# Price paths using input–output data, BEA 2018

In what follows, our focus is mainly empirical, and it is restricted to showing the results of relevant analyses of the U.S. economy for the year 2018, the most recent input—output data released from the Bureau of Economic Analysis (BEA, www.bea.gov/data/economic-accounts/industry). We selected this particular input—output data and year because it has not been tested yet and, in our view, it is detailed enough for conducting the relevant analysis in both the circulating and fixed capital models.

## The fixed capital model, BEA 2018

We start first with the case of a fixed capital model, which is a more realistic representation of the economy, and subsequently, we continue with a circulating capital model utilizing data of the U.S. economy of the year 2018.5 It is important to point out that in the creation of the matrices of depreciation and capital stock coefficients, we utilized the capital flows (investment) matrix of 1997 of 65x65 dimensions, the last capital flows table published by the BEA. Although this matrix was constructed 20 years earlier than the input—output matrix of 2018, we feel that a more recent capital flows table would not be different in its characteristics. For the details of the construction of the matrix of fixed capital coefficients, see Appendix 4. A.

Before we start with the plotting of trajectories of PP relative to DP, it is important to show the proximity of DP and PP to each other and to MP using both circulating and fixed capital models. The first column of Table 4.1 presents the DP, while the next two columns present the PP for both models. The measures of price deviations are shown at the end of Table 4.1. The Mean Absolute Weighted Deviation (MAWD) is computed as the absolute difference of estimated prices relative to the MP, which are by definition equal to one (million dollars worth of output, Miller and Blair 2009, ch. 2) multiplied by the weight of each industry’s output relative to the economy’s total. In the same spirit and independent of the chosen numeraire metric of deviation is the d — statistic = (1 — cos!?), where the cosine oft? is equal to the arcsine

of the tangent of the two vectors estimated by their coefficient of variation (Steedman and Tomkins 1997). Both statistics show reasonable deviations supportive of the proximity of the estimated prices from the MP (Mariolis and Tsoulfidis 2010).

The last two columns of Table 4.1 stand for the capital intensities of industries in both circulating and fixed capital models. The estimations of

Table 4.1 Direct prices, prices of production and capital intensities, BEA 2018

 Industries DP PP Circulating Capital Model PP Fixed Capital Model Capital Intensity Fixed Capital I/R = 1.984 Capital Intensity Circulating Capital 1/R=1.8J4 1 Farms 0.834 0.968 0.976 5.462 2.669 2 Forestry, fishing and related activities 1.186 1.103 1.112 2.208 1.457 3 Oil and gas extraction 0.759 0.804 0.810 9.365 2.168 4 Mining, except oil and gas 0.857 0.893 0.900 4.543 2.064 5 Support activities for mining 1.057 1.024 1.032 2.554 1.673 6 Utilities 0.725 0.726 0.732 9.766 1.850 7 Construction 0.978 0.959 0.967 1.607 1.724 8 Wood products 1.000 1.060 1.069 2.200 2.171 9 Nonmetallic mineral products 0.927 0.954 0.961 2.850 1.995 10 Primary metals 0.970 1.102 1.111 3.291 2.544 11 Fabricated metal products 1.041 1.094 1.103 2.247 2.092 12 Machinery 1.068 1.123 1.132 2.192 2.101 13 Computer and electronic products 1.137 1.023 1.031 2.394 1.293 14 Electrical equipment, appliances and components 0.991 1.014 1.022 2.168 1.946 15 Motor vehicles, bodies and trailers and parts 1.009 1.202 1.212 2.440 2.792 16 Other transportation equipment 0.972 0.993 1.002 2.018 1.956 17 Furniture and related products 1.080 1.122 1.131 1.891 2.034 18 Miscellaneous manufacturing 1.025 1.017 1.026 2.023 1.792 19 Food and beverage and tobacco products 0.876 1.024 1.032 3.274 2.681 20 Textile mills and textile product mills 1.011 1.084 1.092 2.880 2.209 21 Apparel and leather and allied products 1.250 1.239 1.249 1.991 1.793 22 Paper products 0.985 1.087 1.096 2.971 2.380 23 Printing and related support activities 1.032 1.032 1.040 2.206 1.829 24 Petroleum and coal products 0.669 0.792 0.799 7.515 2.829 25 Chemical products 0.817 0.885 0.893 4.176 2.277 26 Plastics and rubber products 0.980 1.050 1.059 2.724 2.209 27 Wholesale trade 0.845 0.804 0.811 2.025 1.590 28 Retail trade 1.009 0.976 0.984 2.791 1.668 29 Air transportation 0.864 0.838 0.845 2.941 1.686 30 Rail transportation 0.918 0.919 0.926 7.148 1.842 31 Water transportation 1.076 1.139 1.148 3.485 2.199 32 Truck transportation 1.033 1.037 1.046 2.346 1.872 33 Transit and ground passenger transportation 0.879 0.845 0.852 2.047 1.640 34 Pipeline transportation 0.563 0.526 0.531 11.577 1.483

(Continued)

