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

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.