An Expanded Decomposition of the Luenberger Productivity Indicator with an Application to the Chinese Healthcare Sector

Productivity growth is an important determinant of the economic well-being of producers, consumers, and society overall. Given its importance, economists have long measured productivity growth, often decomposing the overall measure into constituent pieces to isolate and better understand the sources of productivity change. Typically, productivity change is analyzed at a single level of analysis—e.g., a firm or a country. 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. 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. By shedding light on more dimensions of productivity growth, this expanded decomposition may facilitate policy development and other efforts to improve productivity. The expanded decomposition begins with a standard decomposition of the aggregate Luenberger productivity indicator into its technical progress and efficiency change components. The efficiency change component is then further decomposed into technical, mix, and scale efficiency effects. The decomposition yielding the mix and scale efficiency changes uses both aggregated and disaggregated data, which allows for productivity effects of reallocations of inputs and outputs across members of a group to be measured. 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. Given the rapid growth in the Chinese healthcare sector in recent years and the various healthcare reforms initiated by the government, a deeper understanding of productivity in this traditionally low-productivity sector is warranted. Our results indicate that the growth of the aggregate Luenberger productivity indicator varied across both time and regions; the annual average growth rates were 0.73%, 0.53%, and 0.18% for China’s Central, Eastern, and Western regions, respectively. We find that China’s regional productivity growth in healthcare was primarily driven by technological progress; the contributions of the efficiency related elements of productivity change were smaller and more varied across regions.