A Macroeconomic Model of
Endogenous Systemic Risk Taking
D. Martinez-Miera and J. Suarez
Discussion
Rafal 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 behaviour≠systemic 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 risk
2. 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 force
Due 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
𝜐𝑡+1 (𝑒𝑡 ) of one unit of a banker's wealth
• Upon the realization of the systemic risk:
– Wealth of 'risky banks' is wiped out
– Scarce 𝑒𝑡 ⇒ 𝜐𝑡+1 driven up for save banks: last bank
standing effect (in the spirit of Perotti&Suarez, 2002)
• In equilibrium banks indifferent between projects
⟹ x∈ (0,1)
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 (⟹ 𝜐𝑡+1 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 ∈ (0,1)
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 𝜐𝑡+1 (𝑒𝑡 )
– 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(𝒛,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 given
What 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 deep
b) 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?