GGDC RESEARCH MEMORANDUM 151

Transcription

1 GGDC RESEARCH MEMORANDUM 151 Cross-country income levels over time: did the developing world suddenly become much richer? Robert Inklaar and D.S. Prasada Rao December 2014 university of groningen groningen growth and development centre

2 Cross-country income levels over time: did the developing world suddenly become much richer? Robert Inklaar Groningen Growth and Development Centre University of Groningen, The Netherlands D.S. Prasada Rao School of Economics The University of Queensland, Australia December 12, 2014 A previous version of this paper was circulated under the title Cross-country income levels of time: can ICP 2005 and ICP 2011 be reconciled? The authors would like to thank Angus Deaton, Arvind Subramanian, Marcel Timmer and seminar participants at the University of Graz and the University of Groningen for helpful comments and the World Bank for providing detailed researcher data underlying ICP 2005 and ICP This work was undertaken when Rao was a visiting researcher at the Groningen Growth and Development Centre in August, 2014 and at UNU-MERIT during October, Correspondence to: Robert Inklaar, University of Groningen, Faculty of Economics and Business, PO Box 800, 9700 AV Groningen, The Netherlands (R.C.Inklaar@rug.nl).

3 Abstract The latest global survey on relative prices and income levels showed revisions to income levels that were larger in lower-income countries, thereby shifting the world income distribution. The aim of this paper is to establish whether changes in measurement methodology and price sampling methods between the latest price survey for 2011 and the previous survey for 2005 can explain these large differences. We construct a counterfactual set of relative prices for 2005 that harmonizes measurement and we find that the systematic differences in income levels are substantially reduced or even eliminated, implying that international income inequality had been overstated. Key words: purchasing power parities; International Comparison Program (ICP); extrapolation; price levels; price sampling bias; real incomes; inequality JEL Codes: C43, E01, E31, C83, O57 2

4 1. Introduction Our understanding of differences in living standards across countries, international income inequality and global poverty relies heavily on the periodical global price comparisons of the International Comparison Program (ICP). 1 Without ICP relative prices, comparisons of income levels across countries would have to rely on exchange rates, which tend to systematically underestimate the purchasing power of consumers in low-income countries. 2 But despite the conceptual appeal of ICP relative prices, they are often also a source of controversy. For instance, Deaton (2010) showed how results from consecutive ICP rounds led to upward revisions in income inequality across countries. Similarly, Ciccone and Jarociński (2010) and Johnson et al. (2013) show how various results from the cross-country growth literature change depending on the vintage of relative income data that is used. 3 More broadly, changing the methods and model used to measure relative prices can have a notable effect on the resulting relative income estimates, as shown by Neary (2004), Almås (2012) and Feenstra et al. (2013). The most recent source of controversy is the publication of ICP 2011 (World Bank, 2014a,b). Compared with earlier estimates based on (extrapolations from) ICP 2005 (World Bank, 2008), the average country saw its income and consumption levels increase by about 25 percent. Revisions for developing countries were particularly large, resulting in major changes to the economic geography of the world and a downward adjustment to global inequality. Given the size and systematic pattern of these revisions, they can have farreaching consequences, ranging from a different number and geographical distribution of the world s poor to a different view on income convergence or appropriate policy. 4 It is thus no surprise that the revisions following ICP 2011 have already been the topic of substantial commentary and debate. 5 1 See e.g. Anand and Segal (2008), Deaton (2010), Deaton and Heston (2010), Chen and Ravallion (2010a) and Milanovic (2012). See also Feenstra, Inklaar and Timmer (2013) on how the ICP results are a crucial input in the Penn World Table and World Bank (2013) for details on ICP. 2 The Balassa (1964)-Samuelson (1964) effect, whereby prices of non-traded products tend to be lower in lowerincome countries. 3 Differences between data vintages in these studies reflect revisions to relative prices the focus of our paper and revisions to national GDP statistics a source of differences we exclude. 4 See Chen and Ravallion (2010a) on the impact of ICP 2005 on poverty, (e.g.) Pritchett and Summers (2014) on growth and convergence and Aghion, Akcigit and Howitt (2014) on productivity levels and appropriate policy. 5 See Dykstra, Kenny and Sandefur (2014), Chandy and Kharas (2014), Deaton and Aten (2014) and Ravallion (2014). 1

