The Eurozone Debt Crisis: A New-Keynesian DSGE model with default risk

Transcription

1 The Eurozone Debt Crisis: A New-Keynesian DSGE model with default risk Daniel Cohen 1,2 Mathilde Viennot 1 Sébastien Villemot 3 1 Paris School of Economics 2 CEPR 3 OFCE Sciences Po PANORisk workshop 7 June 2016 Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

2 Motivation Eurozone (EZ) debt crisis does not fit well the literature on sovereign debt models Greece: Unexpected shock on 2009 public deficit (final figure: 15.2% GDP) Then, painful and long reduction of deficit (via fiscal austerity) Standard models assume that deficit is a control variable Ireland: Debt soared because of contingent liabilities in relation to banking sector Large shock to debt-to-gdp ratio, unrelated to deficit (Ireland was fulfilling all Maastricht criteria before the financial crisis) Standard models assume rather smooth process for GDP Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

3 Our modelling strategy Habit consumption (for making adjustment painful) Discontinuous stochastic process for GDP Incorporate standard NK features Small open economy framework, in 2 flavors: flexible exchange regime monetary union Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

4 Outline 1 The model 2 Calibration and baseline results 3 Sensitivity analysis 4 Conclusion Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

5 Outline 1 The model 2 Calibration and baseline results 3 Sensitivity analysis 4 Conclusion Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

6 Main features Small open economy Optimizing households who consume, supply labor and invest in physical capital Firms produce using labor and capital Nominal rigidities: good prices, wages Real rigidities: habit consumption, investment cost Fiscal authority with debt rule Government debt held both domestically and abroad Two model flavors: flexible exchange rate (independant monetary policy) monetary union (nominal interest rate determined abroad) Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

7 Modelling sovereign default The fiscal authority can default on external part of its debt In case of default, two costs: GDP loss, financial autarky Optimal decision by comparing two value functions Technical problem: dimensionality of the problem Our (imperfect) solution: satellite model In normal times, agents do not internalize the possibility of a future default (in particular, no endogenous risk premium) But allows us to compute default probabilities on simulated paths Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

8 Households Program for household ι: E 0 β t Ut ι t=0 where: u ι (C ι t, H t, L ι t) = log(c ι t H t ) ϕ (Lι t) 1+σ L 1 + σ L with H t = h C t 1 Budget constraint: Bt ι + Ct ι = R t 1 + t 1 Bt 1 ι + Yt ι It ι τ t Ct ι π t Y ι t = w ι t L ι t + A ι t + (r k t z ι t ψ(z ι t ))K ι t 1 + Div ι t Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

9 Euler equation Symmetric across households where t is risk premium. ] C t H t 1 τ t R t + t E t [β = 1 C t+1 H t+1 1 τ t+1 π t+1 Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

10 Labor market Differentiated labor varieties Standard Calvo pricing Indexation of non-reoptimized wages on inflation State contingent Arrow-Debreu securities shield against idiosyncratic labor income shock Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

11 Capital accumulation where S E t [ 1 β ( It I t 1 ) [ ( It K t = (1 δ)k t S = κ I 2 ( ) 2 It I t 1 1 ( Ct+1 H t+1 1 τ t+1 C t H t 1 τ t q t [1 S ( It I t 1 I t 1 )] I t )] q t = q t+1 (1 δ) + z t+1 r k t+1 ψ(z t+1 ) )] ( Ct H t 1 + βe t q t+1 C t+1 H t+1 ( ) = q t S It It I t 1 I t 1 r k t = ψ (z t ) ) 1 τ t 1 τ t+1 Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

12 Production Final good firms: Intermediate good firms: with standard Calvo pricing ( 1 Y t = 0 ) ɛ y ɛ 1 ɛ 1 ɛ j,t dj y j,t = A t (z t K j,t 1 ) α K M α M t L 1 α K α M jt Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

