# Measuring Ppp-adjusted Gdp: an Anomaly

This is the second of a series of papers concerned with PPP measures. The papers are in varying presentational styles and also reflect my growing understanding of the issues involved, and my improving presentation of them.See Measuring PPP-adjusted GDP Index for the other papers. This paper, written in December 2003, is an exposition based on tabulations.

Keywords: Statistics;

Introduction

There exists an anomaly in the measurement of PPP-adjusted GDPs, in that there is no need for the production-side and the expenditure-side estimates to be consistent. This arises because the expenditure-side measure values a good which is consumed differently from a good which is exported. The practice is to use an ‘average’ domestic price for all consumed good and to use the internationally traded price for exported (and imported) goods. In principle where there is vigorous market competition and no government intervention, the two prices should be consistent. In practice there may be a substantial difference, especially where there is a high degree of protection.

The problem does not seem to have been observed before, because currently the only comprehensive estimates have used the expenditure-side measure. As more attention is paid to the production-side measure, as a part of industry productivity studies, the anomaly will become more apparent.

An Illustration

Consider two countries, X and Y with a ROW (Rest of the World) so large that it sets the international prices used in the purchasing power parity adjustments.

The two countries make but two goods, A and B, measured in some standard unit (say tonnes). Country X produces 60 tonnes of good A and 40 tonnes of good B, while Country Y produces 40 tonnes of good A and 60 tonnes of Good B.

Each country consumes 50 tonnes of good A and 50 tones of good B, so Country X exports 10 tonnes of good A to Country Y in exchange for 10 tonnes of Good B.

The illustration is so simple we do not need to know the prices that apply in Country A and B. The PPP prices, in effect those of Country ROW are given by

PPP price of good A = \$1 per tonne.
PPP price of good B = \$2 per tonne.

Note that the relative PPP price of the goods is different from the price at which Country A and country B trade (reflecting the protection which ROW does to its production of good B).

The following tables shows the calculations for each country to give the PPP-adjusted GDP.

COUNTRY X: Production-side Estimate

 Quantity PPP Price Value Good A 60 1 60 Good B 40 2 80 Trade n.a. n.a. n.a. Total 140

COUNTRY X: Expenditure-side Estimate

 Quantity PPP Price Value Good A 50 1 50 Good B 50 2 100 Exports 10 1 10 Imports -10 1 -10 Total 150

COUNTRY Y: Production-side Estimate

 Quantity PPP Price Value Good A 40 1 40 Good B 60 2 120 Trade n.a. n.a. n.a. Total 160

COUNTRY Y: Expenditure-side Estimate

 Quantity PPP Price Value Good A 50 1 50 Good B 50 2 100 Exports 10 1 10 Imports -10 1 -10 Total 150

The result of the difference between the PPP and the internationally traded price relativities is that while the expenditure side PPP-adjusted GDP is the same in each country (at 150) , the production side adjusted GDPs differ. In particular Country Y which exports the good which is protected against has a higher relative GDP (160) on the production side than Country X (140).

Note that this happens even if Country X does not protect its own production. The anomaly arises because of world protection.

Interpretation

This difference occurs because the export production of the protected good is valued at the (protected) production cost at the rest of the world (and at the same average world price at which it is consumed in the country and elsewhere), rather that at the price at which it is traded (which is depressed relative to the protection).

The measures of GDP represent different things:

The production-side measure reports the production of the country at the average world prices. It is the cross-country equivalent to real GDP through time.

The expenditure-side measure reports the expenditure of the country at average world prices with an adjustment for the current account deficit (when nominal GDP exceeds nominal GNE). It is the cross-country equivalent to real GDI through time.

Conclusion

The aim of this note is not to argue which measure is the ‘correct’ one, but to point out that they are conceptually different. In this case – there may be others – the difference arises because the international trade price of the good is different from the domestic trade price as a consequence of protection.

The estimates can be reconciled by valuing the internationally traded good in the expenditure side estimate at the PPP price rather than the international traded price. This would make no difference to total World GDP (since the boost to exports in exporting countries would be exactly offset by the reduction to imports in importing countries). It would, however, change the distribution of World GDP between countries.

Whether this effect is large or small is an empirical issue. However, it seems likely that the current procedure may markedly depress the relative GDP of some economies which are significant agricultural exporters. Even if the effect were small, the need to give confidence in the integrity of the published estimates of PPP-adjusted GDP, requires that the effect be measured and that both measures of GDP be reported.

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