Alexander Vaninsky

Computational method of finding optimal structural change in economic systems: an input-output projected-gradient approach

Abstract A method of finding locally optimal structural change in economic systems described by input-output models and aimed to maximization of final product per capita is suggested. The method is based on a projected-gradient. Both projected-gradient and corresponding locally optimal structural change are obtained in explicit form. Numerical examples are provided

Structural change optimization in input-output models

Abstract It is suggested to transform input-output model to structured form, combine it with objective function and apply projected gradient to finding structural change leading to locally maximal increase in the objective function. Theorems providing projection matrix and projected gradient explicitly are proved. Efficiency of structural change is introduced and applied to analysis of structural change of gross output in the US economy for the period of 1988–2005 and to evaluation of prospective structural change in 2014 using GDP as objective function.

R program for estimation of group efficiency and finding its gradient. Stochastic data envelopment analysis with a perfect object approach

The data presented here are related to the research article “Energy-environmental efficiency and optimal restructuring of the global economy” (Vaninsky, 2018) [1]. This article describes how the world economy can be restructured to become more energy-environmental efficient, while still increasing its growth potential. It demonstrates how available energy-environmental and economic information may support policy-making decisions on the atmosphere preservation and climate change prevention. This Data article presents a computer program in R language together with examples of input and output files that serve as a means of implementation of the novel approach suggested in publication [1]. The computer program utilizes stochastic data envelopment analysis with a perfect object (SDAEA PO) to calculate the group efficiency of a collection of decision-making units (DMUs), the efficiency gradient, and the projected gradient. The projected gradient is computed in the case when the SDEA PO inputs and outputs are given as shares in total, to satisfy the constraints of adding up to a unit. By so doing, the program assesses the energy-environmental efficiency of the global economy and determines the ways of its maximum possible increase via locally optimal economic restructuring.

Bridging Calculus and Statistics: Null - Hypotheses Underlain by Functional Equations

Statistical interpretation of Cauchy functional equation f(x+y)=f(x)+f(y) and related functional equations is suggested as a tool for generating hypotheses regarding the rate of growth: linear, polynomial, or exponential, respectively. Suggested approach is based on analysis of internal dynamics of the phenomenon, rather than on finding best-fitting regression curve. As a teaching tool, it presents an example of investigation of abstract objects based on their properties and demonstrates opportunities for exploration of the real world based on combining mathematical theory with statistical techniques. Testing Malthusian theory of population growth is considered as an example.

Integral definition of the logarithmic function and the derivative of the exponential function in calculus

Defining the logarithmic function as a definite integral with a variable upper limit, an approach used by some popular calculus textbooks, is problematic. We discuss the disadvantages of such a definition and provide a way to fix the problem. We also consider a definition-based, rigorous derivation of the derivative of the exponential function that is easier, more intuitive, and complies with the standard definitions of the number e, the logarithmic, and the exponential functions.

Simplified Data Envelopment Analysis: What Country Won the Olympics, and How about our CO 2 Emissions?

This paper introduces a simplified version of Data Envelopment Analysis a conventional approach to evaluating the performance and ranking of competitive objects characterized by two groups of factors acting in opposite directions: inputs and outputs. Examples of DEA applications discussed in this paper include the London 2012 Olympic Games and the dynamics of the United States’ environmental performance. In the first example, we find a team winner and rank the teams; in the second, we analyze the dynamics of CO2 emissions adjusted to the gross domestic product, population, and energy consumption. Adding a virtual Perfect Object – one having the greatest outputs and smallest inputs we greatly simplify the DEA computational procedure by eliminating the Linear Programming algorithm. Simplicity of computations makes the suggested approach attractive for educational purposes, in particular, for use in Quantitative Reasoning courses.