Macroeconomics after the crisis –
hedgehog or fox?
Marcus Miller and Lei Zhang
Currently Houblon-Norman Fellows at the
Bank of England
ESRC Conference on ‘Diversity in Macroeconomics’
University of Essex, February 24/25, 2014
"The fox knows many things, but the
hedgehog knows one big thing"
Archilochus of Paros
• As applied to famous economists?
• One Big Thing: Hedgehogs
• Leon Walras (GE), Karl Marx Capital) , and
Milton Friedman (Money)
• More Eclectic Perspectives: Foxes
• John Maynard Keynes, Amartya Sen and
Joseph Stiglitz
DSGE and its critics
• DSGE approach has DNA of GE in its genes
• seeks to use one modelling framework as the lens with
which to view the world; so it’s a heDGSEhog, no?
• thanks to this unifying, microfounded framework, sees
economics as an essentially scientific endeavour.
• Critics of DSGE ready to use whatever approach seems
most suitable for the problem at hand,
• given this attitude, view economics as a problemsolving discipline rather than a science (cf. John Hicks)
• Let’s meet a couple of foxy types
Greenwald and Stiglitz
Warned of ‘Pecuniary Externalities’ in 1976:
prices may clear markets, but they can lead us
astray too!
Example of ‘Pecuniary Externality’
• insurance companies unable to monitor the effort in
accident prevention being made by individual
households, they price to cover their costs.
• the price an individual pays for insurance will depend
on the average level of accident avoidance of those
who purchase insurance
• this is an externality to an individual purchaser,
• so there will on average be a socially inefficient level
of effort to avoid accidents.
• subsidizing fire extinguishers can reduce the externality
Alan Greenspan
Chairman of the Fed 1987-2006
Did he realise just how powerful these externalities could be?
Let’s consider those affecting the demand and supply of credit
‘Demand-side’ explanations of credit
fluctuations
• ‘the key … is the changing strength of the
borrower’s balance sheet and the resulting
change in the creditworthiness of the borrower’.
• Bernanke and Gertler (1989) and Kiyotaki and
Moore (1997)
• Externality: businesses whose balance sheets
improve as asset prices rise can borrow more;
• Externality :borrowers who sell assets widely
used as collateral in a ‘firesale’ may force other
borrowers to do the same.
The financial accelerator as pecuniary externality
Asset Price
q
t
D'
B'
SC
Bursting asset bubble
B
Initial
conditions
D
S
A
q*
E
θ
qx
X
S
Temporary productivity shock
D'
D
Small Business
Asset Holdings
Insolvency
Solvency
kc
k*
kt
8
‘Supply-side’ mechanisms.
• Adrian and Shin (2007) focussed on balance
sheet pressures that affect the supply of
credit.
• In the subprime crisis, for example, ‘the
greater risk-taking capacity of the shadowbanking system [led] to an increased demand
for new assets to fill the expanding balance
sheets.’
Endogenous Risk Premia (Adrian et al.
2010)
Millenium Bridge
When the London Millennium footbridge was opened in June 2000, it swayed alarmingly
Insurance game with no Arrow-Debreu
equilibrium
• Take a risk averse agent seeking insurance at
‘actuarially fair’ prices, depending on state
probabilities
• Find the AD equilibria given exogenous probabilities;
or endogenous probabilities and contractible effort.
• See whether these AD equilibria survive ( as pure
strategy NE in game) when effort is not contractible
• If not, look for Mixed-Strategy NE
• Look for ‘wishbone’ solution (price quantity pairs as in
Rothschild/Stiglitz)
Pareto-efficient Arrow Debreu equilibria,
with exogenous state probabilities
Agent (the buyer) facing endowment risk who seeks to insure against
downside risk by issuing Arrow securities. Let endowment between two
levels, ‘good’ and ‘bad’ (1,1 − ∆), with state probabilities of 𝜋,1 − 𝜋
respectively, taken to be exogenous and to be common knowledge between
buyer and seller.
