Estimating the Total Pollution Generation by Means of the General Relation between Two Different inverse Matrices

Ho Un Gim 한국지역학회 2000 지역연구 Vol.16 No.1

Until now, in estimating the total pollution generation resulting from economic activities, the Leontief inverse matrix of the traditional input-output model has been used. As it is well known, each element of the Leontief inverse, Cij, represents the direct and indirect output requirements to support a unit of final demand. Moreover, I verified "the general relation" between the notion of direct and indirect input requirements of commodity i to support a unit of final demand of commodity j, γ(f(ij)), and that to produce a unit of gross output of commodity j, γ(g(ij)), in the open static input-output model. Accordingly, the identical meaning cannot exist between two different notions of direct and indirect input requirements. In the same way, we can find the difference between the total requirements matrix for a unit of final demand and that for a unit of gross output. Therefore, we cannot consider two different notions as identical because there is a difference between the notion for a unit of final demand and that for a unit of gross output. The general relation easily helps us convert the Leontief inverse into the other inverse matrix expressed as a unit of output. On the basis of the issues mentioned above, the study objectives of this paper are as follows. (1) Through introducing and understanding the exact theoretical and economic meanings of the general relation, we can apply this relation to estimate another concept of the total pollution generation as an alternative method distinguished from the traditional method using the Leontief inverse. (2) We can obtain three different concepts of the total pollution generation: one from the Leontief inverse and the other two from the general relation. Through three different total amounts of pollution generation, we can analyse theoretically and empirically the impact and difference of the economic meaning between them, and then we can compare the results and findings to get the best-fitting, total pollution generation which coincides with the analysis objectives. This research is mainly limited to estimating the total pollution generation by the general relation; however, we hope and expect that the general relation between two different inverse matrices will be used in many different applications: especially in environmental and energy input-output models, intensity analysis of resources, and impact analysis for one unit of output, etc.

레온티에프 역행렬의 요인별 분해를 통한 투입,산출 승수분석: 한국 경제에 대한 사례 연구를 중심으로

김호언 ( Ho Un Gim ),김군찬 ( Koon Chan Kim ) 연세대학교 경제연구소 2011 延世經濟硏究 Vol.18 No.1

지금까지 레온티에프 역행렬 Cf(최종수요에 대한 생산유발계수행렬)을 통하여 투입·산출승수를 유도하였다. 본 연구에서는 레온티에프 역행렬의 완전한 요인별 분해를 통하여 2개의 투입유발계수행렬(Гf와 Г9)과 산출물에 대한 생산유발계수행렬(C9)을 각각 유도하였다. 이제 Cf와 3개의 새로운 유발계수행렬(C9, Гf, Г9)을 통하여 다양한 투입·산출승수를 정의하고자 한다. Cf와 Гf 행렬을 통해서는 외생적 최종수요의 변화에 대해서, C9 와 Г9 행렬을 통해서는 외생적(혹은 내생적) 산출물의 변화에 대해서 투입 및 생산유발액을 각각 구할 수 있다. 아울러 4개의 유발계수행렬이 최종수요, 생산유발액, 투입유발액 등과의 상호 의존관계를 구체적인 도형으로 도화하였다. 부가적으로 4개의 유발계수행렬에 대한 실제적 유용성을 제고하기 위하여 한국 경제에 대한 다양한 경험적 연구를 수행하였다. The Leontief inverse Cf, also termed as the output requirements matrix for final demand, gave a rise to the formulation of the ordinary input-output multipliers. In this paper, we discuss on the existence and concept of four useful input and output requirements matrices: the Leontief inverse, the output requirements matrix for output, C9, obtained from the decomposition by factors of the Leontief inverse, and two input requirements matrices Гf and Г9 for final demand and output respectively. This paper then focuses on the formulation and analysis of various input-output multipliers based on these four requirements matrices; the multipliers based on Гf and Cf measure the total requirements of changes in final demand and the multipliers based on Г9 and C9 compute the total requirements of changes in gross output. A unifying framework that describes completely how these four requirements matrices are related to inputs, output, and final demand is presented, and a comprehensive empirical analysis is performed in the Korean economy to study the difference of the effects of these newly defined multipliers.

