I distinctly remember the 1980s, during which time Japan was buying up American properties left and right, and looked poised to race past us economically. That was particularly "obvious" in the last few years of that decade, after the market crash of 1987. At some point around then, I vaguely recall reading that the total market value of properties in Tokyo exceeded that of the entire United States.
It was all an illusion, of course. Within a few years, the Nikkei had collapsed, property values had fallen, non-performing loans had skyrocketed, and Japan entered its "lost decade" (which lasted about 15 years) of stagnant growth.
Now that everyone agrees that the era of Japanese dominance is over, the next Asian tiger set to eat our lunch is China. But China has its own unique problems. A country of 1.4 billion people, only about 400 million of them live in a style we might call Western. That's a population a third larger than the United States', but it still leaves a billion people in poverty. And that population has two major demographic challenges: it is rapidly graying, and its youth is heavily skewed towards men (both are consequences of the one-child policy). Furthermore, China's economic growth has started from a much lower base than Japan's did, and the Chinese people lack political freedom. While that last point has not apparently constrained growth up to now, it seems inevitable that at some point a rising middle class will demand more political power.
Mark Steyn believes that China will get old before it gets rich. John Derbyshire basically agrees. Now I read that structural problems in the Chinese economy may finally be throwing enough sand into the gears to cause a major slowdown very soon. It's all speculation at this point, but the slowdown has to come sooner or later.