Monetary Conservatism and Sovereign Default

Joost RöttgerUniversity of Cologne

Fiscal Sustainability, XXI Century

June 8th, 2016

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Overview

1. Introduction2. Model

3. Quantitative Analysis

4. Summary

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MotivationMonetary policy and lack of commitment

I Nominal public debt:I A government faces temptation to relax its budget via surprisein�ation.

I Discretionary policy:I In�ation bias relative to optimal policy under commitment.

I Solution proposed by Rogo¤ (1985):I Delegate monetary policy to a monetary conservative centralbanker.

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MotivationMonetary policy in practice

I Most developed economies have delegated monetary policy toindependent central banks with a focus on price stability.

I Many emerging economies have also recently introducedindependent central banks (see e.g. Carstens and Jácome,2005).

I However, these countries often face frictions that mightundermine the success of such reforms.

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Topic of this paper

Evaluate monetary conservatism when an economy is subject tothree particular frictions:

I Incomplete �nancial marketsI Lack of commitment to debt repaymentI Political economy distortions

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Model environment

I Small open economy as in Arellano (2008)I The economy�s government consists of

I a present-biased �scal authorityI an in�ation-averse monetary authority

I No commitment to future policiesI Quantitative exercise:

I Vary the degree of monetary conservatism

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Preview of results

I Increasing the degree of monetary conservatism leads toI less in�ation, higher average debt and more defaults,I more volatile public spending but more stable in�ation,I sign and size of welfare gains depends on details of theeconomy.

I Monetary conservatism is successful in reducing in�ation andcan be desirable despite considerable negative side e¤ects.

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Related literature

I Time-consistent monetary policy and central bankindependence:

I Rogo¤ (1985), Adam and Billi (2008), Niemann (2011),Martin (2015)

I Monetary policy and sovereign default:I Aguiar et al. (2013, 2015), Hur et al. (2014), Du and Schreger(2015), Nuño and Thomas (2015), Röttger (2015)

I Quantitative sovereign default models with incompletemarkets:

I Aguiar and Gopinath (2006), Arellano (2008), Cuadra andSapriza (2008)

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Overview

1. Introduction

2. Model3. Quantitative Analysis

4. Summary

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Setting

Arellano-Eaton-Gersovitz-type small open economy model:

I HouseholdsI Government

) Two separate authorities that optimize without commitment:

1. Fiscal authority

- chooses �scal policy- is subject to political economy comstraints.

2. Monetary authority

- controls the in�ation rate- might be in�ation averse

I Risk-neutral foreign investors

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Households

I The economy is populated by a representative household withpreferences

U = E0

" 1Xt=0

�tU (gt ; �t)

#; 0 < � < 1;

withU (gt ; �t) = u (gt)� (�t) :

I Interpretation of (convex) in�ation cost function (�t):I Direct utility loss of in�ation (Aguiar et al., 2013, 2015).I Resource losses of in�ation and household utility that is linearin private consumption.

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Fiscal authority

I Inspired by Cuadra and Sapriza (2008) and Aguiar andAmador (2011), there are two political parties i 2 I �f1; 2gwith preferences

Fi = E0

" 1Xt=0

�tUFi (gt ; �t)

#;

whereUFi (gt ; �t) = ~�itu (gt)� (�t) ;

with~�it =

�� > 1; if i is in o¢ ce1; if i is not in o¢ ce

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Fiscal authority (cont�d)

I Given random tax revenue � t , the incumbent party chooses�scal policy without commitment:

I default dt 2 f0; 1g, public good gt , debt issuance bt+1.I Incumbent party remains in o¢ ce with probability � and isreplaced with probability 1� �.

I Political disagreement (� > 1) and turnover risk (� < 1):

) De�cit bias (Persson and Svensson, 1989, Alesina andTabellini, 1990) and suboptimal policies relative to � = 1 (and� = 1).

I Closely related to the present bias in models withquasi-geometric discounting (see e.g. Aguiar and Amador,2011).

