We propose updating a multiplier matrix subject to final demand and total output constraints, where the prior multiplier matrix is weighted against a LASSO prior. We update elements of the Leontief inverse, from which we can derive posterior densities of the entries in input-output tables. As the parameter estimates required by far exceed the available observations, many zero entries deliver a sparse tabulation. We address that problem with a new statistical model wherein we adopt a LASSO prior. We develop novel numerical techniques and perform a detailed Monte Carlo study to examine the performance of the new approach under different configurations of the input-output table. The new techniques are applied to a 196 ×196 U.S. input-output table for 2012.