Reconciling Gross Output TFP Growth with Value Added TFP Growth

This article obtains relatively simple exact expressions that relate value added total factor productivity growth (TFP) in a value added framework to the corresponding measures of TFP growth in a gross output framework when Laspeyres or Paasche indexes are used to aggregate outputs and inputs. Basically, as the input base becomes smaller, the corresponding estimates of TFP growth become larger. A fairly simple approximate relationship between Fisher indexes of gross output TFP growth and the corresponding Fisher index of value added TFP growth is also derived. The methodology developed in this article has a number of applications.