Price Indexes (2) Estimates and Approximations

The difficulties of price index measurement have been well understood for almost a century. Statisticians have always understood that price indexes, like all statistics are estimates.

Statistics are different from accounting. Unlike accountants, who add up every transaction to produce detailed accurate accounts, statisticians make estimates based on partial information. There is nothing wrong with making decisions based partial information; we all have to do that all the time. Statistics is just a way of systematising partial information to clarify what it means.

All statistics are estimates or approximations. The hard part is determining if these approximations produce something useful. Statisticians put a lot of effort into measuring the accuracy of the statistics they produce. Users of statistics and economic commentators can then decide if the approximations are good enough for their purposes. Serious problems arise when they treat statistics as if they were exact measures.

This issue becomes clear with respect to price indexes, when we remember that in any economy, billions of transactions take place every day. Millions of different goods and services are sold in different quantities at different prices. Recording and measuring all these transactions is impossible. Calculating an average price of all the transactions that occur in the economy in one day just does not make sense. The only way to measure prices is to do what is done with most statistics and that is to take a sample.

This is not an unreasonable course of action. Supermarkets generally charge all customer the same price for a size and brand of baked beans, so it is not necessary to observe every single transaction to understand what is happening to the price of baked beans. However, sampling does introduce sampling error so a price index can never be an exact measure.