A Democratic Measure of Household Income Growth: Theory and Application to the United Kingdom

We show that when a nominal household income variable is constructed as the geometric mean of household income and is deflated using a price index whose weights are calculated as the average of each household's expenditure shares, the growth rate of the resulting volume indicator is the average of the growth rate of the real income of each household. This indicator, which treats the income growth experience of a high‐earning household the same as that of a low‐earning household, can be described as democratic. Conventional measures computed from arithmetic means of household incomes and deflated using indices based on aggregate expenditure shares are, in contrast, plutocratic, in the sense that the experience of high‐income households contributes more towards the growth in total income than does the experience of low‐income households. We show that in the UK over the interval 2005/6 to 2015/16, democratic real equivalized household income after housing costs grew by 0.20% per annum while the plutocratic equivalent grew by 0.52% per annum.