Sovereign Default and the Stability of Inflation-Targeting Regimes

Abstract

We analyze the impact of interactions between monetary and fiscal policy on macroeconomic stability. We find that in the presence of sovereign default, macroeconomic stability requires monetary policy to be passive if the feedback from debt surprises back to the primary surplus is too weak. An active monetary policy can however only contribute to the stabilization inflation and output, if the primary surplus is increasing in debt with a slope that increases with the default probability. The results are relevant for the design of fiscal and monetary policy in emerging markets where sovereign credibility is not well established. Recent debt developments in Western Europe and in the United States suggest these results may become relevant for more mature financial markets too once the current low inflation period is over.

Appendices

Appendix I

Equilibrium

A rational expectations equilibrium is a set of sequences {mc_{H, t},w _t ,π _t ,π _Ht ,c _t ,n _t ,q _t ,y_{H, t},R _t ,R* _t ,b_{H, t}+b_{F, t},Z _t ,Z_{1, t},Z_{2, t},s _t }_t+0^∞ satisfying

the transversality condition, and a monetary policy for given sequences {ɛ _t ,g _t }_t+0^∞ and {c* _t ,π* _t }_t+0^∞ satisfying βE _t {(c* _t /c*_t+1)^σ/π*_t+1}=1/R* _t , initial asset endowments and an initial price level.

In a neighborhood of the steady state the equilibrium sequences are approximated by the solutions to the linearized equilibrium conditions. Note that total public debt can be determined, while its distribution between domestic and foreign household is indetermined. We therefore assume that domestic households’ holdings of public debt equals zero, B _{H, t} =0. The equilibrium can be defined as follows (where denotes the percent deviation of a generic variable x _t from its steady-state value ):

Definition

• A rational expectations equilibrium for B_H, t=0 and g _t =g is a set of sequences satisfying

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  (where σ _n =σ _l n_/(1−n), Φ=(b/π)δ′/(1−δ)>0, and ), the transversality condition, and monetary and fiscal policy characterized by

  

  where ρ_π=R′π _H /R≥0 and η=(1−κ)/(1+κ(R−1))∈(0, 1) for {ɛ _t }_t+0^∞ and initial values and Eliminating and with (i) and (v), the aggregate supply constraint (iv) can be rewritten as where α=(1−ϑ)cϑ+ϑ*c*/n(1−ϑ). Further, eliminating and with (iii) and (vi), the set of equilibrium conditions can be reduced to the following system in

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Under certainty, we thus end up with the system (equation (21)).

Proof of Proposition 1

In order to prove the claims made in the proposition, the interest rate is eliminated in Equation (21a–d) by substituting in the policy rule , leading to the following 4 × 4 system in , and the auxiliary variable :

(where Λ=(1−κ)/(β(1−δ))(1)/(1−Φϑ)), which can be rewritten as

The characteristic polynomial of A is given by

One eigenvalue equals zero and can be assigned to . Since there remains one further predetermined variable a uniquely determined convergent equilibrium requires G(X) to exhibit exactly two unstable and one stable eigenvalue. To identify the conditions for this, we first examine G(0),

which is strictly negative, for δ and Φ not exceeding one. One or three negative stable roots are further ruled out, since G(−1) is strictly negative (given that κ≤1):

Two or zero positive stable roots are ruled out, if G(1), given by

is strictly positive. There are two sets of conditions that lead to G(1)>0: For κ>κ₁, where κ₁=1−β(1−δ)(1−Φ), monetary policy has to be active, ρ_π>1, while for κ>κ₁ monetary policy has to be passive, ρ_π<1. Then, there exist either one or three stable eigenvalues, from which at least one is positive. We further examine if the sum of all eigenvalues exceeds 3, which delivers a sufficient (but not necessary condition) for the existence of one unstable eigenvalue and is equivalent to check if G″(1)<0, where

For κ>κ₂⇒G″(1)<0, where κ₂=1+(1−δ)[(1−ϑ)(1−Φ)ψ−(2β−1)(1−Φϑ)], implying that there exists at least one unstable eigenvalue, while κ₁<κ₂ for Φ<1/(1+ψ/β). Then, for ρ_π<1 there exists a uniquely determined equilibrium if and only if κ>κ₁, and for ρ_π>1 there exists a uniquely determined equilibrium if but not only if κ∈(κ₁, κ₂). This establishes the claims made in the proposition.

Appendix II

Consider a closed economy version of the model, ϑ=0, where public debt is held by domestic households, b _t =b _{H, t} , and PPI inflation equals CPI inflation, π _t =π _{H, t} . The set of linearized equilibrium conditions can then be reduced to the following conditions in real debt, consumption, inflation, and the nominal interest rate

and . Eliminating the interest rate, the system can be written as

where Λ=(1−κ)/(β(1−δ))>0 and defining Ψ=χ(σ+σ _n )>0. The characteristic polynomial of A is

There are two sets of conditions that lead to F(1)>0: For κ>κ₁, where κ₁=1−β(1−δ)(1−Φ), monetary policy has to be active, ρ_π>1, while for κ<κ₁ monetary policy has to be passive, ρ_π<1. Then, there exist either one or three stable eigenvalues, from which at least one is positive. We further examine if the sum of all eigenvalues exceeds 3, which delivers a sufficient (but not necessary condition) for the existence of one unstable eigenvalue and is equivalent to check if F″(1)<0, where

For κ<κ₂⇒F″(1)<0, where κ₂=1+(1−δ)[(1−Φ)Ψ−(2β−1)], implying that there exists at least one unstable eigenvalue, while κ₁<κ₂ for Φ<1/(1+Ψ/β). Then, for ρ_π<1 there exists a uniquely determined equilibrium if and only if κ<κ₁, and for ρ_π>1 there exists a uniquely determined equilibrium if but not only if κ∈(κ₁, κ₂). These conditions for equilibrium determinacy correspond to those presented in Proposition 1.

Appendix III

Figure A1

Figure A1

Impulse Responses to Cost Push Shocks