13 Fiscal policy Budget constraint: B t + D t + τ t C t = R t 1 + t 1 B t 1 + R t 1 + t 1 E t D t 1 + G t π t π t E t 1 Fiscal rule: ( τ t C t G t Int t = α B B t 1 + E ) t D t 1 BD t E t 1 where Int t = ( ) ( Rt 1 + t 1 R ) 1 B t 1 + t 1 + t 1 Et 1 D t 1 π t π t E t 1 Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

14 External sector Exports: Balance of payments equilibrium: D t = R t 1 + t 1 π t X t = ε ψ t Y t E t E t 1 D t 1 + ε t M t X t Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

15 Monetary policy and exchange rate Flexible exchange rate (FLEX) Taylor rule: UIP: Risk premium: ( ) R ρπ t R = Rt 1 ( πt ) rπ(1 ρπ) R π R t + t = E t (R t ) E ( ) t+1 + ϑ e (Dt D) 1 E t t = 0 Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

16 Monetary policy and exchange rate Monetary union (EMU) No autonomous monetary policy: Real exchange rate: R t = R t E t E t 1 = π t π t Risk premium (computed on external part of debt): ) t = ψ RP (e Dt D 1 Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

17 Satellite default model After a default, proportional cost on GDP: Y d t = (1 λ Q )Y t Government budget constraint becomes: B t + T t = R t 1 + t 1 B t 1 + G t π t Other equations remain essentially the same This defines a default value function J d Default threshold: D such that J d = J r (given other state variables) Default occurs when J d > J r (given the state variables) Simulation of 10,000 points for computing default probability Simplification: possibility of default not anticipated by agents Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

18 Outline 1 The model 2 Calibration and baseline results 3 Sensitivity analysis 4 Conclusion Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

19 Calibration (selected parameters) For a small country within the Euro area. Standard values for most parameters. Parameter Symbol Value Consumption habit h 0.85 Discount factor β Total debt target BD t 2.4Y t Back to equilibrium debt targets (fiscal rule) α B 1/80 Risk premium in UIP (only FLEX) ϑ Risk premium on debt (only EMU) t ψ RP External debt target D 0.3Ȳ Loss of output in autarky in the FLEX model (% of GDP) λ Q 0.03 Loss of output in autarky in the EMU model (% of GDP) λ Q 0.04 Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

20 Default probabilities and debt thresholds Default probability Mean external debt Default threshold Baseline FLEX 0% 7.5% 60% ( D = 0.3Ȳ ) EMU 0.5% 7.5% 128% D = 0.8Ȳ FLEX 0.5% 20% 60% EMU 2.2% 20% 117% Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

21 Outline 1 The model 2 Calibration and baseline results 3 Sensitivity analysis 4 Conclusion Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

22 Sensitivity to habit consumption (h) Baseline calibration ( D = 0.3Ȳ ) FLEX model EMU model Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

23 Sensitivity to habit consumption (h) Medium external debt ( D = 0.8Ȳ ) FLEX model EMU model Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

24 Sensitivity to external debt target ( D) FLEX model EMU model Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

25 Sensitivity to total debt target (BD) FLEX model EMU model Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

26 Sensitivity to speed of convergence (α B ) FLEX model EMU model Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

27 Outline 1 The model 2 Calibration and baseline results 3 Sensitivity analysis 4 Conclusion Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

28 Main preliminary results Critical differences between flexible regime and monetary union Default thresholds larger in flexible economy but thresholds more likely to be reached in monetary union Fast speed of convergence increases defaults in flexible regime, diminishes them in monetary union In EMU, external debt plays a critical role for stabilization as a consequence, debt more volatile and default risks are more important Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29

29 Future work Incorporate possibility of redemption after default Analyze impact of a discrete shock on debt-to-gdp ratio Allow default on total debt (and not just external debt) Handle (some) nonlinearities Cohen, Viennot, Villemot (OFCE) A DSGE with default risk 7 June / 29