One can estimate the price indexes:
Estimators for the other trends and indexes— and —are defined in the obvious way.
Next, consider the possibility of estimating the price indexes exclusively using store-level data. Let s0 and st denote probability samples of stores, let the subscript k index the store, and let Wk0 and Wkt denote survey weights corresponding to the unbiased estimator of a population total at times 0 and t, respectively. It is easy to imagine estimators
of total dollar volume and
of total unit volume. These estimators obviously require data on prices and unit volume by good at the store level. Current BLS surveys do not collect such data, but surveys based upon scanning technology could produce these data, at least for a subset of goods in a subdomain of stores. Given and , it is possible to estimate the plutocratic price indexes.
The question is whether the price indexes estimated on the basis of store data really estimate TLp, TPp, and TFp. One would anticipate some biases due to such factors as
goods purchased from stores for business use, not for home consumption;