효율성추정과 확률적 생산변경모형에 대한 문헌연구

곽만순(ManSoon Kwack),이영훈(Young Hoon Lee) THE KOREAN ECONOMIC SOCIETY 2005 JOURNAL OF ECONOMIC THEORY AND ECONOMETRICS Vol.16 No.4

본 논문은 확률적 생산변경모형(stochastic production frontier model)에 관한 문헌을 정리하여 소개한다. 효율성 추정에 관한 실증연구에 응용이 되도록 데이터의 종류별로 적합한 계량모형을 고찰한다. 패널자료의 경우 시계열이 긴 자료와 횡단면 관찰치가 많은 자료가 있는데 각각의 경우에 적합한 모형을 심도있게 분석한다. 특히 패널자료를 이용한 확률적 생산변경모형 중 효율성의 평균을 추정하는 '시간불변모형'과 개별 기업의 효율성의 변동패턴을 추정하는 '시간변동모형'을 구분하여 고찰한다. The concept of efficiency is essential to measuring the firm performance. The literature provides a range of methodologies for estimation of efficiency. The purpose of this study is to review stochastic frontier production models and to offer a comparison between established models. The discussion is not exhaustive, but to be up-todate and to provide a significant discussion on stochastic frontier models with panel data.

기술적 비효율성의 오지정이 확률변경모형의 최대가능도 추정에 미치는 영향

양호진(Hojin Yang),이종민(Jongmin Lee),이동혁(Donghyuk Lee) 한국자료분석학회 2023 Journal of the Korean Data Analysis Society Vol.25 No.5

확률변경모형은 투입된 생산요소 대비 산출되는 생산량의 효율성을 평가하기 위하여 널리 사용되는 계량경제학적 모형으로 실제 생산량이 최적 생산량보다 작은 현상을 기술적 비효율성이라는 개념을 도입하여 설명하는 모형이다. 통계학적으로 확률변경모형은 오차항이 정규분포인 일반적인 회귀모형에 기술적 비효율성을 나타내는 음이 아닌(non-negative) 확률변수를 뺀 형태로 구성되며 오차항과 비음의 특정한 확률변수의 차이로 정의되는 합성오차의 분포를 계산하여 최대가능도 추정방법으로 모수들을 추정한다. 하지만 근본적으로 기술적 비효율성은 관측이 불가하기 때문에 특정 확률분포를 가정해야 하므로 잘못된 분포를 가정하여 모형을 적합하게 되는 오지정(misspecification) 문제가 쉽게 발생하게 된다. 본 연구에서는 확률변경모형에서 기술적 비효율성이 오지정된 경우 오지정된 모형의 최대가능도 추정량들이 수렴하는 값들을 살펴보고자 한다. 오지정된 모형의 최대가능도 추정량들은 오지정된 모형과 참모형의 쿨백-라이블러 괴리도(Kullback-Leibler divergence)를 최소화하는 값으로 수렴하는 것을 이용하여 확률변경모형에서 이들을 계산하고, 모의실험을 통하여 확인하고자 한다. 이를 통하여 기존 문헌에서 언급된 기울기 모수들의 최대가능도 추정량이 기술적 비효율성의 분포와 관계없이 비슷하게 얻어지는 현상을 설명하고자 한다. The stochastic frontier model is a widely used econometric method for assessing production efficiency concerning the maximum achievable output given a specific input, where the difference between the maximum and actual production is referred to as technical inefficiency. Statistically, the stochastic frontier model adjusts a standard regression model with normally distributed errors by introducing a non-negative random variable to account for technical inefficiency. By computing the probability density of the composed error, which defined by subtracting the non-negative random variable from the normal error, the maximum likelihood estimators (MLE) for the stochastic frontier model can be obtained. In principle, the technical inefficiency cannot be directly observed so that the distributional assumption is necessary to fit the model. Consequently, it is common to encounter model misspecification problem, which involves inaccurate assumption of the distribution of technical inefficiency. This research aims to explore limiting behaviors of the MLE in the stochastic frontier model under misspecified technical inefficiency distribution. We also investigate the minimizers of the Kullback-Leibler divergence between the true and misspecified model, wherein the MLE obtained from the misspecified model converges. Subsequently, we employ Monte Carlo experiments to examine the finite sample performance and to explain the similarity of MLE for slope parameters regardless of the distributional assumption of technical inefficiency as mentioned in the previous studies.

