Since Benford’s law is an empirical phenomenon that occurs in a range of data sets, this raises the question as to whether or not the same thing might be true in terms of the Chinese income distribution data. We focus on the first significant digit (FSD) distribution of Chinese micro income data from the 2005 Inter-Census sample, which corresponds to 1% of Chinese population and other micro income data from the China family panel studies (CFPS) and Chinese General Social Survey (CGSS). We use information theoretic-entropy based methods to investigate the degree to which Benford’s FSD law is consistent with the FSD of Chinese income data and our findings suggest consistency between the Chinese FSD income distribution and Benford’s distribution. The close connection between the two distributions has implications for the quality of the sample of Chinese micro data.

We use information theoretic information recovery methods, on a 2005 sample of household income data from the Chinese InterCensus, to estimate the income distribution for China and each of its 31 provinces and to obtain corresponding measures of income inequality. Using entropy divergence methods, we seek a probability density function solution that is as close to a uniform probability distribution of income (with the least inequality), as the data will permit. These entropy measures of income inequality reflect how the allocation and distribution systems are performing, and we show the advantages of investigating province variation in income inequality using entropy measures rather than Gini coefficients. Finally, we use a sample of data from the China Family Panel Study to recover an estimate of the 2010 and the 2016 to investigate possible directions of inequality changes using these different additional data sources, given that the 2015 Inter-Census is not yet available.