If a country starts out with low income and capital stock, it ought to be able to grow very quickly as it implements high-productivity techniques borrowed from overseas, as the capital stock per worker rises and as underemployed rural workers move to high-value work such as manufacturing. These above-average growth rates might continue until the economy uses up these convergence opportunities.
The classic example is Japan, where per capita annual growth was over 7% in the three decades after World War II. Japan came out of the war with its production capacity devastated, but with strong institutions, technology and entrepreneurial experience. It experienced a four-decades-long convergence catch-up. It then ran into the lost decade of the 1990s and has since grown slowly, with not the remotest prospect of returning to earlier growth rates.
Taken at face value, the convergence argument doesn’t seem to foretell a slowing in China. Japan slowed only when it could no longer make the easy gains from adaptation of borrowed technology. This would suggest that China, still only one-quarter of the way towards the technological frontier, still has decades of potential convergence ahead.