經濟學에 있어서의 要因分析의 適用 = The Application of Factor Analysis in Economics
저자
邊衡尹 (서울大學校 商科大學 韓國經濟硏究所, 서울大學校商科大學)
발행기관
서울大學校 商科大學 韓國經濟硏究所(INSTITUTE OF ECONOMIC RESEARCH SEOUL NATIONAL UNIVERSITY)
학술지명
권호사항
발행연도
1966
작성언어
Korean
KDC
320.5
자료형태
학술저널
수록면
1-23(23쪽)
제공처
소장기관
Ⅰ. Preface
Factor analysis method, which is an applied branch of mathematics, was devised by J. C. Spearman in 1904, and grew up in this century with the field of psychology. It is increasingly being adopted by other fields, such as economics and sociology. In economics it is applied in economic growth or economic development theory.
The present author is especially interested in the latter applications. But before examining the core of the problem, it may well examine factor analysis itself. And R. Stone's 1947 paper, which deals with the application of the factor analysis to statistical technique, and which is the basis of T. Kloek and L. B. M. Mennes' most advanced paper of the field, is useful for understanding the implication of factor analysis method.
In this paper, therefore, I introduce factor analysis first, examine Stone's paper next, and then M. Megee's paper and I. Adelman and C. T. Morris' paper on the applications of factor analysis to economic development theory.
Ⅱ. Factor Analysis
Factor analysis method is applied to economics in the form of principal component analysis which was devised by Hotelling to deal with the problem of factor analysis in psychology. By principal component or factor analysis we try to answer the question: Is it possible to analyze a set of variables into a more fundamental set of independent components (or factors) possibly fewer in number? Which portion of the total variance can be accounted for by each component? Here, Hotelling's method of solution is introduced,
Assume that we want to replace a set of standardized variables ?? (i=1, 2, …, p) by a more fundamental set of variables ?? (i=1, 2, …, p ), such that
z=Ku,
where z is a p-component column vector, K is a p × p matrix of coefficients, and u, a p-component column vector. The components ?? are principal components and are orthogonal to each other.
We want to maximize the contribution of the fist principal component u₁:i.e., maximize S₁,
??=??,??
under condition that
R=KK′
where R is a p×p symmetric matrix of correlations between the variables ??; and K´,the transpose of K. Here it is found that the solutions of ???are the components of eigenvector of matrix R corresponding to the largest eigenvalue λ₁of that matrix multiplied by the square root of λ₁.Similarly we can find second component (or factor), third component, and so on.
Ⅲ. On Application of Factor Analysis to Statistical Technique.
R. Stone has applied the method of factor analysis or principal components to national income data of American economy taken from the years 1922-38.
Here seventeen variables are reduced to three factors and these three factors together account for more than 97 per cent of the total variance of all variables. Moreover, the three largest factors can tentatively be identified with income ( or output ), rate of changes of income, and time trend respectively.
T. Klok and L. B. M. Mennes have, in their 1960 paper, furthered Stone's analysis and give new economic meaning to that method.
Ⅳ. On Application of Factor Analysis to Economic Development Theory,
I. M. Megee's paper purposes to discuss the usefulness of mathematical model for analyzing problems of economic growth on the one hand, and to analyze briefly the findings from some particular implementations of factor analysis with the hope of discovering some advantages, disadvantages, and implications for the use of the method in economic growth analysis and planning for future growth on the other. Our interest is in the latter.
She introduces three techniques: R, Q, and M-techniques. These there techniques provide the means of testing three kinds of hypotheses related to economic development: R can test hypotheses about variables causing economic development, using the factor loadings ; Q can test hypotheses regarding the area differentiation of patterns of economic development, using the factor scores; and M can test hypotheses involving changes of variables or regions over time.
Although it is quite useful for testing hypotheses, factor analysis is also considered as an ideal way of exploring the unknown without the necessity of assumptions. It is possible to construct a large data matrix of economic and social variables and run factor analysis without any a priori assumptions. But it has some problems in the construction of an economic development matrix.
