Comparison of Gini indices using sequential approach: Application to the U.S. Small Business Administration data

The comparison of Gini inequality indices is an important study related to regional imbalance in equality. In the design of such a study, both the cost constraints and variability of the difference of inequality indices play an active role. In this article, we compare the Gini inequality indices for two regions under cost constraints leveraging on the concept of sequential analysis. Without prior knowledge of the statistical distributions of the data in the two regions of interest, the optimal sample sizes that balance the cost constraint and the accuracy of the comparison cannot be calculated under a fixed-sample-size methodology. Therefore, in this article, we develop a sequential procedure for comparing Gini indices for two regions under a budget constraint. With no specific assumption about the population distribution of the data, we examine and prove the large-sample properties offered by the proposed purely sequential procedure. Further, we use extensive simulations to empirically examine the characteristics of this procedure and illustrate its application using data on the Paycheck Protection Program loan from the U.S. Small Business Administration for the states of Connecticut and Rhode Island.