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Price paths using input–output data, USA 2014Our experiments continue with the U.S. economy using an alternative set of data derived from the WIOD (Timmer et al. 2015) for the year 2014, the most recent input—output data released from this source. The reason for these additional estimations is not only to ascertain the general findings of proximity between different price vectors but mainly because we use data of 2014 to extend our research (in Chapter 5) by making intertemporal comparisons of the WRP curves of the USA. In addition, in Chapter 6, we experiment with these data in our effort to ascertain additional properties of the linear model of production and to reduce largescale description of the economies into a few or even a single hyperindustry. Finally, in Chapter 7, we aggregate the 2014 input—output data into five sectors and proceed with all of our computations in Chapters 4—6 in our effort to show the techniques and the matrices utilized in the estimations. The fixed capital model, USA 2014, WIOD (2016)Based on data provided by WIOD (Timmer et al. 2015), we extract the input—output table of the U.S. economy for the year 2014, the last available input—output table supplemented with data for total compensation, employment and capital stock from the Socio Economic Accounts (SEA, http:// www.wiod.org/database/seasl6). Both sources of data became available in 2016 (see Timer et al. 2015). The lack of capital flow tables compels the use of the best available alternative estimating method of the matrix of capital stock coefficients. This alternative method utilizes the investment data in the final demand column of the input—output table (see Appendix 4. A) to construct the matrix of the vertically integrated capital stock coefficients whose maximum eigenvalue is equal to one and zero is of its subdominant ones. The properties of the soderived matrix of the vertically integrated capital stock coefficients are not too different had we employed a capital flows matrix, as we did with BEA data whose second eigenvalue is particularly small, equal to 0.16. In earlier studies, for the U.S. economy and 39industry detail, gave similar results. More specifically, for the benchmark years, the second eigenvalue shown in parenthesis are as follows: 1947 (0.41), 1958 (0.31), 1963 (0.31), 1967 (0.47), 1972 (0.55) and 1977 (0.46) while using respective data from the OECD for the year 1990 and 33 industries input—output structure gave a second eigenvalue equal to 0.20 (Mariolis and Tsoulfidis 2016a, 2018). The OECD data for the UK of the year 1990 gave a second eigenvalue equal to 0.19 (Mariolis and Tsoulfidis 2016b). The research for the Greek economy for the year 1970 gave a second eigenvalue equal to 0.04 and for S. Korea for the years 1995 and 2000 a second eigenvalues equal to 0.08 and 0.06, respectively.^{7} Finally, for Germany, the input—output data and capital stock matrices aggregated into seven sectors (see Cogliano et al. 2018, pp. 240—244 for details) gave a maximum eigenvalue equal to 1.981 and the second eigenvalue was found to be trivially small. These reported results confirm that both methods give rise to similar matrices of capital stock coefficients. In Table 4.2, we display, as in Table 4.1, the results regarding the PP and DP relative to MP, which by definition is equal to one (million USD). The resulting deviations of PP and DP from MP are relatively small as this can be judged by our usual statistic of deviation, which are in the neighborhood
of 20%. The last two columns of Table 4.2 stand for the capital intensities of industries in both circulating capital and fixed capital models. The standard ratios are also reported in the top two right cells of Table 4.2, and they are equal to 0.931 for the circulating capital (A [I — AJ ') and 1.605 for the fixed capital model К [I —A] The standard deviations and the mean of these capital intensities are displayed in the last two rows of the table. Their respective ratios, that is, the coefficients of variation are 0.36 / 1.46 = 0.24 and 1.31 / 2.26 = 0.58 for the circulating and fixed capital intensities, respectively. Clearly, the coefficient of variation in the fixed capital model is at least twice higher (=2.38) than that of the circulating capital model making more unlikely the crossing of the PPDP line of equality in the fixed capital model. In the graphs of Figure 4.6, we display the price trajectories for the fixed capital model utilizing actual input—output data of the U.S. economy. It is interesting to note that the WIOD Timmer et al. (2015) gives both the Figure 4.6 Price trajectories, fixed capital model, USA 2014. domestic input—output tables as well as the imported along with the row of total output or input, which is the sum of domestic and imported parts. In adding up these two inputoutput tables (domestic and imported) and deriving the (total) input—output coefficients, we get repeated industries. These are industries 11 (chemicals) and 12 (pharmaceutical products) as well as 24 (electricity, gas, etc.) and 25 (water supply). The similar industries include also the following four: namely, industry 46 (architectural and engineering activities), industry 47 (research and development), industry 48 (advertising) and industry 49 (other scientific, technical and related activities). The same is true for the employment input and the capital—output coefficients. Consequently, the actual number of industries in the input—output table is 49. The monotonic movement of prices is in line with Ricardo and Marx’s views about the changes in prices induced by changes in income distribution. This movement is consistent with that of capital intensities. Figure 4.7 Figure 4.7 Capital intensities, fixed capital model, USA 2014. displays the movement of the capital intensities of industries relative to the standard ratio, which is R~ =1.846. The graphs in Figure 4.7 ascertain the parallel movement of capital intensities, as expected by construction in that the subdominant eigenvalues are all equal to zero. The reason is that the columns of the matrix К are linearly dependent derived from a multiplication of two vectors. It is important to stress that had we had the actual capital flows tables, we would not observe anything quite different, unless an industry’s capital—output ratio is near the standard ratio and the elasticity term moves in the opposite direction to the RicardoMarx effect. As we have already mentioned, under these circumstances, it is possible for the feedback effects to change the trajectories of capital intensities and to observe crossings, but not too many as in the case of fixed capital model of the year 2018. Schefold (2013, p. 1177) opined in the case of a circulating capital model that the near linearities in prices could be explained by the small subdominant eigenvalues of the matrix A whose elements he considered as randomly distributed. By contrast, the same configuration of eigenvalue distribution and the resulting near linearities in PRP and WRP curves is explained by the low effective rank of the economic system matrices (Mariolis and Tsoulfidis 2011, 2014, 2016a, 2016b, 2018; lliadi et al. 2014; Shaikh 2016, ch. 9). In the next chapters, we explore more thoroughly the underlying system’s matrices and the resulting eigenvalue distributions and their consequences. 
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