Incorporate Financial Frictions into a Business Cycle Model Business - - PowerPoint PPT Presentation

Incorporate Financial Frictions into a Business Cycle Model 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 lenders are different people, with conflicting interests – Financial frictions: features of the relationship between borrowers and lenders adopted to mitigate conflict of interest mitigate conflict of interest.

Standard Model Firms

consumption Investment goods

Firms

Investment goods Supply labor Rent capital

Households

Backyard capital accumulation: Kt1  1 − Kt  GIt,It−1 y p

t1

 

t

 t, t 1

uc,t  Etuc,t1 rt1

k

 1 − Pk′,t1 Pk′,t

Savers and investors are the same: NO FRICTIONS!

Frictions in Financing of Physical Capital

Money

Savers Have money, but Investors (‘entrepreneurs’) y, no ideas Have ideas, but not enough money.

Frictions in Financing of Physical Capital

Money

Savers Have money, but Investors (‘entrepreneurs’) y, no ideas Problem: ‘stuff’ happens.

Incentive of entrepreneurs to under‐report earnings

A Very Simple Two‐Period Model to h d Get at the Basic Idea

• Bernanke Gertler and Gilchrist 1999 The

Bernanke, Gertler and Gilchrist, 1999, The financial accelerator in a quantitative business cycle framework, in: Taylor, J.B., Woodford, M. y , y , , , (Eds.), Handbook of Macroeconomics, Vol. 1C. North Holland, Amsterdam, pp. 1341‐1393.

• Also, Christiano, Motto, Rostagno, 2003, The

Also, Christiano, Motto, Rostagno, 2003, The Great Depression and the Friedman‐Schwartz Hypothesis. yp

• Period 1

Period 1

– No uncertainty – Households face leisure‐work choice and buy Households face leisure work choice and buy bonds from a bank, with state‐non contingent interest. – Entrepreneurs own equal share of capital, k, in first period, and apply income and loans from bank to buy capital for use in period 2 Experience bank to buy capital for use in period 2. Experience an idiosyncratic productivity shock.

• Period 2

Period 2

– Aggregate uncertainty – Entrepreneurs pay back loans from banks, which Entrepreneurs pay back loans from banks, which repay households.

Households

H h ld f

• Household preferences

Uc,l  Uch,lh  1 − Ucl,ll.

• Budget constraints

c  B ≤ wl c  B ≤ wl, ch ≤ whlh  RB, cl ≤ wlll  RB

• Euler equations:

c ≤ w l  RB.

− Ul Uc  w, − Ul

h

Uc

h  wh, − Ul l

Uc

l  wl

1    Uc

h

Uc  1 −  Uc

l

Uc R,

Goods‐producing firms

• Technology:

y  Fk,l y yh  FhK,lh yl  FlK,ll,

• Competition ensures:

w  Flk,l, wh  Fl

hK,lh, wl  Fl lK,ll h h h l l l

r  Fkk,l, rh  Fk

hK,lh, rl  Fk l K,ll,

Entrepreneurs

• In period 1, each owns equal share of capital

stock, k

• Net worth at end of period, N=rk (100% k

p , ( depreciation)

• Entrepreneurs borrow K‐N from banks at end
• f period 1 and banks get the money by
• f period 1, and banks get the money by

issuing bonds, B, to households.

Idiosyncratic uncertainty

• After purchasing K, entrepreneurs experience

idiosyncratic shock: idiosyncratic shock:

K → K, ~F, E  1.

• Standard debt contract

   ̄ h → pay  ̄ hrhK to bank    ̄ h → pay rhK to bank, bank pays rhK in monitoring costs

Standard Debt Contract, cnt’d Standard Debt Contract, cnt d

   ̄ l → pay  ̄ lrlK to bank    ̄ l → pay rlK to bank, bank pays rlK in monitoring costs

• Parameters of Standard Debt Contract:

 ̄ h,  ̄ l and K

Determination of Parameters of d d b Standard Debt Contract

• Expected utility of entrepreneur at start of

Expected utility of entrepreneur at start of contract:



share of gross entrepreneurial earnings in state h kept by entrepreneur

1 − Γh rhK  1 − 1 − ΓlrlK,

share of gross earnings of entrepreneur taken by bank

 Γh  

 ̄ h

dF   ̄ h 



dF Γ



0 dF     ̄ h dF

Γl  

 ̄ l

dF   ̄ l 



dF



 



 ̄ l

 

Contract

C titi b k fit

• Competition among banks ensures zero profits

for the banks.

f ‘ ’ f – Zero profit condition represents a ‘menu’ of contracts, with different interest rates and loan amounts amounts.

