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On the website https://www.core-econ.org/ in the book provided, there is an exercise 19.10. It asks whether poll tax is progressive, regressive or distributionally neutral. To answer this question of course we need to know first what is regressive, progressive and distributionally neutral tax. First of all a poll tax is a tax levied as a fixed sum on every liable individual.

  • Progressive tax is a tax in which the tax rate increases as the taxable income increases.
  • Regressive tax is the opposite, it takes larger percent from low-income earners and lower percentage from higher income earners.

However I could not find the definition of distributionally neutral tax.

My question: What is the definition of distributionally neutral tax?

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  • $\begingroup$ To me, this question appears to be incomplete or fallacious, at least from a CGE point of view. The only point that matters is how the tax is recycled, be it progressive, regressive or whatever... Which is coherent with Henry's answer actually. $\endgroup$ – keepAlive Oct 4 '18 at 9:58
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It depends on what the writer intended. Here, just over halfway down section 19.10, is a part with the orange title Progressive and regressive redistribution with a paragraph saying

When the direct effect of a tax or transfer policy (compared to what would happen in the absence of the policy) is a reduction in inequality, it is called progressive. We have just seen that expenditures are more progressive than taxes. If a policy’s direct effect is a rise in inequality it is called regressive. Policies that are neither progressive nor regressive are called distributionally neutral.

Clicking on the blue bolded words gives the definitions

progressive (policy) An expenditure or transfer that increases the incomes of poorer households by more than richer households, in percentage terms.

distributionally neutral A policy that is neither progressive or regressive so that it does not alter the distribution of income.

The definition of regressive seems to be missing but presumably is something which increases the incomes of poorer households by less than richer households, in percentage terms. Similarly, presumably all three can also be applied when the policy reduces incomes, with progressive being where the richer households are hit proportionately hardest, regressive being where the poorer households are hit proportionately hardest, and distributionally neutral where all households are hit proportionately the same. There will be other types, such as those which hit rich and poor proportionately the same but middle incomes differently.

The key to answering the exercise comes from considering the proportionate effects on incomes of a poll tax.

Other people have used distributionally neutral in a different sense: for example Michael Linden discussing a flat percentage tax with a single deductible used it to mean a result with the same distributional effect as the income and payroll taxes it might replace; he meant that the change (rather than the policy itself) should be broadly neutral on the current distributional effect of these taxes

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