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On the sovereign debt paradox

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Abstract

Bulow and Rogoff (Am Econ Rev 79(1):43–50, 1989) show that lending to small countries cannot be supported merely on the country’s “reputation for repayment” if exclusion from future credit markets is the only consequence of default. Their arguments are valid under fairly general conditions, but they do not go through when the output of the sovereign may vanish along a path of successive low productivity shocks, or when it may grow unboundedly along a path of successive high productivity shocks. We propose an alternative proof illustrating that their renowned sovereign debt paradox holds in full generality.

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Notes

  1. Bulow and Rogoff (1989) led to a vast literature studying alternative mechanisms to answer why countries repay their debts in the absence of sanctions. It includes, among others, Cole and Kehoe (1995), Cole and Kehoe (1998), Kletzer and Wright (2000), Dutta and Kapur (2002), Kehoe and Perri (2002), Gul and Pesendorfer (2004), Krueger and Uhlig (2006), Amador (2012), and Popov (2014). We refer to Wright (2011) and Aguiar and Amador (2014) for a thorough discussion of this literature.

  2. A “cash-in-advance” contract is just a conventional insurance contract under which a country makes a payment up front in return for a state-contingent, nonnegative future payment.

  3. In that respect the environment in Bulow and Rogoff (1989) is closely related to the one analyzed in Kehoe and Levine (1993) but with a different default option.

  4. Hellwig and Lorenzoni (2009) analyze a slightly different (but equivalent) environment where agents trade sequentially a complete set of contingent bonds with self-enforcing debt limits in place of participation constraints. It is the same environment as in Alvarez and Jermann (2000) but with a different default option. In addition, they show that the risk-neutrality assumption and the ad-hoc separation between a small open economy and investors with “deep pockets” play no role for the impossibility result of Bulow and Rogoff (1989).

  5. Similarly to Hellwig and Lorenzoni (2009) we do not require investors to be risk-neutral.

  6. Formally, we have \((1+r)^{-t} D_t := \sum _{s\geqslant t} (1+r)^{-s} z_s\) and \((1+r)^{-t} N_t := \sum _{s\geqslant t} (1+r)^{-s} y_s\).

  7. The problem is that such a date s may not exist under the general conditions Bulow and Rogoff (1989) impose on primitives. See Sect. 4 for details.

  8. Recall that \(y_s = c_s + D_s - (1+r)^{-1} D_{s+1}\).

  9. Observe that this condition restricts feasible contracts z to be such that the series \({{\mathrm{PV}}}(z \vert s^0)\) is well-defined.

  10. The term \(a(s^0)\) can be interpreted as an initial transfer.

  11. This is equivalent to assuming that the sovereign has access to any consumption-insurance contract. Formally, at any event \(s^\tau \) after default, the country can make the payment \(\sum _{s^{\tau +1} \succ s^\tau } q(s^{\tau +1}) \tilde{a}(s^{\tau +1})\) up front in return for any state-contingent, nonnegative future payment \(\tilde{a}(s^{\tau +1}) \geqslant 0\).

  12. If \({{\mathrm{PV}}}(y \vert s^t) = 0\), we pose \(\kappa (z \vert s^t) = 0\).

  13. We can choose \(z(s^t) := \lambda (s^t) {{\mathrm{PV}}}(y\vert s^t) - \sum _{s^{t+1} \succ s^t} \lambda (s^{t+1}) q(s^{t+1}){{\mathrm{PV}}}(y \vert s^{t+1})\). Since \(\lambda (s^{t+1}) \geqslant \lambda (s^t)\), we have that \(z(s^t) \leqslant y(s^t)\).

  14. Recall that \(p_{t-1} N_{t-1} = p_{t-1} y_{t-1} + p_t N_t \geqslant p_t N_t\).

  15. Since \(D_t \leqslant N_t := {{\mathrm{PV}}}(y\vert t)\), if the sequence \(({{\mathrm{PV}}}(y\vert t))_{t\geqslant 0}\) is bounded, then the sequence \((D_t)_{t\geqslant 0}\) is bounded from above and admits a least upper bound.

  16. Recall that \(S^t(s^\xi )\) is the set of all possible date-t events following \(s^\xi \).

  17. We also refer to Cole and Kehoe (2000), Dutta and Kapur (2002), Aguiar and Gopinath (2006), Arellano (2008), Bai and Zhang (2010), and Mendoza and Yue (2012) for models where default induces a loss in net income in addition to the exclusion from borrowing.

  18. In Bulow and Rogoff (1989) the outside option is \(V(s^t)\) which is larger than the autarchic outside option \(U(y\vert s^t)\) of Kehoe and Levine (1993).

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Authors and Affiliations

  1. Sao Paulo School of Economics, FGV, São Paulo, Brazil

    V. Filipe Martins-da-Rocha

  2. UMR, CEREMADE, CNRS, Unversité Paris-Dauphine, PSL Research University, 75016, Paris, France

    V. Filipe Martins-da-Rocha

  3. Adam Smith Business School, University of Glasgow, Glasgow, Scotland, UK

    Yiannis Vailakis

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  1. V. Filipe Martins-da-Rocha
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Correspondence to Yiannis Vailakis.

Additional information

We would like to thank the referees for their constructive criticism and suggestions which further improved the scope and clarity of the paper. We are also grateful to Gaetano Bloise, Felix Kubler and Herakles Polemarchakis for useful comments. Financial support from CNPq is gratefully acknowledged by V. Filipe Martins-da-Rocha. Yiannis Vailakis acknowledges the financial support of an ERC starting grant (FP7, Ideas specific program, Project 240983 DCFM) and of two ANR research grants (Project Novo Tempus and Project FIRE).

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Martins-da-Rocha, V.F., Vailakis, Y. On the sovereign debt paradox. Econ Theory 64, 825–846 (2017). https://doi.org/10.1007/s00199-016-0971-6

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