Here's a key section of his post, but prior to this he also discusses of the poor quality of the underlying data used by Cox and Alm in coming to their conclusions:
...There is a more fundamental problem with Cox and Alm’s argument. I agree that it is helpful to consider consumption in addition to income, but the point applies more to our assessment of poverty ... than to our assessment of inequality. After all, the portion of their income that high earners don’t spend gets saved. It is therefore available for later spending. And income saved becomes an asset that provides financial and psychological security.
While there is less inequality of consumption than of income, the flip side — because those with high incomes are able to save and invest much more — is that inequality of wealth is much greater than inequality of income. The following chart shows the shares of income and wealth of the bottom two quintiles (fifths) and the top three quintiles of households in 2004 (the most recent year for which wealth data are available). The calculations are by Edward Wolff (here), using data from the Federal Reserve’s Survey of Consumer Finances. The bottom two fifths of households have just 0.2% of the total household wealth. The top fifth have 85%.
If we focus on spending, we miss this key part of the inequality story.