 Industries DP PP Circulating Capital Model PP Fixed Capital Model Capital Intensity Fixed Capital 1/R = 1.984 Capital Intensity Circulating Capital 1/R=1.8J4 35 Other transportation and support activities 1.076 1.050 1.059 2.093 1.706 36 Warehousing and storage 1.144 1.102 1.111 2.653 1.635 37 Publishing industries (includes software) 1.053 0.951 0.959 1.967 1.323 38 Motion picture and sound recording industries 0.932 0.914 0.922 3.888 1.752 39 Broadcasting and telecommunications 0.836 0.860 0.868 4.336 2.023 40 Information and data processing services 0.892 0.874 0.881 2.590 1.758 41 Financial Institutions 0.903 0.862 0.869 2.726 1.609 42 Securities, commodity contracts and investments 1.150 1.098 1.107 1.817 1.625 43 Insurance carriers and related activities 0.841 0.840 0.847 1.868 1.846 44 Funds, trusts and other financial vehicles 0.960 1.091 1.100 2.227 2.658 45 Real estate 0.942 1.011 1.020 9.841 2.269 46 Rental and leasing services and lessors of intangible assets 0.688 0.725 0.731 4.465 2.131 47 Legal services 0.870 0.787 0.793 1.417 1.323 48 Computer systems design and related services 1.191 1.021 1.029 0.701 1.062 49 Miscellaneous professional, scientific and technical services 1.060 0.981 0.990 1.664 1.447 50 Management of companies and enterprises 1.248 1.129 1.138 1.706 1.325 51 Administrative and support services 1.124 1.043 1.051 1.262 1.459 52 Waste management and remediation services 1.356 1.354 1.365 2.384 1.828 53 Educational sendees 1.116 1.006 1.014 3.012 1.293 54 Ambulatory health care services 1.129 1.012 1.020 1.320 1.275 55 Hospitals and nursing and residential care facilities 1.261 1.166 1.176 2.260 1.425 56 Social assistance 1.221 1.127 1.136 1.646 1.409 57 Performing arts, spectator sports, museums, etc. 0.899 0.848 0.855 2.694 1.542 58 Amusements, gambling and recreation industries 1.002 0.954 0.962 3.239 1.574 59 Accommodation 0.899 0.851 0.858 3.324 1.551 60 Food services and drinking places 1.045 1.008 1.016 2.120 1.646 61 Other services, except government 1.053 0.978 0.986 2.217 1.446 62 Federal general government 1.031 0.937 0.945 2.295 1.344 63 Federal government enterprises 1.478 1.334 1.345 8.656 1.300 64 State and local general government 1.250 1.131 1.141 4.646 1.306 65 State and local government enterprise 1.098 1.097 1.106 8.071 1.834 Mean absolute weighted deviation 0.119 0.091 0.092 SD 2.35 SD 0.41 d-Statistic 0.161 0.144 0.144 Avg. 3.36 CV 0.70 Avg. 1.82 CV 0.23

capital intensities in both models are at a relative rate of profit equal to zero and so PP=DP=MP=1. This gives us an initial grasp of the deviations between capital intensities at the starting point of the trajectories of PPs. The standard ratios are also reported in the top two right cells of Table 4.1, and they are equal to 1.984 and 1.834 for fixed and circulating capital models, respectively. 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 2.35 / 3.36 = 0.70 and 0.41 / 1.82 = 0.23 for the fixed and circulating capital intensities, respectively. Clearly, the coef- ficient of variation in the fixed capital model is at least three times higher (=3.11) than that of the circulating capital model. This outcome makes more unlikely the case of crossing the PP—DP line of equality by the PP in the fixed capital model in which PP are expected to move monotonically to the upward or downward direction according to their capital intensity relative to the standard ratio, R.

Figure 4.2 displays the price trajectories of industries of each and every of our 65 industries for 2018. Hence, we used Equation 4.8 and gave the relative rate of profit p prices from zero up to 1. The vector of PP according to

Figure 4.2 Price trajectories, fixed capital model, BEA 2018.

Equation 4.8 is divided, element-by-element, by the corresponding vector of DP, which of course is not affected by changes in p.

Clearly, the movement of relative prices is monotonic with only two exceptions; namely industries, 16 (other transportation equipment) and industry 62 (federal general government) presented in the last right graph of the panel of nine graphs in Figure 4.2 (for the nomenclature of other industries, see Table 4.1). Both exceptional industries attain their maximum at a relative rate of profit much higher than the equilibrium relative rate of profit, p*, which is p = p* = r / R = 0.129 / 0.504 = 25.6%. More specifically, the РР/ DP ratio of industry 16 attains its maximum at p = 40% and crosses the line of PP-DP equality at a relative rate of profit of p = 70%. Industry 62 displays non-monotonic behavior and a maximum at a relative rate of profit of p = 70%. Despite their non-monotonic movement, the price trajectories of both industries are too close to PP—DP line of equality, something that indicates that the capital intensities of these two industries will not be too different from the standard ratio, which is equal to the reciprocal of the maximum eigenvalue 1 / R = 1.984 and is no different from the maximum rate of profit. In the remainder of the graphs, we observe that although the price rate of profit (PRP) curves of some industries are too close to the PP—DP line of equality, do not cross it, and, therefore, do not change the characterization of their intensity. On closer examination, we observe that in all relative rates of profit, the PP—DP deviations are in the neighborhood of one percent, and for the industry 16, the difference is trivially small, even less than 1%!

In the next set of graphs in Figure 4.3 that paint the capital intensities of the 65 industries, we observe that capital intensities move nearly parallel to the standard ratio, in general, or they are so far away that crossing the standard ratio appears as a remote possibility.

The trajectories of the capital—output ratios usually move parallel to the standard ratio as is shown in Figure 4.3. In the last right graph, we present the movement of the capital—output ratio of industry 16, which intersects the standard ratio at a relative rate of profit of 70% and of industry 62, which is approaching the standard ratio but does not intersect it. The capital-output ratios of these two industries start and remain too close to the standard ratio. These findings along with similar others, as we will discuss below, lend support to the view that switching (for positive relative rates of profit) is a remote possibility. Moreover, it is only possible in cases where the initial differences in capital—output ratios from the standard ratio are relatively small; under these rare circumstances, the price feedback effects are quite possible to change the PP—DP differences from positive to negative and vice versa.