When money matters: liquidity
shocks with real effects
John Driffill and Marcus Miller
Birkbeck and University of Warwick
1
Financial
boom…
(Note: US GDP is about $14
trillion)
2
Followed by bust: UK recession (dark blue) relative to earlier
recessions
(dark brown is 1930s; green and yellow follow oil shocks; light brown
follows bursting of housing bubble:)
3
Call for integration of financial factors into real
models
• In ‘The Great Moderation, the Great Panic and the Great
Contraction’ Charlie Bean (2009) calls for further research on
financial factors as an urgent priority.
• In fact, Kiyotaki and Moore (2008) have developed a
‘workhorse model of money and liquidity’ where liquidity
constraints can affect investment and the economy.
• With flex-prices and full employment, their focus is on the
supply side.
• Simulations of such a model by FRBNY- in conjunction with
Kiyotaki - in a fix-price environment produce dramatic results
for liquidity shocks for aggregate demand.
Background: growth and investment
• Before considering how financial factors may
affect investment, we look at three real models of
capital accumulation
• The simplified Solow model of growth
• Neoclassical optimising model
• Tobin’s q –theory of investment
• Reference
• Acemoglou, Daron. Introduction to Modern
Economic Growth. Princeton Univ Press
5
Effect of a liquidity shock in US that lasts 10 quarters, Del Negro et al. (2009)
– with analytical equivalent from Driffill and Miller (2010)
Y
DM
t
6
The Simple Solow Growth Model
(with Fixed Technology and Exponential Depreciation)
y
y, output per head
Shading shows
depreciation
c, consumption
per head
k° = 0
k*
k(o)
k, capital per head
k  k*
7
Neoclassical growth model:
high marginal productivity of capital encourages savings
c° = 0
c, consumption
per head
c
y, output per head
k° = 0
k(o)
k*
k, capital per head
f´(k * )=θ
8
The q-theory of Investment
and Saddle-Path stability
By definition
Let I be an increasing function of q, the present discounted
value of the net marginal product of (installed) capital, and
so
The investment function may reflect represent installation
costs at a micro level or increasing cost of supply at a macro
level.
9
Dynamics of K and q: phase diagram
Equity
Price
q°= 0 Asset price
stationary
q
U
K°= 0
Zero net
investment
S
E
S
U
K(0)
K*
K Capital
Stock
10
Kiyotaki and Moore (2008): “Liquidity, Business
Cycles, and Monetary Policy”
• Assets involved: Money and equity
• Money is liquid
• Equity is not (completely) liquid
– only a fraction of holdings can be sold each period
– only a fraction of newly produced capital goods can be
financed by issuing new equity
Workers – not the focus of attention
• Rational and forward-looking, but credit constrained (no
borrowing)
• Do not have ‘ideas’ for investment
• Can hold money and equity if they choose
• But choose to spend all they get on consumption and save
nothing
• So consumption equals wages
Entrepreneurs – play central role, manage production
and invest and hold assets
• May (prob π) or may not (prob 1-π) have an idea for a
profitable investment
• Those with no ideas (no investment)
– Consume
– Save in form of money and equity holdings
• Those with an idea (Investors)
– Buy new capital goods
– Issue equity against them
– Use money, other equity holdings, and current income to
finance investment
Investment
Entrepreneurs can only finance investment using
money, selling existing equity claims to others, raising
equity on new capital, and spending out of current
income
Liquidity constraints on investment
• Entrepreneurs can raise equity against up to a fraction θ of
new investment.
• They can sell off a fraction φt of pre-existing equity (theirs
and others) nt
• Money is perfectly liquid
nt 1  (1   )it  (1  t ) nt
mt 1  0
Entrepreneur’s budget constraint
• Budget:
ct  ii  qt (nt 1  it   nt )  pt (mt 1  mt )  rt nt
• p – price of money; q – equity price
• λ – 1-depreciation rate
• n equity held by entrepreneur
• Objective - max exp U:

Et  
s t
s t
log(cs )
Production
• CRS / C-D production function, capital and labour
 1
yt  At kt lt
• KM: wage clears labour market
• DM: fix money wage and price level – entrepreneurs keep the
surplus
yt  wt lt  rt kt
Investment and Aggregate (Net) Demand
Investment demand

   rt  t qt  Kt  pt M t  

(1   qt ) It   

R

 1   1  t   qt Kt 

.
Entrepreneurs’ income equals their demand (GM equilibrium)


  r ( xt )  1    t   qt 

r ( xt ) Kt  I t  1     
 Kt  pt M t 
R



   1  t   qt

1   qt
qt 
1
R
Entrepreneur’s Portfolio Balance (AM)
  rt 1   qt 1  / qt  pt 1 / pt 
(1   ) Et 

s
  rt 1   qt 1  N t 1  pt 1M 
 pt 1 / pt   rt 1  t 1 qt 1  (1  t 1 ) qt 1R  / qt 



