Question

1 Consider the continuous time exchange rate crisis model by Flood and Garber (1984) under perfect foresight. Explain the model’s assumptions. Write the equations of the model and explain their meaning.

2 Determine the collapse time of the fixed exchange rate regime and the level of foreign exchange reserves at the collapse time following the speculative attack on the fixed exchange rate regime. Show graphically the time paths of reserves, domestic credit and the money supply during the period surrounding the collapse of the exchange rate regime.

3 Discuss the differences between first- and second-generation models of foreign exchange rate crises.

Answer 1

1) Assumptions is Flood and Garber model are as follows :

1)Money demand takes the Cagan (1956) form, M_t= θP_texp[−η (r +π_t)] , where θ > 0 and t π_t = P'(t)/P(t) is the inflation rate. 2)The government abandons the fixed exchange rate regime when its foreign reserves are exhausted.

3) As soon as foreign reserves are exhausted, the government prints money at a constant rate μ to fully finance its deficit.

The equations for Flood and Garber model could be written as :

M(t) / P(t) = a₀ - a₁i(t) , a(1)>0

M(t) = R(t) + D(t)

D'(t) = μ , μ>0

P(t) = P*(t) X S(t)

i(t) = i*(t) + [S'(t)/S(t)]

Here, ' mark indicates that the variable has been derivated with respect to time

2)

Determining collapse time needs connecting the fixed rate regime to the post-collapse floating regime —shadow floating exchange rate.

Following the attack, money market equilibrium requires

M(z₊) = S(z₊) - S(z₊) = D(z₊)

Here t = z₊ , which is instant after the attack

Prior to the collapse at z, money remains constant, but its components vary. D(t) rises at the rate μ and reserves decline at the same rate.

At time z, both money and reserves fall by

Note: 3 steps

1. know the model
2. solve the shadow exchange rate ()
3. find the timing of collapse ()

3) In first-generation models the government follows an exogenous rule to decide when to abandon the fixed exchange rate regime.

In second-generation models the government maximizes an explicit objective function. This maximization problem dictates if and when the government will abandon the fixed exchange rate regime.

Second-generation models generally exhibit multiple equilibria so that speculative attacks can occur because of self-fulfilling expectations. The level of output is determined by an expectations-augmented Phillips curve. The government decides whether to keep the exchange rate fixed or not.

Suppose agents expect the currency to devalue and inflation to ensue. If the government does not devalue then inflation will be unexpectedly low. As a consequence output will be below its natural rate. Therefore the government pays a high price, in terms of lost output, in order to defend the currency. If the costs associated with devaluing (lost reputation or inflation volatility) are sufficiently low, the government will rationalize agents’ expectations. In contrast, if agents expect the exchange rate to remain fixed, it can be optimal for the government to validate agents’ expectations if the output gains from an unexpected devaluation are not too large. Depending on the costs and benefits of the government’s actions, and on agents’ expectations, there can be more than one equilibrium.