The Indian informal sector (including both farms and household enterprises outside agriculture), much larger than that in China, has been mostly privately owned; even now it employs nearly 94 percent of the labor force. But many of these tiny enterprises, often family owned, cannot quite be described as capitalist business; if market prices are imputed for the inputs they use (such as family labor) their business income is often persistently negative. They operate in the interstices of a low-productivity "involuted" economy, the capitalist parts of which cannot absorb them.
That is from Awakening Giants, Feet of Clay, which looks at China and India. It's a short book, but I am getting a lot out of it. China comes off better than I thought, in part because I did not previously understand the extent to which government there is decentralized and even competitive. India comes off not well, but I cannot say I am surprised. Between Naipul's view of India's culture and politics (in A Million Mutinies Now) and the description of India by William Lewis in The Power of Productivity, I was prepared for the dysfunctionality that Bardhan describes there.
One issue is why there is so much more formal manufacturing in China than in India. Bardhan cites some potential institutional factors, such as restrictive labor laws in India, but he questions their significance. I wonder if the barriers are not more cultural. Maybe there are many in India who are not comfortable in non-family enterprises. Maybe it is easier for Chinese workers to develop a strong attachment to the factories that employ them, but Indian workers are more inclined to quit if some minor issue comes up.
Perhaps India's elite is more dependent than China's on globalization. At an elite level, Indians can move fairly adeptly in the global corporate world, in part because of their knowledge of English and familiarity with western business practices.
Anyway, the book has none of my uninformed cultural speculation. It is filled with facts and useful analysis.