Abstract
In this chapter, to illustrate and test the theory, we refer to time series for the U.S. economy for the years 1890–2009 collected in Appendix 2. The choice of this case is justified by the availability and reliability of the data, which can be easily found on web pages of the U.S. Census Bureau and the U.S. Bureau of Economic Analysis. These organisations have been permanently improving the 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, technological coefficients and bulk productivity of workman.
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Notes
- 1.
The correlation and covariance of two quantities a and b are defined as
$$\begin{aligned}&\mathrm{corr}\; (a,b)=\frac{\mathrm{cov}\; (a,b)}{\varDelta a \, \varDelta b}, \quad (\varDelta a)^2 =\frac{1}{n}\sum _{j=1}^n(a_j-\langle a\rangle )^2, \\&\mathrm{cov}\; (a,b)=\frac{1}{n}\sum _{j=1}^n(a_j-\langle a\rangle )(b_j-\langle b\rangle ),\quad \langle a\rangle =\frac{1}{n}\sum _{j=1}^na_j. \end{aligned}$$.
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Pokrovskii, V.N. (2018). Estimation of Parameters of Production Processes. In: Econodynamics. New Economic Windows. Springer, Cham. https://doi.org/10.1007/978-3-319-72074-6_7
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