음수 값을 처리할 수 있는 Malmquist 생산성 분석 시스템 개발 및 적용

박만희 한국서비스경영학회 2023 서비스경영학회지 Vol.24 No.3

The Malmquist productivity index, a non-parametric productivity analysis technique, is used for productivity analysis in various fields. When the variables considered as input and output variables in the DEA (Data Envelopment Analysis) model have negative values, there is a case where the solution of the DEA model does not exist, and for this reason, the existing methodology has a problem that the Malmquist productivity index cannot be calculated. In order to solve this problem, this study presented a Biennial Malmquist productivity analysis method that can process negative values and developed a system that can support it. The results of this study are summarized as follows. First, the Biennial Malmquist productivity index, which can analyze negative values in input and output variables, is presented, and the productivity index is subdivided into technological efficiency change index and technological change index. Second, an empirical analysis was conducted using performance data from public corporations for five years from 2007 to 2021 to prove the applicability of the Biennial Malmquist productivity index presented in this study. Third, a web-based productivity analysis system was developed to support the analysis of the Biennial Malmquist productivity index proposed in this study. 비모수적 생산성 분석기법인 Malmquist 생산성지수는 다양한 분야의 생산성분석에 활용되고 있다. DEA 모형에서 투입 및 산출변수로 고려된 변수가 음수 값을 가지는 경우 DEA 모형의 해가 존재하지 않는 경우가 발생하고 이로 인해 기존 방법론으로는 Malmquist 생산성지수를 계산할 수 없다는 문제점을 가지고 있다. 본 연구에서는 이러한 문제점을 해결하기 위하여 음수 값을 처리할 수 있는 Biennial Malmquist 생산성분석 방법을 제시하고 이를 지원할 수 있는 시스템을 개발하였다. 본 연구를 통해 도출된 연구결과를 정리하면 다음과 같다. 첫째, 투입변수와 산출변수에 음수 값이 존재하는 경우 이를 분석할 수 있는 Biennial Malmquist 생산성지수를 제시하고, 생산성지수를 기술적 효율성변화지수와 기술변화지수로 세분화하였다. 둘째, 본 연구에서 제시한 Biennial Malmquist 생산성지수 적용 가능성을 입증하기 위하여 2007년부터 2021년까지 5년 동안의 공기업 실적데이터를 이용하여 실증분석을 수행하였다. 셋째, 본 연구에서 제시한 Biennial Malmquist 생산성지수 분석을 지원할 수 있는 웹기반 생산성분석시스템을 개발하였다.

Malmquist 생산성지수와 Luenberger 생산성지수의 이론적 관계와 실증적 분석

박현숙 ( Hyunsuk Park ),양동현 ( Donghyun Yang ) 한국보건행정학회 2015 보건행정학회지 Vol.25 No.2

Background: We measured productivity changes of regional public hospitals using both global Malmquist productivity index?based on global production possibility set over all the periods? and the traditional Malmquist productivity index and analyzed the factors of productivity change. Methods: The data used in this study is two annual inputs and two annual outputs of 32 regional public hospitals in Korea from 2005 to 2009 and the results such as distances and Malmquist productivity index and global Malmquist productivity index are obtained by an R program written for this study. Results: The results can be summarized as follows. Firstly, technical efficiencies of regional public hospitals are affected largely by scale efficiency than pure technical efficiency. Second, productivity progressed and technological change has more significant influence on productivity advance over the period between 2005 and 2009. Third, the circularity problem of the traditional Malmquist index is confirmed, and so the global Malmquist index without this problem are valid for the analysis. Conclusion: Though this study also has some limitations with the data of regional public hospitals with a short time span, it is the first study of hospitals using global Malmquist productivity index and later it can be expanded to private hospitals and longer time periods.