投入模型에서의 産業聯關乘數效果에 관한 연구

金鎬彦(Gim Ho Un) 계명대학교 사회과학연구소 2010 한국사회과학연구 Vol.29 No.2

Recently, Gim and Kim(2005, 2008a, 2009) presented the following research outcomes concerned with the open static interindustry model: (1) the general relation and the complemented general relation between two different input requirements for final demand and total output(γ<SUP>f</SUP>ij and γ<SUP>g</SUP>ij), (2) the entire decomposition by factors in output and input requirements matrices(e.g., C<SUP>f</SUP>, C<SUP>g</SUP>, and Γ<SUP>f</SUP>), (3) the development of a circulation system of production between final demand f, total output χ, and final output ο and (4) the building of a new Output-Output(OO) model without having the overestimation and consecutive connection problems. On the basis of the latest research results, the specific objectives of this paper can be summarized as follows. (1) We explore the economic meanings of four useful input and output requirements matrices: two output requirements matrices for final demand and output(C<SUP>f</SUP>, C<SUP>g</SUP>) and two input requirements matrices for final demand and output(Γ<SUP>f</SUP> and Γ<SUP>g</SUP>), which are obtained from the decomposition by factors of the Leontief inverse. (2) We generalize the interindustry multiplier effects on the various cause-and-effect equations, which can compute the economically induced effects through the relationships between cause and effect variables, in the input model newly considered as an alternative model of the ordinary input-output(IO) model. (3) We examine the economic interpretations for each element and compare the differences between two direct and indirect input requirements for final demand and output(γ<SUP>f</SUP>ij and γ<SUP>g</SUP>ij), which have the different meanings of multi-sector multiplier.

"산출,산출모형"을 통한 새로운 대안적(代案的) 경제분석 방법에 관한 연구: 투입,산출모형과 비교분석을 중심으로

김호언 ( Ho Un Gim ) 연세대학교 경제연구소 2010 延世經濟硏究 Vol.17 No.2

본 연구의 목적은 ① 레온티에프 역행렬(Cf)의 요인별 분해를 통한 유발계수행렬과 유발효과 사이의 관계를 체계화하며, ② 투입·산출(IO)모형에 대한 대안적 경제분석 방법을 소개하고, ③ 대안적 방법에 대한 경제적 파급효과를 추계하는 식을 유도하는 것이라고 할 수 있다. 아울러 이를 활용한 경험적 사례연구를 통하여 개별 모형의 특성과 유용성에 대한 검정을 하는 것이다. Cf 역행렬은 I(단위행렬), A(투입계수행렬), T(기술적 간접행렬), R(연관적 간접행렬)로 요인별 분해가 되며, 이들 요인의 조합을 통하여 총 11가지 유발계수행렬과 그 경제적 의미가 밝혀지게 되었다. 유발계수행렬과 최종수요(f), 총산출(x), 최종산출(o) 사이의 새로운 생산순환체계를 통하여 IO모형, 산출·산출(OO)모형, 최종수요·최종산출 (FF)모형, 투입(I)모형에서의 인과관계와 경제적 파급효과가 규명되었다. 경험적 사례 연구에서는 최종수요와 총산출의 성장 전망은 균등성장률(k=7%)로 하여 위의 네 모형에 대한 각종 유발효과를 추계하였다. 본 연구 는 전통적인 IO모형의 한계를 보완하기 위하여 다양한 대안모형들을 개발 하였다. 이들 모형들은 상호 배타적인 관계에 있는 것이 아니고 개별 연구 목적에 따라서 상호 보완적인 활용이 가능하다. On the basis of the latest research findings, the specific objectives of this paper can be summarized as follows. (1) We formulate a complete system between the varied requirements matrices and the induced economic effects through the decomposition by factors in the Leontief inverse. (2) We develop new alternative models to the traditional Input-Output (IO) model without having overestimation and consecutive connection problems. (3) We derive the cause-and-effect equations on the newly developed alternative models to compute the varied types of induced effects. (4) We perform the empirical case study to do a comparative analysis between the IO and alternative models based on raw data of 2007 Input-Output Tables compiled by the bank of Korea.

사회복지 서비스의 경제적 효과는 COVID-19 이후 변화했는가?

