Use of Artificial Neural Network for the Construction of Lorenz Curve

Use of Artificial Neural Network for the Construction of Lorenz Curve

Sudesh Pundir (Pondicherry University, Puducherry, India) and Ganesan R. (Rajiv Gandhi Institute of Veterinary Education and Research, Puducherry, India)
Copyright: © 2014 |Pages: 12
DOI: 10.4018/ijgc.2014010102
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Abstract

Lorenz curve and Gini index are the most widely used measures of income inequality in Economics. Artificial Neural Networks (ANN) are mathematical models that learn complex relationships in data. ANN is widely used for prediction and classification tasks in many fields of knowledge. In this paper, Lorenz points are generated from a trained ANN by systematically varying some underlying parameters of ANN and the behavior of Lorenz curve is studied. It is shown that ANN technique generates better Lorenz curve in the sense of better distribution of income points and having smaller Gini Index. A real life illustration is provided by taking the per capita Net State Domestic Product at current prices for 32 States / Union Territories of India for the period 1997-1998.
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Introduction

In Economics, Lorenz curve and Gini index are widely used to measure income inequality. Much work is done in this direction (Sen, 1973; Kakwani, 1980; Ullah & David, 1998; Subramanian, 2001; Pundir, 2012). Now-a-days, Lorenz curve is used in other fields also like Reliability, Survival Analysis, Demography, Insurance, Library Science and Medicine for different purposes.

Artificial Neural Network is a computer algorithm inspired by the way information is processed in the nervous system. The aim of ANN is the construction of a system that could compute, learn, remember and optimize in the same way as human brain does. The major advantage of ANN is its flexible nonlinear modeling capability. ANN can be fitted to any kind of data set as it does not require any model assumption. There is also no need to specify a particular form of the model in ANN as the model gets adaptively formed based on the features present in the data (Seber & Wild, 1989). The literature on ANN is vast and expanding rapidly (Zhang & Cao, 2012; Muller & Reinhardt, 1990; Hertz et al., 1991; Antognetti & Milutinovic, 1991; Celenbe, 1991; Johnson & Brown, 1988; Sethi & Jain, 1991; White, 1992; Gurney, 1997; Pacelli et al., 2011; Cheng & Titterington, 1994; Kohonen et al., 1991). Several research journals are dedicated to the field of ANN and their applications in Engineering, Theoretical Biology, Pattern recognition, Computer science, Theoretical Physics and Applied Mathematics.

ANN’s are increasingly being used by Economists for classification and regression problems like classification of customers and prediction of time series in the capital markets (Salchenberger et al., 1992; Li, 1994; Thawornwong & Enke, 2004). Atkinson (1970) showed the rules for ordering risky prospects (called as stochastic dominance rules in finance literature), can be presented in a simple way by Lorenz curves (Hadar & Russel, 1969; Hanoch & Levy, 1969; Rothschild & Stiglitz, 1970). Beltratti et al. (1996) has written a book on Neural Networks for Economic and Financial Modelling. Shalit (2010) concerns the extent to which Lorenz curve is used in financial theory and portfolio risk management. This paper compiles the risk measures associated with Lorenz curve.

With the advancement of information technology and the availability of related software, there are new options that might be more promising than the traditional approach. One such approach is ANN. With increasing interests in ANN and its applications in various disciplines, it is a worthwhile effort to explore such a technique for generating Lorenz curve, a famous and traditional tool in the field of Economics. ANN gives us an alternative approach for the data collected from the field directly as it may have errors which may influence the decision also. In such cases one can use the ANN technique and check the bias in the data so that correct decisions can be taken and income inequality can be measured accurately.

In this paper, our aim is to check how the measurement of inequality gets affected by using ANN methods. The classical approach of construction of Lorenz curve and Gini Index is compared with the ANN approach. It is shown that generation of values through ANN gives better Lorenz curve and the corresponding Gini Index than the results obtained from the classical methods.

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