5 Yet these early commentaries may be misleading because of the major changes to how relative prices were measured in ICP 2011 compared with ICP A particular concern, as identified by Deaton and Aten (2014), is the so-called linking of regions. In both ICP 2005 and 2011, prices are first collected and compared across the countries within a region and in the second stage, the regions are linked to each other to allow for a global price comparison. Some regions consist mostly of low- and middle-income countries (Africa, Asia-Pacific) and some mostly of high-income countries (Eurostat/OECD), which means that changes to the linking approach can shift the prices of lower-income countries relative to higher-income countries. Since the linking approach was considerably improved and refined in 2011, 7 Deaton and Aten (2014) conclude that the linking data and methods are a good starting point for trying to understand why the results from ICP 2011 were so different from the ICP 2005 results. The goal of this paper is to identify the impact of the 2011 methodological and price sampling changes and provide better estimates of the revisions to relative prices and income levels. To this end, we construct a counterfactual price comparison for 2005 using ICP 2011 methods and adjusting for biases in the sampling of the 2005 price data, in particular regarding the linking of regions. We draw upon the early diagnostic work of Deaton and Aten (2014), but provide a more comprehensive and quantitative assessment of the impact of the measurement changes. Given the theoretical problems in measuring relative prices (Van Veelen, 2002) and the practical challenges (Deaton and Heston, 2010), even the counterfactual we construct will show some differences. 8 But if those differences remain systematically larger in lower-income countries, this calls into question the common practice of using a single set of cross-country relative prices to estimate relative income levels across many years, 9 and the research results that depend on such data. To construct our counterfactual price comparison for 2005, we draw upon the original data and methods used in the compilation of ICP 2005 and ICP 2011, including detailed price and expenditure data, and we go through the full compilation of PPPs as detailed in World Bank (2008) and World Bank (2014b). In presenting our results, we focus on the implications for 6 See World Bank (2014b) for a list of major improvements in ICP 2011 methodology compared to ICP See in particular World Bank (2013). 8 See also McCarthy (2013b) for a more practical discussion of why subsequent price comparisons may not be consistent with observed relative inflation patterns. 9 This is standard practice in the World Bank s World Development Indicators, the Maddison Project Database (Bolt and van Zanden, 2013) and for parts of the Penn World Table (Feenstra et al., 2013). 2

6 GDP per capita levels, which are most relevant for research into cross-country economic performance, and consumption per capita, which is used most often in the analysis of poverty and inequality. We make two sets of adjustments to the original ICP 2005 comparison; in the first set, we take all 2005 price data as given, but apply the ICP 2011 methods. In this harmonized methodology counterfactual, the average upward revision to relative income and consumption levels goes down from percent to percent, but especially for consumption, revisions are still systematically larger in lower-income countries. In the second set of adjustments, we correct for a number of biases in the price data collected in Most importantly, we find clear evidence that the price data used in linking the regions in 2005 was based on a product list that was only representative in higher-income countries; a possibility that, notably, Deaton (2010) called attention to. In the sampling bias adjusted counterfactual, the average upward revision goes down to 9-12 percent; making both sets of adjustments simultaneously reduces the average revision further, to 4-10 percent. For both GDP and consumption, lower-income countries no longer show systematically larger upward revisions. Furthermore, the root mean squared revision decreases from percent to percent, which is similar to estimates of the standard error of relative prices. 10 The results from this analysis have important implications. Most importantly, the difference between the original ICP 2005 and ICP 2011 suggested that datasets based on extrapolating GDP per capita levels from a benchmark comparison to earlier years were inherently biased. This, in turn, could have had serious consequences for research based on such datasets, which include the World Development Indicators of the World Bank, the Maddison database (Bolt and van Zanden, 2014) and parts of the Penn World Table (Feenstra et al., 2013). Our success in eliminating the systematic differences with our counterfactual price comparison suggests that such a fundamental reconsideration is not necessary. Furthermore, one concrete outcome of our analysis is two sets of price comparisons based on the same methods and comparable data. This means they can be fruitfully used in combination, such as in the part of the Penn World Table that presents relative price and income levels based on all available ICP benchmarks. Finally, from a statistical point of view, we have demonstrated the usefulness of backward revisions to relative prices, which is similar in spirit to the backwards revision of National Accounts time series when introducing new methods. 10 See e.g. Deaton (2012) and Rao and Hajargasht (2014). 3

