Recent trade theory emphasizes the role of market-share reallocations across firms ("stealing") in driving productivity growth, whereas previous literature focused on average productivity improvements ("learning"). We use comprehensive, firm-level data from India's organized manufacturing sector to show that market-share reallocations were briefly relevant to explain aggregate productivity gains following the beginning of India's trade reforms in 1991. However, aggregate productivity gains during the period from 1985 to 2004 were largely driven by improvements in average productivity. We show that India's trade, FDI, and licensing reforms are not associated with productivity gains stemming from market share reallocations. Instead, we find that most of the productivity improvements in Indian manufacturing occurred through "learning" and that this learning was linked to the reforms. In the Indian case, the evidence rejects the notion that market share reallocations are the mechanism through which trade reform increases aggregate productivity. Although a plausible response would be that India's labor laws do not easily permit market share reallocations, we show that restrictions on labor mobility cannot explain our results.