本文採用一階段隨機邊界分析法（Battese and Coelli, 1995）衡量2004 年第一季至2008 年第三季台灣上市櫃證券商的技術效率，並將Orea（2002）提出的產出導向一般化Malmquist生產力指數改寫成投入導向模式，用來分析台灣上市櫃證券商的生產力變動情形。實證結果顯示，小型券商之經營效率平均而言比大型券商之經營效率高，而大部分的證券商都呈現規模報酬遞增的技術狀態，可見台灣上市櫃證券商整體而言規模不夠大，必須設法再擴大至適當的規模方可發揮規模經濟效果。另外，較多的股本雖然理論上具備較強的競爭優勢，但可能沒有適當的決策支持，造成資源浪費反而降低經營效率；股價指數愈高，在相同的投入之下有較多的產出表現且較有能力調整規模至規模報酬較佳的狀況，因而提高經營效率。

This paper adopts one-stage stochastic frontier analysis (Battese and Coelli, 1995) to measure technical efficiency of listed securities firms in Taiwan from the first quarter of 2004 to the third quarter of 2008. In addition, inspired by the Orea (2002) output orientated productivity model, this paper derives an input orientated generalized Malmquist productivity index to analyze the productivity change of the firms. The empirical results reveal that smaller securities firms are more efficient than larger securities firms in average. The majority of securities firms are operating with increasing returns to scale, indicating that the scale of listed securities firms in Taiwan are generally not large enough, so firms need to enlarge their scale in order to get the effect of economies of scale. Although more capital stocks possess stronger competitive advantage theoretically, without proper strategy to support the firms may waste resources and result in operational inefficiency. Operational efficiency is positively correlated with stock index.

中文文獻
王國樑，翁志強與張美玲（1998），「台灣綜合證券商技術效率探討」，《證券市場發展季刊》，10，93-115。
王媛慧，李文福與翁竹君（2007），「台灣國際觀光旅館業生產力與效率分析：隨機邊界距離函數之應用」，《經濟論文叢刊》，35，55-86。
張雅雯（2004），「台灣綜合證券商之成本效率與生產力分析」，國立台北大學經濟學研究所碩士論文。
黃翔園（2000），「台灣地區網路券商經營績效之實證研究-以資料包絡分析法」，朝陽科技大學財務金融學研究所碩士論文。
楊家豪（2008），「台灣證券商經營效率分析」，國立政治大學行政管理碩士學程碩士論文。
歐陽如虹（2002），「台灣證券商經營效率分析」，銘傳大學國際企業管理學研究所碩士論文。
劉雲霞（1996），「台灣證券商經營狀況之探討-資料包絡分析法的應用」，國立政治大學會計學研究所碩士論文。

