# NSU Research Contributions

### Title : STATISTICAL ANALYSIS FOR THE SIZE DISTRIBUTION OF HOUSEHOLD INCOME OF BANGLADESH

**Authors : **Md. Sharif Hossain

**Abstract : **Nowadays, statistics and econometrics play an important role in almost every field of social and economic research. In statistics and econometrics, different tools and procedures have been developed that are capable of elegant analysis of various phenomena in different fields of research. Econometrics can be thought of as a combination of economic theory, mathematical economics, statistics, and mathematical statistics with computing as vehicle of estimation.
The main concern of mathematical economics is to express theory in mathematical form (equation form) without regarding to measurability or empirical verification of the theory. Econometrics is mainly interested in the empirical verification of the mathematical form of economic theory. But, it is to be born in mind that econometric principles can be applied in almost all fields of human life.
In this paper, a principal attempt has been made for a statistical analysis for the size distribution of household income of Bangladesh. And also on basing upon the econometric principles, empirical analysis has been provided in all aspects of the theoretical constructs. We provided empirical verification of the theoretical constructs in all aspects
based on a data set from BBS ( Bangladesh Bureau of Statistics) publications "Household Expenditure Survey" corresponding to different years for nationwide and also for urban and rural sectors of Bangladesh.
In statistics, theoretical consideration of the distribution of income has changed rapidly since Pareto's (1897) seminal work almost one hundred years ago. Concern with the functional distribution of income, researchers became interested in questions about the personal size distribution of income. The major areas of interest have been the specification of an appropriate hypothetical statistical distribution. Research in this area began as an attempt to explain how the observed personal income was generated, but over time it has become primarily a statistical exercise in searching for a good fitting statistical distribution. Many authors have suggested alternative functional forms to approximate the observed income distribution. All of these forms do not fit the data very well. Some distributions fit well at the tails but not over the lower portion of income data, while other forms have the opposite problem.
Concurrently, many summary measures of income inequality have been suggested, begging with Gini's (1913) measure, Theil (1967), Atkinson (1970), Kakwani (1980), Basmann and Slottje (1987, 1988) and Chakravarty (1988) have all formulated different measures. No single measure appears to satisfy all the criteria that theorists have set down as reasonable description of inequality. Given the problem of specifying a functional form and finding an adequate summary measure of inequality, another approach of measuring inequality has been to look directly at the observed income distribution and at individual's relative position there in.
Lorenz (1905) has started this approach, but latter many authors have refined it. The Lorenz curve is a most powerful tool in the analysis of the size distribution of income and wealth. In the past decades, many authors, see for example, Kakwani and Podder (1973, 76), Rasche et all (1980), Kakwani (1980), Gupta (1984), and Ortega (1991), have proposed different functional forms for estimating Lorenz curves from grouped data. The problem is that, most of these functional forms do not fit the data very well for the size distribution of household income of Bangladesh. That is why, based upon the studies of the income distribution of Bangladesh, in this paper we proposed a new functional form for estimating Lorenz curves from grouped data, which provides a very good fits with compared to other functional forms say; Kakwani's and Podder's (1973, 76), Rasche's (1980), Kakwani's (1980), Gupta's (1984), and Ortega's (1991). On the basis of the new functional form, we derived the formulae of different inequality measures say, Gini index, Kakwani and Chakravarty inequality measures. The relative performance of the new functional form can be compared with others on the basis of the estimated residual sum of squares.
There is a problem of indirect approach for estimating the Lorenz curve is that it is difficult to find any one hypothetical statistical distribution to serve as a good approximation over the entire range of an actual batch of income data. Thus in the past, R.L. Basmann, K. J. Hayes and D. J. Slottje (1990) have considered a general functional form for parametric approximations to estimate Lorenz curves. They have shown that the functional form first proposed by Kakwani and Podder (1973) is very restrictive for describing the Lorenz curve. But, until now no one conducted any general functional form for parametric approximations to show in together that the functional forms first proposed by Kakwani and Podder (1973, 76) and in recent another functional form is proposed by Ortega (1991) are very restrictive for describing Lorenz curves and probably lead to an upward bias. Thus to show this, in this paper another attempt has been made to present a direct parametric approximations of a general functional form for estimating Lorenz curves. We can compare these alternative forms by goodness of fit, F-tests of nested forms and measurement of the Gini coefficients.
Also, as descriptive models for the size distribution of income, in the past decades, many distributions have been developed. These includes, among others, the Lognormal, Log-t, Gamma, Generalized Gamma, Beta, Generalized Beta, Singh-Maddala, and Pareto distributions. All of these functions do not fit the data very well for the size distribution of household income of Bangladesh. That is why, in this paper another purpose has been made to select an appropriate function that fits the size distribution of household income of Bangladesh very well. As a descriptive model for the size distribution of household income of Bangladesh, the appropriate function can be selected on the basis of the estimated sum of squared errors criteria, sum of absolute errors criteria, chi-square value and the predicted probabilities of these functions.
Distribution issues have experienced a renaisance in recent year, especially as consequences of the discussion on the increase of earning inequality in developing countries in the world. Now, income inequality in the Asian countries specially in Bangladesh is a major problem. With high population and limited resources, Bangladesh in general and in particular in rural area, are in the grip of economic disaster which causes the great disparity of income. With respect to income inequality in Bangladesh, in the past decades, a few of works have been done, see for example, Omar H. Chowdhury (1974), S.R. Osmani and Atiq Rahman (1986), Atiq Rahman and Trina Haque (1988), Pk. Md. Motiur Rahman (1988) and Pk. Md. Motiur Rahman and S. Huda (1992). This type of investigation has
an importance in explaining the cause of higher inequality and measuring the inequality within the sub-populations and determining the amount of inequality accounted for between the sub-populations. Most of their investigations reveal that the inequality of income distribution is increasing over time, but until now no one conducted any test of statistics, specially Bootstrap methods to test whether changes in inequality from one period to another period are statistically significant or not.
Thus to know the economic situation and condition of social welfare policy of Bangladesh, another attempt has been made to estimate a variety of inequality measures. To test whether changes in inequality from one period to another period are statistically significant or not, Bootstrap methods are applied. Also, another attempt has been to compare in income inequality between urban and rural sectors of Bangladesh. To test, whether their income differentials are statistically significant or not, we also, applied Bootstrap methods. We also try to compare the urban-rural income disparity of Bangladesh internationally. Also, by analyzing the urban-rural income distributions, we highlighted the following issues; (i) is the income distribution of Bangladesh improved or worsened? (ii) is the income distribution of Bangladesh going to follow the Kuznets hypothesis? (iii) what factors have caused the income disparity? (iv) what are the impacts of income disparity on economic development, social and political stability in Bangladesh?

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Year : 2002 |
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Pages : 190 |
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Institution : kyushu University, Japan |
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