Theory and Practice of Contagion in Monetary Unions: Domino Effects in EMU Mediterranean Countries

Abstract

This paper analyzes strategic interactions and contagion effects in the peripheral countries of a monetary union. Using game theory and cost-benefit analysis, the paper determines the set of equilibrium solutions under which country-specific shocks are transmitted to other member countries giving rise to contagion. Numerical simulations, obtained by a simple calibration of the model on some key Mediterranean countries of the Euro Zone, show the probabilities of contagion from Greece, Spain and Italy.

Appendix – Proof of Proposition 2

Proof. The incentive to move between alternative regimes can be written in compact form as: ${a}_1={L}_{D^B}^A-{L}_E^A$, ${a}_2={L}_{D^A}^A-{L}_N^A$, ${b}_1={L}_{D^A}^B-{L}_E^B$, ${b}_2={L}_{D^B}^B-{L}_N^B$. Thus, if a ₂ > 0, for example, country A has no incentive to leave the monetary union. Setting u ^B _t  = 0, it is easy to check that

$$ {a}_1>0\iff {v}_t>{v}^{\ast \ast \ast } $$

(12)

$$ {b}_1>0\iff {v}_t>{v}^{\ast \ast } $$

(13)

$$ {a}_2>0\iff {v}_t<{v}^{\ast } $$

(14)

$$ {b}_2>0\kern1em \mathrm{always}, $$

(15)

where ${v}^{\ast }=\frac{1}{\sigma}\sqrt{\left({\sigma}^2+\theta \right)\phi }$, v ^∗ ∗ = Q v ^∗, ${v}^{***}=\frac{\beta_i{\sigma}^2}{\sigma^2+\theta }{v}^{**}$. As Q > 1, v ^∗ < v ^∗ ∗ > v ^{∗ ∗ ∗}. Accordingly, from proposition 1 and (12)-(15), it follows that: i) E is a Nash equilibrium if and only if a ₁ and b ₁ are both positive, i.e. v _t  > max(v ^∗ ∗, v ^{∗ ∗ ∗}) = v ^∗ ∗; ii) Regime N is a Nash equilibrium if and only if a ₂ > 0 and b ₂ > 0, i.e. v _t  < v ^∗; iii) regime D ^B is never a Nash equilibrium as it would require b ₂ < 0.