The statistical reconciliation of time series of accounts between two benchmark revisions

The 2003–2007 U.S. annual input–output accounts, GDP‐by‐industry accounts, and expenditure‐based GDP are reconciled with the 2002 and 2007 quinquennial benchmarks and all contemporaneous constraints of the input–output accounts for the in‐between years. The reconciliation is performed at a very detailed level (six‐digit NAICS) according to feasible statistical procedures able to deal with very large systems of accounts. Our objective is to adjust the preliminary levels of the annual 2003–2007 series such that they are consistent with the quinquennial benchmarks available, fulfill all the accounting relationships for any given year, and show movements that are as close as possible to the preliminary information. We use a simultaneous least‐squares procedure based on the proportional first difference criterion, a well known movement preservation principle proposed by Denton. We evaluate the possible adoption of (i) a pure proportional (PROP) adjustment for small series and series with both negative and positive values that deteriorate the meaningfulness of growth rates, and (ii) a priori assumptions for groups of variables according to their different reliabilities, where this can reasonably be imposed.