Consider two examples. Suppose American entrepreneurs create many products that foreigners want to buy, and start many companies they want to invest in. That will increase the demand for dollars and so cause the dollar’s price to rise. Such innovation will also make Americans want to buy more goods and assets in the United States — and fewer abroad. The supply of dollars to the foreign exchange market will fall, further strengthening the dollar. This example describes very well the conditions of the late 1990s — when the dollar was indeed strong.
Now suppose the United States runs a large budget deficit that causes domestic interest rates to rise. Higher American interest rates make both foreigners and Americans want to buy more American bonds and fewer foreign bonds. Thus the demand for dollars increases and the supply decreases. The price of the dollar will again rise.
This example describes conditions in the early 1980s, when President Ronald Reagan’s tax cuts and military buildup led to large deficits. Those deficits, along with the anti-inflationary policies of the Fed, where Paul A. Volcker was then the chairman, led to high American interest rates. The dollar was very strong in this period.
BOTTOM LINE: a strong dollar, by itself, doesn't tell you very much. You have to look at the reasons for its strength. Some are good, but some are not.
HT: Greg Mankiw