This matters because in Mr Matsuyama's model manufacturing is special. If this were to happen, agriculture could have a special role in stimulating growth, just as Mr Matsuyama assumes manufacturing does. The empirical evidence on this point is mixed. However, the consequences may not be as bleak as he expected. This is because, so far, productivity growth in agriculture has been as fast as in manufacturing.
Chile provides a good test case.
Since the country opened up to trade in 1976, the relative size of its manufacturing sector has declined. The decline of manufacturing has not meant slow growth, however. Exports have been the engine of growth and agricultural products have been star performers. Chile went from being a small player in the global fruit market, exporting just apples in the 1960s, to become one of the world's largest fruit exporters in the 1990s. Such exports may not be manufactured, but the businesses that make and export them have been using increasingly sophisticated production technology and management methods.