The problem can be formulated as:
max𝑐𝑖 𝜋𝑢 𝑐𝐺 + 1 − 𝜋 𝑢 𝑐𝐵
subject to the budget constraint
𝑐𝐺 + 𝑞𝑐𝐵 = 1 + 𝑞(1 − ∆),
𝑐𝑖 ≥ 0
where 𝑖 = 𝐺, 𝐵 represents either “good” or “bad” state, ∆ represents the
adverse shock to GDP; and solvency requires
1 + 𝑞(1 − ∆) > 0.
Indifference curves cross as
they are for different
probabilities
Bad
state
Iso- Expected Utility curves of sovereign
where
𝜋𝑢 𝑐𝐺 + 1 − 𝜋 𝑢 𝑐𝐵 is constant .
Shown for for High and Low probabilities
of good state, 𝜋𝐻 > 𝜋𝐿
c
H,c
x
L,x
E
1/q
Borrower
Good state
Two interpretations of these equilibria
• The first, more obvious interpretation, is that the state
probabilities are simply exogenous.
• The other, to be used in what follows, is that state
probabilities endogenous , depending on discrete ‘effort’ of
sovereign; but this effort is ‘contractible’.
• So the sellers of insurance offer a menu of contracts each
depending on the observed level of effort.
• Note that expected utility shown in the figure is gross of
the cost of effort. The net utility with high effort, as
measured by certainty equivalent consumption ,will move
down the 45-degree line from H,c depending on the cost of
effort.
• What if effort is ‘non-contractible’?
Non-contractible effort
• With asymmetric information, the buyer is aware
of its effort levels, but the sellers of insurance are
not.
• We construct the ‘offer curves’, OH OL , of the
sovereign buyer depending on the level of effort,
and these curves pass through H,c and L,c
identified as AD equilibrium in the full
information case.
• Are these still competitive equilibria with
asymmetric information?
Arrow-Debreu equilibria
c
Offer curves of borrower;
Low effort to the Left
L,c
Bad
state
H,c
x
L,x
H,x
E
1/q
Buyer
Good state
Buyer chooses effort level, H or L given ‘fair’ price of insurance, c or x
17
A simple insurance game
Actions.
Cheap insurance
Expensive insurance
High effort
H,c
↓
← H,x
Low effort
L,c
→
↑
L,x
Payoffs
Cheap insurance
Expensive insurance
High effort
(𝑢 𝑐 𝐻,𝑐 − 𝑒, 𝑢(𝐸))
↓
← (𝑢 𝑐 𝐻,𝑥 − 𝑒, 𝑢(𝐸′′))
Low effort
(𝑢 𝑐 𝐿,𝑐 , 𝑢(𝐸′))
→
↑
(𝑢 𝑐 𝐿,𝑥 , 𝑢(𝐸))
Non existence of AD equilibrium
c
seller
Offer curves of borrower;
Low effort to the Left
L,c
Bad
state
H,c
x
E’
L,x
H,x
E
E’’
Buyer
Good state
Convergence to a polymorphic
equilibrium (Binmore et al.)
1*
1*
2
2
-2
←
↑
3
-1
↓
→
-2
Price and quantity contracts
• An alternative way to increase effort by the
sovereign is the use price and quantity contracts,
as in Rothschild and Stiglitz (1976). To ensure
incentive compatibility, sellers could restrict the
amount of insurance so that the expected utility
with high effort (net of the cost of effort) is at
least as good as that with low effort.
• The relevant restriction for given cost of effort is
shown in the following “wish-bone” diagram.
Price and quantity contracts (cont.)
• The “wish-bone” shows the level of insurance for
which the buyer is indifferent between applying
high and low effort.
• This is not of course perfect insurance, i.e., it’s
Pareto inefficient.
• How can this be implemented? Industry wide
deductible on all insurance contracts. (Rating
agencies could perhaps recommend appropriate
deductibles, based on cost of effort.)
Lender
Red arrow shows ‘cost of effort’
Bad
state
H,c
C
L,x
Quantity constrained insurance
RS Rothschild/Stiglitz
E
1/q
Buyer
Good state
23
Connection with adverse selection
• Clearly as the cost of effort increases, quantity
constraints head towards that of Rothschild
and Stiglitz needed to separate high risk and
low risk “types” of buyer.
• In other words, for this cost of effort or
higher, the dominant strategy for the buyer
will be to choose low effort, i.e., it is a high
risk type. So the problem becomes one of the
adverse selection, rather than moral hazard.