C t t hi h t d i ilib i i th

• Contract which trades in equilibrium is the
• ne entrepreneurs most prefer.

max

 ̄ s,K1 − ΓhrhK  1 − 1 − ΓlrlK

 hΓh − GhrhK − K − NR G ̄ s  

 ̄ s f d.

  Γ G r K K NR  lΓl − GlrlK − K − NR,   



f 

Characterizing Equilibrium Contract

• First order condition for K (K‐N is loan

amount) amount)

1 − Γhrh  1 − 1 − Γlrl  hΓh − Ghrh − R  lΓl − Glrl − R

• First order condition for :

 ̄ h and  ̄ l h  Γ′h Γ′h G′h Γ′h − G′h 1 1 Γ′l l  1 − 1 − Γ l Γ′l − G′l .

Equations Characterizing Contract: q g

• Optimality:

1 − Γhrh  1 − 1 − Γlrl Γ′h 1 − 1 − Γ′l  Γ′h Γ′h − G′h Γh − Ghrh − R  1 1 Γ  Γ′l − G′l Γl − Glrl − R

• Competition (i.e., zero profits)

Γh − GhrhK  K − NR Γl − GlrlK  K − NR. Γ G r K K NR.

Equilibrium

• Three equations for loan contract (optimality

and competition) and competition)

• Resource constraints:

c  K ≤ Fk,l

household consumption

 ch 

resources used in monitoring

G ̄ hrhK 

entrepreneur consumption

1 − ΓhrhK ≤ FK,lh cl  G ̄ lrlK  1 − ΓlrlK ≤ FK,ll

• Household and firm first order conditions:

h l

− Ul Uc  Flk,l, − Ul

h

Uc

h  Fl hK,lh, − Ul l

Uc

l  Fl lK,ll

Uh Ul 1    Uc Uc  1 −  Uc Uc R,

Equilibrium Equilibrium

• Ten equations in 10 unknowns:

Ten equations in 10 unknowns:

l,lh,ll,c,ch,cl,K, ̄ h, ̄ l,R

Incorporating BGG Financial Friction d l into a Monetary Model

Vt1  real earnings on capital (rent plus capital gains)t i l t f i t t − nominal rate of interestt−1 t real debt to bankst−1 Net Wortht1  Vt1  Wt1

e   1 − Wt1 e

Prediction of financial friction model: Prediction of financial friction model:

• Shocks that drive output and price in the same

Shocks that drive output and price in the same direction (‘demand’) accelerated by financial frictions.

– Fisher and earnings effects reinforce each other.

• Shocks that drive output and price in opposite

directions (‘supply’) not much affected by ( pp y ) y financial frictions.

– Fisher and earnings effects cancel each other.

Model with Financial Frictions

Firms Labor L K Entrepreneurs Labor market Capital Producers C I Producers household

Model with Financial Frictions

Firms Labor Entrepreneurs Labor market Capital Producers K’ Producers household banks Loans

The equations of the financial friction d l model

• Net addition of two equations to consensus

model: model:

– Subtract the household intertemporal equation for capital. Add three equations pertaining to the entrepreneurs – Add three equations pertaining to the entrepreneurs

Three equations pertaining to entrepreneur

• Law of motion of net worth

a

• t o o

et

• t
• Zero‐profit conditions of banks

p

revenues from non-bankrupt entrepreneurs  quantity of non-bankrupt entrepreneurs  receipts from bankrupt entrepreneurs net of bankruptcy costs  receipts from bankrupt entrepreneurs net of bankruptcy costs  payment obligations on bank debt to households

• Optimality condition associated with

entrepreneur’s choice of contract.

Empirical Analysis of Financial Friction d l Model

Ch i i (2008) b d

• Christiano‐Motto‐Rostagno (2008), based on

Bernanke‐Gertler‐Gilchrist (1999) model of fi i l f i i financial frictions.

