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An Application to Sovereign Debt 11 Essays on Macroeconomics and Contract Theory ARCHIVES by MASSACHUSETTS INSTITUTE OF TECHNOLOGY Juan Passadore B.A. Economics, Universidad de Montevideo (2006) OCT 15 2015 Submitted to the Department of Economics LIBRARIES in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY September 2015 @ 2015 Juan Passadore. All rights reserved. The author hereby grants to MIT permission to reproduce and distribute publicly paper and electronic copies of this thesis document in whole or in part. redacted A u th o r ............................................Signature . .. ... .-- j - --- -- -- --- - Department of Economics August 15, 2015 redacted C ertified by ........................... .... .Signature . .C,, - --- - Robert M. Townsend Elizabeth & James Killian/Professor of Economics ..I -1 Thesis Supervisor Certified by..........................Signature redacted.. -- ~~ Ivan Werning Robert Solow Professor of Economics Thesis Supervisor Accepted by ......... Signature redacted- .................. Ricardo J. Caballero nternational Professor of Economics Chairman, Departmental Committee on Graduate Studies Essays on Macroeconomics and Contract Theory by Juan Passadore Submitted to the Department of Economics on August 15, 2015, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract This thesis studies how contracting frictions affect the outcomes that the public sector or individual agents can achieve. The focus is on situations where the government or the agent lacks commitment on its future actions. Chapter 1, joint work with Juan Xandri, proposes a method to deal with equilibrium multiplicity in dynamic policy games. In order to do so, we characterize outcomes that are consistent with a subgame perfect equilibrium conditional on the observed history. We focus on a model of sovereign debt, although our methodology applies to other settings, such as models of capital taxation or monetary policy. As a starting point, we show that the Eaton and Gersovitz (1981) model features multiple equilibria-indeed, multiple Markov equilibria-when debt is sufficiently constrained. We focus on predictions for bond yields or prices. We show that the highest bond price is independent of the history, while the lowest is strictly positive and does depend on past play. We show that previous period play is a sufficient statistic for the set of bond prices. The lower bound on bond prices rises when the government avoids default under duress. Chapter 2, joint work with Yu Xu, studies debt policy of emerging economies accounting for credit and liquidity risk. To account for credit risk we study an incomplete markets model with limited commitment and exogenous costs of default following the quantitative literature of sovereign debt. To account for liquidity risk, we introduce search frictions in the market for sovereign bonds. In our model, default and liquidity will be jointly determined. This permits us to structurally decompose spreads into a credit and liquidity component. To evaluate the quantitative performance of the model we perform a calibration exercise using data for Argentina. We find that introducing liquidity risk does not harm the overall performance of the model in matching key moments of the data (mean debt to GDP, mean sovereign spread and volatility of sovereign spread). At the same time, the model endogenously generates bid ask spreads, that can match those for Argentinean bonds in the period of analysis. Regarding the structural decomposition, we find that the liquidity component can explain up to 50 percent of the sovereign spread during bad times; when the sovereign is not close to default, the liquidity component is negligible. Finally, regarding business cycle properties, the model matches key moments in the data. Chapter 3, studies the implications of reputation on equilibrium multiplicity in a model of sovereign debt. These models can exhibit multiple equilibria. In the worst equilibrium the government is in autarky. However, in reality, we do not observe the autarkic solution. Motivated by an apparent disconnection between theory and reality, I characterize a lower bound on the utility that the government can obtain for any positive probability that the government is from a commitment type that always repays debts. Chapter 4, joint with Ignacio Presno, studies the optimal risk sharing contract between a risk neutral money lender and an agent that faces Knightian uncertainty about the distribution of her endowment and cannot commit on future transfers. We find that in the optimal contract model uncertainty contributes to increase consumption of the agent over time independently of which shocks have been realized. This differs qualitatively from