Purchasing Power Parity Estimates for Canada and Implications for Volume Comparisons
Katharine Kemp and Gaston Levesque
Statistics Canada

Abstract

Introduction

(Tables and Charts of three comparisons and the exchange rate and the volume comparisons follow).

Year	OECD multilateral	OECD bilateral STC (projections)	PENN Mark 5.6a	Market Exchange rate
1980	1.27	1.21	1.15	1.17
1981	1.28	1.20	1.16	1.20
1982	1.31	1.21	1.21	1.23
1983	1.32	1.24	1.22	1.23
1984	1.30	1.25	1.22	1.30
1985	1.29	1.24	1.21	1.37
1986	1.29	1.23	1.21	1.39
1987	1.30	1.23	1.21	1.33
1988	1.31	1.25	1.21	1.23
1989	1.32	1.23	1.21	1.18
1990	1.30	1.22	1.21	1.17
1991	1.29	1.23	1.19	1.15
1992	1.28	1.23	1.18	1.21
1993	1.26	1.23
1994	1.25	1.21
1995	1.24	1.20
1996	1.22

Real Gross Domestic Product per head, Canada/US

1. Bolded data indicates years of OECD-EUROSTAT benchmark studies.
2. 1996 is a projection. The benchmark study is not yet complete.
3. OECD columns are based on current dollar data; PENN data has been adjusted to use Canada and US published data from OECD National Accounts, Vol I.

Description

In general, some axiomatic properties are required in spatial comparisons (as are also required in time series, depending on the purpose of the price indexes). For example, the results must be transitive. This means that the results will be consistent whichever country (or group of countries) is used as the base. This requirement leads to the use of Fisher formula price ratios between countries. The Fisher formula also has a drawback for some purposes in that the derived volume components do not sum to the total volume for the GDP. For some analysis this is not a serious concern while for other types of analysis, such consistency in aggregation is important. Another requirement is factor reversibility; that is, the restatement of the value series deflated by the PPPs will yield the volume indexes and vice versa, with no remainder.

The OECD multilateral benchmark studies, in which all countries are related to each other and to the whole, incorporate price and expenditure data from all the countries included in the comparisons. Comparisons (PPPs) between any two countries therefore take into account the economic structures of all countries in the comparison. Each PPP takes into account the market composition and economic structures of all countries in the comparison, not just the goods and services on the markets being compared. Complexities arise from the different markets for consumer and investment and the variety of goods and services consumed in all the countries. The potential exists for strong negative or unpredictable correlations between price and quantity on a cross-country basis. Otherwise stated, a relative price increase between two countries gives little intuitive feel for what the relative quantity impact might be, unlike the case in time series where a rise in price for an item is expected to produce substitution effects, decreasing the quantity purchased. This phenomenon in a spatial context leads to much wider differences than are seen in time series between the Laspeyres and Paasche indexes. (In spatial comparisons, the base or given country’s weights are used to compile the PPPs)

Following a look at the three sets of results for the Canada /US comparisons of price and volume, this paper reviews the factors and their impacts which contribute to the differences in levels and trends of these PPPs and volume comparisons and describes some initiatives underway to develop and improve the comparisons. The discussion concerns the macro level of the PPPs, as well as estimation procedures at more detailed levels (micro PPPs).

Results

The first table and chart show results of the three Canada/US PPP comparisons for the period 1981-1995, ³ and the exchange rate, all in Canadian dollars per US dollar. The PPPs in all cases refer to the Gross Domestic Product, that is, micro PPPs weighted with GDP expenditure categories. The first column presents the time series created by the OECD from its benchmark studies (bolded) for all countries in the multilateral comparisons. For this multilateral comparison, the PPP projections are calculated using the ratio of the growth rates of the Implicit Price Indexes for the Canadian and US GDPs. The years between benchmarks use forward projections for years near the earlier period and retro-projections for years nearer the later benchmark. The second column also uses the results of the OECD benchmark studies in the same years but for the direct bilateral Canada/US comparisons. In this case, the PPPs are projected and interpolated in all the intervening years, weighting the PPPs projected forward and backwards between benchmarks to smooth the transition. Again, the ratio of the growth rates of the IPIs for Canada and the US are used as projectors of the PPPs, but at the level of the 55 published categories. The PENN World Table brings together comparisons in space and time, using adjustment factors to convert or smooth time series and benchmark data and to fill in gaps where actual country data are missing. The results cannot be precisely compared with the OECD studies due to the inclusion of price and expenditure data for many more countries. Incorporating the economic structures and prices for 150 countries also affects the relationship between each pair of countries in the study.

