Real versus nominal, constant price versus current price: A comment on some terminology that is used in economic statistics

In a recent critique of this paper by Dr Andrew Leigh and Dr Chris Ryan, Dr David Zyngier has suggested that a time series on education expenditure that is constructed by Leigh and Ryan is wrong. One of Zyngier's reasons for making this claim is his belief that Leigh and Ryan (2008) did not adjust for inflation. While it is true that Leigh and Ryan did not adjust the education expenditure data in Appendix Table 2 of their paper to account for inflation, they did not claim to do so. Indeed, the title of that table is "Nominal education expenditure (Spending per child per year, in current dollars)". Zyngier appears to have confused nominal data with real data. Specifically, he has interpreted "current dollars" to mean "constant 2003-2004 dollars". I suspect that this confusion may have been caused by a lack of familiarity with the terminology of economic statistics on the part of Zyngier. While Leigh and Ryan (2008) are correct to use the term "current dollars" to refer to nominal data, it is not difficult to see why someone who is unfamilar with the terminology employed in economic statistics might misinterpret this to mean "constant prices for this year" or maybe "constant prices for the most recent year in the data set". Such a mistake is understandable. After all, the everyday meaning of "current" is "now", not each of many previous points in time. Nonetheless, while such a mistake is understandable, it still renders this aspect of Zyngier's criticism of Leigh and Ryan (2008) invalid.

In economic statistics, current dollar figures refer to nominal values. These are valued in terms of the dollars of the year in which the expenditure took place. On the other hand, constant dollar figures refer to real values. These are valued in terms of a particular years dollars. I suspect that misinterpreting "current dollars" to mean "constant dollars of the the most recent year in the time series" is probably an easy and understandable mistake to make for people who are not familar with the terminology employed in economic statistics.

The distinction between nominal (or current price) data and real (or constant price) data exists because time series data on pure quantities is sometimes unavailable in circumstances where time series data on expenditure and time series data on prices is available. In these circumstances, it is possible to obtain an index that represents the implicit time series data on quantities by:

1. Constructing an expenditure index from the nominal expenditure time series;

2. Constructing a price index from the price time series; and

3. Deflating (that is, dividing) the nominal expenditure index by the price index.

4. Renormalising the resulting quantity index so that it has a base year.

The result of this is an index of the underlying quantities. If the time series of nominal expenditure itself is deflated by the price index, then the resulting data will be a time series of real expenditure. This is simply actual expenditure valued at the prices that prevailed in whatever year is chosen as the base year.

When it comes to actual data, things are, of course, much more complicated. In particular, it is necessary to deal with both aggregation and quality changes when constructing the underlying price index. There are also other techniques for constructing volume (or quantity) indices, including the use of chain weights. There is a large literature on the properties of various different types of indices. An overview of this literature can be found at this website for a course on index numbers that is taught by Professor Erwin Diewert at the University of British Columbia in Canada.

Note 1. The full reference for Leigh and Ryan (2008) is: Leigh, A and C Ryan (2008), "How has school productivity changed in Australia?", mimeo The Australian National University, Canberra.

Note 2. Dr Zyngier's criticisms of Leigh and Ryan (2008) appear in three places. The first place they appear is in this article in the online version of the Australian's Higher Education Supplement from Wednesday 19 March 2008. The second place they appear is in a letter to the editor of the online version of the Age from Tuesday 1 April 2008. However, it should be noted that this letter does not explicitly mention the current doolar versus constant dollar issue. The third place in which it appears is in this comment on this post at Dr Leigh's blog site. Andrew addresses a different aspect of Dr Zyngier's critiques in the post mentioned above.

Note 3. While Leigh and Ryan (2008) privide a time series of nominal education expenditure in their Appendix Table 2, they also provide three alternative time series of real education expenditures in their Appendix Table 4. The real data is presumably based on the nominal expenditure data in their Appendix Table 2 and three alterenative price indices that are provided in their Appendix Table 3.

Update: I have made some edits to this post, including the addition of point four in the section of the post that discusses the construction of a quantity index from a time series on nominal expenditures and a time series on prices.