연쇄지수에 의한 실질 경제성장률과 GDP의 가법분해
Additive decomposition of economic growth rate and real GDP by chain index
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기술발전의 가속화로 가격구조의 변동성이 증대됨에 따라 기존의 고정가중법에 의한 실질 국내총생산(GDP) 추계는 현실을 제대로 반영하지 못하는 한계를 보이기 시작하였다. 이에 1996년 미국과 캐나다는 실질 국내총생산(GDP)의 추계에 연쇄지수 (chain index)를 도입하였으며 이후 대부분 OECD 국가들도 연쇄지수 방법을 채택하였다. 우리나라는 2009년 3월부터 Laspeyres 연쇄지수에 의한 실질 GDP를 공표하였다. 그러나 기존 문헌들에는 연쇄지수 방법에 대한 이론적 설명이 부족하며 실질 GDP 와 부문별 실질 부가가치의 합이 일치하지 않는 비가법성(non-additivity)의 문제가 남아있다. 본고는 연쇄지수의 필요성을 경제학적 지수이론의 이론모형과 Divisia 적분지수(integral index) 간의 관계 및 Divisia 적분지수에 대한 바람직한 이산근사식의 형태를 통하여 설명한다. 다음은 연쇄지수의 비가법성 문제에 대한 대안으로 다기간(multi-period) 경제성장률에 대한 기여도를 이용하여 부문별 실질 부가가치를 정의한다. 새로운 부문별 실질 부가가치의 정의는 가법성을 가지며 기여도 분해와 내적일관성을 가진다. 실증분석으로 한국은행이 공표한 16개 산업부문에 대한 데이터로부터 Laspeyres 연쇄지수와 Paasche 및 Fisher 연쇄지수에 의한 다기간 기여도 분해와 가법성이 성립하는 부문별 실질 부가가치의 추계 결과를 제시하였다. 본고의 다기간 기여도 분해는 산업구조의 장기 추세를 간명하게 설명할 수 있으며 부문별 실질 부가가치의 가법성은 국민계정의 정합성을 제고한다.
Abstract
The increasing volatility in price structure due to the accelerating technical progress makes the substitution bias of the conventional fixed weight method of compiling the real GDP obvious. Recognizing this problem, the national statistical agencies of the U.S. and Canada substituted the fixed weight method of compiling real GDP with the chain method as from 1996. Following the two countries, most of OECD countries have gradually adopted the chain method of real GDP compilation. As of March 2009, the Bank of Korea released new real GDP in 2005 price compiled by the chain method. However, there have remained two issues unanswered regarding this new method. The first is the lack of theoretical rationale of the chain method itself and the second is the so called non-additivity of sectoral real value added. In this paper, we provide an answer to the first issue by linking the theoretical economic index number with the Divisia integral index for which numerical integration is in order. Regarding the second issue, we provide a solution to the non-additivity problem together with a numerical demonstration using the official real and nominal 16 sectoral value added data. The proposed new method is expected to enhance the internal consistency of national account.
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