Generations of macro econometric
models
Vintage
Approximate dates
Comment
First Generation Models (1G) 1936-1960’s
Tinbergen pre-WWII and
Klein post-WWII
Second Generation Models
(2G)
Third Generation Models
(3G)
“emerging in the early
70’s and staying for
around ten or twenty
years”
(late 80’s to end of the
century)
Include ECM and RE, plus
equations for financial
system based on flow
funds
Have steady state model
at the core
Fourth Generation Models
(4G)
“have arisen in the
2000’s”
Counterpart of DSGE
Where is the 5th (post-crisis) generation?
Conclusions
• We end with a puzzle
– Why does the hedgehog not listen to the barking
of the foxes?
26
References
• Akerlof, G. and R. Shiller (2013), “Phishing for Phools: the economics of
manipulation and deception”, Lectures in Finance, Princeton Bendheim,
October 10, 2013
• Allen, F. and D. Gale (2009), Understanding Financial Crises, Oxford: Orford
University Press.
• Geanakoplos, J. D. and H., M. Polemarchakis (1986), “Existence, regularity
and constrained suboptimality of competitive allocations when the asset
market is incomplete," in W. Heller, R. Starr and D. Starrett (eds.),
Uncertainty, Information and Communication: Essays in Honor of K. J.
Arrow, Vol. 3, pp. 65-95, Cambridge University Press (1986).
• Greenspan, A. (2002), “World Finance and Risk Management”, Speech
presented at Lancaster House, London, U.K., September 25, 2002.
• Foster, D. P. and H. P. Young (2010), “Gaming Performance Fees By
Portfolio Managers”, The Quarterly Journal of Economics, 125 (4): 14351458.
References (cont.)
• Magill, M. M. Quinzii and J., C. Rochet (2012), “Who owns this firm? A
Theoretical Foundation for the Stakeholder Corporation”, Swiss Finance
Institute Working Paper, University of Zurich, available at
http://sticerd.lse.ac.uk/seminarpapers/et23022012.pdf.
• Mas-Colell, A., M. D. Whinston and J. Green (1995), Microeconomic
Theory, New York: Oxford University Press.
• Vickers, J. (2011), “How to regulate the capital and corporate structures of
banks?’” Speech made to LBS. Available at:
http://bankingcommission.s3.amazonaws.com/wpcontent/uploads/2011/01/John-Vickers-2201111.pdf (last accessed on 6th
November 2012).
• Rothschild, M. and J. Stiglitz, (1976), “Equilibrium in Competitive Insurance
Markets: An Essay on the Economics of Imperfect Information”, Quarterly
Journal of Economics, Vol. 90, No. 4, (Nov., 1976), pp. 629-649.
• Tett, G. (2013), “An interview with Alan Greenspan”, Financial Times,
October 2013.
Arrow-Debreu equilibria with complete insurance
Bad
state
Iso- Expected Utility curves of sovereign
where
𝜋𝑢 𝑐𝐺 + 1 − 𝜋 𝑢 𝑐𝐵 is constant .
Shown for for High and Low probabilities
of good state, 𝜋𝐻 > 𝜋𝐿
c
H,c
x
Indifference curves cross as
they are for different
probabilities
L,x
E
1/q
Borrower
Good state
Borrower chooses complete insurance depending on probability of good state,
1−𝜋
H or L , given ‘fair’ price of insurance, q =c or x, where 𝑞 = 𝜋 .
29
State space diagram
The endowment point for the sovereign is at point E, with less
output is available in the Bad state, measured vertically, than
the Good (horizontal). The state probabilities are (1-π, π,
respectively) are common knowledge and affect both the
desire for insurance by the buyer and the cost of insurance, q,
charged by sellers. The indifference curves have slope π/(1-π )
as they cross the 45% line, so they will be flatter the greater
the risk of loss.
With ‘fair’ priced insurance, the budget lines, have slope 1/q =
π/(1-π). Ex, for example, reflects a higher prospect of the bad
state, so insurance will be more expensive. The amount of
insurance purchased is πΔ.
Two full-insurance, competitive equilibria are shown: (H,c)
with higher probability of the good state and cheap insurance;
(L,x) with more risk of loss and expensive insurance.