Vol.:(0123456789) SN Bus Econ (2021) 1:148 https://doi.org/10.1007/s43546-021-00151-9 ORIGINAL ARTICLE Some confdence intervals and insights for the proportion below the relative poverty line Dilanka S. Dedduwakumara 1,2  · Luke A. Prendergast 1  · Robert G. Staudte 1 Received: 14 March 2021 / Accepted: 14 September 2021 / Published online: 13 October 2021 © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 Abstract We examine a commonly used relative poverty measure called the headcount ratio ( H p ), defned to be the proportion of incomes falling below the relative poverty line, which is defned to be a fraction p of the median income. We do this by consider- ing this concept for theoretical income populations, and its potential for determin- ing actual changes following transfer of incomes from the wealthy to those whose incomes fall below the relative poverty line. In the process we derive and evaluate the performance of large sample confdence intervals for H p . Finally, we illustrate the estimators on real income data sets. Keywords Confdence intervals · Headcount ratio · Poverty · Quantile ratio index Introduction Simple-to-interpret and scale-free measures of poverty are commonly used to assess economic health of a country, either in comparison to other countries, or as a meas- ure of change within a country compared to historical measures. One commonly used measure, often referred to as the ‘headcount ratio’, is the proportion of indi- viduals whose income is less than a fraction, p, of the median income. Usually, p is chosen to be between 40 and 60% (e.g. Burkhauser et al. 1996 see who use these rates with p equal to 40%, 50% and 60% as measures of poverty in Germany and the United States) and for many countries a specifc choice of p is used to defne the ofcial poverty line. The Organisation for Economic Co-operation and Development (OECD) specifcally defnes the poverty rate using p = 0.5 (https://data.oecd.org/ inequality/poverty-rate.htm) and this has been adopted by many governments. For example, in Hong Kong it is p = 0.5 and recently this defnition of poverty has been * Luke A. Prendergast luke.prendergast@latrobe.edu.au 1 Department of Mathematics and Statistics, La Trobe University, Melbourne, Australia 2 School of Mathematical Sciences, The University of Adelaide, Adelaide, Australia