Private Leverage and Sovereign Default

Private Leverage and Sovereign Default Cristina Arellano Yan Bai Luigi Bocola FRB Minneapolis University of Rochester Northwestern University Economic Policy and Financial Frictions November 2015 1 / 37

Motivation Debt crisis in Southern European Countries Government spreads rose substantially Decline in economic activity, since 2007 GDP drops by 10-20% Question: Did crisis originate in the government sector? Or is crisis due to aggregate shock with government as a veil? 2 / 37

Key Idea In cross section of firms response to shocks depend on characteristics If aggregate shock, same effect for all firms If government shock affects financial sector, high leverage firms exposed more Build a model of firms heterogeneity and sovereign default Use micro data to identify source of crisis 3 / 37

What we do Develop a model of heterogenous firms with default risk Financial conditions depend on government default risk Subject to aggregate shock: disaster risk Use Italian firm micro data to calibrate model Government default risk affects high leverage firms more Disaster risk affects firms equally Micro-level data good for identifying macro shocks Use calibrated model to interpret the recent crisis in Italy Government default risk accounts for 2/3 of fluctuations Disaster risk accounts for 1/3 of fluctuations 4 / 37

Literature Government crises affects aggregates through financial channel Neumeyer-Perri (2005), Uribe-Yue (2005), Bocola (2015) Aggregate shocks drive fluctuations and sovereign crisis Arellano (2008), Aguiar-Gopinath (2006), Mendoza-Yue (2012) Decomposition of shocks in Euro Crisis Philippon-Martin (2014) Literature mostly uses aggregate data 5 / 37

Model Heterogeneous firms that borrow and default Government that borrows and defaults Firm financing costs depend on own default risk and gov. spread Households invest and provide labor Aggregate shocks: Disaster risk and government expenditure 6 / 37

Model: Firms Heterogeneous in productivity z it and leverage λ i Produce with capital and labor and pay fixed cost Choose k it before shocks Finance λ i fraction of capital with loan at price q it Firms profits are q it b it = λ i k it π it = z it (kitl α 1 α it ) ν w t l it rt k k it b it ξ + λ i k it Default d it = 1 if profits negative If default firm exits, output used to pay for input costs, debt holders get zero 7 / 37

Model: Disaster Shock Firm productivity has idiosyncratic and aggregate component There are two regimes s = 0, 1 Regimes s = 0, probability ps = 1 p t, z it = y it Regimes s = 1, probability ps = p t, where 0 < µ θ < 1 and z it = (1 µ θ )y it ln y it = ρ ln y it 1 + σ y ε it Aggregate private shock: p t probability of idiosyncratic disaster 8 / 37

Model: Government Government budget constraint B g t = q g t+1 Bg t+1 + S t Default d g t = 1 if cannot roll over the debt where the surplus is max{q g t+1 Bg t+1 } < Bg t S t S t = τ l w t L t + τ c C t G t T t Aggregate public shock: G t government expenditure shock 9 / 37

Model: Bond Price Functions Government price compensates for default loss [ q g (1 d g ] t ) t = E 1 + r Government spread is s g t = 1 q g t (1 + r) Firm price compensates for default loss and depends on govt. spread [ ] (1 dit ) q it = E βs g t 1 + r Implication arises in models where intermediaries have leverage constraints (Bocola 2015) 10 / 37

Model: Households Own firms Provide labor such that U C,t /U L,t = w(1 τ L )/(1 + τ C ) Decide on investment such that U C,t = βeu C,t+1 (r k t+1 + (1 δ)) 11 / 37

Analysis for Today Partial equilibrium model with endogenous firm default risk Exogenous government spread shock s g t Abstract from feedback from private sector to government sector Two shocks: Government spread and disaster risk 12 / 37

Firm Capital and Leverage Firm capital decreases with government spread and disaster risk Government spread increases effective marginal cost and firm default risk Firms with high leverage affected more Disaster risk decreases expected marginal productivity and increases firm default risk Effects similar across firms 13 / 37

Firm Problem Choose capital and default cutoff v(y 1 ) = max k,{y (s)} 1 p s s=0 y (s) [ π(k, z(y, s)) + 1 ] 1 + r v(y) df (y y 1 ) Profits and financing requirement combined π(k, z(y, s)) = M(z(y, s))k θ r k k ξ b(k) + λk Financing requirement b(k) from [ 1 s p s F (y (s)) βs g ] b = λk Default cutoff y (s), s π(k, z(y (s), s)) = 0 14 / 37

Characterization of Firm s problem Default cutoffs ( ) M(z(ys, s))k θ r k 1 k ξ = λk 1 s p sf (ys) βs g 1 High k or high s g increase default cutoff y s Optimal capital E[MP K] = r k + λ βsg 1 βs g + [ y p s f(y ] s) s k 1 F (y s s) v(y s) }{{} >0 Default costly for firms: Lose future profits v(y) 15 / 37

Firm Problem and Government Spread E[MP K] = r k + λ βsg 1 βs g + s p s [ y s k f(ys) ] 1 F (ys) v(y s) Capital is decreasing in s g more for high λ firms Absent default, s g increase MC of investing and more for high λ With default, capital further decreases, more for high λ firms Default incentive higher with high repayment due to high s g More for high λ firms: increase in loan is larger 17 / 37