7 2. Basic framework The basic aim of the ICP is to measure the overall price level P in a country j relative to any other country k. Implicit in this aim is the idea that the law of one price does not hold, because if it did hold we would only need to observe market exchange rates to put GDP or consumption on a comparable basis. The presence of non-traded goods in an economy can be one reason for the law of one price to fail, but also see Rogoff (1996) for other reasons. As a result, a procedure is needed to estimate the economy-wide price level using data on prices p and expenditures v for individual products i. One could take a welfare-theoretic approach and aim to compare the cost-of-living, as in e.g. Neary (2004). However, as argued by Deaton and Heston (2010), such an approach leads to questions that are extremely hard to provide sensible answers on, such as whether tastes or identical or, if not, how best to envisage comparing countries that do not only differ in price and income levels but also along dimensions such as climate or religion. What is done in ICP can thus best be thought of as comparing an index of the price level, not the cost of living. If we choose a so-called superlative index for this purpose, we know from Diewert (1976) that such an index will provide a second-order local approximation to arbitrary preferences. Let us, for expositional purposes, assume the superlative Törnqvist index. The relative price level of country j relative to k at time t can then be written as: t t log P j P k 1 t s 2 ij t i s ik t p ik, (1) t log p ij where s ij are the expenditure shares of product i, v ij v i ij. An important feature of equation (1) is that the relative price level between j and k depends on expenditure shares in both countries. 11 How will this relative price index evolve over time? The standard approach, used in e.g. the World Bank s World Development Indicators, is to assume the change in the relative price level is equal to relative inflation. Let country inflation also be measured by a Törnqvist index: t t t 1 log P j log P j P j 1 t s 2 ij t 1 i s ij t 1 p ijk (2) t log p ij 11 In the more general, so-called multilateral indexes used in ICP, the price level between j and k also depends (to a lesser degree) on expenditure shares in all countries, see Diewert (2013). 4

8 Since the price level in equation (1) depends on both country s expenditure shares, while national inflation only depends on national expenditure shares, the change in the price level is not exactly equal to relative inflation, as shown by Deaton and Aten (2014). If we assume that expenditure shares do not change over time, we can write the change in the price level by combining equations (1) and (2) as: log P j t P k t log P t t j log P k 1 s 2 ij s ik i log p t t ij log p ik. (3) This equation shows that the expected change in PPPs is given by relative inflation the first term in brackets and a term reflecting differences in expenditure patterns and (average) relative price changes across products. If there are no differences in expenditure patterns, no changes in relative prices or if differences in expenditure patterns are uncorrelated with average changes in relative prices, this term will be zero. In the absence of detailed data about product level inflation, log p t ij, it is not feasible to implement equation (3) in full. 12 To extrapolate PPPs from 2005 to 2011, we will therefore rely only on data about relative inflation, which according to equation (3) should be a fair approximation on conceptual grounds. On practical grounds, discrepancies may well occur if, for example, country-specific products are used to estimate national inflation but (for lack of cross-country comparisons) are not used in ICP. McCarthy (2013b) details a comprehensive set of practical considerations, but for none of these would we expect a larger effect in lower-income or higher-income countries. Given this framework, we now turn to a comparison of ICP 2011 with extrapolations from ICP For ICP 2011, we use the results as published in the Summary Report (World Bank, 2014a) and specifically the purchasing power parities (PPPs) and expenditure levels for GDP and final consumption expenditure ( consumption ). For ICP 2005, we use the PPPs as originally published in World Bank (2008). 13 The combined data set is constrained mostly by ICP 2005, which covered 146 countries. Argentina, Syria and Lebanon participated in ICP 2005 but not in ICP 2011 and Zimbabwe participated in ICP 2005 but the coinciding period of hyperinflation led to unreliable results. This leaves us with a data set of 142 countries, 12 Experiments with inflation data for (at most) four products in the consumption bundle shows small relative price changes over the period, which suggests that the second term in equation (3) will be small. However, more detailed data could in principle reveal larger changes, so definite statements are not possible. 13 Or, to be more precise, the ratio of the PPP over the exchange rate. This avoids having to explicitly control for changes in currency units, such as the adoption of the euro in a number of countries. 5

