生產效率估計之非線性考量：平滑轉換迴歸在台灣農業部門生產效率估計之應用

Nonlinear Estimation of Production Efficiency: Application of the Smooth Transition Regression on the Agricultural Sector in Taiwan

過去研究生產效率的文獻都是以線性的生產函數或成本函數迴歸模型為基礎，而線性的迴歸模型卻同時隱含迴歸係數為常數的假設。這樣的假設無法適用於樣本資料跨長期之時間序列模型，因為模型中可能存在結構性轉變。因此，本文利用Granger and Terasvirta（1993）所提出非線性之STR模型，結合定性邊界法來估計台灣農業部門之生產效率，並與以線性OLS模型之估計結果進行比較。實證結果發現，以CD生產函數為基本模型，再結合STR模型的估計結果，其對產出的解釋力較線性OLS模型為佳。本文也發現以線性OLS模型所估計之台灣農業部門生產效率，自1960年代以後顯示呈現逐漸下降，到了1980年代中，又很快回升到最高的效率水準，在1990年以後，則又有下滑的走勢。而以LSTR模型所估計之效率的變化來看，我們發現自1960年起至1999年，台灣農業部門之生產效率並無明顯的上升或下降趨勢，估計值約莫在90%～100%之間變動。這顯示台灣農業部門生產效率，變化程度應該是相當穩定的，平均維持在96%之間，亦無效率之程度僅約4%。

Most of the past studies on production efficiency were based on the assumption of linearity in production functions. A linear production function implicitly assumes constancy in coefficients of the empirical specification of linear regression of the production function. Such assumptions of constancy in coefficients of regression are particularly inadequate in modeling empirical analysis with long time series data due to possible structural changes in the model specifications. Compared with the OLS estimation under the assumption of constancy in coefficients of regression, this paper proposes to employ Granger and Terasvirta's (1993) STR model and deterministic frontier approach to consider the possible structural changes in estimating production efficiency of the agricultural sector in Taiwan. It is shown that the results of the STR estimation outperform the one of the OLS estimation by using the Cobb-Douglas production function as the underlying model. The empirical results also show that the changes in production efficiency in the agricultural sector of Taiwan were rather smooth from 1960 to 1999. It indicates that production efficiency of Taiwan's agricultural sector varied around 90%-100% and the average estimated inefficiency was 4%.