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When money matters: liquidity shocks with real effects

John Driffill and Marcus MillerBirkbeck and University of Warwick

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Financial boom…

(Note: US GDP is about $14 trillion)

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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:)

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.

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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

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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

t

DM

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y

k k*

y, output per head

k* k, capital per head

k° = 0

c, consumption per head

Shading shows depreciation

k(o)

The Simple Solow Growth Model (with Fixed Technology and Exponential Depreciation)

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Neoclassical growth model:high marginal productivity of capital encourages savings

c

f´(k * )=θ

y, output per head

k* k, capital per head

k° = 0

c, consumption per head

k(o)

c° = 0

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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.

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Dynamics of K and q: phase diagram

q

Equity Price

K Capital Stock

S

U

K*

Zero net investment

Asset price stationary

U

S

K°= 0

q°= 0

K(0)

E

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

1 (1 ) (1 )t t t tn i n

1 0tm

Entrepreneur’s budget constraint

• Budget:

• p – price of money; q – equity price

• λ – 1-depreciation rate

• n equity held by entrepreneur

• Objective - max exp U:

1 1( ) ( )t i t t t t t t t t tc i q n i n p m m r n

log( )s tt s

s t

E c

Production

• CRS / C-D production function, capital and labour

• KM: wage clears labour market

• DM: fix money wage and price level – entrepreneurs keep the surplus

1t t t ty A k l

t t t t ty w l r k

Investment and Aggregate (Net) Demand

(1 )1 1

t t t t t t

t t Rt t t

r q K p Mq I

q K

( ) 1

( ) 11

t t t

t t t t t tRt t

r x qr x K I K p M

q

Investment demand

Entrepreneurs’ income equals their demand (GM equilibrium)

1

1R t

t

qq

.

Entrepreneur’s Portfolio Balance (AM)

1 1 1

1 1 1 1

1 1 1 1 1 1

1 1 1 1 1 1 1

/ /(1 )

/ (1 ) /

(1 )

t t t t tt s

t t t t

Rt t t t t t t t

t R st t t t t t t

r q q p pE

r q N p M

p p r q q qE

r q q N p M

1 (1 )st t t t tN I K K

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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?

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.

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Using AM and RI to get phase diagram

q

Equity Price

K

AM

E

Capital Stock

RI

SU

K*

K Zero net investment

ΔK/Δt = 0

Asset price stationary

Δq/Δt = 0 U

S

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q

Equity Price

K

AM

E

Capital Stock

RI'

K*

AM'

RI

Note that, at E’, the price level is lower than at E.

E'

Flex-price comparative statics as in KM (2008): φ increases, liquidity driven expansion,

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Figure 2. ‘Big Bang’ - with anticipated encore

q

K

E

K**

C

K*

E'

B

U'

U'

A

A

I

N

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q

Equity Price

K

AM

E'

Capital Stock

RI'

K*

Zero net investment

ΔK/Δt = 0

GM

AM'

RI

Fixed price, 2D dynamics with respect to AM and RI, output is demand determined

E

Y

Fix price comparative statics DM (2010): tightening liquidity shifts RI and AM to left

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Dynamics: stock market fall leading to recession – or recovery if shock is to be reversed

q

K

E

K**

U'

D

K*

E'

U'

L

A

A

I

PY

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.

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45°

L

wage bill (w*L)

X

‘workers spend what they earn;

entrepreneurs earn what they

spend’

Marginal Product of Labour

Aggregate Demand

Bargaining Wage

w*

X

Xf

real wage rate

L

D(X;q,K,)

μ

E

E*

D

D*

Net Output (X = r(Y)K)

Net Output (X=r(Y)K)

Figure 3. Short-run determination of X and Y

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

t

Y

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%

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100.00 105.00 110.00 115.00 120.00 125.00 130.00 135.00 140.00 145.00 150.000

0.5

1

1.5

2

2.5

1937

1920-1929

1929-1937

K

q

Figure 8. Tobin’s q and the capital stock between the wars

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Figure 9. Bubble collapse preceding liquidity shock: like 1929

q

K

U

E

K**

U

E'

D

K*

U'

U'B

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

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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’