# Alexander Y. Vaninsky

## Publications

##### 7 Optimal Economic Restructuring Aimed at an Increase in GDP Constrained by a Decrease in Energy Consumption and CO2 Emissions

**Authors:**
Alexander Y. Vaninsky

**Abstract:**

The objective of this paper is finding the way of economic restructuring - that is, change in the shares of sectoral gross outputs - resulting in the maximum possible increase in the gross domestic product (GDP) combined with decreases in energy consumption and CO_{2} emissions. It uses an input-output model for the GDP and factorial models for the energy consumption and CO_{2} emissions to determine the projection of the gradient of GDP, and the antigradients of the energy consumption and CO_{2} emissions, respectively, on a subspace formed by the structure-related variables. Since the gradient (antigradient) provides a direction of the steepest increase (decrease) of the objective function, and their projections retain this property for the functions' limitation to the subspace, each of the three directional vectors solves a particular problem of optimal structural change. In the next step, a type of factor analysis is applied to find a convex combination of the projected gradient and antigradients having maximal possible positive correlation with each of the three. This convex combination provides the desired direction of the structural change. The national economy of the United States is used as an example of applications.

**Keywords:**
Economic Restructuring,
input-output analysis,
divisia index,
factorial decomposition,
E3 models

##### 6 Economic Factorial Analysis of CO2 Emissions: The Divisia Index with Interconnected Factors Approach

**Authors:**
Alexander Y. Vaninsky

**Abstract:**

This paper presents a method of economic factorial analysis of the CO_{2} emissions based on the extension of the Divisia index to interconnected factors. This approach, contrary to the Kaya identity, considers three main factors of the CO_{2} emissions: gross domestic product, energy consumption, and population - as equally important, and allows for accounting of all of them simultaneously. The three factors are included into analysis together with their carbon intensities that allows for obtaining a comprehensive picture of the change in the CO_{2} emissions. A computer program in R-language that is available for free download serves automation of the calculations. A case study of the U.S. carbon dioxide emissions is used as an example.

**Keywords:**
Economic analysis,
Co2 Emissions,
divisia index,
factorial analysis,
Interconnected factors

##### 5 Data Envelopment Analysis with Partially Perfect Objects

**Authors:**
Alexander Y. Vaninsky

**Abstract:**

This paper presents a simplified version of Data Envelopment Analysis (DEA) - 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. DEA with a Perfect Object (DEA PO) augments the group of actual objects with a virtual Perfect Object - the one having greatest outputs and smallest inputs. It allows for obtaining an explicit analytical solution and making a step to an absolute efficiency. This paper develops this approach further and introduces a DEA model with Partially Perfect Objects. DEA PPO consecutively eliminates the smallest relative inputs or greatest relative outputs, and applies DEA PO to the reduced collections of indicators. The partial efficiency scores are combined to get the weighted efficiency score. The computational scheme remains simple, like that of DEA PO, but the advantage of the DEA PPO is taking into account all of the inputs and outputs for each actual object. Firm evaluation is considered as an example.

**Keywords:**
Data Envelopment Analysis,
Explicit Solution,
Perfect Object,
Partially
perfect object,
Partial efficiency,
Simplified
algorithm

##### 4 Theory of Fractions in College Algebra Course

**Authors:**
Alexander Y. Vaninsky

**Abstract:**

**Keywords:**
Mathematics curriculum,
teacher preparation,
fractions,
mathematics
education

##### 3 Interstate Comparison of Environmental Performance using Stochastic Frontier Analysis: The United States Case Study

**Authors:**
Alexander Y. Vaninsky

**Abstract:**

Environmental performance of the U.S. States is investigated for the period of 1990 – 2007 using Stochastic Frontier Analysis (SFA). The SFA accounts for both efficiency measure and stochastic noise affecting a frontier. The frontier is formed using indicators of GDP, energy consumption, population, and CO2 emissions. For comparability, all indicators are expressed as ratios to total. Statistical information of the Energy Information Agency of the United States is used. Obtained results reveal the bell - shaped dynamics of environmental efficiency scores. The average efficiency scores rise from 97.6% in 1990 to 99.6% in 1999, and then fall to 98.4% in 2007. The main factor is insufficient decrease in the rate of growth of CO2 emissions with regards to the growth of GDP, population and energy consumption. Data for 2008 following the research period allow for an assumption that the environmental performance of the U.S. States has improved in the last years.

**Keywords:**
Environmental Performance,
stochastic frontier analysis,
interstate comparisons

##### 2 Environmental Performance of the United States Energy Sector: A DEA Model with Non-Discretionary Factors and Perfect Object

**Authors:**
Alexander Y. Vaninsky

**Abstract:**

**Keywords:**
Environmental Performance,
energy sector,
DEA with Non Discretionary Factors,
Explicit Solution,
Perfect Object

##### 1 Environmental Efficiency of Electric Power Industry of the United States: A Data Envelopment Analysis Approach

**Authors:**
Alexander Y. Vaninsky

**Abstract:**

Importance of environmental efficiency of electric power industry stems from high demand for energy combined with global warming concerns. It is especially essential for the world largest economies like that of the United States. The paper introduces a Data Envelopment Analysis (DEA) model of environmental efficiency using indicators of fossil fuels utilization, emissions rate, and electric power losses. Using DEA is advantageous in this situation over other approaches due to its nonparametric nature. The paper analyzes data for the period of 1990 - 2006 by comparing actual yearly levels in each dimension with the best values of partial indicators for the period. As positive factors of efficiency, tendency to the decline in emissions rates starting 2000, and in electric power losses starting 2004 may be mentioned together with increasing trend of fuel utilization starting 1999. As a result, dynamics of environmental efficiency is positive starting 2002. The main concern is the decline in fossil fuels utilization in 2006. This negative change should be reversed to comply with ecological and economic requirements.

**Keywords:**
United States,
DEA,
Environmental efficiency,
electric power industry