중국 도시별 생산성의 추계와 비교

김상욱 한중사회과학학회 2009 한중사회과학연구 Vol.7 No.1

The DEA efficiency and Malmquist productivity index are used to measure productivity growth in many fields. This paper use the two method, estimate the urban productivity in China from 1990-2005. The results of DEA efficiency shows that most of urban are not exist DEA efficiency. But DEA method is the static method, so it has limits in analyzing the urbanization dynamic process. Using Malmquist method, this paper try to analyze the dynamic changes of productivity. This paper establish two models. Model 1 include two input variables, labor and capital, and one output variable, GDP. Model 2 include two input variables, labor and capital, and two output variables, GDP and government revenue. This paper use 196 urban data, it is data available. From total urban’s Malmquist index, model 1 shows the productivity’s improvement, annual average 6.7%, in 1990-2005, model 2 also shows the improvement, 3.0%. From each Malmquist index, the 189 urban have the productivity’s improvement in model 1, and the 152 urban have the productivity’s improvement in model 2. From regions’s Malmquist index, the Eastern region shows the higher improvement respectively, and the North-Eastern region shows the lower improvement. The relation between urban scale and productivity find that urban population and productivity have negative relation, and urban economic scale and productivity have positive relation. It means that urban population scale need to control in urbanization process.

중국 도시별 생산업의 추계와 비교

김상욱 ( Sang Wook Kim ) 한중사회과학학회 2009 한중사회과학연구 Vol.7 No.1

The DEA efficiency and Malmquist productivity index are used to measure productivity growth in many fields. This paper use the two method, estimate the urban productivity in China from 1990-2005. The results of DEA efficiency shows that most of urban are not exist DEA efficiency. But DEA method the static method, so it has limits in analyzing the urbanization dynamic process. Using Malmquist method, this paper try to analyze the dynamic changes of productivity. This paper establish two models. Model 1 include two input variables, labor and capital, and one output variable, GDP. Model 2 include two input variables, labor and capital, and two output variables, GDP and government revenue. This paper use 196 urban data, it is data available. From total urban`s Malmquist index, model 1 shows the productivity`s improvement, annual average 6.7%, in 1990-2005, model 2 also shows the improvement, 3.0%. From each Malmquist index, the 189 urban have the productivity`s improvement in model 1, and the 152 urban have the productivity`s improvement in model 2. From regions`s Malmquist index, the Eastern region shows the higher improvement respectively, and the North-Eastern region shows the lower improvement. The relation between urban scale and productivity find that urban population and productivity have negative relation, and urban economic scale and productivity have positive relation. It means that urban population scale need to control in urbanization process.

