A paper by David Agrawal is set to be published in the American Economic Journal: Economic Policy. 

If online transactions are tax-free, increased online shopping may lower tax rates as jurisdictions seek to reduce tax avoidance; but, if online firms remit taxes, online sales may put upward pressure on tax rates because internet sales help enforce destination-based taxes. I find that higher internet penetration generally results in lower municipal tax rates, but raises tax rates in some jurisdictions. The latter effect emerges in states where many online vendors remit taxes. A one standard deviation increase in internet penetration lowers local sales taxes in large municipalities by 0.15 percentage points or 16% of the average rate.