Question

1. Suppose that PPP holds between Japan (the home country) and the US (the foreign, starred country), so that in logs: se+pi-P-0 Also suppose that UIP holds. Money demand in Japan is given by: and in the US by (a) Derive the fundamental equation of the monetary model of the (log) exchange rate. (b) Suppose that the relative money supply in logs is given by m -m, and that = 0.5 + 0.82t-1 + Eg, tencie with mean zero. Solve for the exchange rate ", in terms of the current value of t. (c) How does the variance of the exchange rate compare to the variance of the fundamen tals?

Answer 1

(b)

s_t + p_t* - p_t = 0

So, s_t = p_t -p_t*+

Now, m_t - p_t + i_t = 0 , therefore, p_t = m_t + i_t

and, m*_t - p*_t + i*_t = 0 , therefore, p*_t = m*_t + i*_t

So, s_t = m_t + i_t - m*_t - i*_t

Since, x_t is equivalent to m_t - m*_t

hence, s_t = x_t + i_t - i*_t