3.5 Capital 6 Spread 3 low-leverage firm 5 4 high-leverage firm 2.5 3 2 1.5 high-leverage firm 1 2 3 Government Spread 2 1 0 low-leverage firm 1 2 3 Government Spread Capital decreases/firm spread increases with government spread More so for high leverage firms 18 / 37

Firm Problem and Disaster Risk E[MP K p s ] = r k + λ βsg 1 βs g + s p s [ y s k f(ys) ] 1 F (ys) v(y s) Disaster risk lowers expected productivity, capital decreases Default penalty s p sv(y s ) drops with higher disaster risk Not differentially for high λ 19 / 37

3.5 Capital 6 Spread 3 2.5 2 low-leverage firm high-leverage firm 1.5 2 4 6 8 10 Disaster Risk 5 4 3 2 1 0 high-leverage firm low-leverage firm 2 4 6 8 10 Disaster Risk Capital decreases/firm spread increases with disaster risk Effect similar across firms 20 / 37

Data Compustat Global from Italy (2000+ obs), 2002 to 2013 Sales growth: (sit s it 1 )/0.5(s it + s it 1 ) Leverage: liabilitiesit /assets it Distribution of growth rates changes over time Use to discipline disaster risk Find differential correlation of growth rates with government spread depending on leverage Use to discipline effect of government spread 21 / 37

Firm growth Sales Growth -.2 -.1 0.1.2 2002 2004 2006 2008 2010 2012 year 50 Pct 25 Pct 75 Pct Growth declines in 2009 and 2012 22 / 37

Firm growth Firm Distributions Fraction 0.05.1.15.2.25-2 -1 0 1 2 Sales Growth 2007 2009 Sales growth distribution fat left tail in 2009 23 / 37

Growth disaster Growth disaster 0 2 4 6 8 10 2002 2004 2006 2008 2010 2012 year gd t : Fraction of firms with growth< 0.43 (=5 percentile panel) Proxy for disaster risk 24 / 37

Regression on Sales Growth s g t 1.8 2.7 0.5 s g t leverage it 4.4 3.2 gd t 2.7 2.1 3.0 gd t leverage it 0.7 0.5 controls no no yes yes firm fixed effect no no no yes Adjusted R 2 0.01 0.04 0.07 0.19 Growth in negatively correlated with government spread and disaster 25 / 37

Regression on Sales Growth s g t 1.8 2.7 0.5 s g t leverage it 4.4 3.2 gd t 2.7 2.1 3.0 gd t leverage it 0.7 0.5 controls no no yes yes firm fixed effect no no no yes Adjusted R 2 0.01 0.04 0.07 0.19 Growth falls by 1.1% more with a 1% increase in s g t for firms with 0.25 higher leverage 26 / 37

Quantitative Analysis Strategy Use firm level moments to parameterize model Leverage dispersion, growth dispersion Effect of government spread on economy calibrated to get differential effect Match interaction coefficient of s g t leverage it in similar regression Quantify the effects of aggregate shocks on GDP and corporate spreads in event study 27 / 37

Calibration Spread process AR(1) to fit data, α = 0.33, ν = 0.9, r = 2%, ρ y = 0.9 Moment Parameter Data Model Std of growth disaster σ p 2.9 2.7 5 percentile growth µ θ -0.43-0.40 IQR sales growth σ y 0.20 0.28 IQR leverage λ 75,t λ 25,t 0.25 0.25 Int coeff [λ 75,t λ 25,t ] β g -1.10-1.10 Mean Leverage λ 25,t 0.52 0.02 Default rate ξ 0.01 0.01 28 / 37

Aggregate implications With calibrated model, feed observed shocks Evaluate effect on GDP and corporate spreads Decompose contribution of government spread and disaster risk 29 / 37

Event: Spread shock 6 5 4 3 2 Government Spread 1 0 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 Feed spread shock s g t is as in data 30 / 37

Event: Disaster shock 14 12 Disaster Risk 10 8 Growth Disaster 6 4 2 0 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 Disaster shock p t to match time path of growth disaster 31 / 37

Event: GDP 0.05 Event 0-0.05 Data -0.1-0.15-0.2 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 Model explains 90% of movement in GDP 32 / 37

Event: GDP Decomposition 0.05 Event Only disaster risk 0-0.05 Only gov. spread -0.1-0.15-0.2 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 Government spread accounts for 83%; disaster risk accounts for 44% 33 / 37

Event: Firm Spreads 7 6 5 4 3 Event 2 Data 1 0-1 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 Model explains 90% of movement in corporate spreads 34 / 37

Event: Firm Spread Decomposition 7 6 5 4 3 Event 2 Only gov. spread 1 0 Only disaster risk -1 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 Government spread accounts for 97%; disaster risk accounts for 5% 35 / 37

Ongoing work Use Amadeus dataset (130000+ observations) Empirical findings robust: differential effect of government spread based on leverage Measure directly aggregate private shock from firms productivity evolution Feedback from private sector to government Government spread responds to private shock Current results are upper bound on the role of public shocks Rely more heavily on structure of model for decomposition of shock contribution 36 / 37

Conclusion Use model of heterogeneous firms and micro data to measure effects of government crisis on private sector Government crisis accounts for large portion of decline in GDP 37 / 37