Forrester says that store retailers need to excel at cross-channel selling to thrive.

The web’s influence over all retail spending in the United States promises to increase as more consumers use mobile devices inside stores to read product information and compare prices, according to a new report by Forrester Research Inc.

Thanks in part to that practice, called “showrooming,” the web will influence an estimated $1.66 trillion in U.S. retail sales by 2016, up from $1.10 trillion in 2011 and from about $400 billion in 2007, the report says.

Forrester also says that by 2016, web-influenced offline spending and online retail sales combined will account for $1.99 trillion, or 52% of all retail spending in the United States, which the research firm estimates will reach $3.80 trillion.

Forrester analyst and report author Sucharita Mulpuru says that while showrooming behavior until now has had the greatest impact on hard goods categories such as consumer electronics, no product category is immune to the impact of showrooming and the instant access the mobile web provides consumers. “We foresee a future in which the ability to receive targeted messages and coupons easily and instantaneously will impact categories that have been weaker with respect to online sales, such as grocery,” she writes.

The report emphasizes the importance of excelling at cross-channel retailing for retailers that sell in stores and online. Mulpuru advises these retailers to reduce pricing discrepancies between the web and stores, and to create diversified merchandise assortments that makes consumers less likely to successfully comparison shop those products with other retailers, such as adding private label items or making items sold on the retailer’s web site available for ordering in stores.