They are bad for equality
Value added tax (VAT) diminishes the equalizing effect of progressive taxation. And therefore, increases in VAT rates are undesirable while the world is worried about rising inequality.
Value added tax (VAT) is the consumption tax that consumers pay on most they buy: a portion of the price of goods and services goes to the tax authority. In several countries, those on low incomes pay a lower income tax rate than those on high incomes. This is called progressive taxation, and means before tax income is taxed in such a fashion that after tax income is more equally distributed.
VAT potentially regressive
Adding a consumption tax on top of that progressive income tax diminishes the effect of different tax levels:
Assume that the low income tax level is 30%, the high income tax level is 50%, and the VAT is 20%.
When your after tax income is 70% of your before tax income, the VAT adds 14% to your tax burden, relative to your before tax income.
When your after tax income is 50% of your before tax income, the VAT adds 10% to your tax burden, relative to your before tax income.
Takeaway
The takeaway is that when your income is less taxed by the income tax, this is partly counteracted by the VAT. A VAT increase (as seen in several European countries recently) counteracts the redistributive effect of a progressive tax.
When people save, the counteracting effect of the VAT becomes stronger. As saving is (obviously) not taxed by the VAT, the more you save the less you pay VAT relative to your income. And saving is more common among those on higher incomes. A VAT (increase) hence raises the tax burden relatively more for those on lower incomes, because they save less and often pay a lower income tax rate.