Must the growth rate decline? Baumol's unbalanced growth revisited

According to Baumol's model of unbalanced growth, if resources are shifting towards industries where productivity is growing relatively slowly, the aggregate productivity growth rate will slow down. This conclusion is often applied to the advanced economies, where resources are indeed shifting towards the relatively stagnant service industries. But Baumol's conclusion only follows logically if the stagnant industries produce final products. If instead they produce intermediate products, the aggregate productivity growth rate may rise rather than fall. This is empirically relevant since the most rapidly expanding service industries, e.g. business services, are producing mainly for intermediate use.