運用考慮交互效果的真實固定效果模型探討各國總體生產效率

Abstract

本研究在Greene (2005a, 2005b) and Wang and Ho (2010) 真實固定或隨機效果模型架構下，利用 Bai (2009) 所稱的交互效果 (interactive effects) 將無法觀察到的共同衝擊因子 (unobserved common shocks) 納入考量。分別探討我國銀行業的技術效率以及各國總體生產效率。將這種無法觀察到的共同衝擊因子納入迴歸模型，表示各國生產活動具有橫斷面相依性與來自共同因子的異質衝擊。迴歸模型若忽略這種交互效果，易造成係數與效率估計值的偏誤。 根據 Hsu et al. (2012) 發展的方法，利用Pesaran (2006) 的方法先對迴歸模型進行轉換，設法消除交互效果，再針對轉換後模型以最大概似法進行估計，就可得到具備一致性的係數與效率估計值。研究對象為各國總體隨機生產邊界函數，並進一步將樣本國家分成低與高所得兩群組，採用Huang et al. (2014) 發展的新共同生產邊界模型進行生產效率與生產力之比較。 研究結果發現這兩群組國家採用不同的生產技術進行生產，確認應採用共同邊界模型估計和比較兩群組的生產效率。此外，高所得國家的技術進步速度較低所得國家快且生產技術較為接近固定規模報酬；然而低所得國家的總技術效率優於高所得國家，主要原因為低所得國家的群組技術效率高於高所得國家，兩群國家的技術缺口比率幾無差異。 This paper applies the true fixed effects model of Greene (2005a, 2005b) and Wang and Ho (2010), together with interactive effects of Bai (2009), to examine the production efficiency of countries. To compare efficiency scores of the sample countries, we suggest the use of the meta-production frontier, developed by Huang et al. (2014). The inclusion of the interactive effects allows us to explain why different countries (firms) might be influenced by various degrees of impacts coming from observed/unobserved common economic/technology shocks. These effects are modeled as the product of firm-specific parameters (loadings) and common shocks (factors). The exclusion of these effects from models may lead to bias parameter estimates and efficiency measures. Following Hsu et al. (2012), we first employ the transformation procedure, proposed by Pesaran (2006), to purge the interactive effects, and then estimate the transformed model by the maximum likelihood. This leads to consistent parameter estimates and efficiency scores. Panel data of aggregate output produced by labor and physical capital for countries are used to investigate issues related to production efficiency. The sample countries are further divided into two groups, i.e., low and high income countries. The low and high income countries are found to utilize different production technologies and to take the increasing returns to scale technology, but the latter countries are closer to the constant returns to scale. The speed of technical advance for high income countries is faster than that of low income countries. However, the overall technical efficiency score of low income countries is greater than that of high income countries, due mainly to technical efficiency rather than TGR, while the difference between the two groups is not large.