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Monetary authority

I The monetary authority (or central bank) has preferences

M = E0

" 1Xt=0

�tUM (gt ; �t)

#;

whereUM (gt ; �t) = u (gt)� � (�t) ;

with � � 0.I central bank sets the in�ation rate �t without commitment.I Parameter � re�ects degree of monetary conservatism(Rogo¤, 1985, Niemann, 2011)

I For � 6= 1 (� 6= �� � 1=�), the relative weight on the in�ationcost deviates from that for the households (�scal authority).

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Government budget constraintRepayment case

I Fixed debt structure (see Chatterjee and Eyigungor, 2012):I Constant nominal debt share �:

bNt+1 =BNt+1Pt

= �bt+1;

bRt+1 = (1� �)bt+1;

withbt+1 = bNt+1 + bRt+1:

I Government budget if debt is honored:

� t + (�qNt + (1� �) qRt) bt+1 = gt +����1t + 1� �

�bt ;

with random tax revenues � t .

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Government budget constraintDefault case

I Following Arellano (2008), there are two types of defaultcosts:

I Resource losses �(� t) � 0.I Temporary exclusion from �nancial markets.

I Government budget in default case:

� t � �(� t) = gt :

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International investors

I Homogeneous risk-neutral foreign investors can borrow at therisk-free rate rf and maximize expected pro�ts.

I The price of a real bond is given as

qR (bt+1; � t) =1

1+ rfEt [1�D(bt+1; � t+1)] ;

while a nominal bond is priced according to

qN (bt+1; � t) =1

1+ rfEt�1�D(bt+1; � t+1)�r (bt+1; � t+1)

�;

where D(�) and �(�) determine the default and in�ationdecisions dt+1 and �t+1.

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Policy interaction

I Interaction between periods:I Markov-perfect policy game with state (b; �)I Authorities take as given future policies but can a¤ect themvia b0.

I Interaction within periods:I Timing after tax revenues � are realized:

1. Fiscal authority chooses d 2 f0; 1g.2. Central bank chooses �.3. Fiscal authority chooses g and b0.

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Public policy problemsStep 1: Fiscal policy problem

I After tax revenues � are realized, the �scal authority solves

F(b; �) = maxd2f0;1g

n(1� d)F r (b; �) + dFd (�)

oI The beginning-of-period values of the central bank and theparty not in o¢ ce satisfy

M(b; �) = (1�D(b; �))Mr (b; �) +D(b; �)Md (�);

F�(b; �) = (1�D(b; �))F�r (b; �) +D(b; �)F�d (�);

with D(�) denoting the policy function for the �scalauthority�s default decision.

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Public policy problemsStep 2: Monetary policy problem

The central bank solves

Mr (b; �) = max�

(u(Gr (�; b; �))� � (�)

+�E� 0j�hM(Br (�; b; �); � 0)

i ) ;if the �scal authority repays and

Md (�) = max�

8<: u(Gd (�; �))� � (�)

+�E� 0j��

�M(0; � 0)+ (1� �)Md (� 0)

� 9=; ;

if it defaults.

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Public policy problemsStep 3: Fiscal policy problem

In the repayment case, the �scal authority solves

F r (�; b; �) = maxg ;b0

8<:�u(g)� (�)

+�E� 0j��

�F(b0; � 0)+ (1� �)F�(b0; � 0)

� 9=;subject to 0 � � � g �

����1 + 1� �

�b

+��qN

�b0; �

�+ (1� �)qR

�b0; �

��b0

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Public policy problemsStep 3: Fiscal policy problem (cont�d)

In the default case, the �scal authority solves

Fd (�; �) = maxg

8>>>><>>>>:�u(g)� (�)

+��E� 0j��

�F(0; � 0)+ (1� �)F�(0; � 0)

�+(1� �)�E� 0j�

��Fd (� 0)

+ (1� �)F�d (� 0)

�9>>>>=>>>>;

subject to 0 � � � g � �(�)

