Are sales taxes regressive?

There are competing definitions of regressive taxes out there:

On Wikipedia:

A regressive tax is a tax imposed in such a manner that the tax rate decreases as the amount subject to taxation increases.

In a textbook I use (Case, Fair, and Oster's Principles of Economics):

A regressive tax is a tax whose burden, expressed as a percentage of income, decreases as income increases.

By the Wikipedia definition, a sales tax would technically be a proportional tax as the rate is fixed regardless of how the base (consumption) changes.

However, by the textbook definition, and assuming that households with lower income consume a greater percentage of that income than households with higher income (i.e. have lower savings rates), a sales tax with a fixed rate would be regressive.

You might be inclined to suggest that the textbook was defining it specifically for income taxes where the Wikipedia article is defining it generally. Actually, though, the authors of the text make it clear they mean their definition to be general. They say that they define it in terms of income because "all taxes are ultimately paid out of income." I think that statement is a bit imprecise, but whatever. They go on to show an example that demonstrates that sales taxes are regressive (conditional on lower-income households saving less).

I agree with them on an intuitive level that sales taxes are regressive. But then why has Wikipedia decided on a definition that is independent of income, with one consequence being that sales taxes are proportional?

• You're oversimplifying. Sometimes "critical goods" such as food have a reduced sales tax rate or are even exempt from sales tax or "luxury goods" have a higher rate. Also, you are assuming that people of all incomes spend the same percentage of their income and that's not true. I'm pretty sure I pay sales tax on a higher percentage of my income than Bill Gates did. – David Schwartz Jul 6 '16 at 19:21
• @DavidSchwartz I specifically mention my assumption that people with higher incomes have higher saving rates (which you agree with). And let's abstract from sales tax exemptions -- I mean this as a precise theoretical question regarding definitions. The question is whether, even with the assumption, the Wikipedia definition would allow us to call a sales tax regressive. From my reading, it would not, and I find this odd. – Shane Jul 7 '16 at 2:57
• Definitions don't work that way. Definitions are not tests that you can apply to things to see if they "really are" instances of the thing defined. You cannot look up "car" in the dictionary and find out some test you can use to tell what is a car and what is not. If you keep reading that very Wikipedia article, it explains that in the second paragraph, "if the activity being taxed is more likely to be carried out by the poor and less likely to be carried out by the rich, the tax may be considered regressive". Regressiveness is a judgment, not a precise test. – David Schwartz Jul 7 '16 at 8:13
• @DavidSchwartz Sir I do hope your last sentence is intended as humor. – Giskard Jul 7 '16 at 15:27
• @Shane Come to think of it this question is primarily opinion based because it asks us to speculate about the reasoning of Wikipedia... – Giskard Jul 7 '16 at 15:28