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This paper contains a General Equilibrium model of an economy with Incomplete Markets (GEI) with money and default. The model is a simplified version of the real world consisting of a non-bank private sector, banks, a Central Bank, a government and a regulator. The model is used to analyse actions by policy makers and to identify policy relevant empirical work. Key analytical results are: A financially fragile system need not collapse; efficiency can be improved with policy intervention; and that a system with heterogeneous banks is more stable than one with homogeneous ones. Existence of monetary equilibria allows for positive default levels in equilibrium. It also characterises contagion and financial fragility as an equilibrium phenomenon. A definition of financial fragility is proposed. Financial fragility occurs when aggregate profitability of the banking sector declines and defaults in the non-bank private and the banking sectors increase. Thus, equilibria with financial fragility require financial vulnerability in the banking sector and liquidity shortages in the non-bank private sector. The model will be used as a basis to carry out empirical work on the costs of financial instability, to quantify the effectiveness of particular regulatory tools such as capital requirements, and to identify tradeoffs between increasing stability through action by authorities and the efficiency of the financial system. Keywords: Financial fragility, contagion, competitive banking, capital requirements, incomplete markets, default.

Leith and Wren-Lewis (2007) have shown that government debt is returned to its pre-shock level in a New Keynesian model under optimal discretionary policy. This has two important implications for monetary and fiscal policy. First, in a high-debt economy, it may be optimal for discretionary monetary policy to cut the interest rate in response to a cost-push shock--thereby violating the Taylor principle--although this will not be true if inflation is significantly persistent. Second, the optimal fiscal response to such a shock is more active under discretion than commitment, whatever the degree of inflation persistence.

We analyse optimal discretionary games between a benevolent central bank and a myopic government in a New Keynesian model. First, when lump-sum taxes are available and public debt is absent, we show that a Nash game results in too much government spending and excessively high interest rates, while fiscal leadership reinstates the cooperative outcome under discretion. Second, we show that this familiar result breaks down when lump-sum taxes are unavailable. With government debt, the Nash equilibrium still entails too much public spending but leads to lower interest rates than the cooperative policy, because debt has to be adjusted back to its pre-shock level to ensure time consistency. A setup of fiscal leadership does not avoid this socially costly outcome. Imposing a debt penalty onto the myopic government under either Nash or fiscal leadership raises welfare substantially, while appointing a conservative central bank is less effective.

Leith and Wren-Lewis (2007) have shown that government debt is returned to its pre-shock level in a New Keynesian model under optimal discretionary policy. This has two important implications for monetary and fiscal policy. First, in a high-debt economy, it may be optimal for discretionary monetary policy to cut the interest rate in response to a cost-push shock--thereby violating the Taylor principle--although this will not be true if inflation is significantly persistent. Second, the optimal fiscal response to such a shock is more active under discretion than commitment, whatever the degree of inflation persistence.