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Public policy problemsStep 3: Political party not in o¢ ce

The value functions for the party not in o¢ ce satisfy

F�r (�; b; �) =

8<:u(Gr (�; b; �))� (�)

+�E� 0j��

�F(Br (�; b; �); � 0)+ (1� �)F�(Br (�; b; �); � 0)

� 9=; ;

F�d (�; �) =

8>>>><>>>>:u(Gd (�; b; �))� (�)

+��E� 0j��

�F(0; � 0)+ (1� �)F�(0; � 0)

�+(1� �)�E� 0j�

��Fd (� 0)

+ (1� �)F�d (� 0)

�9>>>>=>>>>; :

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Public policy problemsStep 3: Monetary authority

The value functions for the central bank satisfy

Mr (�; b; �) =

(u(Gr (�; b; �))� � (�)

+�E� 0j�hM(Br (�; b; �); � 0)

i ) ;Md (�; �) =

8<:u(Gd (�; b; �))� � (�)+��E� 0j� [M(0; � 0)]

+ (1� �)�E� 0j��Md (� 0)

�9=; :

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Equilibrium policies

In equilibrium, all values and policies will only be functions of thebeginning-of-period state variables:

X r (b; �) = X r (�r (b; �); b; �);X d (�) = X d (�d (�); �);

for X 2fB;F ;F�;Gg, and

X (b; �) = (1�D(b; �))X r (b; �) +D(b; �)X d (�);

for X 2fB;F ;F�;G;M;�g.

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Overview

1. Introduction

2. Model

3. Quantitative Analysis4. Summary

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Functional forms

I CRRA utility:

u(g) =

(g 1�

1� if 6= 1ln g if = 1

I Quadratic in�ation costs as in Calvo and Guidotti (1992):

(�) =�

2(� � 1)2 ; � > 0;

I Asymmetric default costs as in Arellano (2008):

�(�) = max f0; � � ��g ;

I Tax revenues follow a log-normal AR(1)-process:

� t = ��t�1 exp (�"t) ; "ti :i :d :� N(0; 1); 0 < � < 1:

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CalibrationModel calibration (no CBI, one model period is one quarter):

Parameter Description Value Target

rf Risk-free rate 0.017 Arellano (2008)

� Discount factor 1/(1+rf ) - CRRA 2 Standard value

� Probability of reentry 0.1 Aguiar/Gopinath (2006)

� Share of nominal debt 0.58 Du/Schreger (2015)

� Probability of reelection 0.9 Cuadra/Sapriza (2008)

� Persistence revenue process 0.9 Standard value

� Std. dev. revenue process 0.022 Std. of g in Mexico� Probability of reelection 0.9 Cuadra/Sapriza (2008)

�� Default cost parameter 0.982 1% default prob.

� Weight on public good 2.75 20.68% avg. in�ation

� In�ation cost parameter 1.53 Mean(b=� ) = 0.05

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Bond price schedules and policy functions at � = E [� ]

0 0.05 0.10.7

0.8

0.9

1q N

b'0 0.05 0.1

0.75

0.8

0.85

0.9

0.95

1

b'

q R

0 0.05 0.10

0.02

0.04

0.06

0.08

0.1

b

π ­1

0 0.05 0.10.03

0.04

0.05

0.06

0.07

0.08

b

b' α=αθ

α=2αθ

α=10αθ

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Simulation results

I Quantitative model analysis compares model statisics fordi¤erent monetary policy regimes

I Values for � relative to �� � 1=�

No CBI � = �� � = 2�� � = 10��Avg. default prob. (annual) 0.0087 0.0085 0.0155 0.0192Mean(b=� ) 0.0531 0.0519 0.0654 0.0708Mean(� � 1) (annual) 0.2095 0.2116 0.1322 0.0291Std(g )/Std(� ) 1.1041 1.0957 1.1956 1.2614Std(�)/Std(� ) 1.3399 1.3118 1.2152 0.3263Welfare measure ! (in %) - 0.0005 0.0523 0.1051

