A Macroeconomic Model of Endogenous Systemic Risk Taking

D. Martinez-Miera and J. Suarez

DiscussionRafal Raciborski

DG ECFIN, European Commission

Norges Bank, Oslo, 29 - 30 November 2012

Disclaimer

The views expressed are the author’s alone and do not necessarily correspond to those of the

European Commission.

Context

• It's been almost 5 years that the world has been in the financial and economic crisis…

• …with its causes still not yet fully understood…• …but with a contribution of the financial sector

generally unquestioned

Most economists would agree the financial sector (banks in particular) may contribute to and perhaps

generate systemic risk

This paper

• Discusses one particular channel via which systemic risk may originate in the banking sector– Idea most closely linked to the 'risk-shifting literature’

• Embeds it into a general equilibrium model– May be disputed whether the systemic risk is truly

endogenous; more on it later• Solves nonlinearly to discuss optimal bank capital

requirements

The model: general idea• General result (Jensen&Meckling, 1976;

Stiglitz&Weiss, 1981; Allen&Gale, 2000):– Limited liability non-convexities in the profit

maximizer's problem– The maximizer may then prefer a riskier project,

pushing its risk on other agents (=risk shifting)• Banks protected by deposit insurance (limited

liability) they like riskier projects• But: riskier behavioursystemic risk– Assume that riskier projects are systematically linked

The model: available projects

• 2 types of projects:1. Less risky projects (in terms of its variance and its mean):

idiosyncratic risk2. More risky projects: risk perfectly correlated

• Higher variance of the risky projects to induce risk-shifting in the banks

• Correlation of risky projects=systemic risk• Lower unconditional mean of the risky project

probably makes things harder; conveys the idea of systemic risk being "bad"

The model: equilibrating forceDue to limited liability banks like riskier projects; why don't we observe only the riskier ones being

chosen (share of risky projects x=1)?• Crucial variable: stochastic marginal value of

one unit of a banker's wealth• Upon the realization of the systemic risk:– Wealth of 'risky banks' is wiped out– Scarce driven up for save banks: last bank standing

effect (in the spirit of Perotti&Suarez, 2002)• In equilibrium banks indifferent between

projects x

Welfare• Banks’ agency problem affects negatively the

economy via 2 channels:– Static losses: picking inefficient projects– Dynamic losses: loss of bank equity (and, hence,

lending capacity) in the event of a systemic shock• Measurement:– All agents risk neutral; but GDP does not reflect

welfare well– GDP (=added value) excludes capital losses– Does output (y=GDP+undepreciated K) correlate

perfectly with welfare in your model?

Capital requirements

• Increased capital requirements γ make capital scarcer ( higher) higher incentive to choose safer projects higher proportion of bank equity invested in safer projects

• But, banks’ lending capacity reduced lower average efficiency

• Trade-off optimal γ

Results

• For the benchmark calibration:– With low γ=7% fraction of capital invested in

systemic projects very large (70%) – Systemic shocks very painful (31% drop of GDP)– Optimal γ large (14%)– Optimal γ welfare higher by about 1%

• Number of extensions– Interesting perverse results

Minor remarks (I)

• You assume a pooling equilibrium– Are there other types of equilibria?– If so, how do we know yours is the relevant one?

• One of your main contributions: quantitative results (“high optimal γ”); but your model ‘very stylized’. For example:– Crucial role of the slope of – It would be less steep if labour were variable…

Minor remarks (II)

• An issue with calibration?– You assume 35% depreciation in failed firms– For γ=7%, 70% of all projects are systemic– This gives 35%×70%=25% capital depreciation in

the economy in the event of a systemic shock– Also the fall in GDP (30%) very large

• Develop the sensitivity analysis– “The choices for the values of […] ψ and φ are

quite tentative.”

General equilibrium?

Is systemic risk endogenous?• Yes: share of bad projects x=f(,regulation) • No: systemically-risky projects are always

there to be picked only the severity of the crisis endogenous

I believe we cannot do w/o opening the black box – see next 2 slides

Take the black box as givenWhat are the systemic projects?

• Allen&Gale (2000): oil shock – convincing, but with a limited application (Norway!)

• Your footnote 1: housing bust:– Is it systemic? What makes it so?– Was it (before 2007) considered risky? (The notion

that “house prices never fall”)• Even so: Is it plausible? Convince the reader!• What happens in your model if you have 2 types

of risky projects: identical payoffs, but projects of the 2nd type independent

Bring your channel to the data“Systemic Banking Crises facts” (Boissay et al.):

a) SBC’s are rare and deepb) SBC’s are closely linked to credit developments

Ad. a) Your model can obviously match it, but:– by imposing exogenous prob. of a systemic crisis– endogenous risk correlation in recessions,

Brunnermeier&Sannikov, 2011 (parsimony)Ad. b) Nothing to say about it– again, endogenous link (Boissay et al., 2012)– hard to make policy advice w/o a crucial channel

Need to open up the black box

Interesting perverse effect?

• Your results sensitive to the exogenous probability of a systemic crisis– Benchmark: ε=0.03

• One view: makes your results fragile• Alternative view: innovations that make the

economy safer (ε↘) make crises deeper…

Worth exploring?