Risk Shock and News Risk Shock and News

• Assume

iid i i t i ti t ̂

Assume h d i f i b

 ̂ t  1 ̂ t−1 

iid, univariate innovation to t

 ut

• Agents have advance information about

pieces of ut

ut  t

0  t−1 1

...t−8

8

t−i

i

~iid, Et−i

i 2  i 2

t−i

i

~piece of ut observed at time t − i

Estimation

• EA and US data covering 1985Q1‐2007Q2

Δlog

Nt1 Pt

t logper capita hourst Δl

per capita creditt

Δlog

p p

t

Pt

Δlogper capita GDPt Δlog

Wt Pt

Δlogper capita It Xt  Δlog

per capita M1t Pt

Δlog

per capita M3t Pt

Δlogper capita consumptiont E t l Fi P i , External Finance Premiumt Rt

long − Rt e

Rt

e

ΔlogPI,t Δlogreal oil price

• Standard Bayesian methods

Δlogreal oil pricet Δlog

per capita Bank Reserves t Pt



• We remove sample means from data and set steady

state of X to zero in estimation.

Summary of Empirical Results With Fi i l F i ti Financial Frictions

• Risk shocks:

– important source of fluctuations. – news on the risk shock important

h h b fl h l h b l

• The Fisher debt‐deflation channel has a substantial impact on

propagation. M d d d h i f d i i id

• Money demand and mechanism of producing inside money:

– relatively unimportant as a source of shocks – modest contribution to forecast ability

• Model accounts or substantial fraction of fluctuations in term

structure.

• Out‐of‐Sample RMSEs of the model perform well compared with

BVAR and simpler models.

Risk Shocks are Important Risk Shocks are Important

Actual data versus what actual data would have been if there were only risk Shocks: Note: (1) as suggested by the picture, risk shocks are relatively important at the lower frequencies (2) We find that they are the single most important source of low frequency (2) We find that they are the single most important source of low frequency fluctuation in the EA, and a close second (after permanent tech shocks) in the US

Table: Variance Decomposition, HP filtered data, EA x shock

• utput

consumption investment hours inflation labor productivity interest rate f 15.02 23.05 2.63 16.37 35.74 1.40 20.46 x b 0.59 1.29 0.02 0.44 0.52 1.44 0.24  0.32 0.01 0.12 0.18 0.08 0.01 0.04

Markup Banking tech Capital tech

 0.32 0.01 0.12 0.18 0.08 0.01 0.04  0.02 0.06 0.00 0.02 0.00 0.00 0.00 g 3.26 3.11 0.00 3.34 0.87 0.21 0.48 z

∗

3.72 1.16 0.24 1.42 1.07 10.29 0.72  0 43 0 06 0 92 0 80 0 24 1 52 0 30

Capital tech Money demand Government Permanent tech Gamma shock

 0.43 0.06 0.92 0.80 0.24 1.52 0.30  10.54 21.68 0.49 7.46 16.10 27.52 8.56 policy 6.22 11.27 1.01 4.14 5.40 0.10 33.15  2.88 0.19 5.11 6.57 0.88 13.17 1.08  20 09 1 81 38 09 15 96 9 22 38 24 9 80

Gamma shock Temporary tech Monetary policy Risk, contemp Si l i k

signal 20.09 1.81 38.09 15.96 9.22 38.24 9.80  and signal 22.96 2.00 43.20 22.53 10.09 51.41 10.88 c 11.68 32.75 0.15 12.20 11.26 0.83 10.15 i 24.57 1.72 51.14 30.69 10.17 5.22 11.56

Signals on risk Risk and signals Discount rate Marginal eff of I f l

oil 0.42 1.39 0.03 0.24 2.21 0.04 1.32 long 0.00 0.00 0.00 0.00 0.00 0.00 0.00 measurement error 0.00 0.00 0.00 0.00 0.00 0.00 1.26 inflation target 0.24 0.43 0.05 0.16 6.23 0.01 0.87

