Download How do shocks and frictions within financial

HOW DO SHOCKS AND FRICTIONS
WITHIN FINANCIAL MARKETS AFFECT
THE REAL ECONOMY?
Stephen Millard (Bank of England, Durham University
Business School and Centre for Macroeconomics)
Alexandra Varadi (Bank of England)
Eran Yashiv (Tel Aviv University, CfM, and CEPR)
17 March, 2017
Roadmap
• Introduction and motivation
• Relevant literature
• Model
• Effects of shocks
• Effects of frictions
• Conclusions and next steps
What is our research question?
• How do financial and real frictions affect the transmission
of shocks (including financial) onto the real economy
• Three key question we want to consider:
• How do financial frictions and frictions in the real economy, such as
labour market frictions, interact in the presence of shocks?
• What does this mean for the transmission of monetary and
macroprudential policies?
• What does this mean for the transmission of problems in the
financial sector into the wider macroeconomy?
Where do we fit in the literature?
DSGE models with financial frictions
• Gertler and Kiyotaki (2015)
• Bernanke, Gertler and Gilchrist (1999)
DSGE models with labour/investment frictions
• Yashiv (2015)
DSGE models with housing
• Iacoviello (2015)
We incorporate all these frictions into one model to move
away from studying them in isolation
Our Model
• Two types of households – patient and impatient – who
get utility out of consumption, housing and leisure.
Impatient households borrow subject to a collateral
constraint (mortgage borrowing).
• We think of the loan-to-value ratio in this constraint as a potential
policy tool and examine the effects of a temporary shock to this.
• Firms subject to costs of adjusting prices, hiring costs and
investment adjustment costs. Have to borrow to finance
investment and hiring costs.
• Banks lend to firms and households and are subject to
Gertler-Kiyotaki frictions.
Our model: Patient Households
• Mass of 1-s patient housheholds
• ‘Patience’ implies low discount rate
• These households save via bank deposits
• Get utility out of consumption and housing
• Disutility from members of the household working
• Nj is the proportion of household j in employment
• Total employment of patient households equals NP
Our Model : Patient Households
• Maximize:


1 
E0    1    ln c j ,t  cH ,t 1   jA j ,t ln H j ,t 
N j ,t 
1 
t 0



t
P
• Subject to:
D j ,t  Qt H j ,t  Rt 1 D j ,t 1  Qt H j ,t 1  Wt N j ,t   j ,t  Pt c j ,t  T j ,t
N j ,t  1   N N j ,t 1  h j ,t
Our model: Impatient Households
• Mass of
s impatient housheholds
• ‘Impatience’ implies high discount rate
• These households borrow via mortgages
• Get utility out of consumption and housing
• Disutility from members of the household working
• Nj is the proportion of household j in employment
• Total employment of impatient households equals NI
Our Model : Impatient Households
• Maximize:


 
E0    1    ln c j ,t  cH ,t 1   jA j ,t ln H j ,t 
N j ,t 
1 
t 0



t
I
• Subject to:
Qt H j ,t  L j ,t  Qt H j ,t 1  RL ,t 1 L j ,t 1  Wt h j ,t  Pt c j ,t  T j ,t
L j ,t  ltvt Qt H j ,t
N j ,t  1   N N j ,t 1  h j ,t
Our model: Firms
• Monopolistically competitive
• Owned by the patient households
• Maximise present discounted utility value of dividends
• Face costs of adjusting investment and hiring costs
• Have to borrow from banks to finance hiring costs
• Also have to borrow from banks to finance investment
• Face quadratic costs of adjusting prices
• Wages are set so that all the surplus of job matches goes
to firms
• Households will be indifferent between supplying an extra worker
and not supplying an extra worker
Our Model : Firms
• Maximize:

  h    P
 Pt 1    
 h  l ,t    l ,t  1
P
y

P
I

W
N

L

R
L


t l ,t
t l ,t
l ,t
L ,t 1 l ,t 1
 l ,t l ,t
 2 N 
2  Pl ,t 1 
t 1 Pt c P ,t  c P ,t 1 
l ,t 




