産業別生産函数とその規模係数 : 綿紡績業と製糸業を中心として

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1. This is a sequel to my paper "Production Functions and their Scale Coefficients in Ten Textile Industries." published in the last issue of this Review, which were read at the 1959 Keio Joint Meeting of Japanese Economic Association and Econometric Society (Oct. 15～16). In the discussion many suggestive and valuable comments were presented by Mr. M. Hisatake, Chairman, Mr. T. Watanabe, Reporter, and Messrs. K. Nakamura, Y. Shionoya, H. Shishido, I. Ozaki and H. Matsusaki, Commenters. This succeeding paper contains my reply to these comments with further consideration of the hypothesis (i. e. the model and method of estimation) and more close scrutiny of estimated results especially for Silk Reeling, and Cotton Spinning Industries. 2. In Section II the structural parameters k and j are tentatively estimated from three different procedures, of which differences depend upon the properties of used V^^o_L, V^^o_R and V^^o_<LR>, the time-series estimates of variances and co-variance of cross-sectionaly estimated reduced-form disturbances. They are, in principle, consistent estimates of their population parameters, so it should were preferable for us to have longer series of them. However, in order to test the constancy and stability of k and j, the author derives here twenty-one sets of (k,j) from three possible way. First, V^^o_L, V^^o_R and V^^o_<LR> are supposed to be their estimates of each year, [TABLE 10' Nos. (1)～(8)]; secondly to be year-by-year accumulating-averages [Nos. (9)～(16)]; and lasty to be four-years moving-averages [Nos. (17)～(21)]. These tentative results are examined in the following four aspects. (i) There is more fully developed the discriminant formulae of the domain of k^^∧ (or j^^∧) in terms of used V^^o_L, V^^o_R and V^^o_<LR>. (ii) The validity of an a priori assumption U_<12>=0 is scrutinized in rather simple way. If U_<12>≠0, k^^∧=k-(U_<12>/U_2). There-fore, the increasing tendency of k^^∧ for Silk Reeling and decreasing one for Cotton Spinning are due to some systematic variation of U_<12> or covar (u_1u_2) over time. (, for Silk Reeling it always would be negative, while for Cotton Spinning positive.) (iii) The [(α_L/β_L)-(α_R/β_R)] gives the estimated relative price of factors of production (w/r), that goes, in general, upward in the course of technical progress and of capital accumulation. The estimated series of [(w/r)t/(w/r)](FIG. 3' base year =1931) exhibits that (w/r) increases sharply in 1937 for Cotton Spinning, and for Silk Reeling it changes upward rather slightly in 1940, that corresponds to our experiences on the differences of economic, growth between these two industries. (iv) During the period 1929～31, Japanese economy experienced deep depression and whole industries endeavoured to compact it through capital accumulation and concentration, and introduction of new machines and techniques (TABLE 12'). Some rough outside information derived from historical records and engineering data (TABLE 13' and 14') suggests us that such antidepression policy are taken up in Silk Reeling after 1932, and while in Cotton Spinning had already finished during 1929～31. These records are consistent with our results of estimation. In the light of above discussion, the constancy of (k, j) could not be distorted, but the stability of them might be affected not only by sampling variations, also by any other factors. It may be supposed that in Silk Reeling Industry, technical progress and capital accumulation took place in such a way as affecting the yearly variation of scale variation, while in Cotton Spinning in another way as affecting both scale coefficients and stability of (k, j). However this is not decisive conclusion and must be tested by any further experiment. During the post-war period two industries experienced more drastic technological innovations, that offers to us one of the suitable chance for testing this maintained hypothesis. 3. The yearly, and inter-industry variation of scale coefficients are discussed again in Section III. With respect to yearly variations, additional estimation of s_L and s_R are presented for Cotton Spinning (TABLE 15') and deflated by selected index of cross-section variation coefficient of intensity utilization. The comparison between deflated and undeflated series of s_R (or s_L) (FIG. 4') illustrates explicitly that our s_L and S_R are affected by utilization variation among firms of different size. In the next subsection interindustry differences of them are discussed based upon their average levels (TABELE 17'). Essentially s_L (and S_R) is determined within the framework of labor market. The fact that S_L-level of Cotton Spinning is the highest and of Silk Reeling is the lowest, coincides Mr. Obi's empirical finding on wage and working-hour relation in textile industries about during same period with respect to labor supply. However, these descriptions never be the autonomous explanation, so there remains the necessity of constructing the model explaning the scale ceofficient inter-temporal and interindustry variation. 4. Lastly the author described his opinion about the very nature of production function and the essense of scale coefficients.
慶應義塾大学の論文
1959-12-10

産業別生産函数とその規模係数 : 綿紡績業と製糸業を中心として

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