Stratified price indices

The starting point for a stratified price index is a partitioning of goods along some set of observable characteristics that determine price, so that each good is placed into a stratum based on these characteristics. For example, a simple stratification scheme is to separate goods according to geography, so that goods are grouped by where they are sold. But goods can be partitioned according to more complex rules—any combination of characteristics can, in principle, be used to stratify goods into distinct groups. A stratified price index is then simply a collection of sub-indices, one for each stratum, along with a set of weights to aggregate these sub-indices into an overall price index.

The usefulness of stratification is that it provides a means to justify an independence assumption that gives each sub-index a constant quality interpretation. Rather than requiring full independence between potential prices and the time when goods sell, however, independence need only hold conditional on the characteristics used for stratification. That is, independence only needs to hold for each stratum individually, rather than all strata simultaneously. With independence, stratification non-parametrically controls for the characteristics that can confound changes in price over time with changes in the composition of goods sold at different points in time. These stratified sub-indices can then be aggregated to get an overall constant-quality index (this is the job of the weight) because the index for each stratum has a constant-quality interpretation.

A stratified approach for constructing a constant-quality price index is just a direct application of the results in the previous section. It is useful to start with stratified indices because these indices require the fewest assumptions and, in some sense, the other approaches for constructing a constant-quality index attempt to mimic a stratified index.

📖 RPPI Handbook: Chapter 4.

📖 PPI Manual: Chapter 7, sections A, C.