Price of oil Long rate error

all shocks 100.00 100.00 100.00 100.00 100.00 100.00 100.00

Table: Variance Decomposition, HP filtered data, EA x shock

• utput

consumption investment hours inflation labor productivity interest rate f 15.02 23.05 2.63 16.37 35.74 1.40 20.46 x b 0.59 1.29 0.02 0.44 0.52 1.44 0.24  0.32 0.01 0.12 0.18 0.08 0.01 0.04  0.32 0.01 0.12 0.18 0.08 0.01 0.04  0.02 0.06 0.00 0.02 0.00 0.00 0.00 g 3.26 3.11 0.00 3.34 0.87 0.21 0.48 z

∗

3.72 1.16 0.24 1.42 1.07 10.29 0.72  0 43 0 06 0 92 0 80 0 24 1 52 0 30  0.43 0.06 0.92 0.80 0.24 1.52 0.30  10.54 21.68 0.49 7.46 16.10 27.52 8.56 policy 6.22 11.27 1.01 4.14 5.40 0.10 33.15  2.88 0.19 5.11 6.57 0.88 13.17 1.08  20 09 1 81 38 09 15 96 9 22 38 24 9 80

It’s the

signal 20.09 1.81 38.09 15.96 9.22 38.24 9.80  and signal 22.96 2.00 43.20 22.53 10.09 51.41 10.88 c 11.68 32.75 0.15 12.20 11.26 0.83 10.15 i 24.57 1.72 51.14 30.69 10.17 5.22 11.56

It s the signals!

oil 0.42 1.39 0.03 0.24 2.21 0.04 1.32 long 0.00 0.00 0.00 0.00 0.00 0.00 0.00 measurement error 0.00 0.00 0.00 0.00 0.00 0.00 1.26 inflation target 0.24 0.43 0.05 0.16 6.23 0.01 0.87 all shocks 100.00 100.00 100.00 100.00 100.00 100.00 100.00

Table: Variance Decomposition, HP filtered data, EA x shock stock market credit spread term structure real M1 real M3 shock stock market credit spread term structure real M1 real M3 f 1.83 13.15 0.16 12.36 44.28 1.82 x b 0.00 0.14 0.00 0.10 5.04 42.39  0.18 0.07 0.03 0.07 0.03 0.02

Markup Banking tech Capital tech

 0.00 0.00 0.00 0.00 13.17 22.63 g 0.03 0.10 0.01 0.07 0.44 0.02 z

∗

0.17 0.07 0.05 0.14 0.42 1.29  5 37 25 82 1 86 0 33 0 13 0 15

Money demand Government Permanent tech Gamma shock

 5.37 25.82 1.86 0.33 0.13 0.15  0.10 4.06 0.00 3.40 9.89 0.61 policy 4.89 1.81 0.99 25.76 13.15 1.58  13.94 5.07 20.58 0.97 1.39 0.76

Gamma shock Temporary tech Monetary policy Risk, contemp

signal 68.29 44.23 75.90 6.79 5.98 6.20  and signal 82.22 49.30 96.48 7.76 7.38 6.96 c 0.02 1.72 0.02 3.99 2.46 15.40 1 90 2 54 0 27 8 77 1 18 6 17

Signals on risk Risk and signals Discount rate Marginal eff of I

i 1.90 2.54 0.27 8.77 1.18 6.17 oil 0.14 0.94 0.05 0.56 1.87 0.15 long 0.00 0.00 0.00 36.05 0.00 0.00 measurement error 2.89 0.19 0.02 0.32 0.21 0.02

Marginal eff of I Price of oil Error in long rate

inflation target 0.24 0.10 0.05 0.34 0.35 0.80 all shocks 100.00 100.00 100.00 100.00 100.00 100.00

Table: Variance Decomposition, HP filtered data, EA x shock stock market credit spread term structure real M1 real M3 shock stock market credit spread term structure real M1 real M3 f 1.83 13.15 0.16 12.36 44.28 1.82 x b 0.00 0.14 0.00 0.10 5.04 42.39  0.18 0.07 0.03 0.07 0.03 0.02

