An expanded decomposition of the Luenberger productivity indicator with an application to the Chinese healthcare sector

The objective of this research is to combine productivity analysis at the “firm-level” and the “industry-level” so that a novel, fuller decomposition of the sources of productivity change can be undertaken. Productivity change is decomposed into technological progress, technical, mix, and scale efficiency effects. Specifically, our decomposition allows us to capture changes in productivity due to the reallocation of inputs or outputs across productive units. In practice, such reallocation might take place across plants operated by the same firm, across regions within a country, or via mergers and acquisitions. The new decomposition of the aggregate Luenberger productivity indicator is illustrated using data at both the provincial and regional levels for China's healthcare sector over the period 2009–2014. Our results indicate that the growth of the aggregate Luenberger productivity indicator varied across both time and regions. We find that China's regional productivity growth in healthcare was primarily driven by technological progress, while the contributions of the other components of productivity change were smaller and more varied across regions.