誘發係數行列과 부문 사이의 連續的 連結

金鎬?(Gim Ho Un) 계명대학교 사회과학연구소 2008 한국사회과학연구 Vol.27 No.1

Gim and Kim(1998, 2005, 2008a, 2008b), recently, presented the following research results: (1) the general relation and the complemented general relation between two different notions of total input requirements(r<SUP>f</SUP>ij and r<SUP>g</SUP>ij), (2) the decomposition by factors in the Leontief inverse C<SUP>f</SUP>, and (3) the circulation system of production between final demand(f), total output(x), and final output(o). From the latest research findings above, the study objectives of this paper can be summarized as follows. (1) We clarify the exact economic meanings of consecutive connections between sectors, and between cause and effect variables. (2) We examine the relation between output and input requirements matrices as multi-sector multipliers and consecutive connections, (3) We propose the criteria necessary to estimate various induced effects in the models of Input-Output(IO), Output-Output(OO), and Final demand-Final output(FF) on the basis of consecutive connections. The major findings from the analysis include: (1) In the Input-Output model, it is obvious that there is consecutive connection between the Leontief inverse C<SUP>f</SUP> and the final demand f, but that there is no consecutive connection between the inverse C<SUP>f</SUP> and the total output x. And also the product (I-A)C<SUP>f</SUP> is consecutively connected between the sectors, but the expression C<SUP>f</SUP>(I-A) is not consecutively connected although it has no problem mathematically. (2) In the Output-Output model, it is proved that there is consecutive connection between the output requirements matrix for output C<SUP>g</SUP> and x, but that there is no consecutive connection between the inverse C<SUP>g</SUP> and f. (3) In the Final demand-Final output model, it is also verified that there is consecutive connection between the output requirements matrix for final demand of final output C<SUP>gf</SUP> and f, but there is no consecutive connection between the matrix C<SUP>gf</SUP> and x.

A Study on the Requirements Matrix through the Concept of “Correct Consecutive Connections”

Gim, Ho Un(김호언) 한국산업경제학회 2015 산업경제연구 Vol.28 No.3

Gim and Kim (1998)은 투입ㆍ산출(IO)모형에서 서로 다른 두 종류의 직ㆍ간접 투입요구량(Γ<SUP>f </SUP>행렬의 원소 γij<SUP>f</SUP>와 Γ<SUP>g</SUP> 행렬의 원소 γ ij<SUP>g</SUP>) 사이에 존재하는 수리적(혹은 경제적) 일반적 관계를 처음으로 규명하였다. 그러나 Sancho (2012)는 Gim and Kim (1998)의 연구 결과에서 나타나는 부문 사이에서 존재하는 연속적 연결(consecutive connections)의 문제를 지적하였다. 다만 Sancho (2012)의 이러한 언급에 앞서서 Gim and Kim (2005, 2008a, 2008b, 2009)은 매우 지속적인 다양한 후속 연구를 수행하였다. 이를테면 (1) 유발계수행렬이 4가지(I, A, T, R) 요인별 행렬로 분해가 이루어지며, (2) 부문 사이에 존재하는 “올바른 연속적 연결” 개념을 통하여두 직ㆍ간접 투입요구량 사이에 존재하는 “보완된 일반적 관계”(complemented general relation)를 새롭게 증명하였다. 아울러 이러한 연구 결과를 다양한 분야에 경험적으로도 활용하였다. 이제 새롭게 밝혀진 “보완된 일반적 관계”를 통하여, (1) 두 개념(Γ<SUP>g</SUP> 행렬의 원소 γij<SUP>g</SUP>와 레온티 에프 역행렬(C<SUP>f</SUP>)의 대각항의 원소 cjj<SUP>f</SUP>) 사이에는 연속적 연결이 잘 이루어지며, (2) 또한 두 행렬의 원소를 곱한 형태 γij<SUP>g</SUP> cjj<SUP>f</SUP>는 경제학적으로도 그 의미가 분명하게 밝혀지게 되었다. 더욱이 레온티에프 역행렬(C<SUP>f</SUP>)의 요인별 분해를 통하여 유발계수행렬 체계를 일반화함으로써(<그림 1> 참조) 새로운 산출ㆍ산출(OO)모형과 최종수요ㆍ최종산출(FF) 모형을 각각 유도할 수 있게 되었다. 뿐만 아니라 세 모형(IO, OO, FF)에서 “올바른 연속적 연결” 개념이 각각 어떻게 적용되는지를 상호 비교 분석하였다. 이와 같이 새롭게 개발된 OO모형과 FF모형을 활용하여 전통적인 IO모형에서는 전혀 분석할 수 없었던 다양한 인과변수 사이의 의존관계와 파급효과 등도 손쉽게 분석할 수 있게 되었다. Sancho (2012) showed that the first general relation between two different notions of direct and indirect input requirements (γij<SUP>f</SUP> and γ ij<SUP>g</SUP>), proposed by Gim and Kim (1998), is actually faulty. However, Gim and Kim (2005, 2008a, 2008b, 2009), prior to Sancho’s comment, verified continuously the requirements matrices can be decomposed by factors and also proposed the complemented general relation on the basis of the correct consecutive connection. Through the complemented general relation, we definitely point out that there is a “consecutive connection” between γij<SUP>g</SUP> and cjj<SUP>f</SUP> and moreover the product γ ij<SUP>g</SUP> cjj<SUP>f</SUP>makes sense economically, where cjj<SUP>f</SUP> is the diagonal element of the Leontief inverse. By using a complete framework of the requirements matrices, we can finally derive a new output-output (OO) and final demand-final output (FF) models, which are of great use in calculating the various impacts among the assorted cause and effect variables.

