本文以貝氏方法估計隨機方向距離函數，加入單調性與曲度等限制條件，並連結無效率項與環境變數。為突顯包含非意欲產出的方向距離函數之優點，本文同時估計產出面距離函數，並與方向距離函數之結果比較。實證分析資料為1970至2010年各國總體經濟變數，分別在有無加入限制條件與環境變數的設定下，估計兩種距離函數，從效率分數與技術進步率等角度，分析兩種函數的差異。發現產出面距離函數因忽略非意欲產出，傾向高估各國的技術效率與低估技術進步率；而同時加入限制條件與環境變數的方向距離函數，估計結果最為合理。

This paper applies the Bayesian approach to estimate the directional distance function (DDF) with the imposition of monotonicity and curvature, using national data covering 1970–2010. The inefficiency term is further specified as a function of several environmental variables. The salient feature of DDF is its ability to take undesirables into account. For the purpose of comparison we also estimate the output distance function. Evidence is found that the output distance function tends to overestimate the measure of technical efficiency and underestimate the rate of technical change. DDF that imposes monotonicity and curvature is found to be superior to the output distance function in terms of estimated efficiency scores and the rate of technical progress.