt contract, entrepreneur either pays the interest rate on the debt,
or (if  is too low) declares bankruptcy, in which case he/she is monitored and
loses everything to the bank.

35. Five Adjustments to Standard DSGE
Model for CSV Financial Frictions
• Drop: household intertemporal equation for capital.
• Add: characterization of the loan contracts that can be
offered in equilibrium (zero profit condition for banks).
• Add: efficiency condition associated with
entrepreneurial choice of contract.
• Add: Law of motion for entrepreneurial net worth
(source of accelerator and Fisher debt-deflation
effects).
• Introduce: bankruptcy costs in the resource constraint.

36. Risk Shock and News
• Assume ̂
iid, univariate innovation to  t
̂ ̂ 
 t   1  t−1  ut
• Agents have advance information about
pieces of u t
u t   0   1 . . .  8
t t−1 t−8
2
 it−i ~iid, E it−i    2
i
 it−i ~piece of u t observed at time t − i

37. Economic Impact of Risk Shock
lognormal distribution:
20 percent jump in standard deviation
1
0.9
 Larger number of
 *1.2
0.8
entrepreneurs in left
0.7 tail problem for bank
density
0.6
Banks must raise
0.5 interest rate on entrepreneur
0.4
Entrepreneur borrows less
0.3
Entrepreneur buys less capital,
0.2
investment drops, economy tanks
0.1
0.5 1 1.5 2 2.5 3 3.5 4
idiosyncratic shock

38. Monetary Policy
• Nominal rate of interest function of:
– Anticipated level of inflation and change.
– Slowly moving inflation target.
– Deviation of output growth from ss path.
– Monetary policy shock.

39. Estimation
• Use standard macro data: consumption,
investment, employment, inflation, GDP,
price of investment goods, wages, Federal
Funds Rate.
• Also some financial variables: BAA-AAA
corporate bond spreads, value of DOW,
credit to nonfinancial business.
• Data: 1985Q1-2008Q4

40. Key Result
• Risk shocks:
– important source of fluctuations.
• Out-of-Sample evidence suggests the
model deserves to be taken seriously.

41. Risk Shocks
• Important
• Why are they important?
• What shock do they displace, and why?

42. Role of the Risk Shock in Macro and Financial Variables

43. Variance Decomposition In
Business Cycle Frequencies
Risk shock,  t
Output
49
Credit
63
Slope of Term Structure
33
Risk spread
98
Real Value of Stock Market
76

44. Why Risk Shock is so Important
• A. Our econometric estimator ‘thinks’
risk spread ~ risk shock.
• B. In the data: the risk spread is strongly
negatively correlated with output.
• C. In the model: bad risk shock generates
a response that resembles a recession.
• A+B+C suggests risk shock important.

46. What Shock Does the Risk
Shock Displace, and why?
• The risk shock crowds out some of the
role of the marginal efficiency of
investment shock.

48. Why does Risk Crowd out
Marginal Efficiency of
Investment?
Supply shifter:
Price of capital marginal efficiency
of investment,  i,t
Demand shifters:
risk shock,  t ;
wealth shock,  t
Quantity of capital

49. • Marginal efficiency of investment shock
can account well for the surge in
investment and output in the 1990s, as
long as the stock market is not included in
the analysis.
• When the stock market is included, then
explanatory power shifts to financial
market shocks.

50. CKM Challenge
• CKM argue that risk shocks (actually, any
intertemporal shock) cannot be important in
business cycles.
• Idea: a shock that hurts the intertemporal
margin will induce substitution away from
investment and to other margins, such as
consumption and leisure.
• CKM argument probably right in RBC model.
• Not valid in New Keynesian models.

51. Failure of Comovement Between C & I
in RBC Models With Risk Shocks
• In RBC model, jump in risk discourages
investment.
• Reduction in demand leads to reduction of price of
current goods relative to future goods, i.e., real
interest rate.
• Real interest rate decline induces surge in
demand, partially offsetting drop in investment.
• This Mechanism does not necessarily work in NK
model because real rate not fully market
determined there.

53. ‘Out of Sample Evidence’
• Out of sample forecasting performance
good.
• Predictions for aggregate bankruptcy rate
good.
• Correlates well with Bloom evidence on
cross-sectional uncertainty.

54. Conclusion
• Much of the dynamics of past data can be
explained as reflecting a risk shock.
• In this analysis, shock is treated as
exogenous.
• Interesting to investigate mechanisms that
make that ‘shock’ endogenous.