“연속적 연결” 개념을 고려한 기간산업 지표 개발에 관한 연구 : IO, OO, FF모형을 통한 산업연관효과를 중심으로

김호언(Gim, Ho Un),이춘근(Lee, Choon Keun) 한국지역개발학회 2021 韓國地域開發學會誌 Vol.33 No.1

Essentially, the concept of the correct consecutive connections, originally proposed by Gim and Kim(2008a), must be satisfied in the area of interindustry analysis such as balance equations, solutions of the equations, matrix products, etc. For instance, it is clear that there is a consecutive connection between the total output requirements matrix or the Leontief inverse and the final demand , but that there is no consecutive connection between the total requirements matrix and the total output in the solution of the IO model; that is, should not be multiplied by. On the basis of the latest research findings and results on the development of key industry indicators, the specific objectives of this paper can be summarized as follows. (1) We review the traditional measures introduced by Rasmussen(1957) to verify key sectors in interindustry analysis. And then, we can get a more accurate indicator to reflect the economy-wide effects of key industries. (2) We critically introduce the major critics’ arguments which were pointed out by many researchers, so far, in key industry indicators. (3) By using the concept of net backward linkage, we newly propose the net key sector, which is more meaningful and practicable in the models of IO, OO, and FF. Moreover, the numerical illustrations have been done to examine the validity of the net key industry indicator.

産業聯關模型에서 經濟的 波及效果의 過大推定은 왜 發生하는가? 새로운 “産出?産出模型”을 통한 代案을 中心으로

김호언 한국경제학회 2008 經濟學硏究 Vol.56 No.1

The concept of net multipliers, as introduced by Oosterhaven and Stelder(2002), accepts outputs as entries instead of final demand to avoid the overestimation of the importance of the sector at hand. However, this new concept only makes the real meaning of the multipliers meaningless and trivial. It was clearly shown by Gim(2007) and de Mesnard(2007) that net multipliers have the homogeneous characteristics with no causal relation between the cause(endogenous or exogenous outputs) and the effect(total output requirements). And also it is obvious that there is “consecutive connection” between the Leontief inverse [기호] and the final demand f, but that there is no consecutive connection between the inverse [기호] and the total output x. The primary aim of this paper is to present a clear interrelation of the Leontief inverse with final demand and total output and to propose another alternative input-output multipliers based on “the output-output model,” developed by the author, which can solve overestimation and consecutive connection problems naturally together. I hope that the findings and results obtained from the output-output model can also be utilized in many different input-output areas. 개방형 정태 투입·산출모형에서 레온티에프 역행렬은 외생적인 최종수요 변화 에 대한 내생부문의 (직·간접)산출요구량을 추계하는 데 매우 유익하게 사용되 고 있다. 그러나 최종수요가 아니라 산출물의 변화에 대한 (직·간접)산출요구량 을 계산하기 위하여 레온티에프 역행렬을 그대로 사용하게 되면 내생 중간수요에 대한 이중 계산으로 경제적 제반 파급효과가 과대추정된다는 사실이 밝혀지게 되 었다. 본 논문에서는 우선적으로 “파급효과의 과대추정은 왜 발생하는가?”에 대해 서 원인 규명을 하고자 한다. 최근 이러한 과대추정에 대한 대안적 승수로 개발된 “순승수” 개념의 한계와 부문 사이의 “연속적 연결”의 문제를 집중적으로 분석하고 자 한다. 아울러 경제학 문헌에서 나타나고 있는 파급효과에 대한 과대추정 및 연 속적 연결에 대한 오해 사례를 제시하고자 한다. 이러한 실제적 오해 사례에 대한 새로운 대안 모형으로서 “산출·산출모형”을 개발하고자 한다. 산출·산출모형은 레온티에프 역행렬의 요인별 분해를 통하여 총산출과 최종산출 사이의 새로운 승 수적 인과관계를 밝힌 것이다. 따라서 산출·산출모형을 통하여 산출물에 대한 제반 파급효과를 과대추정 및 연속적 연결에 대한 우려없이 편리하게 추계할 수 있게 되었다.

