NEW DELHI—India today doesn't look quite like the economic dynamo that, just a few years ago, some predicted would overtake China as emerging-markets champion.

But the race looks a lot closer if you account for one key fact: China got a 13-year head start on India in opening its economy and giving companies greater freedom to invest and produce. In exports, capital spending and foreign investment, India today is remarkably similar to China circa 2001.

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