Problems with (dis)aggregating productivity,and another productivity paradox

Using a standard definition of productivity growth, it is shown that a country may have higher productivity growth than another country in each sector, but may have a lower productivity growth rate overall. Also, it is shown that popular methods for aggregating firm/industry estimates of productivity growth have a serious problem in that productivity of all firms/industries can go up, but aggregate productivity can fall. This is not necessarily due to changes in the reallocation of resources across firms/industries. Hence, there are problems for the interpretation of previously published articles which use these methods. There can be inappropriate assessments of the cyclical properties of productivity, and the productivity impact of industry dynamics, micro-economic reforms and regulatory change. Index-number methods that avoid these aggregation problems are introduced.