India and China are growing at a high, approximately constant rate. But will their growth continue at the current rate? Hong Kong, as a more mature economy, provides a good example as to what may be expected to happen as China and India continue to grow. As Hong Kong developed, it's progression was approximately linear until about 1988- and it's been slowing down since then. That's not really a surpise: high growth rates are easier to maintain the lower is your GDP, as you can grow simply by adopting the technology of others. But at some point, that process will run out of steam.
And the point where growth starts to slow is likely to be a function of the level of "social infrastructure" (Hall and Jones, QJE, 1999) in society. Short of a major change in institutional quality in China and India, resulting in substantial reductions in corruption, expect GDP growth to slow at much lower per capita levels in these countries than it did in Hong Kong, which enjoys an excellent, corruption-free administration, at least by comparison.
Even this may be optimistic. Hong Kong has endured no major crises over that period shown on the grapth. Sure, 1989 and the Asian Financial Crisis shook up markets, but there have been no major events that have significantly threatened the functioning of the economy or the political structure of Hong Kong since our data begins in 1961. Will the same hold true for China and India over the coming decades? We can only hope so.