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Sensitivity Analysis
Background
In an international GDP and price comparison, any mistake in the base data of one country influences the overall results. The OECD has been conducting some tests of the sensitivity of PPP results to errors in weights or in the prices supplied by countries using GDP per capita indices for 1996 (US = 100). The testing was based on some EKS results for 28 countries, the results of which are shown in the tables below. Broadly, the first part of the testing involved shifting part of the weight from one component to another. The countries selected were France and Japan, and the components selected for the weight shift had relatively high PPPs and relatively low PPPs in order to maximise the effect of the change. Results indicated that the impact on the country concerned was relatively small and that the effect on other countries was negligible. The second part of the testing involved halving the prices for one component of the overall PPPs. As would be expected, the full effect of this change impacted on the individual country concerned in each case but there was a negligible impact on the comparisons between other countries. In other words, errors in reported prices directly affected the country that reported the incorrect prices but had a negligible impact on comparisons between the other countries involved.
Test I: Influence of expenditure data
Table Set 1: Transferrals of expenditure
In the first sensitivity test, half of the housing expenditure for France was transferred to Food, Beverages and Tobacco ( Table 1.1). Both Gross Rents, Fuel and Power and Food, Beverages and Tobacco are important expenditure categories representing more than ten per cent of GDP in France. These categories was chosen because of differing PPPs, meaning that housing is relatively expensive in France while food is relatively cheap (see Annex tables 1 to 3).
Results indicated that the transfer of expenditure from a cheap category to an expensive one increased Final Consumption in France by less than one per cent. At GDP level the change was 0.72 per cent. For other countries the results remained almost unchanged. Due to increased weight of food, countries with similar price structures to France showed a slight increase in Final Consumption while countries with different price structures indicated a decrease.
In the second example ( Table 1.2), expenditure data for Japan was transferred from an expensive category (Food, Beverages and Tobacco) to a cheap one (Clothing). Results were similar to those seen in the French case.
Table Set 2: Changes in GDP - results using unweighted expenditures
Like temporal price indices, overall PPPs or volumes are not very sensitive for incorrect expenditure weights. This has been demonstrated in table set 2. Table 2.1 shows original volume indices and Table 2.2 demonstrates change in results if the same GDP structure is applied for all 28 countries. Table 2.3 shows the difference in results displayed in Table 2.1 if for each row heading (39 categories) the underlying structure of sub-aggregates is the same for all countries. The structures are estimated as an unweighted average of all countries.
Table 2.2 shows that when using the same GDP structure, change in GDP volume is outside the range of +/-2 for only five countries. As expected, at a detailed level results often change significantly. If structures within sub-aggregates are fixed ( Table 2.3), volume indices for GDP differ much less from the original ones: +/-1 is exceeded only for Spain, Czech and Hungary. At a detailed level, variations are often much larger, but the errors offset as data are aggregated into broader expenditure categories.
In conclusion, incorrect expenditure data seemed to have only a minor effect on overall results. Concerning inter-temporal indices, PPPs are not particularly sensitive to erroneous weights.
Test II: Influence of price data
Table Set 3: Halving PPPs
In Table 3.1, PPPs for Housing in France have been halved and the results compared with original ones. In Table 3.2, PPPs for Food, Beverages and Tobacco for Japan have also been halved.
Due to the high importance of the two categories, the GDP of France and Japan increased significantly. For other countries, the influence on GDP is fairly minimal. Countries in which the volume of housing is low despite low prices will see a slight increase in GDP, while countries with higher volumes and prices will see a slight decrease in GDP (see Annex tables 1-3).
Table Set 4: Influence of basic headings on results
Table 4 shows roughly the influence of the number of basic headings on results. The test was undertaken by basic heading (not using price data). For each aggregate category, PPPs are estimated as a geometric average of underlying basic heading PPPs.
Table 4 is based on eleven basic headings. GDP results are for most countries close to original results. However there are large changes within some areas of household consumption. These changes may also arise as a result of the unreliability of detailed expenditure data.
Conclusions
These examples show clearly that erroneous data from one country do not essentially distort results for other countries. In other words, the influence of incorrect weighting data for one country is negligible as far as other countries are concerned. These tests also demonstrate that if the main purpose is to obtain reasonable overall PPP volumes, the quality of expenditure is not critically important. However, if the aim is to obtain plausible volumes for any sub-categories of GDP then greater attention should be paid to acquiring reliable expenditure data. Unexplainable differences between countries undermines the credibility of the PPP Programme in the same way as anomalies in price levels.
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