After Amazon collects sales taxes, households increase their spending on Amazon's taxed competitors, but not its untaxed competitors. I find no evidence that households change their browsing or shift their spending offline. Collecting sales taxes online will help governments recapture lost taxes and increase online competition, but will not shift customers back offline.

Working Paper
A World Without Borders Revisited: The Impact of Online Sales Tax Collection on Shopping and Search
August 2020
WP 20-34: I study the effect of closing the online sales tax loophole on online spending and search. Using online shopping data, sales taxes, and Amazon’s staggered sales tax collection, I estimate that household price elasticity is -1.9, implying a 13% decline in Amazon’s revenues upon sales tax collection.