Today saw a rather depressing milestone: the dollar has hit a new all-time low against the yen. This chart helps explain why: the yen's long-term appreciation against the dollar has been largely driven by the fact that inflation in Japan has been much lower than U.S. inflation since the late 1970s.
According to Japan's Nationwide General Price Index, prices are on average at the same level today as they were in March 1993. Meanwhile, over that same period, the U.S. Consumer Price Index has risen by 58%. This alone would account for a 58% appreciation of the yen vis a vis the dollar since 1993, since that is what would be required to keep prices stable between both countries (if the yen/dollar exchange rate had not changed, U.S. prices would have risen 58% relative to Japanese prices). So its not surprising to find that the yen has risen about 50% against the dollar since then. The green line in the chart above shows how the value of the yen should have moved over time in order to keep price levels constant between the U.S. and Japan. It moves consistently higher because U.S. inflation has been consistently higher than Japanese inflation.
The fact that the current exchange rate is 76 yen/$, while my calculation of Purchasing Power Parity is 117 yen/$, is one way of estimating how strong the yen is. I figure it's about 50% "overvalued" relative to the dollar, which means that a U.S. tourist in Japan would find that, on average, things there cost about 50% more than they do in the U.S. This is also an indication of how little confidence the world has in the underlying fundamentals of the dollar relative to the yen.