A Study on the Requirements Matrix through the Concept of “Correct Consecutive Connections”: Based on the Three Different Models of IO, OO, and FF

김호언 한국산업경제학회 2015 산업경제연구 Vol.28 No.3

Sancho (2012) showed that the first general relation between two different notions of direct and indirect input requirements ( and ), proposed by Gim and Kim (1998), is actually faulty. However, Gim and Kim (2005, 2008a, 2008b, 2009), prior to Sancho’s comment, verified continuously the requirements matrices can be decomposed by factors and also proposed the complemented general relation on the basis of the correct consecutive connection. Through the complemented general relation, we definitely point out that there is a “consecutive connection” between and and moreover the product makes sense economically, where is the diagonal element of the Leontief inverse. By using a complete framework of the requirements matrices, we can finally derive a new output-output (OO) and final demand-final output (FF) models, which are of great use in calculating the various impacts among the assorted cause and effect variables.

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.

산업연관분석(産業聯關分析)과 부문 사이의 연속적(連續的) 연결(連結): 두 투입요구량(投入要求量) 사이의 보완된 일반적(一般的) 관계(關係)를 중심으로

김호언 ( Ho Un Gim ) 한국경제통상학회 2008 경제연구 Vol.26 No.1

유발계수행렬에서 발생하는 추정오차 문제에 관한 연구: IO, OO, FF모형을 통한 과대추정을 중심으로

김호언 ( Ho Un Gim ),이춘근 ( Choon Keun Lee ) 경남대학교 산업경영연구소 2018 지역산업연구 Vol.41 No.2

투입·산출(IO)모형이 갖는 연속적 연결의 문제와 순승수 개념의 한계를 동시에 해결하기 위하여 레온티에프 역행렬(C^f)의 요인별 분해가 이루어지게 되었다. 유발계수행렬을 통하여 각종 경제분석(승수효과, 연관효과, 파급효과 등)을 수행할 때에 원인변수와 결과변수 사이의 논리적 인과관계에서 연속적 연결이 되지 않는 경우 심각한 추정오차가 발생하게 된다. 최근 유발계수행렬에 대한 다양한 논의와 연구 성과에 대하여 유념하면서 다음과 같은 연구 목적을 설정하고자 한다. (1) 산업연관분석의 유발계수행렬에서 나타나는 추정오차 문제의 본질을 경제 이론 및 경험적 분석 측면에서 규명하고자 한다. (2) 여러 형태의 추정오차가 발생하는 구체적인 사례를 투입·산출(IO)모형, 산출·산출(OO)모형, 최종수요·최종산출(FF)모형을 통하여 제시하는 것이다. (3) 개별 유발계수행렬을 통한 인과관계식에서 나타나는 추정오차를 실제 경험적 자료를 통하여 추계하고자 한다. 연구 범위와 선행 연구와 구별되는 본 논문의 차별적인 성격은 다음과 같다. (1) 다양한 인과변수 사이에서 존재하는 추정오차는 과대추정과 과소추정으로 대별하여 분석할 수 있지만, 본 연구에서는 우선적으로 과대추정 문제를 집중적으로 다루고자 한다. (2) IO모형의 균형식, OO모형의 균형식, FF모형의 균형식을 토대로 하여 추정오차를 분석하는데 연구의 주안점을 두는 것이다. (3) 세 모형(IO, OO, FF)에서 총산출 증분(△x)과 최종산출 증분(△o)에 따른 이중계산, 과대추정, 과대추정 비율 등을 실제로 추계하는데 본 과제의 차별성을 부여할 수 있다. 경험적 연구를 위한 기초 자료는『2013년 산업연관표』30기본부문으로 하였다. 개별 분석 모형에서 추정오차가 발생하는 구체적인 사례는 다음과 같다. (1) 투입·산출모형에서는 외생적인 최종수요(△f) 대신에 총산출(△x)을 C^f역행렬에 후승하게 되면, (2) 산출·산출모형에서는 외생적 총산출(△x) 대신에 최종산출(△o)을 C^g역행렬에 후승하게 되면, (3) 최종수요·최종산출 모형에서는 외생적 최종수요(△f) 대신에 최종산출(△o)을 C^gf행렬에 각각 후승하게 되면, 경제변수 사이의 연속적 연결도 되지 않으며 이중계산에 의한 과대추정이 존재하게 된다. Specifically, we show that there is a consecutive connection in the interrelation of intersectoral interdependence between elements in the Leontief inverse L = (I-A)^-1=C^f and final demand f, but there is no consecutive connection between elements in L and total output x. Through the exact concept of consecutive connection, we then introduce the four requirements matrices in the models of input-output (IO) and output-output (OO): the two input requirements matrices Γ^f and Γ^g for final demand f and gross output x and the two output requirements matrices C^f and C^g for final demand f and total output x, respectively. On the basis of the latest research findings and results from the decomposition by factors in the Leontief inverse L and the buildings of models without having the estimation error and consecutive connection problems, the specific objectives of this paper can be briefly summarized as follows. (1) We primarily clarify the nature of estimation error problem, in all its aspects, especially in economic theory and empirical analysis, which occur in the various requirements matrices of interindustry analysis. (2) We secondly illustrate the specific examples of estimation error in the different double countings based on the consecutive connections between the intersectoral relations through the diverse cause and effect models of IO, OO, and FF. (3) We empirically calculate the varied estimation errors happen in the cause-and-effect equations drawn from each requirements matrix based on a new circulation system of production in the three economic variables (final demand f, total output x, and final output o). The basic data for computing estimation error is the 2013 national IO tables compiled by the BOK on the basis of 30 endogenous sectors of the Korean economy.