 Et 
R
s
  rt 1  t 1 qt 1  (1  t 1 ) qt 1  N t 1  pt 1M 
N t 1s   I t  t K t  (1   ) K t
Basic structure of KM model
• 3 equations :Investment Demand, Aggregate
Demand (C+I) and Portfolio Balance, between
money and shares.
• 3 unknowns: price level, Tobin’s q, and K.
• Two regimes :
• Flex-price: full employment via Pigou effect
determines the price level.
• Fix-price: agg demand determines
employment.
• What about K and q?
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Stationary conditions for K and q.
• The Investment equation and Portfolio
Balance determine evolution of K and q.
• Stationarity for K is when all capital spending
is for Replacement Investment, on upward
sloping RI schedule in K,q space.
• Stationarity for q, is on downward sloping AM
equilibrium schedule where there are no
capital gains.
Using AM and RI to get phase diagram
Equity
Price
q
Asset price stationary
Δq/Δt = 0
U
AM
S
RI
K
E
Zero net investment
ΔK/Δt = 0
S
U
Capital Stock
K*
K
22
Flex-price comparative statics as in KM (2008):
φ increases, liquidity driven expansion,
Equity
Price
q
AM
AM'
E
RI
E'
RI'
Capital Stock
K*
K
Note that, at E’, the price level is lower than at E.
23
Figure 2. ‘Big Bang’ - with anticipated encore
q
A
U'
I
B
C
E'
N
E
A
U'
K*
K**
K
24
Fix price comparative statics DM (2010): tightening
liquidity shifts RI and AM to left
Equity
Price
AM'
q
AM
Zero net investment
ΔK/Δt = 0
E'
RI'
E
GM
RI
Y
Capital Stock
K*
Fixed price, 2D dynamics with respect to AM and
RI, output is demand determined
K
25
Dynamics: stock market fall leading to recession – or recovery if
shock is to be reversed
q
U'
A
I
L
E
E'
D
P
U'
K*
K**
A
Y
K
26
Linearised fix-price model:
Fix price macro
• If prices are inflexible downward, there will be no Pigou effect
to stabilise aggregate demand in the face of a fall of
investment
• A fall in demand will contract employment if the real wage is
determined by bargaining, as argued for the UK in Layard and
Nickell, Alan Manning.
• Graphical representation follows of how liquidity contraction
can cut income conditional on K and q.
Figure 3. Short-run determination of X and Y
Aggregate
Demand
D(X;q,K,)
E
‘workers spend what they earn;
entrepreneurs earn what they
μ
D
spend’
X
45°
Bargaining
Wage
w*
Xf
Net Output (X = r(Y)K)
real wage rate
X
D*
wage bill
(w*L)
Marginal
Product of
Labour
Net Output (X=r(Y)K)
E*
L
L
29
Calibration using FRBNY parameters (qtly)
• φ = 0.13 (fraction of existing assets an entrepreneur can sell);
• discount factor β = 0.99;
• fraction of new capital against which an entrepreneur can
raise equity, θ = 0.13;
• probability of an entrepreneur having an idea for an
investment, π = 0.075;
• the quarterly survival rate of the capital stock λ = 0.975
• [ our base case steady state: q = 1.12, r = 0.0374,
• Mp/K =0.1171, K = 152.5, y =17.26]
Figure 6. Numerical Results from DM simulation using FRBNY parameters
Temporary and permanent liquidity shock
Y
t
Table 2. Impact effects of a 20% cut in ϕ
for different lengths of time
Short (2 years)
Long (8 years)
Permanent
q
-1.25%
-2.86%
-3.57%
r
-10.90%
-12.23%
-12.50%
X
-10.27%
-11.48%
-11.73%
y
-18.65%
-20.54%
-20.92%
Figure 8. Tobin’s q and the capital stock between the wars
2.5
2
1929
1.5
q
1920-1929
1
1929-1937
1937
0.5
1920
0
100.00
110.00
120.00
130.00
K
140.00
150.00
34
Figure 9. Bubble collapse preceding liquidity shock: like 1929
q
U
U'
B
E
E'
D
U'
U
K*
K**
K
35
Conclusion
• Switching from a flex-price to a fix-price framework means
that demand failures can emerge after a liquidity shock.
• AM and RI offer simple analytical treatment of impact and
dynamic effects.
• Adding bubble might help explain the origin of the shock- it’s
when the bubble bursts
• Need to add financial intermediaries to get to the heart of
the matter
References
• Acemoglou, Daron. Introduction to Modern Economic
Growth. Princeton Univ Press
• Del Negro, Marco, Gauti Eggertsson, Andrea Ferrero and
Nobuhiro Kiyotaki (2009). ‘The Great Escape? A
Quantitative Evaluation of the Fed's Non-Standard Policies.’
FRBNY working paper.
• Dale, Spencer (2010), ‘QE – one year on’, speech a CIMF
and MMF conference at Cambridge on 12th March.
• Driffill, John and Marcus Miller(2010) ‘When money
matters: liquidity shocks with real effects’
• Kiyotaki, Nobuhiro and John Moore (2008) ‘Liquidity,
Business Cycles, and Monetary Policy’
37