Knowledge production function and Malmquist index regression equations as a dynamic system

Abstract

In this study, we demonstrate that when the popular data envelopment analysis (DEA)-based Malmquist productivity indexes are used in regression analysis, the set of linear equations involved can be treated as a system. With reference to a special structure of the knowledge production function, the regression equations can be further specified as a dynamic system. Cross-equation restrictions are explored to reveal the rich structures for the relationship between productivity growth, productivity growth components, and their determinants. Preliminary empirical results using community innovation survey (CIS) data show that knowledge production in terms of technical progress can exhibit diminishing returns with respect to level of knowledge while technical efficiency may improve at an increasing rate. We expect that the study may have important implications for micro studies on the relationships between innovation and productivity and for macro modeling of endogenous economic growth.

Keywords:

• total factor productivity
• dynamic analysis
• technical progress
• efficiency change
• knowledge production function

JEL Classification:

• D24
• C61
• O30

Notes

1. Phelps (1966) uses the term ‘technology function’ in referring to the relationship between research inputs and research outcomes; Gomulka (1970) mentioned ‘the production function of innovations’; and Jones (1999, 2002, 2005) prefers to phrase the relationship as ‘the idea production function’.

2. Concerning the ‘the future of the new economy’, Jones (2001) notes ‘Economists cannot say what it takes to generate knowledge at a permanently faster rate and thereby raise the productivity growth rate permanently’ and ‘It is certainly possible that the economy becomes increasingly better at producing new ideas, … However, it is also possible that it becomes increasingly difficult to discover new ideas, as the most obvious ideas are discovered first’.

3. If we assume that TFP growth cannot be negative, log linearization in principle should be feasible. But in practice, it is better to be able to accommodate negative values of TFP change or growth at this stage.