Post on 14-Nov-2020
Financial Frictions Under Asymmetric Information and Costly
State Verification
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.
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 dsgemodel.– 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.
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.
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
Banks, Households, Entrepreneurs
HouseholdsBank
entrepreneur
entrepreneurentrepreneur
entrepreneur
entrepreneur
Standard debt contract
~ F, 0
dF 1
• 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 assets
A
net worth
N
loans
B
• 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’.
1Rk A−ZBdF
N1R
• 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
Z1Rk
L−1L →L→
Z1Rk
• 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.
‘Indifference Curves’ of Entrepreneurs
• Think of the loan contract in terms of the loan amount (or, leverage, (N+B)/N) and the cutoff,
1Rk A−ZBdF
N1R
− dF 1Rk
1R L
2 3 4 5 6 7
1
2
3
4
5
6
7
-
bar
leverage
Indifference curve, (leverage, - bar) space
L AN NB
N
Utility increasing
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)
Banks, cont’d• Monitoring cost for bankrupt entrepreneur with
• Bank zero profit conditionfraction of entrepreneurs with
1 − Fquantity paid by each entrepreneur with
ZB
quantity recovered by bank from each bankrupt entrepreneur
1 − 0
dF1 Rk A
amount owed to households by bank
1 RB
Bankruptcy cost parameter
1 Rk A
Banks, cont’d• Simplifying zero profit condition:
• Expressed naturally in terms of
1 − FZB 1 − 0
dF1 Rk A 1 RB
1 − F1 Rk A 1 − 0
dF1 Rk A 1 RB
1 − F 1 − 0
dF 1 R
1 RkB/NA/N
1 R1 Rk
L − 1L
,L
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
-
bar
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, becauseentrepreneurs would never select a high value of if a lowerone was available at the same leverage.
,L
Some Notation and Results• Let
• Results:
G
expected value of , conditional on
0
dF , Γ 1 − F G,
G′ dd 0
dF
Leibniz’s rule F′
Γ′ 1 − F − F′ G 1 − F
Moving Towards Equilibrium Contract• Entrepreneurial utility:
− dF 1 Rk
1 R L
1 − G − 1 − F 1 Rk
1 R L
share of entrepreneur return going to entrepreneur
1 − Γ 1 Rk
1 R L
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 − 1
L
Γ − G 1 R1 Rk
L − 1L
L 11 − 1Rk
1R Γ − G
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 − 1Rk
1R Γ − G
log
higer drives share of profits to entrepreneur down (bad!)
1 − Γ log 1 Rk
1 R
higher drives leverage up (good!)
− log 1 − 1 Rk
1 R Γ − G
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 − F1 − Γ
elasticity of leverage w.r.t.
1Rk
1R 1 − F − F′
1 − 1Rk
1R Γ − G
L 11− 1Rk
1R Γ−G
risk spread ≡ Z1R 1Rk
1R LL−1
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 B
N 1 BN
B L − 1N
1 Rk
1 R , , F
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
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.
Results for log‐normal• Need: G
0
dF, F′
0
dF
change of variables, xlog 1
x 2−
log exe
−x−Ex2
2x2 dx
E1 requires Ex− 12 x
2
1x 2
−
log exe
− x 12 x2
2
2x2 dx
combine powers of e and rearrange 1
x 2−
log e− x− 1
2x22
2x2 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
Results for log‐normal, cnt’d• The log‐normal cumulative density:
• Differentiating (using Leibniz’s rule):
F 0
dF 1
x 2−
log e− x 1
2x22
2x2 dx
F; 1
12
exp−
log 12
2
2
2
1 Standard Normal pdf
log 12
2
1.08 1.1 1.12 1.14 1.16 1.18
1
2
3
4
5
6
7
8
9
leverage, L = (B+N)/N
risk
spre
ad, 4
00(Z
/R-1
)
Figure : Impact on standard debt contract of a 5% jump in
Entrepreneur Indifference curve
Risk spread= 2.67Leverage = 1.12
Risk spread=2.52Leverage = 1.13
Zero profit curve
Put this Into DSGE Model
Standard Model
Firms
Households
Supply labor Rent capital
consumptionInvestment goodsYt
0
1Yjt
1f,t dj
f,t
, 1 ≤ f,t ,
Yjt tKjtztljt
1−
uc,t Etc,tuc,t1Rt1
k
t1
other toilautKt Gt Ct
It,t
≤ Yt.
Kt1 1 − Kt Gi,t, It, It−1
Rt1k
ut1rt1k 1 − Pk ′,t1
Pk ′,t
Backyard capital accumulation:
‘Marginal Efficiency of Investment’
Standard Model
Firms
household
Market for Physical Capital
Labor market
L
C I
K
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.
Financial Frictions with Physical K
Firms
household
Entrepreneurs
Labor market
Capital Producers
L
C I
K
Entrepreneurssell their Kto capital producers
Financial Frictions with Physical K
Firms
household
Entrepreneurs
Labor market
banks
Capital Producers
Loans
K’
Banks, Households, Entrepreneurs
HouseholdsBank
entrepreneur
entrepreneurentrepreneur
entrepreneur
entrepreneur
~F,t, E 1
Standard debt contract
Accounts for nearly 50% of GDP
• Net worth of an entrepreneur who goes to the bank to receive a loan in period t:
An entrepreneur who bought capital in t-1 experienced an idiosyncratic shock, .
This log-normal shock has mean unity across all entrepreneurs, .
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.
~ F,t
nt
value of capital after production
Pk ′,t1 − Kt
earnings from capital after utilization costs
rtkKt −Bt−1
Zt−1 t
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.
Risk Shock and News
• Assume
• Agents have advance information about pieces of
t 1t−1 iid, univariate innovation to t
ut
ut
ut t0 t−1
1 . . . t−88
t−ii ~iid, E t−i
i 2 i2
t−ii ~piece of ut observed at time t − i
Economic Impact of Risk Shock
0.5 1 1.5 2 2.5 3 3.5 4
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
idiosyncratic shock
dens
itylognormal distribution:
20 percent jump in standard deviation
*1.2
Larger number of entrepreneurs in lefttail problem for bank
Banks must raise interest rate on entrepreneur
Entrepreneur borrows less
Entrepreneur buys less capital, investment drops, economy tanks
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.
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
Key Result• Risk shocks:
– important source of fluctuations.
• Out-of-Sample evidence suggests the model deserves to be taken seriously.
Risk Shocks
• Important
• Why are they important?
• What shock do they displace, and why?
Role of the Risk Shock in Macro and Financial Variables
Variance Decomposition In Business Cycle Frequencies
Risk shock, t
Output49
Credit63
Slope of Term Structure33
Risk spread98
Real Value of Stock Market76
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.
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.
Why does Risk Crowd out Marginal Efficiency of
Investment?Price of capital
Quantity of capital
Demand shifters:risk shock, t;wealth shock, t
Supply shifter:marginal efficiencyof investment, i,t
• 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.
CKM Challenge• CKM argue that risk shocks (actually, any
intertemporal shock) cannot be important in business cycles.
• Idea: a shock that hurts the intertemporalmargin 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.
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.
‘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.
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.