PISA投入產出績效國際比較：情境相依模型與拔靴法的應用

國際學生能力評量計畫（Programme for International Student Assessment，簡稱PISA）是由經濟合作暨發展組織（Organisation for Economic Cooperation and Development）所主辦的跨國學生素養調查。其所評量的關鍵能力是呼應著全球教育課程目標的主流趨勢，並且評量結果大多呈現良好的信效度。目前大多數的PISA研究都是直接看各個國家的學科成就表現，沒有探討到各個國家的國情背景、經濟因素等投入項的因素。因此本文想藉由績效分析法的效率模型、拔靴法、情境相依模型，來探討各個國家的投入產出績效，根據2012年的PISA評量結果，將數學、閱讀、科學能力等評量項目為產出項，再以人均國內生產毛額（gross domestic product, GDP）、人類發展指數（human development index, HDI）、教育支出、城市化、生師比等經濟指標為投入項，探討台灣與OECD 34個國家的教育績效差異。資料包絡分析法（DEA）是學術上常用的投入產出績效法，其可以客觀地衡量每一個決策單位的投入產出績效。DEA中的情境相依模型，可分成不同層級的效率前緣，讓後段班國家地區仿效中段班國家地區教育成效，中段班國家地區學習前段班國家地區的教育績效。此外，本文納入標準差的資料，利用拔靴法進行經由多次重複抽樣，提高研究的準確性。研究結果顯示，在高所得國家之中，台灣、愛沙尼亞、芬蘭、德國、愛爾蘭、日本、韓國之相對效率表現最優，是其他高所得國家學習模仿的對象，而在低所得國家當中，智利、墨西哥、波蘭、斯洛伐克、斯洛文尼亞、土耳其之教育績效表現最好，是其他低所得國家學習模仿的對象。在情境相依模型當中，我們運用上下層級的相對吸引力和相對進步力，來分析各層級國家的改善方向與競爭情形，在相對吸引力方面，墨西哥、匈牙利、義大利分別對各種不同階層的國家有著最大的相對吸引力，亦表示該國的教育績效較優，足以吸引其國家來學習。在相對進步力方面，盧森堡、西班牙、挪威、瑞典、冰島則各有不同的進步力的改善空間，必須檢視目前的教育政策，找出改善的方向，才能提高教育績效。在拔靴法的績效分析中，我們可以得知教育績效較不佳的國家，可以學習參考哪些國家為對象，另外我們也發現低所得的國家可以學習模仿這些低所得且教育績效佳的國家，因為如果國情背景相差太大，短時間是無法立刻被學習模仿而達成效率的。所以我們也發現有一些投入低的國家，被學習模仿的次數是很多的，例如土耳其學習次數有21次，其次為波蘭有16次。情境相依模式和拔靴法效率分析，這些研究方法所得的教育績效皆可以互相印證，互相對照找出確切的政策方向，學習的楷模。

關鍵字

資料包絡分析模型；情境相依模型；拔靴法；國際學生能力評量計畫

並列摘要

The Programme for International Student Assessment (PISA) is a survey conducted by the Organization for Economic Cooperation and Development (OECD) on the skills of international students. The critical abilities assessed correspond with the trending course and educational objectives worldwide, and the assessment results have mostly exhibited satisfactory reliability and validity. Currently, most studies based on the PISA have focused directly on the academic achievements of students in each country without considering the country’s input factors such as national circumstances and economy. Therefore, this study investigated the input–output performance by applying the efficiency model, bootstrapping, and context-dependent model of performance analysis. According to the 2012 PISA results, this study involved assigning mathematics, reading, and scientific capability as input items and designating gross domestic product, the human development index, educational expenditure, urbanization, and student–teacher ratio as output items to investigate the difference in the educational performance of Taiwan and 34 OECD countries. In academic research, data envelopment analysis is a commonly used method for measuring input–output performance, enabling input–output performance of each decision unit to be objectively assessed. The context-dependent model in data envelopment analysis can be divided into different levels of efficient frontiers, enabling low-ranked countries to emulate the educational performance of middle-ranked countries, and middle-ranked countries to emulate the performance of high-ranked countries. Furthermore, this study incorporated standard deviation and performed bootstrapping through repeated sampling to enhance accuracy. The results indicated that, among high-income countries, Taiwan, Estonia, Finland, Germany, Ireland, Japan, and South Korea exhibited the highest relative efficiency and were worth imitating by other high-income countries. Among low-income countries, Chile, Mexico, Poland, Slovakia, Slovenia, and Turkey demonstrated the most satisfactory educational performance and were worth imitating by other low-income countries. In the context-dependent model, we employed the relative attractiveness and progress between high and low levels to analyze the improvement directions of and competition among countries of each level. Mexico, Hungary, and Mexico individually exhibited the highest relative attractiveness towards the countries of other levels, indicating that their educational performance was superior and sufficiently satisfactory for imitation by other countries. Luxembourg, Spain, Norway, Sweden, and Iceland required different improvements in progress and should therefore inspect their current educational policies and seek directions of improvement to promote educational performance. In the performance analysis of bootstrapping, we determined the countries that could be referred to and emulated by countries exhibiting unfavorable educational performance. Moreover, we found that low-income countries can emulate countries with low income and unsatisfactory educational performance because overly discrepant national circumstances inhibited immediate efficiency improvement through imitation. Several low-input countries were imitated numerous times; for example, Turkey was imitated 21 times, followed by Poland (16 times). The educational performance data acquired using the context-dependent model and bootstrapping efficiency analysis can be mutually compared and verified to identify the exact policy orientations and role models for emulation.