Charles L. Ballard (Michigan State University, Department of Economics) & Jaimin Lee (Korea Transport Institute) have published Internet Purchases, Cross-Border Shopping, and Sales Taxes, 60 Nat’l Tax J. 711 (2007). Here is the abstract:

Using data from the Current Population Survey for 1997 and 2001, we estimate the probability that a consumer engages in online shopping. We use variation in sales–tax rates by county to identify the effects of the sales–tax rate in the home county and adjacent counties. We also control for the sales–tax base. The estimates are consistent with the interpretation that consumers use Internet shopping to avoid sales taxes. In addition, consumers who live adjacent to counties with lower sales–tax rates are less likely to shop via the Internet, all else equal. We interpret this as evidence of cross–border shopping.