Decomposing the Luenberger–Hicks–Moorsteen Total Factor Productivity indicator: An application to U.S. agriculture

Abstract

This paper introduces a decomposition of the additively complete Luenberger-Hicks-Moorsteen Total Factor Productivity indicator into the usual components: technical change, technical inefficiency change and scale inefficiency change. Our approach is general in that it does not require differentiability or convexity of the production technology. Using a nonparametric framework, the empirical application focuses on the agricultural sector at the state-level in the U.S. over the period 1960 − 2004. The results show that Luenberger-Hicks-Moorsteen productivity increased substantially in the considered period. This productivity growth is due to output growth rather than input decline, although the extent depends on the convexity assumption of the technology. Technical change is the main driver, while the role of technical inefficiency change and scale inefficiency change also depends on the convexity assumption of the technology.

Exact and Superlative Measurement of the Luenberger-Hicks-Moorsteen Productivity Indicator

“…It can be decomposed in technical change and technical inefficiency change (Chambers et al, 1996), but the exact contribution of output and input change cannot be determined. This is because, in general, g t = (g i t , g o t ) > 0 and inputs are contracted simultaneously as outputs are expanded in the directional distance functions (Ang and Kerstens, 2016). Hence, it is not "additively complete" (O'Donnell, 2012).…”

“…Recently, Ang and Kerstens (2016) show that the LHM productivity indicator is "additively complete" and, following Diewert and Fox (2017), provide a decomposition in the usual components of technical change, technical inefficiency change and scale inefficiency change under minimal assumptions of the technology set. However, an exact and superlative approximation of the LHM productivity indicator is presently absent in the literature, which disallows easy computation of the LHM productivity indicator in practice.…”

“…However, the Luenberger productivity indicator is not "additively complete", preventing decomposition into output and input changes (O'Donnell, 2012). Although Briec and Kerstens (2004)'s Luenberger-Hicks-Moorsteen (LHM) productivity indicator does have this desirable property (Ang and Kerstens, 2016), no superlative and exact approximation is currently known in the literature.…”

“…Determinateness of the index does not necessarily carry over to its components. This occurs for example in the empirical application ofAng and Kerstens (2016), where the technical change component is undefined for one of the observations.…”

Carbon Sequestration Total Factor Productivity Growth and Decomposition: A Case of the Yangtze River Economic Belt of China

“…Actually, even if all regions are efficient, it is still required to optimize resource utilization for the TFP growth at the regional level through coordination for improvement of input-output mixes [67]. Recognizing the shortage of previous research, some scholars have tried to improve analysis on the structural effect or/and scale effect in decomposition of TFP growth [68][69][70][71], such as a decomposition of TFP indicator into components of technical change, technical inefficiency change, and scale inefficiency change on the agricultural sector at the state-level in the U.S. [68] and measurement of green productivity evolution for 30 OECD countries with decomposition for green productivity growth changes into technological progress, technical efficiency change, and structural efficiency change [35]. But, integration of technology progress, technical efficiency change, factor allocation efficiency change, and scale efficiency change has yet to be discussed in literature.…”