Markup Banking tech Capital tech

 0.00 0.00 0.00 0.00 13.17 22.63 g 0.03 0.10 0.01 0.07 0.44 0.02 z

∗

0.17 0.07 0.05 0.14 0.42 1.29  5 37 25 82 1 86 0 33 0 13 0 15

Money demand Government Permanent tech Gamma shock

 5.37 25.82 1.86 0.33 0.13 0.15  0.10 4.06 0.00 3.40 9.89 0.61 policy 4.89 1.81 0.99 25.76 13.15 1.58  13.94 5.07 20.58 0.97 1.39 0.76

Gamma shock Temporary tech Monetary policy Risk, contemp

signal 68.29 44.23 75.90 6.79 5.98 6.20  and signal 82.22 49.30 96.48 7.76 7.38 6.96 c 0.02 1.72 0.02 3.99 2.46 15.40 1 90 2 54 0 27 8 77 1 18 6 17

Signals on risk Risk and signals Discount rate Marginal eff of I

i 1.90 2.54 0.27 8.77 1.18 6.17 oil 0.14 0.94 0.05 0.56 1.87 0.15 long 0.00 0.00 0.00 36.05 0.00 0.00 measurement error 2.89 0.19 0.02 0.32 0.21 0.02

Marginal eff of I Price of oil Error in long rate Signal matters!

inflation target 0.24 0.10 0.05 0.34 0.35 0.80 all shocks 100.00 100.00 100.00 100.00 100.00 100.00

Importance of Risk Signals Importance of Risk Signals

News Specification on Risk and Marginal Likelihood (EA data)

1 2 p

 ̂ t  1 ̂ t−1  t−0  t−1

1

 t−2

2

...t−p

p

p log, marginal likelihood odds (exp(difference in log likelihood from baseline)) 8 (baseline) 4397.487 1 ( ) 6 4394.025 31 1 4325.584 

Why is Risk Shock so Important?

• According to the model, external finance

premium is primarily risk shock premium is primarily risk shock. T l k f id h i k i h b

• To look for evidence that risk might be

important, look at dynamics of external finance premium and gdp finance premium and gdp. E l fi i i i l di

• External finance premium is a negative leading

indicator

Why is Risk Shock so Important?: d A second reason

• Our data set includes the stock market

Output stock market investment all procyclical – Output, stock market, investment all procyclical (surge together in late 1990s) – This is predicted by risk shock.

Impact of Financial Frictions on Propagation

• Effects of monetary shocks on gdp amplified

by BGG financial frictions because P and Y go by BGG financial frictions because P and Y go in same direction.

• Effects of technology shocks on gdp mitigated

b BGG fi i l f i ti b P d Y by BGG financial frictions because P and Y go in opposite directions.

Baseline model with no Fisher Effect Baseline model Blue line: baseline model with no financial frictions

Out of Sample RMSEs Out of Sample RMSEs

• There is not a loss of forecasting power with

There is not a loss of forecasting power with the additional complications of the model.

• The model does well on everything, except

h i k i the risk premium.

Models with Financial Frictions Can be U d Add I P li Used to Address Important Policy Questions

• When there is an increase in risk spreads, how should

monetary policy respond?

• How should monetary policy react to credit variables and

the stock market?

• Does monetary policy cause excess asset price volatility?

– Taylor: deviations from Taylor rule may cause asset price volatility – Christiano‐Ilut‐Motto‐Rostagno: Taylor rule may cause asset – Christiano‐Ilut‐Motto‐Rostagno: Taylor rule may cause asset price volatility

How Should Policy Respond to the Risk d Spread?

• Taylor’s recommendation:

Taylor s recommendation:

R e  y Risky rate Risk free rate  Rt  t

e  yt − Risky ratet − Risk free ratet

 1

• Evaluate this proposal by comparing

  1

Evaluate this proposal by comparing performance of economy with and against Ramsey‐optimal benchmark

  1

  0

against Ramsey optimal benchmark.

  0

Get a recession, just like in earlier graph g p

Taylor suggestion creates a boom Is it too much? Is it too much?

Taylor’s suggestion overstimulates Taylor’s suggestion overstimulates

Conclusion of Empirical Analysis with Fi i l F i i Financial Frictions

• Incorporating financial frictions changes

p g g inference about the sources of shocks and of propagation p p g

risk shock – risk shock. – Fisher debt deflation

• Opens a range of interesting questions that

can be addressed