Stochastic Frontier Models for Temporal Patterns of Technical Efficiency

Lee, Young-Hoon 한국생산성학회 1999 THE JOURNAL OF PRODUCTIVITY Vol.5 No.1

This paper compares the three stochastic frontier models with time-varying technical efficiency which differ to a great extent in specification and estimation; Cornwell, Schmidt, and Sickles(1990, CSS), Battese and Coelli(1992, BC), and Lee and Schmidt(1993, LS). For Monte Carlo experiments, we generate the data sets of technical inefficiency by CSS, BC, and LS specifications with different sample size combinations of cross-section and time-series(N/T) and different variance-ratios of an inefficiency and a statistical noise(σu/σv). The Monte Carlo results indicate that the LS model provides with the most robust estimator. The LS estimates outperform the CSS and BC estimates when the LS-type data are used. In many cases, the LS model performs more or less equal to or better than the other models even when CSS or BC-types of data used. The LS model also seems to have the properties that it fits especially well with panel data of a large N and a small T and that it estimates relative technical inefficiency significantly better than the other models. The BC estimator is relatively insensitive to changes in a sample size combination and changes in variance-ratio. On the other hand, the CSS model is sensitive to changes in variance-ratio(σu/σv) so that it performs relatively better when (σu/σv) is high.

농가 이질성과 생산기술효율성: 베이지안 확률경계분석

권오상 ( Oh-sang Kwon ),조현경 ( Hyunkyoung Cho ) 한국농업경제학회 2020 農業經濟硏究 Vol.61 No.4

This study constructs a multiple error component Bayesian stochastic frontier model to analyze production efficiencies of Korean farm households incorporating farm heterogeneity. A sampled data set of 400 farms for the period 2008-2012 is used. The analysis combines a Bayesian random effect multilevel/hierarchical model with a panel data stochastic frontier model. The results show that the usual SFA models without incorporating producer heterogeneity substantially over-estimate the level and dispersion of farm technical inefficiencies. It is also found that incorporating producer heterogeneity into the production frontier reduces the contribution of technical efficiency change to productivity change significantly. The study identifies the sources of frontier heterogeneity using the constructed multiple error component Bayesian SFA model.

Application of the Information Matrix Test on the National Productivity Analysis as the Cause of International Trade

Dong-Joo Lee 한국무역연구원 2021 무역연구 Vol.17 No.6

Purpose In order to analyze the national competitiveness of the Korean economy, it is necessary to estimate the total factor productivity correctly, because incorrect assumptions in the model can lead to serious estimation errors. Therefore, in order to estimate the suitability of the model, an information matrix test was proposed as an applicable method to the actual stochastic frontier production function. Design/Methodology/Approach We first examine the large sample distribution properties of maximum likelihood estimation (MLE) and quasi-maximum likelihood estimation (QMLE), and introduce several versions of the stochastic frontier product function models proposed by different scholars. Finally, we derive the Information Matrix Test (Battese and Coelli, 1992) for the stochastic frontier production function model. Also, a Monte Carlo simulation was applied to verify the correctness of the model. Findings From the results, we derive an analytical form of the Information Matrix Test (Battese and Coelli, 1992) on the stochastic frontier production function model using the simplified form proposed by Lancaster (1984). and as a result of empirical analysis by applying this process to each of the seven countries (Korea, China, Japan, the United States, United Kingdom, Germany, France), each  value was below the 95% significance level in all countries, indicating that the translog production function model was specified correctly. Research Implications The Information Matrix Test by White (1982) is an important solution for misspecified regression models. To solve this issue, Lancaster (1984) suggested the simpler form of the Information Matrix Test of White (1982). However, this method is also complex to apply in a real model. Therefore, until now, the Information Matrix Test has not been properly implemented in a regression model. This study presents an analytical form of the Information Matrix Test for the stochastic frontier production function, which is very important for analyzing national, industrial, and corporate competitiveness.

Robust estimation in stochastic frontier models

Song, J.,Oh, D.h.,Kang, J. North-Holland Pub. Co ; Elsevier Science Ltd 2017 Computational statistics & data analysis Vol.105 No.-

This study proposes a robust estimator for stochastic frontier models by integrating the idea of Basu et al. (1998) into such models. It is shown that the suggested estimator is strongly consistent and asymptotic normal under regularity conditions. The robust properties of the proposed approach are also investigated. A simulation study demonstrates that the estimator has strong robust properties with little loss in asymptotic efficiency relative to the maximum likelihood estimator. Finally, a real data analysis is performed to illustrate the use of the estimator.

확률변경모형(Stochastic Frontier Model)을 이용한 공공병원의 기술적 비효율성(Technical Inefficiency) 분석

양동현 ( Dong Hyun Yang ),장영재 ( Young Jae Jang ),노재확 ( Jae Whak Rho ) 한국보건경제정책학회 2012 보건경제와 정책연구 Vol.18 No.4

This analysis studied on the technical inefficiencies of regional public hospitals using a stochastic production frontier model. For the empirical analysis the five year data from 2005 to 2009 of 32 regional public hospital data are used. The main focuses are given to reveal whether the technical inefficiency are improved as time goes by, and what is the prior causes of inefficiencies, if there exists. The results can be summarized as follows; First, the proper production model is the 5 elements translog production function rather than the simple labor and capital Cobb-Douglass production model. Second, the technical efficiency of in-patients has not being improved for the considered time of periods. Our findings have some policy implications. In case of in-patients, it is confirmed that there exists some inefficiencies, and those inefficiencies can not be overcome through just improving the inner management system. Rather than, the fact that the business environments which can be upgraded by the policy are needs to be improved is revealed.