전기공사업 효율성 및 생산성 변화 분석: DEA 및 Malmquist 생산성지수 모델을 중심으로

김예정(Yejung Kim) 대한경영학회 2019 大韓經營學會誌 Vol.32 No.5

지역경찰활동의 효율성과 맘퀴스트 생산성 분석

이승철(Lee Seung Chal),송건섭(Song Keun Sub) 한국공안행정학회 2012 한국공안행정학회보 Vol.21 No.3

정부행정의 효율화에 대한 관심이 증가되면서 지역경찰청의 효율성을 개선하기 위한 투자와 노력은 지속되고 있다. 하지만 지역경찰청 성과에 대한 적절한 평가가 선행되어야 하는데, 지역경찰서의 양적자료 수집의 한계, 경찰활동 산출물에 대한 측정문제 등으로 평가가 어려운 것이 사실이다. 지역경찰청의 효율적인 경찰활동을 위해 적절한 정책과 투자가 이루어지고 있는지를 파악해 볼 필요가 있다. 이를 위해 본 연구는 생산성 변화요인을 파악하기 위해 DEA-Malmquist생산성 지수를 활용하여 효율성을 평가하였다. 분석자료는 2001년부터 2010년까지 시계열데이터를 활용하였는데, 투입변수는 경찰인력, 1인당 관할면적, 관할인구이며 산출변수로 범죄발생 및 검거건수, 검거율이다. 분석된 연구결과를 정리하고 방향을 제시하면 다음과 같다. 첫째, DEA분석에서 효율적인 지역경찰서는 11개이며, 3개는 비효율적으로 나타났다. 둘째, DEA결과에서 나타난 지역경찰서의 기술적 효율성을 향상시키기 위해서는 적극적인 지역사회경찰활동으로 범인 검거활동을 증가시켜야 한다. 또한 정부는 인력에 대한 적절한 정책이 필요하다. 셋째, 맘퀴스트 생산성 지수를 이용하여 보면, 생산성이 2001/2002년, 2006/2007년에 높았지만, 2005/2006년, 2009/2010년에 크게 감소하고 있다. 이러한 생산성을 떨어뜨리는데 주도적인 역할을 한 것은 기술적 효율성 변화보다는 기술변화라고 볼 수 있다. 넷째, 기술변화의 상승폭을 늘이기 위해서는 효율성이 높은 지역의 벤치마킹이나 기술혁신을 통하여 높은 수준으로 기술을 발전시켜야 하고 생산성 향상을 위한 정부차원의 구조개선이나 정책이 필요하다. A concernment is on the increase, related with local administration efficiency, so inputs and endeavors are made continuously to improve local police agencies' effectiveness. First of all, an appropriate appreciation on the fruits of local police agencies is essential. But it's very difficult to appreciate the fruits because of the limitation of quantitative material collection by the local police agencies and difficulty in measurement of materials produced by police activities. It is necessary to grasp appropriate input policies and inputs, helpful to effective police activities of local police agencies. This study put into a practical use DEA-Malmquist productivity index to grasp productivity change factors. This study measured effectiveness and productivity of local police agencies from 2001 to 2010.In addition this study measured productivity change index by dividing it into skill effectiveness change index and skill change index. The result of the study, arranged, and direction, presented, are as followings. First, the effective police stations in the analysis of DNA were those of 11 regions. The regional police stations classified to be ineffective were those of Chungnam, Chungbuk, Gyeongbuk, whose effectiveness values were less than average. It is possible for the regional polices appreciated to be ineffective to benchmark with remark synthesis values, classified with regions. Second, it is necessary to increase crime prevention and arrest activities actively to promote skill effectiveness of regional police agencies. In addition, it is necessary for the government to assist in human power and appropriate policies continuously. In addition to human power supplement, budget increase and equipment reinforcement are indispensible in increasing demand of police. Structure arrangement and management innovation in the inside of local police stations will lead to their effectiveness by themselves. Third productivity index of Malmquist shows that productivity in 2001/2002 and 2006/2007 was high, but the productivity in 2005/2006, 2009/2010 decreased greatly. The important factor in decreasing productivity is a change in skill, rather than effectiveness in skill. The productivity index of Seoul, Chungbuk, Jeoonnam, and Gyeongbuk was higher than 1, but that of the rest was low. For example, the regional police stations which regressed in skill were those of Daegu, Incheon, Gyeonggi, Gangwon, Chungbuk, Chungnam, Jeonnm, Gyeongbuk, Gyeongnam. The productivity of wide-area province was low, except Daegu and Incheon. In the aspect of areas, the productivity index of capital area was high a little, but in average, that of Chungcheong Honam area was the highest for 10 years. It is due to changes in skills. Fourth, It is necessary to develop skills at a high level through bench marking of the regions with high effectiveness or skill innovation to increase rise span of skills. In addition it is necessary for the government to change structures in the governmental level or to display policies to enhance productivity.

