Suppose that the half-life of deviations from PPP is five years (it takes five years for the difference between the actual and equilibrium real exchange rate to narrow by half) and the nontraded share of consumption is 0.50. What will be the annual rate of change of the real exchange rate if a country initially has a 20% gap between its actual and equilibrium real exchange rates and its GDP is growing 5% faster than GDP in the rest of the world?
A) 70%
B) 22%
C) 4.5%
D) 2.0%

Question

Quizplus · Accepted Answer

The annual rate of change of the real exchange rate can be approximated using the formula for the half-life of a process, which in this case is 5 years for deviations from PPP to halve. Given a 20% initial gap, after 5 years, this gap would reduce to 10%, implying an annual rate of convergence of approximately 4.5% when considering the rule of 70 (70/5 years = 14% per year halving rate, but since only half of consumption is affected due to the nontraded share, it's effectively 7% per year, and over 5 years this approximates to a 4.5% annual rate when considering compounding effects and the specific dynamics of PPP adjustment).

Suppose That the Half-Life of Deviations from PPP Is Five