本文針對Rao(2006)的共同邊界Malmquist生產力指數(MMPI),進行二個層面的延伸:首先,考量生產力指數衡量的完全性,嚐試透過距離函數的推導,在參數法下,提供一般化共同邊界Malmquist生產力指數(gMMPI)的拆解,與可行估計架構;另外,亦針對MMPI構成項目中的「追趕」,進一步再拆解為純粹技術追趕(PTCU)與潛在技術相對變動(PTRC)二項,以獲得更為明確的意涵。實證上,利用1980-2003年間,26個高所得國家(DCs),以及40個中所得與低所得國家(LDCs)的總體資料,進行參數法的生產力推估與拆解。結果發現,在MMPI的架構下,LDCs的生產力高於DCs,而在gMMPI的架構下,LDCs的生產力則低於DCs,此反轉的結果,說明了未考量規模效率變動的MMPI,所潛藏的衡量不完全的風險。其次,將焦點轉向亞洲國家的比較,可更清楚了解PTCU所捕捉的,為個別國家的技術追趕,而PTRC則反應出潛在技術發展空間的變化,其意涵與可應用的範圍不同。最後,本文亦對純粹技術追趕過程進行一簡單的實證,結果發現,技術水準較低的國家,技術追趕的速度較快,推論原因,主要可能與技術取得的差異有關。
This study extends Rao (2006) Metafrontier Malmquist Productivity Index (MMPI) to two dimensions. First, to increase the measure's completeness this paper attempts to subsume a scale efficiency term (SEC) in the MMPI. Second, the 'catch-up' term in the MMPI is further divided into two subcomponents: pure technological catch-up (PTCU) and potential technological relative change (PTRC), to achieve a more meaningful decomposition. An empirical study is then conducted using data on two country groups: 26 high income level countries (DCs) and 40 middle and low income level countries (LDCs) for 1980-2003. The results reveal that: (i) the MMPI shows a higher productivity of LDCs. However, the gMMPI shows a lower productivity of LDCs. Such a reversal suggests the risk of using the MMPI without considering the SEC effects; (ii) when focusing on the Four Asian Tigers, the implication of the PTCU and PTRC are more unambiguous. Finally, this study also inspects the pattern of pure technological catch-up. The results show that a country with a lower level of technology will exhibit a higher catch-up rate. This is due to the differences in acquiring technology between DCs and LDCs.