A Macroeconomic Model of Endogenous Systemic Risk Taking

1. A Macroeconomic Model of Endogenous Systemic Risk Taking Discussion Rafal Raciborski DG ECFIN, European Commission Norges Bank, Oslo,  29 - 30 November 2012 D. Martinez-Miera and J. Suarez

2. Disclaimer The views expressed are the author’s alone and do not necessarily correspond to those of the European Commission.

3. 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

4. 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

5. The model: general idea • General result (Jensen&Meckling, 1976; Stiglitz&Weiss, 1981; Allen&Gale, 2000): • Limited liabilitynon-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

6. The model: available projects • 2 types of projects: • Less risky projects (in terms of its variance and itsmean): idiosyncratic risk • 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"

7. 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 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 projectsx

8. 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?

9. 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

10. 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

11. 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…

12. 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.”

14. 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

15. 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

16. Bring your channel to the data “Systemic Banking Crises facts” (Boissay et al.): • SBC’s are rare and deep • 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

17. 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?