An Interest Rate Defense of a Fixed Exchange Rate From Flood and Jeanne

M = base-money, S = exchange rate, R* = international reserves, B = world-wide private holding of domestic government debt, r = domestic-currency interest rate, r* = foreign-currency interest rate, D = CB domestic credit, s = lnS, m= lnM, b = lnB 1/

N =outstanding domestic nominal government bonds, B= world- wide private holding of domestic government debt, D= Central Bank domestic credit, r(N-D) = net interest payment of consolidated government, r*SR* = interest payments on international reserves,  real level of taxes. /2

/3 An anticipated attack takes place when the shadow exchange rate equals the fixed exchange rate. Under assumption that the domestic credit grows at the same rate, g, before and after the collapse, the collapse time T is the solution to g = domestic credit growth = rate of depreciation Money Demand Money Supply

Dynamics of the economy becomes more complicated, but the results still hold for  small enough. /4

Assume that interest rate is constant before and after the attack but may jump at the time of the attack: /5 Pegging the Interest Rate

The monetary authority intervenes in the domestic bond market and in the foreign exchange market to fix the exchange rate, and prices. Asset market equilibrium is: /6 Pre-Collapse Regime = money demand is constant, since r is determined by the central bank at the level:. Foreign reserves move to clear market.

Pre-Collapse Debt Path /7 from (8),

/8 where

/9 The variable is strictly increasing with T and strictly decreasing in . Hence, given, the level of nominal debt at any given time t > 0, before the speculative attack, is strictly increasing in T and strictly decreasing in the real tax receipts.

/10 Following the collapse, the economy settles immediately into a real steady state, with constant real level of government debt, N/S. Because, the primary surplus is constant and seignorage is determined by the post-attack interest rate, the only remaining balancing variable is the level of debt, Post-Collapse Regime which must satisfy: where denotes the real quantity of money in the post-collapse regime.

/11 Equation (12) is a second-order polynomial equation in n, whose unique positive root is a function of the interest rate and fiscal receipts:

/12 the interest parity disappear andtakes the simple form: Which is increasing in the level of tax receipts and in the post- collapse interest rate, when the economy is on the increasing branch of the seignorage Laffer curve.

/13 it remains true that and

/14 The Collapse The shadow exchange rate at time t is the value of the exchange rate such that the exchange rate neither depreciate nor appreciate, And the value of the outstanding domestic nominal government bonds is unchanged is proportional to the state variable The currency peg collapses if and when the shadow exchange rate crosses the fixed peg, i.e., if there is a time T such that:

/15 The collapse is inevitable if nominal debt explodes, i.e., if In this case the time of collapse is given by equation (16). (1) It is always possible to raise the level of taxes such that which prevents public debt from expanding. (2) The time of the collapse is decreasing with the pre- collapse interest rate and increasing with the post-collapse interest rate.

/16 Raising the interest rate before the attack and lowering it after the attack hastens the collapse. Intuition: Raising the interest rate before the attack worsens the fiscal imbalance, since it amounts to financing a stock of low-interest- rate-bearing foreign assets by borrowing at a high interest rate. A higher nominal interest rate is then reflected one-to-one in a higher real rate of interest since the exchange rate and prices are fixed. Higher interest rates after the collapse are associated with higher seignorage revenues, allowing the government to service a larger real debt in the steady state. After the collapse an increase in the nominal rate of interest improves the fiscal situation by raising seignorage revenues.