In 1985, the bilateral PPP for Canada (US=100) was 1.24 at the level of the GDP, compared with the multilateral results of 1.29. In 1990, the bilateral result was 1.22, compared with multilateral result of 1.30. In 1993, a limited bilateral US/Can study was undertaken, yielding a bilateral PPP of 1.23 compared to 1.26 for the multilateral result at the level of GDP. The PENN result was 1.21 in 1985 and 1990, closer to the bilateral result.

Differences exist between the Canada/US PPPs shown by the OECD-EUROSTAT multilateral and bilateral benchmark results, with the PPPs from the bilateral results always lower than the multilateral results. This means, it takes relatively fewer Canadian dollars in Canada to buy the same amount as one US dollar purchases in Canada, across all the GDP components, when looking at the bilateral results than when using the multilateral results. Such results imply an intuitive result that the closer match of specifications, prices, markets, and economic structures between the two countries brings the price comparisons closer together.

In the series calculated for the PENN real output, the current price estimates have been adjusted, substituting the national published estimates for GDP in current dollars and population ⁴ for the data shown in the PENN Table itself. (PWT 5.6a). This brings the volume measure to levels just above those for the bilateral study, as would be expected from the slightly lower PPPs.

A consistent result demonstrated by the three time series of volumes for Canada relative to the US, is that the output per head has been declining since 1990. In this period both Canada and the US experienced slowdowns in growth. If the hypothesis that Canada’s cycle is steeper and slower to recover, the volume results are plausible.. Some other factors which also affected the downward trend were downward data revisions in the GDP expenditure series in Canada and an upward revision to the population counts, following the 1991 census of population.

PPP estimations

Many empirical considerations, techniques and measurement approaches are involved in the estimation of the PPPs and the derived volume estimates, both for the benchmark studies, and for the interpolated time series. The price index theory and choice of formula issues are largely left for discussion elsewhere. The purpose of this discussion is to look at more statistical estimation aspects, which play a critical role in the comparative result.

It should be noted first, that spatial price comparisons contain all the same issues and problems that are found in time series, and usually they are much more complex. As in time series, the measurement of non-market services (government health and education) causes particular difficulty. These are measured using the same convention as in time series, that is, inputs are used to measure outputs. A major shortcoming of the input-cost approach is that it does not account for differences in productivity levels among countries. Wage rates and purchased goods and services as well as capital consumption allowances must be estimated. Does the doctor’s wage rate in different countries reflect the increased or decreased productivity of having fewer tools and less equipment to work with? This is a more serious problem spatially than in time series, where the equipment and technology would be expected to change more slowly, not causing major shifts in productivity over time. Spatially, depending on the countries being compared, wide differences are possible. No adjustment for intercountry productivity differences are attempted when using these inputs as proxy measures for the desired outputs, although research is ongoing in this area. Such adjustments could be very significant, depending on the GDP component and countries being compared. These are often referred to as “comparison-resistant” goods. The closer countries’ economic, institutional and market structures are, the less will be the concern with such issues.

The individual price comparisons among countries are the key element in the PPP estimations. It is much more difficult to measure price differences across space than through time. Growth rates for one country’s market through time are easier to identify than differences in price levels across markets at a point in time. The latter require item specifications that are sufficiently representative of a country’s consumption and at the same time are comparable among countries. The specifications developed and used in the OECD-EUROSTAT program tend to be Euro-centric, that is, they are more representative of consumption in the western European countries than they are of non- European countries, such as North America, Australia, New Zealand, or Japan.
 

