Macroeconomics after the crisis – hedgehog or fox?

Marcus Miller and Lei ZhangCurrently 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 problem-

solving discipline rather than a science (cf. John Hicks)• Let’s meet a couple of foxy types

Warned of ‘Pecuniary Externalities’ in 1976:prices may clear markets, but they can lead us astray too!

Greenwald and Stiglitz

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 GreenspanChairman 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.

8

The financial accelerator as pecuniary externality

Insolvency Solvency

k *

S

θ

qt

Asset PriceSC

E

S

kt

D

D

B

B'D'

D'

kc

Initial conditions

X

qx

Aq*

Temporary productivity shock

Bursting asset bubble

Small Business Asset Holdings

‘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 shadow-banking 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’ ), with state probabilities of , respectively, taken to be exogenous and to be common knowledge between buyer and seller.The problem can be formulated as:

subject to the budget constraint

,

where represents either “good” or “bad” state, represents the adverse shock to GDP; and solvency requires.

Good stateBorrower

Bad state

1/q

Iso- Expected Utility curves of sovereign where is constant . Shown for for High and Low probabilities of good state,

H,c

L,x

E

Indifference curves cross as they are for different probabilities

x

c

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?

17

Arrow-Debreu equilibria

Good state

Buyer chooses effort level, H or L given ‘fair’ price of insurance, c or x

Buyer

Bad state

1/q

Offer curves of borrower; Low effort to the Left

H,c

L,xE

L,c

H,x

x

c

A simple insurance game

Cheap insurance Expensive insurance

High effort H,c H,x

Low effort L,c L,x

Actions.

Cheap insurance Expensive insurance

High effort

Low effort

Payoffs

Non existence of AD equilibrium

Good stateBuyer

Bad state

Offer curves of borrower; Low effort to the Left

H,c

L,xE

L,c

H,x

x

c

E’’

E’

seller

Convergence to a polymorphic equilibrium (Binmore et al.)

1* 2

1* -2 ← ↑ 3

2 -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.)

23

Good stateBuyer

Bad state

1/q

LenderRed arrow shows ‘cost of effort’

H,c

L,xE

Quantity constrained insuranceRothschild/Stiglitz

CRS

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)

“emerging in the early 70’s and staying for around ten or twenty years”

Include ECM and RE, plus equations for financial system based on flow funds

Third Generation Models (3G)

(late 80’s to end of the century)

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?

26

Conclusions

• We end with a puzzle– Why does the hedgehog not listen to the barking

of the foxes?

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): 1435-1458.

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/wp-content/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.

29

Arrow-Debreu equilibria with complete insurance

Borrower chooses complete insurance depending on probability of good state, H or L , given ‘fair’ price of insurance, q =c or x, where .

Good stateBorrower

Bad state

1/q

Iso- Expected Utility curves of sovereign where is constant . Shown for for High and Low probabilities of good state,

H,c

L,x

E

Indifference curves cross as they are for different probabilities

x

c

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.

State space diagram