英文文獻
Aigner, D. J., C. A. K. Lovell and P. Schmidt (1977), “Formulation and Estimation of Stochastic Frontier Production Function Models,” Journal of Econometrics, 6, 21- 37.
Balk, B. M. (2001), “Scale Efficiency and Productivity Change,” Journal of Productivity Analysis, 15, 159-183.
Battese, G. E. and G. S. Corra (1977), “Estimation of a Stochastic Production Frontier Model: With Application to the Pastoral Zone of Eastern Australia,” Australian Journal of Agricultural Economics, 21, 169-179.
Battese, G. E. and T. J. Coelli (1995), “A Model for Technical Inefficiency Effects in a Stochastic Frontier Production Function for Panel Data,” Empirical Economics, 20, 325-332.
Caves, D. W., L. R. Christensen and W. E. Diewert (1982), “The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity,” Econometrica, 50, 1393-1414.
Diewert, W. E. (1976), “Exact and Superlative Index Numbers,” Journal of Econometrics, 4, 115-145.
Färe, R., S. Grosskopf, M. Norris and Z. Zhang (1994), “Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries,” American Economic Review, 84, 66-83.
Färe, R. and D. Primont (1995), Multi-Output Production and Duality: Theory and Applications, Kluwer Academic Publishers, Boston.
Farrell, M. J. (1957), “The Measurement of Productive Efficiency,” Journal of the Royal Statistical Society, 120, 253-290.
Fisher, I. (1922), The Making of Index Numbers, Houghton Mifflin, Boston.
Fukuyama, H. and W. L. Weber (1999), “The Efficiency and Productivity of Japanese Securities Firms, 1988-93,” Japan and the World Economy, 11, 115-133.
Goldberg, L. G., G. A. Hanweck, M. Keenan and A. Young (1991), “Economies of Scale and Scope in the Securities Industry,” Journal of Banking and Finance, 15, 91-107.
Grifell, E. and C. A. K. Lovell (1997), “The Sources of Productivity Change in Spanish Banking,” European Journal of Operational Research, 98, 364-380.
Huang, C. J. and J.-T. Liu (1994), “Estimation of a Non-Neutral Stochastic Frontier Production Function,” Journal of Productivity Analysis, 5, 171-180.
Koopmans, T. C. (1951), “ An Analysis of Production as an Efficient Combination of Activities,” in T. C. Koopmans, ed., Activity Analysis of Production and Allocation, Cowles Commission for Research in Economics, Monograph No. 13, Wiley, New York.
Kozo, H. and O. Eiji (2006), “The Changing Structure of Cost for Japanese Securities Firms,” International Journal of Business, 11, 17-33.
Kumbhakar, S. C. and C. A. K. Lovell (2000), Stochastic Frontier Analysis,
Cambridge University Press, Cambridge.
Kumbhakar, S. C., S. Ghosh and J. T. McGuckin (1991), “A Generalized Production Frontier Approach for Estimating Determinants of Inefficiency in U.S. Dairy Farms,” Journal of Business and Economic Statistics, 9, 279-286.
Malmquist, S. (1953), “Index Numbers and Indifference Surfaces,” Trabajos de Estadistica, 4, 209-242.
Meeusen, W. and J. van den Broeck (1977), “Efficiency Estimation from Cobb- Douglas Production Functions with Composed Error,” International Economic Review ,18, 435-444.
Nishimizu, M. and J. M. Page (1982), “ Total Factor Productivity Growth, Technological Progress and Technical Efficiency Change: Dimensions of Productivity Change in Yugoslavia, 1965-78,” Economic Journal, 92, 920-936.
Orea, L. (2002), “Parametric Decomposition of a Generalized Malmquist
Productivity Index,” Journal of Productivity Analysis, 18, 5-22.
Ray, S. C. (1998), “Measuring Scale Efficiency from a Translog Production Function,” Journal of Productivity Analysis, 11, 183–194.
Ray, S. C. and E. Desli (1997), “Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries: Comment,” American Economic Review, 87, 1033-1039.
Reifschneider, D. and R. Stevenson (1991), “Systematic Departures from the Frontier: A Framework for the Analysis of Firm Inefficiency,” International Economic Review, 32, 715-723.
Schmidt, P. and R. C. Sickles (1984), “Production Frontiers and Panel Data,” Journal of Business and Economic Statistics, 2, 367-374.
Shephard, R. W. (1970), The Theory of Cost and Production Functions, Princeton University Press, Princeton.
Stevenson, R. E. (1980), “Likelihood Functions for Generalized Stochastic Frontier Estimation,” Journal of Econometrics, 13, 57-66.
Törnqvist, L. (1936), “The Bank of Finland’s Consumption Price Index,” Bank of Finland Monthly Bulletin, 10, 1-8.
Wang, H.-J. and P. Schmidt (2002), “One-Step and Two-Step Estimation of the Effects of Exogenous Variables on Technical Efficiency Levels,” Journal of Productivity Analysis, 18, 129-144.
Wang, K.-L., Y.-T. Tseng and C.-C. Weng (2003), “A Study of Production Efficiencies of Integrated Securities Firms in Taiwan,” Applied Financial Economics, 13, 159-167.
Zellner, A., J. Kmenta and J. Drèze (1966), “Specification and Estimation of Cobb-
Douglas Production Function Models,” Econometrica, 34, 784-795.
Zhang, W. D., S. Zhang and X. Luo (2006), “Technological Progress, Inefficiency, and Productivity Growth in the US Securities Industry, 1980-2000,” Journal of Business Research, 59, 589-594.