A virtual regulation analysis for inequality of opportunity: Statistical significance test for the difference of gini coefficients by bootstrap method

Hamada and Ishida (2003) formulated the Virtual Regulation Analysis for Inequality of Opportunity, based on Roemer's idea, equality of opportunity principal. This analytical method enables us to measure the degree of inequality under the virtual state that inequality of opportunity, such as sex or his/her parents' status, is regulated. However, the assumptions of their model were ambiguous and their method did not take into account the way of testing statistical significances for the difference of Gini coefficients between before and after virtual regulation of opportunity. In this article, we clarify the differences between Roemer's model and Virtual Regulation Analysis and propose a method of statistical significance test for the difference of Gini coefficients between before and after the regulation. In order to compute a standard error of Gini coefficient, we use Efron's bootstrap method. We also present some examples of analysis with SSM 1985 and 1995 data. Furthermore, we discuss the methodological problem about the partition of the data of achievement level and give one theoretical answer. As one of applications of our method, we analyze the effect of inequality of opportunity as to the amount of inherited immovable property on the amount of family immovable property and family income corresponding to different numbers of partition intervals.