Malmquist 생산성 지수를 이용한 학교기업지원사업의 생산성 변화 분석

강경종,이건남,정철영 한국농·산업교육학회 2009 농업교육과 인적자원개발 Vol.41 No.3

The purpose of this study was to analyze productivity change of school-based enterprise according to Malmquist Productivity Index. This study analyzed productivity change and the related factors by school size, and session of school-based enterprise. Input factor was government financial support in this study, and output factors were net sales, the number of students who participated in field trip and the number of employees. The major conclusions of this study were as follows. First, considering the productivity, the school-based enterprise was successful project. Second, according to school size, the efficiency and productivity were more influenced by technical change than net efficiency. Third, the support should be conducted in the long term. Fourth, customized strategies should be studied for each school-based enterprise. Fifth, scanning the effect and counterplan of school-based enterprise should be conducted more by school size continuously. Sixth, additional support such as teacher training and accounting support should be planned. 이 연구의 목적은 2004년부터 정부의 국고지원으로 운영되고 있는 학교기업지원사업을 Malmquist 생산성 지수를 이용하여 생산성 변화를 분석하는데 있다. 그리하여 투입요소로 국고지원금을, 산출요소로 매출액(순수익), 현장실습참여 학생수, 직원채용수로 하여 학교기업지원사업의 기수에 따른 학교급별 생산성 추이와 학교기업지원사업의 생산성의 변화 요인을 분석하였다. 이 연구의 결과는 첫째, 학교기업지원사업을 통한 전체 학교기업의 생산성이 신장된 것으로 나타나 의미있는 사업이었음을 시사한다. 둘째, 학교급에 따른 학교기업의 효율성과 각 기간간의 생산성 변화에 대해 학교기업 모두는 상대적으로 기술변화가 순수 효율성보다 더 영향을 받았다. 셋째, 학교기업지원사업의 장기적 성장을 위한 노력이 필요하다. 넷째, 학교기업 특성에 따른 생산성 증대 전략이 필요하다. 다섯째, 지속적으로 학교급에 따른 학교기업의 대응 정도 및 효과를 파악해야 한다. 여섯째, 내부의 효율성에도 민감하게 영향을 받고 있는 것으로 나타난 전문계 고등학교에서 운영하고 학교기업에 대해서는 국고지원 외에 교사연수, 회계지원 등의 별도의 추가적인 지원방안이 마련되어야 한다.

글로벌 Malmquist 생산성지수를 활용한 의료기기 수출제조기업의 생산성변화 분석

황경연 한국무역연구원 2019 무역연구 Vol.15 No.5

Purpose - The purpose of this study is to analyze the trend of productivity changes of medical device export manufacturers by using the global Malmquist productivity index. Design/methodology/approach – The global Malmquist productivity index was used in this study. In the productivity analysis, total assets, equity, tangible assets, intangible assets, employment costs, selling expenses, and general administrative costs were used as input variables while sales and gross profit were used as output variables. Data for this empirical analysis were obtained from 128 medical device manufacturers for a period of six years from 2013 to 2018 using the KISVAUL DB. Findings - The results of this study are as follows: First, the productivity of medical device manufacturers declined by 2.3% every year for six years due to pure technical efficiency change and best practice gap. Second, during the same period, productivity of exporting firms declined by 2.5% per year, while non-exporting firms experienced an average annual decline of 2.2%. Third, corporate group productivity and stand-alone firms’ productivity declined 2.3% each year over the same period. Fourth, productivity of large-sized firms increased by 1.8% per year, while that of small and medium-sized firms decreased by 0.3% per year. Research implications or Originality - Exporting firms should improve productivity by enhancing their pure technical efficiency and promoting technological progress.

