Decompositions of Productivity Growth into Sectoral Effects: Some Puzzles Explained

An earlier paper by Diewert (2013) provided some new decompositions of economy wide labour productivity growth and Total Factor Productivity (TFP) growth into sectoral effects. The economy wide labour productivity growth rate turned out to depend on the sectoral labour productivity growth rates, real output price changes and changes in sectoral labour input shares. A puzzle is that empirically, the real output price change effects, when aggregated across industries, did not matter much. The economy wide TFP growth decomposition into sectoral explanatory factors turned out to depend on the sectoral TFP productivity growth rates, real output and input price changes and changes in sectoral aggregate input shares. The puzzle with this decomposition is that empirically all of these price change effects and input share effects did not matter much when they were aggregated over sectors; only the sectoral TFP growth rates contributed significantly to overall TFP growth. The present paper explains these puzzles.