A major problem is lack of availability of data for desired information categories, resulting in their omission from the study. Another major problem is that of subjectivity, the selection of variables, the naming of the factors, the delineation of economic and social regions and the choice of the factor analysis method itself all introduce a certain amount of subjectivity into the analysis, though it would seem to be less encumbered by restrictions than is multiregression analysis. Unlike other multivariate techniques, factor analysis cannot show inter- and intra-regional structure and flows, though some can be inferred from Q-technique.
The most important use of factor analysis for the social scientist is to isolate important or strategic variables for further study and to eliminate extraneous information. And factor analysis model can be used to identify and measure the relative importance of certain sectors of the economy as well as to indicate regional differentiation.
Ⅴ. On the Application of Factor Analysis to Economic Development Theory, Ⅱ
In their paper, I. Adelmen and C. T. Morris attempt to gain some semiquantitative insights into the interaction of various types of social and political changes with the level of economic development.
For this purpose the techniques of factor analysis are applied to per capita GNP and to twenty-two indexes representing the social and political structure of seventy-four less developed countries in the period 1957-62. And to see the regional differences in the interrelationship between per capita GNP and sociopolitical influences the countries are divided into three groups: African countries, Near Eastern and Far Eastern countries, and Latin American countries.
In their analysis, the remarkably high percentage of intercountry variations in the level of economic development (66%) are associated with differences in non-economic characteristics. And a strong association was derived between per capita GNP (or the level of economic development ) and two aspects of sociopolitical change: the socio-cultural concomitants of the industrialization-urbanization process (Factor I) and the Westernization of political institutions (Factor Ⅱ). In contrast, a rather weak relationship appears between per capita GNP and indicators summarizing the character of leadership (Factor Ⅲ) and the degree of social and political stability in the past decade ( Factor Ⅳ) .
In addition, the results of regional studies indicate that Factor I is overwhelmingly important for low income economies in which the absorptive capacity is sharply limited by the inhibiting nature of the social structure. However, even among countries at higher stages of evolution, the social variables remain the most important element associated with intercountry differences in per capita GNP. As for factor Ⅱ, it is of negligible importance at the early stages of development. This result probably arises because both the ability to generate sustained economic growth and the evolution of more sophisticated political institutions require fundamental changes in mentality characteristic of Western thought pattern.
And at the last part of the paper they emphasize that the relationships found between levels of economic development and differences in social and political structure are neither caused nor causal.
Ⅵ. Conclusion
As M. Megee points out, factor analysis has deficiencies such as lack of availability of data for constitutions of factor matrix, incorporation of subjectivity, and impossibility of showing inter-and intra-regional structure and flows. And in the application of tactor analysis to economic development theory, there are many to-be-solved problems: we must construct matrices to find weights for variables on economic development; incorporate political, social and psychological variables into the study of economic development ; and vary the numbers and kinds of variables. Further, this analysis is a laborious method because of complexity in calculation and is subject to the type of computer. But this analysis is as Megee says, useful for isolation of important or strategic variables for further study, and for elimination of extraneous information at an initial stage of research. This is the most important use of factor analysis for the social scientist. And it is also a merit of factor analysis that it is a highly complex model which can incorporate many more variables than the ordinary sorts of models constructed for dealing with economic problems.
In Korea, econometric studies are beginning to be applied to real problems. In these studies efficient model building is the most important process. Here factor analysis method may function usefully. And it may be thought that economic forecasting will be more accurate with the use of factor analysis.
In Korea, more attention is paid to the gross national product or per capita GNP. But there have been no attempts similar to Adelman and Morris'. It may be a valuable attempt to examine how much per capita GNP is influenced by noneconomic or political and social factors. Further, the method can suggest something about treatment of noneconomic factors in econometrics. Therefore, a proper study on factor analysis is much required in Korea.
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