Aggregating and Decomposing Productivity

We illustrate how the aggregate level of total factor productivity, as obtained from aggregate input and output statistics, can be replicated by summing appropriately weighted firm-level measures. This exact aggregation has a number of advantages over existing practices. First, the contribution of different sub-samples to a well-defined aggregate is easily identified. Second, the importance of patterns at the micro level, such as larger size or higher capital intensity for more productive firms, for the aggregate can be calculated. Third, it allows the exact decomposition of aggregate output growth into the contribution of several factors, among which firm-level total factor productivity growth, an inherently relative concept. A sample of all Chinese manufacturing firms with annual sales above five million RMB is used to illustrate the usefulness of the different decompositions.