Bias concerns statisticians in spatial comparisons even more than in time series. Bias can be introduced at many different levels. To increase comparability and reduce possible biases in the comparisons, the prices incorporated rely on a combination of the following characteristics and filters. Generic and specific specifications are used. Specific specifications are quoted in terms of manufacturer and model number and produce the most exact matches, but are not always available among countries, or may not be typical of spending patterns. To fill in gaps, more generic specifications are combined, in which the characteristics of the item to be priced are described. While these specifications lead to price estimations for representative goods and services in most countries, they also embody quality differences between countries. They may therefore be closer to a unit value comparison, rather than a measurement of pure price differentials. A third approach used is the functional equivalence group, specifications which lie between the specific brand and model (which may not be typical or even available in certain markets) and the generic specifications which are not specific enough. The functional equivalence approach identifies more technical characteristics of the good and a range of “qualities” (high end, popular-priced, etc.) so that representativity can be improved in individual countries. To counterbalance bias that may be introduced, each country prices both typical items in its market and atypical items which are representative in another country. It is hoped that in combining the typical item PPP by the atypical one, the result should be reasonably objective. Possible errors may still arise if the degree of bias is different in the two directions, due, for example, to the type of outlet chosen in different countries, or the sample sizes. As is often the case, the statisticians count on offsetting errors in such comparisons. Bias is still less of a problem between Canada and the US than among other countries, however.
 

In addition to the price issues raised above, a number of other factors can influence the results. In the OECD-EUROSTAT comparisons, the individual PPPs themselves are not revised. However, the extent and timing of revisions to National Accounts expenditure data can and do affect the volume comparisons. In Canada, the biggest downward revision in the GDP in at least 25 years occurred in 1990 (1.2%). This was also the year of a benchmark study. The results of the census of population conducted every 5 years are introduced when the results become available. For the intervening years, the population is extrapolated. When the 1991 results became available, the projections were found to be too low, due to a technical undercounting, and the population counts were raised by 4% for the census year, and adjusted for the entire series. The effect of these two revisions was to lower output per person by 5-6%. In the bilateral time series constructed in Statistics Canada the macro PPPs are revised through revisions that re-weight the micro PPPs. The accuracy of population counts in other countries is hard to evaluate. Intuitively, we expect undercoverage in the United States as a result of the number of illegal residents in the country. Furthermore, if all the comparisons are not using data at the same point of timeliness (i.e preliminary or revised estimates), the results will be different. For example, in the PENN work, the data on population and GDP may be taken from indirect sources, and lack the latest revisions, as noted above. Canada has just incorporated a historical revision based on the 1993 international guidelines for the System of National Accounts. These are not yet incorporated for countries in the published OECD version of National Accounts nor are they incorporated in the PPP comparisons. To the extent that other countries are on a different time schedule, the comparisons among countries will be less accurate to some extent.

The accuracy of the National Accounts expenditure data in all countries in the comparisons and the classification system used for the expenditures are significant factors. The United States, for example, has never been an adherent of the System of National Accounts, although they are moving closer to it. They do special tables for the OECD incorporating some special classes of expenditure, which are not available in their National Income and Product Accounts. As a result, some expenditure matches are not as precise as would be desirable. The PPPs are calculated by the OECD-EUROSTAT programme using two classifications, the System of National Accounts (SNA) which is an expenditure classification, and the ICP, the consumption-based classification used in the United Nations’ International Comparison Program and incorporated in the PENN tables. These classification differences impact results for goods and services paid for by government and consumed by individuals., such as health and education. The ICP results are more relevant in cases where the analytical emphasis is on the consumer.

The classification system used for the expenditure data, especially for personal expenditure categories is moving towards the COICOP, that is, the SNA 1993 classification to be adopted by all countries. This should eventually improve the consistency of the program among all the countries.

The definitions and measurements of key concepts embedded in the National Accounts expenditures and the accuracy of the surveys and administrative data sources also play a role in the measurements. We have seen a growing gap between unemployment rates for Canada and the US. This may reflect definitional differences, undercounts, or measurement tools to a greater or lesser extent. Again, expectations are that such differences would be less between the US and Canada than between many other country comparisons.
 