COMPARISON OF STOCHASTIC FRONTIER APPROACHES FOR ESTIMATING NATIONAL EFFICIENCY: AN APPLICATION TO SUB-SAHARAN AFRICAN COUNTRIES

MICHAEL DANQUAH,BAZOUMANA OUATTARA 중앙대학교 경제연구소 2018 Journal of Economic Development Vol.43 No.3

In this paper, we attempt to estimate pure national (technical) efficiency for 19 SSA countries over the 1960-2010 periods. In doing this, we compare conventional stochastic frontier models for panel data with a number of recently developed models which seek to control for unobserved heterogeneity in the inefficiency component. We find that the ‘true’ random effects model that treats unobserved heterogeneity in our national dataset generates more reasonable efficiency estimates. Moreover the results confirm that most SSA countries operate far from the efficient frontier.

R&D와 생산효율성 관계에 관한 계량모형 비교연구 : 확률적 생산변경모형을 중심으로

이영훈 한국은행 2011 經濟分析 Vol.17 No.1

연구개발 및 정부의 연구개발지원의 성과에 대한 실증연구결과의 중요성에도 불구하고 연구개발투자의 생산성에 대한 영향을 분석하는 계량모형에 관한 논의는 상대적으로 활발하지 않았다. 본 연구에서는 연구개발투자의 생산성에 관한 기존 실증분석연구에서 활용한 계량모형들을 비교하여 모형의 장단점을 논하며 최근 발전된 관련 계량모형을 논함으로써 향후 응용연구에서 모형설정에 필요한 정보를 제공하고자 한다. 특히 기존 연구에서 가정하였던 연구개발투자와 생산성의 관계에 단조성을 완화하여 비단조성을 추정할 수 있는 모형을 소개하고 이를 기반으로 단조성 가정에 대한 검정방법을 논한다. 광공업통계DB에 있는 기업자료 및 OECD국가 패널자료에 논의한 계량모형을 적용함으로써 모형특성의 차이에 따른 추정결과의 차이점을 논한다. This paper intends to provide applied economists which study the effects of research and development with valuable information on econometric model selection. It includes extensive discussion on econometric models which have been applied for the study on the relationship between research and development and productivity. In particular, it compares various stochastic production frontier models which have been developed recently. The discussion decomposes them into models with scaling property and the ones with nonscaling property as well as models with monotonic and nonmonotonic relationships between research and development and productivity. Finally, this paper applies the models to two different panel data sets (firm level data and country level data) and compare estimation results from competing econometric models.

문화적 거리가 한국 무역에 미치는 영향: 확률적 변경 중력 모형을 기반으로

곡만군,임형록 국제지역학회 2023 국제지역연구 Vol.27 No.3

글로벌 통합이 지속적으로 진행됨에 따라 문화는 한국 무역 발전에 영향을 미치는 중요한 요소가 되었다. 본 논문에서는 문화적 거리를 착안점으로 하여, 한국과의 무역량이 비교적 많은 43개 국가와 지역의 2005-2019년 데이터를 확률적 변경 중력 모형(Stochastic Frontier Gravity Model, SFGM)에 따라 분석함으로, 문화적 거리가 한국의 무역에 미치는 영향에 대해 연구하였다. 실증 결과 다음과 같은 점들을 알 수 있게 되었다. 첫째, 문화적 거리와 한국의 무역액은 역U자형의 관계에 있다. 둘째, 한국의 1인당 GDP, 무역국의 1인당 GDP, 무역국의 인구, 무역국과 한국의 FTA 체결 여부, 무역국의 APEC 가입 여부, 무역국의 무역 자유도, 품질 규제와 정부 기능에 관한 점수 등과 같은 요소는 모두 한국의 무역액과 양의 상관관계를 나타낸다. 셋째, 한국은 전반적으로 무역 효율이 높지 않고 무역 효율의 국가별 차이가 크므로 발전할 수 있는 잠재력이 비교적 크다. 따라서 본 논문은 국가 차원과 기업 차원에서에서 제안을 하였다. With the continuous development of the global integration process, culture has become an essential factor affecting the development of Korea's trade. This paper uses cultural distance as the entry point, investigating the impact of cultural distance on Korea's trade based on the data of 43 countries and regions with which Korea has a large trade volume from 2005-2019, using a stochastic frontier gravity model. The empirical results show that: 1. Cultural distance has an inverted U-shaped relationship with Korea's trade volume 2. GDP per capita of Korea, GDP per capita of trading countries, the population of trading countries, the signing of FTA between trading countries and Korea, joining of APEC by trading countries, trade freedom, regulatory quality, and government effectiveness scores of trading countries have a positive relationship with Korea's trade volume; geographical distance between the two countries, financial freedom of trading countries have a negative relationship with Korea's trade volume 3. Korea's overall trade efficiency is not high, the trade efficiency gap between countries is large, and Korea's trade efficiency has great potential for development. The paper concludes with policy recommendations at the national and enterprise levels, respectively.