Longitudinal Analysis, Part 3 – Index Numbers

Index numbers are unique to socio-economic statistics and are well-established. The need for index numbers has never been seriously questioned. They also pursue the longitudinal study of socio-economic phenomena, but are not recognized as belonging to the analysis of time series. Index numbers seem to be different, with theories and problems of their own. The discussion has not really gone much beyond the thinking of Laspeyres and Paasche some 125 years ago. It reflects the scienceinspired ideal of that epoch concerning the measurement of ‘prices’ p, ‘quantities’ q, and the role of weights.¹ There was a time when the discussion of Price-indexnumbers dominated the scene. By simply reversing prices p and quantities q, a price-index-number formula seemed readily convertible to a quantity-index-number with price weights. As will be discussed in the following, the classic ‘index-numberproblem’ is really a pseudo problem. Price measurement can be greatly simplified by recognizing the misconceptions about the nature of ‘price’, about the complex nature of ‘quantities,’ and about the unrecognized features of socio-economic data. All this has been ‘off the radar screen’ of statistical theory.

Grau, teurer Freund, ist alle Theorie, doch grün des Lebens goldner Baum

Johann Wolfgang von Göthe, Faust I Studierzimmer, Mephisto 2038; translated: “Gray, my dear friend, is all theory, but green is life’s golden tree”.