산출물에 대한 生産誘發係數行列의 經濟的 含意에 관한 연구

金鎬彦(Gim Ho Un) 계명대학교 사회과학연구소 2009 한국사회과학연구 Vol.28 No.2

Most recently, the authors (Gim and Kim, 2009) showed the following research outcomes concerned with the Input-Output (IO) model and table pioneeringly developed by W. Leontief in the early 1930s: (1) the general relation and the complemented general relation between two different input requirements for final demand and total output, (2) the entire decomposition by factors in output and input requirements matrices, and (3) the consecutive connection and overestimation problems in the inter-industry model. Moreover, we found out that there is no consecutive connection between the Leontief inverse matrix C<SUP>f</SUP> and the total output x and that there are some limits to computing the impact effects of the initial change in output. Finally, we developed a new??Output-Output(OO) model??and compiled a new??Output-Output table??to solve the problems and limits in the IO model together through the output requirements matrix for output C?. On the basis of the latest research findings, the specific objectives of this paper can be summarized as follows. (1) We closely examine into the characters and characteristics of the OO model used as an alternative to the IO model. (2) We test the consecutive connection problem, in the interpretation of inter-sectoral interdependence, in the OO model between the output requirements matrix C?, the total output x, and the final demand f. (3) We derive the varied economic interpretations and implications from the inverse matrix C?. Therefore, we truly understand that the IO and OO models are not completely separate or independent even though they differ essentially on the impact (the initial change on final demand vs. total output).

새로운 “産出ㆍ産出表” 作成은 왜 필요한가?

김호언(Gim, Ho-Un) 한국지역개발학회 2008 韓國地域開發學會誌 Vol.20 No.1

The complemented general relation between two different notions of direct and indirect input requirement(γ<SUP>f</SUP>ij and γ<SUP>g</SUP>ij) and the decomposition of factors in the output requirements matrix for final demand C<SUP>f</SUP> were proposed by Gim and Kim(2005, 2008). Furthermore we showed that there is consecutive connection between the Leontief inverse C<SUP>f</SUP> and the final demand f, but there is no consecutive connection between C<SUP>f</SUP> and the total output x. From the research results above, the study objectives of this paper can be summarized as follows. (1) We develop an alternative "Output-Output(OO) model" without having overestimation and consecutive connection problems and compile a new "Output-Output table" on the basis of the OO model to analyse the various economic impacts. (2) We make a comparative study between the input-output table and the output-output table for the complementary using. For the performance of the empirical illustration, we consider an economy with 5 sectors which has been obtained by reaggregating the 28 basic sectors given in the 2003 Input-Output Tables of Korea. Moreover as a specific example for the usefulness of the OO model and table, we formulate the OO multipliers, corresponding to input-output multipliers, that can accept output as an initial change.