• Benchmarks

Most of the discussion concerns the two OECD comparisons: Canada/US from the multilateral comparison and from the bilateral comparison. The PENN tables are constructed differently, taking into account many more countries and deriving some estimates using statistical methods rather than direct price data. Because of the similarity in tastes, markets and institutions between Canada and the United States, the OECD bilateral comparison is the most robust comparison. This similarity, which is reflected in expenditure baskets in both countries minimizes the bias due to the aggregation process. The range of goods and services consumed are similar, item specifications can be well matched, similar outlets are the source of purchases in the two countries, income levels are broadly similar and statistical classifications and definitions are also very similar in many instances. This is one set of factors contributing to the strength of the comparisons for the benchmark studies. Still, the comparisons are faced with different types of price data banks in the two countries, where in Canada we are using a much thinner range of prices and in the US it is a probability sample, not necessarily geared to a spatial comparison.

• Time series

Price index theory tells us that an index number problem always exists. Changing price structures over time and through space alter the trend of a price index and rebasing of price series is necessary to bring the growth rates into line. This is true of spatial comparisons as well as time series. When we compare relative rates of growth using national GDP and those implied from successive PPP benchmark studies, the change in price structures both within countries over time and among countries spatially has the effect that the projected growth rates and new benchmark levels will not match. The implication is that any projection of the time series can never be an accurate reflection of new PPP levels. The projection of the multilateral PPPs, using the growth rates of each country’s GDP results in apparent discontinuities whenever the benchmark results are completed. These are not usually severe, but they do represent a conceptual issue. In the bilateral series the smoothing process was not based on index number theory, but rather averages out the trend between the benchmark levels, projecting ahead from the most recent study until the results are completed. The PPPs using these results have stayed within a narrower band.

Another point concerns the price indexes embedded in the GDP deflator. Recent discussion suggests that the CPI for the US has been overstated for the past few years. One reason cited is that it does not take adequate account of changes in outlets where consumer purchases are made. (Department stores to “big box” bulk purchasing outlets, for example). Other factors mentioned include the micro and macro aggregation formulas, as well as the treatment of the introduction of new goods and the continuing issue of quality change adjustments. The suggestion has been made that the Canadian CPI is less biased upwards. If this hypothesis holds, the lower rate of inflation in Canada may be at least partly illusory. The comparison between the two CPIs is, however, bringing down the level of the projected PPP time series after the latest benchmark study, since the CPI is used to measure prices for about two-thirds of the GDP. With lower PPPs we would intuitively expect the reciprocal volume series to rise in Canada relative to the US. The charts show otherwise. Behind the trend shown are two other factors: a revision in the population estimates for Canada, which were raised as a result of the 1991 census, bringing down the GDP per person as well the downward revision in the GDP estimates for 1990. Combined these two revisions lowered the GDP per head in Canada by almost 6%.
 

Thoughts for the future

Although strong support exists to use PPPs rather than market exchange rates in comparing and analyzing price levels and real or volume comparisons among countries, it is recognized that improvements are needed at the micro levels. More confidence can be placed at the macro GDP level in the comparisons, while some components are more problematic (as is also true in the time series). Several initiatives are underway. These include the establishment of a working group for non-European countries to examine and adapt the specifications and pricing methods particularly in the area of personal consumption, so as to reflect the tastes and markets of the different component countries. More analytical resources could be applied to examine unusual results in different studies for different countries and try to explain or improve them. Other data sources are becoming available which can be utilized. These include scanner data, which will provide a much broader range of price data than are currently collected in most countries. Additional data are available through the international agencies, for example, for automobile sales and direct volume measures for items such as telephone calls, from which PPPs could be implicitly derived. Examination of both the volume side and the price comparisons may help strengthen the analysis as well for specific components. Further use can be made of regression and hedonic methods as is now applied to rents, for example, as well as the model approach used for parts of construction. Some thought is being given to productivity adjustment factors where inputs are used, but this has been an issue difficult to overcome in time series as well.

A number of concerns have been identified in undertaking spatial comparisons of price and volume among countries. We believe that progress is possible and that the results will continue to improve, as analysts continue to identify better approaches to the desired measures, as has been the case with time series. Finally, the PPP comparisons and their reciprocal volume measures at aggregated levels are better price converters than exchange rates and the direct bilateral Canada/US results are believed to be the most robust.