임상수 서울행정학회 2024 한국사회와 행정연구 Vol.35 No.2

본 연구는 COVID-19 이후 한국의 사회복지 서비스 부문의 경제적 효과의 변화를 살펴보는 것을 목적으로 한다. 이러한 분석을 위해 본 연구는 한국은행에서 최근 발표한 2020년 실측 기준 산업연관표를 활용했다. 이러한 경제적 효과의 변화 분석을 위해 본 연구는 비중과 함께 파급효과를 분석했다. 분석 결과, 사회복지서비스 부문이 최종수요에서 차지하는 비중은 COVID-19 이후 상승했고 정부소비에 의존하는 경향이 더 커진 것으로 나타났다. 또한 사회복지서비스 부문에서 부가가치가 차지하는 비중 역시 상승하여 사회복지서비스 부문의 효율성이 개선되고 있는 것으로 나타났다. 다음으로 경제적 파급효과 분석을 위해 Leontief 역행렬과 Ghosh 역행렬을 활용하여 분석했다. 사회복지서비스 부문의 Leontief 역행렬 기준 생산유발계수는 전산업 평균, 농림수산업 평균, 제조업 평균, 서비스업 평균 수준에 미치지 못한 반면 부가가치유발계수는 COVID-19 이후 상승세가 확대되었고, 전산업 평균, 농림수산업 평균, 제조업 평균, 서비스업 평균 수준보다 높은 것으로 나타났다. 또한 Ghosh 역행렬 기준으로 산출한 사회복지서비스 부문의 생산유발계수는 COVID-19 이후 상승세가 확대되었고, 전산업 평균, 제조업 평균, 서비스업 평균 수준에 미치지 못하지만 농림수산업 평균보다 높은 것으로 나타났다. This study is trying to examine changes in the economic effects of Korea's social welfare service sector after COVID-19. For this analysis, this study used the input output table based on 2020 actual measurements recently announced by the Bank of Korea. To analyze changes in these economic effects, this study analyzed the change of the proportion and that of the inducement effect. The results of the analysis showed that the social welfare service sector's share of final demand has risen since COVID-19 and there has been a greater tendency to rely on government consumption. In addition, the proportion of added value in the social welfare service sector also increased, showing that the efficiency of the social welfare service sector is improving. Next, to analyze the economic inducement effect, the Leontief inverse matrix and the Goshian inverse matrix were used for analysis. The production inducement coefficient based on the Leontief inverse matrix in the social welfare service sector did not reach the level of the all-industry average, the agriculture, forestry and fisheries industry average, the manufacturing average, and the service industry average, while the value-added inducement coefficient showed an upward trend after COVID-19, and the all-industry average, agriculture and forestry average It was found to be higher than the fishing industry average, manufacturing average, and service industry average. In addition, the production inducement coefficient of the social welfare service sector, calculated based on the Ghoshian inverse matrix, has expanded its upward trend since COVID-19, and although it does not reach the level of the all industry average, manufacturing average, and service industry average, it is higher than the agriculture, forestry and fisheries industry average.

On the Interrelation of the Leontief Inverse with Final Demand and Total Output: Based on the Correct Consecutive Connections

김호언,김군찬 한국경제통상학회 2008 경제연구 Vol.26 No.3

In the literature especially concerning input-output multipliers, the multiplication of the Leontief inverse L = (I-A)-1 by the total output x often occurs. This paper clarifies the interrelation of L with final demand f and total output x. Specifically, we show that there is “consecutive connection” between L and x, but there is no consecutive connection between L and x; that is, L should not be multiplied by x. We give reasons why Lx does not make sense and discuss what makes practitioners and researchers to think that the Leontief inverse can be multiplied by the total output. We illustrate that overlooking such misconceptions could cause erroneous results, for instance, in the formulation of net multipliers which can accept outputs as entries.

The Decomposition by Factors and Partial Derivatives in Direct and Indirect Requirements of the Input-Output Model

Ho Un Cim 한국지역학회 2002 지역연구 Vol.18 No.3

Gim and Kim (1998) proposed the general relation between the notion of direct and indirect requirements of commodity i to support a unit of final demand of commodity j and that to produce a unit of gross output of commodity j in the open static input-output model. Recently, Gim (2000) also showed that the elements of the Leontief inverse can be decomposed into four different parts (the final demand, the direct effect, the technical indirect effect and the interrelated indirect effect) : that the elements of the total requirements matrix for a unit of final demand can be decomposed into three different parts (the direct effect, the technical indirect effect and the interrelated indirect effect) : and that the elements of the total requirements matrix for a unit of gross output can be decomposed into two different parts (the direct effect and the technical indirect effect). In this paper, we examine and show that the findings of the decomposition by factors drawn from Gim`s 2000 paper can also be expressed as the partial derivatives with respect to the final demand and gross output. Using this method, we obtained the same results as the major findings of Gim (2000). Through a practical illustration, we interpret the significance and economic meanings of the components of the partial derivative decomposition, Some useful applications are also presented for the effectiveness and validity of the decomposition by different factors in direct and indirect requirements. Therefore, we hope and expect that these results can be applied in many different areas: especially in environmental and energy input-output models, intensity analysis of resources, multiplier and impact analysis.

