Based on the money demand function and purchasing power parity, the long-run  exchange rate can then be expressed as follows: M/P  ∗  kY,  / ∗  ∗ ∗  ,  ∗ ∗  e  ∙ ∗  ∗  ∗  ∗ ∗ ∗  ̂  ∗  ∗  ∗  ∗  Thus, the exchange rate is expressed as a decreasing function of monetary expansion in the United States and an increasing function of monetary expansion in Japan.
The two countries try to achieve their inflation targets by adjusting their monetary bases. We assume that under price rigidities, there is a short-run negative spillover effect as a result of monetary policy interdependence, the so-called "beggar-thy-neighbor effect of monetary policy."