As the U.S. government shutdown postpones the Jan. 11 release of monthly market-moving agriculture data, forecasting firms and traders are trying to plug the gap with their own crop estimates.

Gro Intelligence, a closely held data and analytics company, will endeavor to fill the void in two days with its own version of the U.S. Department of Agriculture’s giant data dump at noon New York time. The agency last week postponed its monthly World Agricultural Supply and Demand Estimates, or WASDE, because of the shutdown, approaching a third week.

“This is really critical data for markets,” Sara Menker, chief...