글로벌 공급망 충격의 경제적 파급효과 분석: 희토류 및 천연가스를 중심으로

조무상,노현숙,권이남,박완 조선대학교 지식경영연구원 2024 기업과 혁신연구 Vol.47 No.2

본 연구는 글로벌 공급망 충격이 우리 경제에 어떠한 파급효과를 야기하는지 평가할 수 있는 분석틀을 마련하는 것을 목적으로 한다. 경제안보의 관점에서 위험도가 높은 희토류와 천연가스를 분석대상 산업으로 선정하고 OECD의 국제투입산출표를 KITA의 수입데이터 등 관련 자료와 연계한 자료를 이용하여 국제산업연관분석 방법론을 통해 공급망 충격의 경제적 파급효과를 분석한다. 공급망 충격은 중간재 투입의 감소를 의미하므로 중간재를 포함하는 총투입을 충격벡터로 이용하는 외생화 공급유도형 모형을 적용한다. 분석결과, 최근 10년간의 수입현황 분석을 통해 추정된 공급망 충격금액 대비 희토류의 전·후방연계효과는 각각 2.99배와 2.89배인 반면 천연가스의 전·후방연계효과는 각각 2.68배와 0.16배로 나타났다. 이러한 결과는 희토류의 공급망 충격이 국내산업에 미치는 영향은 크고 넓게 나타날 수 있는 반면, 천연가스의 공급망 충격은 수요유도형 모형에서는 과소평가되므로 외생화 공급유도형 모형이 적절한 분석방법임을 시사한다. 또한 본 연구의 분석틀은 국가 및 품목을 특정한 다양한 시나리오별로 분석할 수 있다는 장점이 있다. This study aims to provide an analytical framework for assessing the impact of global supply chain shocks on the Korean economy. Rare earths and Natural gas, which are high-risk industries from the perspective of economic security, are selected to be analyzed, and the economic impact of supply chain shocks is analyzed using Input-Output analysis methodology by linking related data such as the OECD's international input-output table and import data from the Korea International Trade Association. As supply chain shocks imply a decrease in intermediate inputs, we apply an exogenous Ghosh Inverse matrix model that uses total inputs, including intermediate inputs, as the shock vector. As a result, the backward and forward linkage effects of Rare earths are 2.99 times and 2.89 times, respectively, compared to the size of supply shocks estimated by analyzing imports over the past 10 years. But, for Natural gas, the effects are 2.68 times and 0.16 times. These results suggest that the supply chain shocks of Rare earths can have a large and far-reaching impact on domestic industries, while the supply chain shocks of natural gas are underestimated in the demand-driven model, suggesting that the exogenous Ghosh Inverse matrix model use applied is an appropriate analysis method. The analytical framework of this study also has the advantage of being able to analyze different scenarios across countries and commodities.

레온티에프 역행렬의 최종수요 및 산출물과의 상호 의존관계

김호언 ( Ho Un Gim ),김군찬 ( Koon Chan Kim ) 한국경제통상학회 2008 경제연구 Vol.26 No.3

동북아 역내 제조업의 글로벌 공급망 변화와 특징 분석: 한중일을 중심으로

吉元浩二,이홍배 한일경상학회 2022 韓日經商論集 Vol.97 No.-

Purpose: This paper analyzes how the manufacturing supply chain has changed over the past 20 years according to the trilateral division of labor between Korea, China and Japan. Also, by measuring changes in the trade structure and competitiveness between Korea, China and Japan during the same period, the effect on the changes in the supply chain between the three countries is examined. Research design, data, and methodology: This study analyzes the trade structure, export competitiveness, and supply and distribution structure of 10 manufacturing industries in Korea, China and Japan. The analysis period was set from 2000 to 2020. The statistics use the UN Comtrade and the Asian International Input-Output Table. In the analysis of the trade structure between Korea, China and Japan. The Revealed Symmetric Comparative Advantage (RSCA) index was introduced to analyze the trade structure between Korea, China and Japan. And for the supply chain structure between the three countries, the Leontief inverse multiplier decomposition of the International Input-Output Analysis was used. Results: As a result of the analysis, it was observed that the supply chain of the manufacturing industry between Korea, China and Japan has changed to an interdependent structure since 2010, and the reason for this is that the production technology gap between the three countries has been greatly reduced. Accordingly, the supply chain of the manufacturing industry between the three countries has shifted from the past one-way dependence structure to a two-way dependence structure. In terms of industry, the deepening dependence among the three countries centered on electrical/electromechanical machinery, metal products, general machinery, chemical products, transportation machinery, precision machinery and textile products, which are key export industries for both Korea, China and Japan, means that the supply and distribution structure is being strengthened. Implications: Considering the relationship between the supply chain between Korea, China and Japan from 2000 to 2020, institutional integration, such as the trilateral FTA, is delayed, but functional integration is deepening due to interdependence and complementarity and increased production and trade. However, if trade frictions or disputes between Korea, China and Japan occur between specific countries, it is interpreted that this can lead to negative effects, so-called big losses, not only for the country concerned but also for the other country.