On Chained Price and Quantity Measures that are Additively Consistent

The international movement to convert the real (deflated) components of the NIPAs to chain indexes, in order to assure timeliness, has introduced grave inconsistencies. Most importantly, the components no longer add up to the totals. The U.S. accounts which employ a Fisher chain have additional inconsistencies. For example, the product of the price and quantity indexes does not reproduce the change in nominal expenditure. The paper presents a unified approach to the construction of price and quantity measures which can be chained while maintaining every kind of consistency. The solution is based on a combination of elements from the theories of price indexes and consumer surplus.