This is an addition to The Impact of International Price Discrepancies on PPP-adjusted GDP and expands on material in Estimating Production and Income Across Nations: Reconciling the Differences: the New Zealand Experience .
While the nominal output of an economy, usually called ‘Gross Domestic Product’ or GDP is exactly the same whether it is measured by what is produced or how it is disposed – on the production side or the expenditure side of the economy. This occurs because the incomes the expenditure generates exactly matches the outlays (including investments) the incomes finance. However this mathematical congruency does not apply when a different set of prices is applied to the production and expenditure sides of an open economy, even if the prices are consistent. The difference arises because the goods and services consumed in an open economy differ from that which is produced because some of the domestic production is exchanged for foreign production, that is it is exported to in exchange for imports. The ratio of the exchange values can vary, and that leads to the difference when, for instance, constant price GDP estimates are made over time. This exchange ratio can be measured as the ration of export prices over import prices. Note that the exchange rate does not directly influence the terms of trade ratio, providing the prices are measured either in the local currency or the international currency.
The difference between the two over time has long been understood in New Zealand, which is a small open multi-sectoral economy much prone to changes in its terms of trade as the following Chart shows. There can be substantial changes in the terms of trade both on a year to year basis and secularly.
The issue was important practically in the 1950s and 1960s when the Court of Arbitration made a General Wage Order, which changed all the award wage rates in the economy. There was no express reference to the terms of trade in the law guiding the court but it was required to take into consideration ‘any increase or decrease in productivity and in the volume and value of production in the primary and secondary industries of New Zealand’ (as well as changes in consumer prices). (See In Stormy Seas p.93) How then to measure productivity? To simplify, it could be measured as volume GDP per unit of labour input, in which case the different measures of volume become significant. In any case workers were keen to a share any benefit from a rise in export prices, while businesses were keen to share their fall.
The resolution was to have two measures of volume GDP (or in those days GNP). Today they would be called RGDP and RGDI, although the latter was then called ‘effective GDP’. RGDP was calculated on the production side, indicating what had been produced in constant prices. RGDI, calculated on the expenditure side, was a measure of the purchasing power the production generated. It differed from RGDP by valuing exports in terms of the imports they would purchase. The relationship, ignoring the details of the price bases, between them is
RGDI = RGDP + (value of exports)/(import price index)
RGDI = RGDP + (volume of exports)* (terms of trade)
= RGDP*(1 + (volume of exports/RGDP)* (terms of trade)). 
In an economy with exports as a low proportion of output, and not prone to major changes in its terms of trade, the difference between RGDP and RGDI would be small. But in an economy of New Zealand’s characteristics the effect is not insignificant
Chart 2 of the ratio of RGDI to RGDP shows an overall pattern of a downward trend in the ratio, implying that RGDI has grown more slowly that RGDP by about .1 percent a year. The downward trend reflects that New Zealand had faced deteriorating terms of trade in the post-war era. (There were two main drivers. The largest traditional export, wool, was undercut by synthetics, and the other two traditional exports, meat and dairy products – still the largest good exports today – are subject to widespread international protectionism including restrictions of access in affluent markets and dumping by producers in those affluent markets into third markets. The effect is that RGDI has grown less than RGDP in the post 1950 era by about 5.5 percent.
There is considerable variation around this postwar decline, reflecting swings in the terms of trade. The standard deviation of the year to year changes is 2.0 percent compared to an average annual change in RDGP and RGDI of 1.5 and 1.4 percent respectively. In about half the years the growth of RGDP and RGDI diverged by more than their trend growth rate.
Thus for New Zealand the distinction between RGDP and RGDI is important in the short run, and the long run. The production story is quite different from the income/expenditure story.
Does PPP-adjusted GDP measure RGDP or RGDI?
The New Zealand divergence may be large for an OECD country (although Australia and Norway may be comparable). Even so, whenever price adjustments to GDP are made we need to ask whether the resulting measure is conceptually RGDP or RGDI.
In the case of international comparisons involving GDP adjusted for differences in purchasing power parity, the practice is to calculate the measure on the expenditure side. It therefore corresponds to RGDI. This is not an unimportant point, since most volume GDP statistics are conceptually derived on the production side.
Does this matter? It is well known that PPP-adjusted measures do not appear to track through time very well. Could the effect be from using RGDP for the track rather than RGDI?
To explore this issue a comparison was made between the 19990 and 1999 OECD estimates for PPP-adjusted GDP.
In 1990 PPP-adjusted GDP estimates were estimated for the 24 OECD, although Germany has to be omitted for the 1999 comparison because of the merger with East Germany shortly after. Table 1 shows the 1990 GDP figures, and the projections as to what they would be in 1999 based on the OECD reported increases in RGDP, and RGDI.*
[*RGDI was calculated from the reported terms of trade change over the period and the proportion of exports in nominal GDP in 1995 (see equation 2). This is only an approximate estimate, and could be refined if the data was available. A particular worry is that the terms of trade are only for goods, whereas service exports are becoming significant and have a different track to goods prices.]
Table 1: 1990 and 1999 Volume GDP Levels
* = RGDI gives a better projection than RGDP
underline indicates economies in which the projection is more than 9 percent in error.
(The table is constructed as follows. The ‘Actual’ columns (2 and 7) are the PPP-adjusted figures as reported by the OECD for the 23 relevant countries. Note that the first is in 1990 prices and the last is in 1999 prices. The 1990 Actual was then increased by the reported RGDP growth (column 3) and the RGDI growth (column 4) to give estimates of 1999 GDP but in 1990 prices, so they are not comparable with the 1999 Actual.
We do not know the actual increase in prices between 1990 and 1999, so we assume that the increase over the two periods was exactly enough to increase the aggregate GDP for the 23 countries to the level in 1999. (Insofar as this assumption is wrong, this adds a further source of error.)
For 16 starred countries the RGDI figure derived from the 1990 base is closer than the RGDP figure. For 7 the RGDP projection is superior. (I also tried the assumption that the US (rather than 23) price inflator was correct and the EU (rather than the individual 23) price inflator was correct. Neither made a great difference to the outcome. Nor did projecyting to 1999 from 1993 or 1996.) This gives a little support to the argument that PPP-adjusted GDP is a RGDI conceptual measure, although the case is not conclusive.
Far more importantly, however, the exercise suggests that the 1990 PP-adjusted GDP projected by either volume GDP growth is not a very good predictor of the 1999 figure. In the 5 italicised countries in the table, the error is in excess of 9 percent. Among the remaining 18, the standard deviation of the error is 4.6 percent for the RGDP projection and 3.6 percent for the RGDI projection.
We conclude then that while there is a case that RGDI projections are superior to RGDP projections, supporting the analytical proposition that expenditure side PPP-adjusted GDP is analogous to RGDI, there are other factors which reduce the usefulness of projecting PPP-adjusted GDP from past years. Insofar as these factors are measurement errors they will be eliminated with time. Indeed, some appear to be ‘start-up errors’.
But this paper’s concern with the RGDI versus RGDP difference leaves open the possibility that there may be conceptual errors too. That analysis belongs to another paper.