2
 Pt
yl ,t  
 Pl ,t

1
y

A
k
N
z ,t l ,t 1
l ,t
• Subject to: l ,t

 I l ,t  


kl ,t  1   k kl ,t 1  I l ,t 1  S 


 I l ,t 1  

h  hl ,t
Ll ,t  Pt I l ,t  Pt yt 
2  N l ,t




N l ,t  1   N N l ,t 1  hl ,t
2


 yt


2


P y 
 t t 


Our Model : Firms
• First-order conditions:
• New Keynesian Phillips curve
  1  rmct 
 t   P Et t 1 
ln


rmc


• Value of installed capital
QK ,t 
 rmct 1 yt 1

1
Et 1   t 1 
 1   k QK ,t 1 
Rt
kt


• Investment demand

ˆ  Rˆ  Rˆ
Q
1

L ,t
t
P
Iˆt 
Iˆt 1 
Et Iˆt 1  k ,t
1 P
1 P
k 1   P 

Our model: Firms
• Definition of real marginal cost
wt N t
h RL ,t ht  ht 
1  
rmct 

1    yt 1   Rt N t  N t 
RL ,t 1 ht 1 yt 1 N t

1   N  h

Et 1   t 1 
Rt 1  
Rt 1 N t 1 yt N t 1
• This is the usual expression for real marginal cost plus an
additional term reflecting the cost of hiring additional
workers and this term depends on the spread
• This is the key link between financial frictions and the real economy
and inflation
Our model: Banks
• Banks are funded through capital (retained earnings) and
•
•
•
•
deposits
Bank assets are loans to impatient households
(mortgages) and firms
Banks are owned by the patient households
Each period banks either continue to accumulate net
worth (probability z) or ‘die’ and distribute their
accumulated net worth to patient households as dividends
(probability 1-z)
The 1-z ‘dead’ banks are replaced by 1-z new banks with
initial net worth Pn, provided lump sum by the patient
households
Our model: Banks
• For a surviving bank, net worth evolves according to:
n j ,t  n j ,t 1  RL ,t 1  1L j ,t 1  Rt 1  1D j ,t 1  y ,t n j ,t 1
• Where
y is a shock to bank profits (and, by implication,
net worth)
• Net worth will equal assets less liabilities (deposits)
n j ,t  L j ,t  D j ,t
• So, aggregate net worth in the banking sector evolves
according to:
nt  z RL ,t 1 Lt 1  Rt 1 Dt 1  y ,t nt 1   1  z Ptn
Our model: Banks
• Bankers have the opportunity to ‘run away’ overnight with
•
•
•
•
•
a proportion, q, of the bank’s assets.
To stop them doing so, it must be more profitable for them
to keep the bank open as an ongoing business than to run
away with the assets.
This implies the incentive constraint: Vt  qLt
This leads to a spread between lending and deposit rates,
which is increasing in leverage and this friction, q.
We implement regulatory policy as affecting q .
We also implement a shock to bank equity prices, V,
which will directly affect the spread.
Our model: Banks
• Dividends will be given by
DivB ,t  1  z RL ,t 1 Lt 1  Rt 1 Dt 1   t nt 1 
• So, banks will solve the following profit maximisation
problem:
• Maximise

Vt  Pt Et  
j 1
• Subject to
j
P
z
j 1
1  z 1    R
L ,t  j 1 Lt  j 1  Rt  j 1 Dt  j 1   t  j nt  j 1 
Pt  j cP ,t  j  cP ,t  j 1 
Vt  qLt
Our model: Banks
• The Bellman equation for this problem implies:
y ,t 1  1

q
 
 1  Et 

Rt
 1  z  zqj t 1  jt Rt  jt
RL ,t
• That is, the spread is increasing in leverage
j, the
(expected value of) the shock, y, and the friction, q
Our model: Public sector and market clearing
• The government is assumed to run a balanced budget:
Pt Gt  Tt
• The Central Bank operates a Taylor rule:
 1
ln Rt  1   R ln 
 H


y
   R ln Rt 1  1   R n   t n y ln  t
 y


• Finally, market clearing implies:
yt 
ct  I t  Gt
 2 h  ht 
1   t   
2
2  Nt 
2

