Quantitative Sovereign Default Models and the European Debt Crisis

Quantitative Sovereign Default Models and the European Debt Crisis Luigi Bocola Gideon Bornstein Alessandro Dovis ISOM Conference June 2018

This Paper Use Eaton-Gersovitz model to study European debt crisis Applications to EME model emphasize external debt position Focus on counter-cyclical trade balance Is it appropriate for European debt crisis?

Results Show total public debt better predictor of spreads than measures of external debt typically used for EME If private credit markets are sophisticated then total public debt is sufficient statistic in government problem Same problem as EME model but different interpretation for debt Matching counter-cyclicality of total public debt issuances allows model to better account for empirical distribution of spreads Most of the time zero spreads

Related Literature Quantitative Eaton-Gersovitz models Arellano (2008), Aguiar-Gopinath (2006), Hatchondo-Martinez (2009), Chatterjee-Eyigungor (2012), Arellano-Ramanarayanan (2012), Mendoza-Yue (2012), Aguiar et al. (2016) European debt crisis applications: Bocola-Dovis (2016), Salomao (2016), Arellano et al. (2018), Paluszynski (2016) Government debt behavior in Ramsey tax models Aiyagari et al. (2002), Presno-Pouzo (2014) Domestic-foreign debt interactions Dovis et al. (2016), D Erasmo-Mendoza (2013) Spillovers Bocola (2016), Arellano et al. (2017), Perez (2015)

MOTIVATING EVIDENCE

Spreads and Output GDP -.05 0.05.1.15 Spain Italy Portugal 2002 2004 2006 2008 2010 2012 Spread (%) 0 5 10 15 2002 2004 2006 2008 2010 2012

Measures of Indebtedness Net external debt (% of GDP) 0 50 100 Spain Italy Portugal 2002 2004 2006 2008 2010 2012 Total public debt (% of GDP) 40 60 80 100 120 140 Public external debt (% of GDP) 20 40 60 80 2002 2004 2006 2008 2010 2012 2002 2004 2006 2008 2010 2012 External debt goes down or constant from 2008

Total Public Debt Better Predictor Consider spr t = α + β 1 y t + β 2 debt t + ɛ t The R 2 for the regression is Country Output only Debt only Output and debt PED NED TPD PED NED TPD Spain 0.39 0.30 0.46 0.79 0.40 0.85 0.91 Italy 0.30 0.02 0.10 0.67 0.31 0.41 0.67 Portugal 0.67 0.34 0.34 0.83 0.66 0.67 0.84 When debt is only covariate: R 2 when using total public debt is between 2 to 7 times larger than other two debt indicators. Similar result if consider both output and level of debt

MODEL

Environment State s t µ( s t 1 ) Households Preferences: ( ) ( β t µ s t s 0 [u c(s t ) ) + ω ( g(s t ) ) ]) t s t The consumer receives an income Y (s t ) in each period. Foreign lenders: Stochastic discount factor M (s t+1, s t ) Benevolent government Tax revenues T (s t ) = τy (s t ) Chooses g Market structure Government can issue defaultable bonds Private credit markets are sophisticated: trade securities contingent on s and gov t policies, in particular government default

Primal Markov Problem Equilibrium outcome {g(s t ), B(s t ), q(s t )} from t 1 solves: where W (B, s) = max { W r (B, s), W d (s) } W r (B, s) = max G,B ω (G) + β s µ ( s s ) W ( B, s ) subject to the budget constraint G + B τy (s) + q (s, B ) B, W d (s) = ω (τy (s) χ (s))+β s µ ( s s ) [ (1 ζ) W d ( s ) + ζw ( 0, s )] and q ( s, B ) = s M ( s, s ) I {W r (B,s ) W d (s )}

Primal Markov Problem Equilibrium outcome {g(s t ), B(s t ), q(s t )} from t 1 solves: W (B, s) = max { W r (B, s), W d (s) } where W r (B, s) = max G,B ω (G) + β s µ ( s s ) W ( B, s ) subject to the budget constraint G + B τy (s) + q (s, B ) B, W d (s) = ω (τy (s) χ (s))+β s µ ( s s ) [ (1 ζ) W d ( s ) + ζw ( 0, s )] and q ( s, B ) = s M ( s, s ) I {W r (B,s ) W d (s )} Debt distribution does not matter, only total public debt B Same problem as EG but B has different interpretation

QUANTITATIVE ANALYSIS

Functional Forms Follow Bocola-Dovis (2016) and assume ω (g) = ( g g ) 1 σ 1 1 σ where g 0 is subsistence level for public consumption good Foreign lenders risk neutral so M (s, s) = Pr (s s) / (1 + r ) The process for Y = exp{y} is y = ρ y y + σ y ε, ε N(0, 1) As in Chatterjee-Eyigungor (2013), the default costs are χ (Y) = max{0, d 0 τy + d 1 (τy) 2 }

Calibration Set σ, ζ, output process to standard values β, d 0, d 1, and g chosen to match behavior of outstanding debt and interest rate spreads Statistic Data Our calibration Trad.calibration Average spread 0.32 0.30 0.53 Spread volatility 0.88 0.95 0.55 Average debt service/gdp 8.43 8.60 8.69 Debt/GDP cyclicality -0.78-0.61 - Trade balance cyclicality -0.69 - -0.14 In traditional calibration: corr(b /Y, ln Y) > 0 Coefficient of variation small, Aguiar et al. (2016)

Our Calibration Better Matches Distribution of Spreads 0.8 0.7 0.6 Data Model 1 Model 2 Frequency 0.5 0.4 0.3 0.2 0.1 0 [0, 0.1) [0.1, 0.5) [0.5, 2) [2, 10) Spread (%)

Why? Front-loading and precautionary motives Canonical Model Our Model qb 1/(1 + r ) qb 1/(1 + r ) B goes down if output low B goes up if output low B B

Debt Cyclicality Critical for Spread Behavior Why spreads in our calibration more volatile? Debt price is q(y, B (B, Y)) so income shock has two effects Direct Indirect: through effect on B In our model with counter-cyclical debt As Y goes down spreads rise via both direct and indirect (B (B, Y) ) effect In canonical calibration with pro-cyclical debt As Y goes down spreads rise via direct effect but moderating force via indirect effect (B (B, Y) )

Typical Default Event 0 0.6 3.5 Income -0.01-0.02-0.03-0.04-0.05 Debt to income (pp) 0.4 0.2 0-0.2 Spread (%) 3 2.5 2 1.5 1 0.5-0.06-10 -5 0 Periods prior to default -0.4-10 -5 0 Periods prior to default 0-10 -5 0 Periods prior to default In our model, spreads Less than 50 bp until 4 quarters prior to default Then jumps and reaches about 3.50% quarter before default Under canonical calibration, spreads In all periods between 50 basis points and 1% No substantial jump in the period before default

Conclusion Show Eaton-Gersovitz model can be applied to study European debt crisis Emphasize role of total public debt as determinant for spreads Matching counter-cyclicality of total public debt issuances allows model to better match behavior of spreads