RDP 2018-08: Econometric Perspectives on Economic Measurement 5. Conclusion

There is a material difference between modelling, say, the price of dwellings (distinct residences), and the price of housing (the infrastructure providing shelter). Modelling the price of housing is a more macro-oriented task and implies a synthetic population of interest. A simple way to implement the macro orientation is to write the model in terms of what I call units of equal interest.

In the field of economic measurement it is common to model prices from macro perspectives, so units of equal interest come up a lot. In fact this paper shows that practically all price index functions are defined by their choice of average, their definition of quality, and their stance on equal interest. For instance, the Törnqvist function, used in the official chained version of the US consumer price index, is defined by the geometric average, any definitions of quality that are constant over adjacent time periods, and units of equal interest that are proportional to expenditure shares. The Laspeyres function, used in the Australian consumer price index, is defined by the arithmetic average, definitions of quality that are proportional to (closing period) prices, and units of equal interest that are proportional to transacted amounts of quality.

This new framework for differentiating between index functions is free of ambitious modelling assumptions. Hence it is more defensible and conceptual than the so-called stochastic approaches that preceeded it. By covering practically all index functions, it is also more comprehensive. And the time investment needed to understand it is small. This hopefully makes it useful for other macro researchers wanting to appreciate the strengths and weaknesses of the tools they are routinely using.

For measurement specialists, the new framework might offer new avenues to understand and tackle measurement problems. To illustrate, I use it to challenge the use of the Goldberger (1968) bias correction, the widespread reliance on unit values, and some common views on quality adjustment with dynamic populations. At a high level, this work is a stochastic complement to recent research on the economic approach to index functions by Redding and Weinstein (2018), because it unifies a wide range of measurement methods.