Modeling Guarantees, Over-Indebtedness and Financial Crises in an Open Economy

Abstract

This work develops a simple framework to analyse how financial intermediaries’ balance sheet problems combined with financial guarantees make an economy more vulnerable to financial crises. A ‘double default’ problem – that is, the default of financial intermediaries on their debt repayments and of the government on its guarantees to bailout intermediaries’ losses – is modelled in this study. The possibility of multiple equilibria, including a crisis equilibrium where the government is not able or willing to honor its guarantees towards the domestic financial sector, arises from the interplay of all the above elements: financial intermediaries’ level of indebtedness, government implicit guarantees and high-risk creditors’ lending. This work also produces predictions concerning the vulnerability to a financial crisis: multiple equilibria are possible only in certain ranges of the fundamentals.

Keywords:

• Financial guarantees
• risk premium
• multiple equilibria

JEL CLASSIFICATIONS :

• E44
• F31
• F34

Acknowledgements

The author wishes to thank an anonymous referee for his valuable comments and suggestions on the work. The usual disclaimer applies.

Notes

¹As is commonly assumed by the existing models of open monetary macroeconomics (Obstfeld & Rogoff, 1996), the shock that occurs in periods 1 and 2 is wholly unanticipated and thus it is not taken into account by the domestic market when setting prices.

²The shock causes a deviation from the PPP in periods 1 and 2 since prices are set at the beginning of each period and remain fixed; while nominal exchange rate and domestic interest rates have to adjust to absorb the shock.

³The UIP applies with risk neutrality as it is the outcome of arbitrage from fully diversified investors.

⁴This share of wages is directly determined from the Cobb-Douglas production function:

⁵Since FIs’ produce y and pay a share of wage equal to (1−α)y, which is determined from the assumed Cobb-Douglas production function, the resulting sales net of wage payments will be equal to α y.

⁶Both prices and exchange rate at time 0 have been normalized to 1.

⁷The assumption of FIs’ limited liability, implies that if FIs’ owners have insufficient funds to make debt repayments, they can default losing their equity investment without additional costs.

⁸By using equation (15), relationship (20) can be also written as a function of the exogenous and constant world interest rate: for t≥3.

⁹The assumption is that government guarantees cover both principal and interest repayments.

¹⁰This can be thought as one way of financing lending of last resort operations. There are several ways of carrying out lending of last resort facilities and, for the purpose of the model, the easiest alternative is a lump-sum tax, including the issue of new public debt to distribute this tax over a longer period. The injection of domestic currency by the Central Bank is not considered in this analysis since such an injection of liquidity by driving up prices might have feedback effects on the exchange rate.

¹¹As recalled in the previous section both prices and the nominal exchange rate at time 0 have been set equal to 1.

¹²As the threshold level of the productivity shock, û, above which creditors expect that the government will intervene to bailout the FIs, increases then the risk premium, τ, given by relationship (31) rises and the implied nominal interest rate on lending, equation (29), will be higher.

¹³At this long-run boundary solution equilibrium, the domestic interest rate is equal to .