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Role of political frictions

I Consider model versions with � < 1=(1+ r f ):I No political frictions: � = 1, � = 1I No turnover risk: � > 1, � = 1

I Parameters �� , � and � re-calibrated to match long-run targets

� = �� � = 2�� � = 3�� � = 10��� = 1, � = 1 0 -0.0227 -0.0244 -0.0272� > 1, � = 1 0 0.0458 0.0729 0.0973� > 1, � < 1 0.0005 0.0523 0.0789 0.1051

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Overview

1. Introduction

2. Model

3. Quantitative Analysis

4. Summary

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Summary

I The role of monetary conservatism has been revisited in aquantitative sovereign default model with

I incomplete �nancial markets,I lack of commitment to debt repayment,I political economy distortions.

I Increasing a central bank�s degree of monetary conservatismleads to

I higher average debt, more defaults and less in�ation,I more volatile public spending but more stable in�ation,I welfare gains or costs depending on political frictions.

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References

Adam, K. and R. Billi (2008): "Monetary Conservatism and Fiscal

Policy," Journal of Monetary Economics, 55(8), 1376-1388.

Aguair, M. and M. Amador (2011): "Growth in the Shadow of

Expropriation," Quarterly Journal Of Economics, 126(2), 651-697.

Aguiar, M., M. Amador, E. Farhi, and G. Gopinath (2013): "Crisis and

Commitment: In�ation Credibility and the Vulnerability to Sovereign Debt

Crises," mimeo.

Aguiar, M., M. Amador, E. Farhi, and G. Gopinath (2015): "Coordination

and Crisis in Monetary Unions," Quarterly Journal of Economics, 130(4),

1727-1779.

Alesina, A. and G. Tabellini (1990): "A Positive Theory of Fiscal De�cits

and Government Debt," Review of Economic Studies, 57(3), 403-414.

Arellano, C. (2008): "Default Risk and Income Fluctuations in Emerging

Economies," American Economic Review, 98(3), 690-712.

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References (cont�d)

Calvo, G.A. and P.E. Guidotti (1992): "Optimal Maturity of Nominal

Government Debt: An In nite-Horizon Model," International Economic

Review, 33(4), 895-919.

Carstens, A. and L.I. Jácome (2005): "Latin American Central Bank

Reform: Progress and Challenges," IMF Working Papers 05/114.

Chatterjee, S. and B. Eyigungor (2012): "Maturity, Indebtedness, and

Default Risk," American Economic Review, 102(6), 2674-2699.

Cuadra, G. and H. Sapriza (2008): "Sovereign Default, Interest Rates and

Political Uncertainty in Emerging Markets," Journal of International

Economics, 76(1), 788-811.

Du, W. and J. Schreger (2015): "Sovereign Risk, Currency Risk, and

Corporate Balance Sheets," mimeo.

Hur, S., I. Kondo, and F. Perri (2014): "Infation, Debt, and Default,"

mimeo.

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References (cont�d)

Martin, F.M. (2015): "Debt, In�ation and Central Bank Independence,"

European Economic Review, 79, 129-150.

Niemann, S. (2011): "Dynamic Monetary-Fiscal Interactions and the Role

of Monetary Conservatism," Journal of Monetary Economics, 58(3),

234-247.

Nuño, S. and C. Thomas (2015): "Monetary Policy and Sovereign Debt

Vulnerability," mimeo.

Persson, T. and L.E.O. Svensson (1989): "Why a Stubborn Conservative

Would Run a De�cit: Policy with Time-Inconsistent Preferences,"

Quarterly Journal of Economics, 104(2), 325-345.

Röttger, J. (2015): "Monetary and Fiscal Policy with Sovereign Default,"

mimeo.

Rogo¤, K. (1985): "The Optimal Degree of Commitment to an

Intermediate Monetary Target," Quarterly Journal of Economics, 100(4),

1169-89.36 / 36