Abstract
In this chapter, to illustrate and test the theory, we refer to time series for the U.S. economy for years 1890–2009 collected in Appendix B. The choice of this case is justified by the availability and reliability of the data, which can be easily found on webpages of the U.S. Census Bureau and the U.S. Bureau of Economic Analysis. These organisations have been permanently improving methods of estimation of time series, and the data has been permanently revised in order for the numbers to be as accurate as possible. We have used the latest available series to illustrate the methods of estimation of some quantities: substitutive work, technological index, marginal productivities and technological coefficients.
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Notes
- 1.
The correlation and covariance of two quantities a and b are defined as
- 2.
Here the reader can be pertinently reminded of the contradictions arising if one uses for an assessment of output the neo-classical production function in the Cobb–Douglas form,
$$Y=Y_0 \frac{L}{L_0} \biggl(\frac{L_0}{L} \frac{K}{K_0}\biggr)^{\alpha'}, \quad 0 <\alpha' <1.$$Considering exponential growth (7.10), the expression for output is determined in the form of
$$Y=Y_0 e^{[(1 - \alpha') \nu+ \alpha' \delta]t}.$$It is easy to see that the Cobb–Douglas production function describes empirical data for the U.S. for years 1950–2000 at α′≈1, which excludes the influence of labour. Moreover, the index α′ can be interpreted as a share of capital in total expenses for maintenance of production factors—the quantity that is equal to 0.3–0.4 for the U.S. economy. This is a well-known fact [4, p. 4] which has led to the introduction of the full factor of productivity [6] and to numerous modifications of the neo-classical production function [7, 8].
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Pokrovskii, V.N. (2012). Application to the U.S. Economy. In: Econodynamics. New Economic Windows. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2096-1_7
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