    R,t

Effects of frictions
We compare results from four models:
1.
Model with no other friction than sticky prices
• Firms are 100% equity financed and face no investment or hiring adjustment costs
• No role for banks, one representative household
2.
Model with hiring and investment frictions
• Same as Model 1, but firms face costs of hiring and adjusting investment
3.
Model with financial frictions
• Firms have to borrow to finance investment
• Impatient households borrow for housing purchases
4.
Model with all the frictions
• Financial frictions : LTV ratios, leverage constraint, firms have to borrow to finance
investment, costs of adjusting investment, and hiring costs , and impatient households
borrow for housing purchases
• Hiring and investment frictions
Effects of a monetary policy shock
Model 1: Only price frictions
Per cent
5
Model 2: Just price, hiring and investment frictions
Per cent
0.05
Consumption
Consumption
0.00
0
House prices
GDP
GDP
-5
-0.05
Investment
-0.10
-10
Employment
-0.15
Employment
-15
-0.20
-20
-0.25
House prices
Investment
-25
-0.30
-30
-0.35
-35
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
-0.40
0
1
2
3
4
5
6
Quarters after shock
Model 3: Just price and financial frictions
7
8
9
10 11 12 13 14 15 16 17 18 19 20
Quarters after shock
Per cent
1
Model 4: All frictions
Per cent
0.05
Consumption
Consumption
0.00
0
House prices
GDP
GDP
-1
-0.05
Investment
-0.10
-2
-0.15
Employment
Employment
-3
-0.20
-4
House prices
Investment
-5
-0.30
-6
-0.35
-7
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
Quarters after shock
-0.25
-0.40
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
Quarters after shock
Effects of shocks
Look at shocks to:
• Bank equity prices, y
• Mortgage loan-to-value ratio, ltv
• Banking regulation (proxied by q)
Effects of a bank equity price shock
Effect of a bank equity price shock
Per cent
0.05
Effect of a bank equity price shock on
interest rates and inflation
Basis points
700
600
Consumption
0.00
500
Spread
GDP
-0.05
400
-0.10
Investment
Employment
Loan
rate
300
-0.15
200
-0.20
100
Inflation
-0.25
0
Deposit rate
-100
-0.30
0
1
2
3
4
5
0
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Quarters after shock
Effect of a bank equity price shock on
bank lending and net worth
Per cent
20.0
1
2
3
4
5
6
7 8 9 10 11 12 13 14 15 16 17 18 19 20
Quarters after shock
Effect of a bank equity price shock on
the housing market
Per cent
4
Housing stock
held by patient
households
15.0
6
2
Net worth
0
10.0
House
prices
-2
-4
5.0
-6
Housing stock
held by impatient
households
Lending to firms
-8
0.0
-10
Deposits
Mortgage lending
0
1
2
3
4
5
6
7
8
9
-5.0
10 11 12 13 14 15 16 17 18 19 20
Quarters after shock
-12
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
Quarters after shock
Effects of a mortgage loan-to-value shock
Effect of a rise in LTV ratios
Per cent
Effect of a rise in LTV ratios on
interest rates and inflation
0.06
Basis points
40
Lending
rate
20
0.04
Inflation
0.02
Consumption
0
Deposit
rate
-20
0.00
GDP
-40
Spread
-0.02
Employment
Investment
-0.04
-60
-0.06
-80
-100
-0.08
0
1
2
3
4
5
6
7 8 9 10 11 12 13 14 15 16 17 18 19 20
Quarters after shock
Effect of a rise in LTV ratios on bank
lending and net worth
Per cent
2.0
Mortgage lending
0
1
2
3
4
5
6
7 8 9 10 11 12 13 14 15 16 17 18 19 20
Quarters after shock
Effect of a rise in LTV ratios on the
housing market
Per cent
2.0
1.5
1.5
1.0
Deposits
Housing stock
held by impatient
households
0.5
1.0
0.0
0.5
Lending to firms
House prices
-0.5
0.0
-1.0
Net worth
-2.0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
Quarters after shock
-0.5
Housing stock
held by patient
households
-1.5
0
1
2
3
4
-1.0
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
Quarters after shock
Effects of a loosening in regulation (q)
Effect of a loosening in regulation
Per cent
Effect of a loosening in regulation on
bank lending and net worth
0.18
Per cent
4
Deposits
0.16
Mortgage lending
0.14
Investment
2
0
Lending to firms
0.12
-2
0.10
Employment
0.08
-4
0.06
-6
0.04
GDP
Consumption
Net worth
-8
0.02
-10
0.00
-12
-0.02
0
1
2
3
4
5
6
7 8 9 10 11 12 13 14 15 16 17 18 19 20
Quarters after shock
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
Quarters after shock
Conclusions
• According to our model, a loosening of bank regulation
leads banks to lend more while allowing their net worth
(capital) to fall
• A shock to bank equity valuations leads to a marked rise
in the spread but a relatively small fall in output
• Raising the LTV ratio on mortgage lending leads to a rise
in mortgage lending but only a small rise in house prices
• But we are still not happy with the quantitative
implications of the model: in particular, for the spread
• Need for a more careful calibration of the model
• In future work we hope to estimate the model!