산업단지 쇠퇴와 이에 따른 생산성 변화 분석 - 대구성서산업단지를 중심으로 -

전경구 대한부동산학회 2018 大韓不動産學會誌 Vol.36 No.1

This study analyzes the declining processes and productivity changes with Malmquist productivity index of dilapidated industrial estates focusing on the Seongseo industrial estate in Daegu City. This paper suggests that the deteriorated industrial estates are characterized by the increase in the density of the firms since new small scale firms enter into the estates while large ones exit from them. This paper suggests the declining of the industrial estate may indicate the path dependent process. This paper examines the productivity changes of the deteriorating estates with MPI. It is suggested that the absolute average productivity of the declining estates tends to be lower as the estates get older. However, MPI of the old estates tends to indicates the steady state while that of the young estates shows the declining trends, indicating path dependent characteristics. The paper decomposes the MPI with the efficiency change index and technical change index. It is suggested that the decrease in the MPI is due to the low level of efficiency index in the early stage of 2010s while the declining of the MPI results from the low level of technical change index. Also, this paper argues that the efficiency change effect originates form the scale efficiency index rather than the pure efficiency effects. Based on the findings, this paper discusses some policy implications for regeneration of the declining industrial estates that emphasize the technological innovation of the existing firms and careful considerations of development of new industrial estates. 본 연구는 대구의 성서산업단지를 중심으로 산업단지의 쇠퇴과정을 분석하고, 자료포락분석법(DEA)의 일종인 Malmquist 생산성지수(MPI)를 이용하여 쇠퇴산업단지의 생산성 변화를 분석하며 이를 토대로 바람직한 재생 정책과제를 모색하는 것을 목적으로 하고 있다. 분석결과 성서산업단지의 쇠퇴는 시간이 경과함에 따라 비교적 규모가 큰 기업이 퇴장하고 상대적으로 규모가 작은 기업들이 입지함에 따라 소규모의 영세업체가 많이 증가하고 임대공장도 증가함으로써 단지의 밀도가 높아지는 특성이 있는 것으로 나타났다. 그리고 최근에 조성된 단지도 그 전에 조성되어 쇠퇴하고 있는 단지와 유사한 경로를 그대로 따르는 경향이 있어 산업단지의 쇠퇴과정이 경로의존적인 특성을 보이는 것으로 나타났다. 그러나 쇠퇴산업단지는 새로운 기업의 창업보육기능을 제공하고 클러스터를 구축할 수 있는 여건을 제공하는 긍정적인 효과도 있는 것으로 나타났다. 본 연구는 성서산업단지의 구조변화와 쇠퇴에 따른 생산성의 변화를 효율 프론티어(frontier)를 기준으로 측정하는Malmquist 생산성지수(MPI)를 이용하여 분석한 결과 산업단지가 쇠퇴하면 생산성도 일정 수준까지 하락하는데 늦게 조성된 단지일수록 생산성의 하락 시기도 늦어지는 경로의존적인 경향을 보이는 것을 밝혔다. 생산성의 변화 요인과 관련하여 2010년대 전반기에는 기술효율성이 기술변화에 비하여 상대적으로 낮은 것이 생산성 저하의 중요한 원인이고 2010년대 중반기부터는 기술효율성보다 기술변화의 수준이 낮은 것이 생산성 저하의 중요한 원인임을 밝혔다. 그리고 기술효율성의 경우 순수 기술효율성보다는 규모효율성이 생산성의 변화에 영향을 미치는 중요한 요인임을 밝혔다. 본 연구는 산업단지의 쇠퇴를 극복하기 위한 정책과제로서 입주기업들의 혁신성을 제고하고 혁신기술을 보유한 기업의 유출을 방지하는 한편 혁신기업의 유치를 추진할 필요가 있다는 것을 제시하였다. 그리고 기존 단지의 생산성을 향상시키는 각종 정책을 추진하는 한편 기존 단지의 쇠퇴를 촉진하는 신규 산업단지의 신중한 개발이 필요하다는 것을 제시하였다.

중국 주요 조선사의 효율성 및 생산성 분석에 관한 연구

구종순(Jong-Soon Koo),이정선(Jung-Sun Lee),가월위(Yue-Wei Jia) 한국무역연구원 2014 무역연구 Vol.10 No.3

This study analyzed the trend and causes of changes in efficiency and productivity based on the results of 12 shipyards including Chinese state-run and private shipbuilders for 4 years from 2010 to 2013 by using the Malmquist productivity index. Considering the current situation of Chinese shipbuilding industry such as stiff competition against Korea and second movers like Vietnam and India, it is necessary to figure out the productivity of shipyards. The total average efficiency change from 2010 to 2013 was 1.039, increased 3.9% annually, and the total average technology change was 1.118, increased 11.8%, and the total average Malmquist index increased 17.8% annually. For the average Malmquist index from 2010 to 2013 by DMUs, the productivity of other shipbuilders except Jiangsu New Century are generally increasing. And most of the shipbuilders showed that the average productivity was improving due to a change in technology owing to technical advancement rather than a change in efficiency. The Zhoushan Shipyard showed the highest average Malmquist index, which means that the productivity was largely improved due to the improvement in the efficiency change and technology change together through management, technology and service innovation.