the case without Knigthian uncertainty. Thesis Supervisor: Robert M. Townsend 3 Title: Elizabeth & James Killian Professor of Economics Thesis Supervisor: Ivan Werning Title: Robert Solow Professor of Economics 4 Acknowledgments My time at MIT has been a tremendously rewarding experience both in academic and personal terms. I owe special thanks to my advisors Robert Townsend and Ivan Werning. Both have been outstanding mentors and role models; along countless discussions during these years I have not only learned about economics, but more importantly, how to approach problems with an open and critical mind. I would also like to thank George Marios Angeletos and Alp Simsek; both have been incredibly generous with their time. This dissertation has benefited from many discussions with them and from their insightful comments. I am also grateful to Arnaud Costinot for helpful comments, advice and support. Special thanks to my Professors at Universidad de Montevideo, Fernando Borraz, Marcelo Caffera, and Juan Dubra, and at Universidad Di Tella, Leandro Arozamena, Rodolfo Manuelli, Emilio Espino, and Martin Sola, whose encouragement and mentoring as an undergraduate student has been fundamental for my graduate years. I have been fortunate to share this experience with an amazing group of friends and colleagues. I would like to thank Juan Pablo Xandri, Luis Zermeno, Sofia Barrera, Sebastian Di Tella, Mercedes Politi, Jose Montiel, Nicolas Caramp, Andres Sarto, Maria Fazzolari, Felipe Severino, Joaquin Blaum, Dejanir Silva, Giovanni Reggiani, Natalia Rigol, Joey Neggers, Marco Tabellini, Yu Xu, Miikka Rokkanen, Benjamin Feigenberg, Dan Rees, and Annalisa Scognamiglio, for making this journey both productive and fun. I would also want to thank an outstanding group of classmates and colleagues at the department who have been a constant source of inspiration. The love from my family and friends back home has been fundamental during this journey. I thank my mother for her affection, unconditional support and constant encouragement. My brother has been a friend that provided wise words when needed. I would also like to thank Celia, Pedro, Martha, Maria and Jose, for always being there in spite of the distance. Last, but certainly not least, I would like to thank to an incredible group of friends back home for reminding me where I come from and where I am going. 5 To my father. 6 Contents Acknowledgements 5 1 Robust Conditional Predictions in Dynamic Games: An Application to Sovereign Debt 11 1.1 Introduction ........... .............................................. 11 1.2 A Model of Sovereign Debt .................................... 15 1.2.1 Dynamic Game: Notation and Definitions ...... ......................... 16 1.3 Multiple Equilibria in Sovereign Debt Markets .......................... 18 1.3.1 Lowest Equilibrium Price and Worst Equilibrium ..................... 19 1.3.2 Highest Equilibrium Price and Best Equilibrium ..................... 20 1.3.3 M ultiplicity .... ............................... ....... 22 1.3.4 Equilibrium Consistency: Focus on Outcomes ....................... 23 1.4 Equilibrium Consistent Outcomes ........................... ....... 24 1.4.1 Equilibrium Consistency: Definitions ............................ 24 1.4.2 Equilibrium Consistency: Characterization ........................ 25 1.4.3 Equilibrium Consistent Prices ................................ 27 1.4.4 Interpretation: Robust Bayesian Analysis ............ ............. 31 1.5 Extensions: Excusable Defaults and Savings . ........................... 32 1.5.1 Excusable Defaults ............................... ....... 32 1.5.2 Best SPE ........................................... 34 1.5.3 Excusable Defaults and Savings ............................... 35 1.6 Sunspots ..................... ........................... 35 7 1.6.1 Equilibrium consistent distributions .......... ... 36 1.6.2 Expectations of Equilibrium Consistent Distributions . 38 1.6.3 Probability of Crises ... .. ............ 39 1.7 Discrete Income ............ ....... .... 41 1.8 Conclusion and Discussion ...... ............ 44 1.9 Appendix A . .......... ............ 45 1.10 Appendix B: Characterization of U (b, q S ... ....... 51 1.11 Appendix C: Computing U (b, q) . .. ............ 54 1.12 Appendix D: Sunspot Proofs . ... .. ....... ... 58 1.13 Appendix E: A connection to Robust II ayesian Analysis .. 62 1.13.1 Robust Bayesian Analysis .. .. ....... ... 62 1.13.2 Main Result ......... ............ 64 1.13.3 Further Results ........ ............ 65 1.13.4 Proofs ............ ............ 66 2 Illiquidity in Sovereign Debt Markets 70 9 . 1 In+rodr1t-in .mal . ................ 70 2.2 Model .nvestors..................... 73 2.2.1 Small Open Economy
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