Does the "missing" high-income matter? -Income distribution and inequality revisited with truncated distribution

Abstract

The issue of missing high-income data in household surveys has been a constant concern among researchers and practitioners when drawing inferences on inequality measures, discussing the relationship between poverty and growth, and examining the relationship between expenditure and income. We introduce a truncated distribution technique to correct the potential bias caused by the missing high-income data. Using 2002/2007/2013 Chinese Household Income Project Survey data and the 2002/2007/2014 US Consumer Expenditure Survey data, we test and estimate three commonly used income distributions: lognormal, Singh Maddala, and Beta II distribution with/without the truncation assumption. We find that the truncated Beta II distribution best describes income distribution in China, while the truncated Singh Maddala best fits the income in the US. The missing high-income in China has a significant but small effect on the Gini and Theil coefficients for 2007, whereas the missing high-income in the US has significant effects for 2007 and 2014. The Gini coefficient increases from the sample mean 0.44 to the simulation mean of truncated Beta II distribution as 0.47 for China in 2007 and increases from the sample mean 0.4422/0.4485 to the simulated mean of truncated Singh Maddala distribution 0.4506/0.4588 for 2007 and 2014 respectively. We also check the impact of missing low-income individuals on inequality assessment and find that the missing low-income data does not appear to underestimate inequality.