9 which is used in the remainder of the paper. To extrapolate GDP PPPs, we use GDP deflators; to extrapolate consumption PPPs, we use the consumer price index (CPI). 14 Let P Yjt be the PPP for GDP (Y) in country j at time t based on a benchmark year and let p Yjt be the GDP deflator in year t in country j. Whenever t the PPP is extrapolated from the benchmark year as: p p Yjt Yj Yjt PYj (4) pybt pyb P where b refers to a base or reference country usually the United States. We can then compare GDP per capita (y) or household consumption per capita (c) based on the PPP extrapolated from ICP 2005 with the corresponding numbers based on the new ICP 2011 benchmark. We use the following relative difference measure: d y P P 1 1 (5) j2011 Yj2011 Yj2011 Yj yj2011 PYj2011 PYj2011 As all the subsequent comparisons are for the year 2011, we drop the subscript Figure 1 shows a plot of d Y against the log of GDP per capita converted using exchange rate E, ln ( y E ), and d C against the log of consumption per capita, ln ( c E ). The GDP and j j consumption per capita numbers are those reported in World Bank (2014a). The figure illustrates the very large upward revisions to income and consumption levels resulting from the downward revisions to PPPs when moving from extrapolations from ICP 2005 to ICP As the range of the graphs shows, relative income and consumption levels have increased by more than half in a large number of countries. Differences in GDP per capita extrapolations are between 30 to 40 percent also for large countries like Brazil, China and India and differences are quite large in oil-rich economies including Indonesia. However, the relative differences exhibit a slightly different pattern for per capita consumption. Differences for India are around 50 percent whereas the difference for Indonesia is more moderate. More generally, there is a clear negative correlation with the j j 14 An alternative would be the implicit price deflator of household consumption expenditure from the National Accounts but the results are very similar. 15 The figure is qualitatively similar to Figure 1 in Deaton and Aten (2014, p. 31), though for OECD/Eurostat countries, their consumption levels are extrapolated from a more recent benchmark comparison than ICP

10 highest-income countries typically showing only small revisions. The lower-income countries typically show larger revisions and this effect is stronger for consumption. 16 Figure 1, Differences between extrapolating ICP 2005 and ICP 2011 To summarize the patterns in Figure 1 and compare these to alternative PPP series in the remainder of this paper, we use three statistics based on the difference measure in (5). Mean difference across the set of J countries: d i 1 J J j P ij 2011 P 1, for i Y,C ij Root mean squared difference (RMSD): d i 2 1 J J j P ij 2011 P 1 ij 2, for i Y,C Slope coefficient of the regression: d ij a i b i ln e ij E j u ij, for j 1,, J and i Y,C, where e ij is either GDP or consumption per capita. These summary measures are best understood by viewing the problem as a forecasting exercise. Until the release of the benchmark ICP 2011 PPPs, the typical approach was to forecast PPPs for 2011 by 16 The difference between the GDP and consumption pattern suggests that revisions to the price levels of investment and government consumption are not related with income levels. 7

11 extrapolating 2005 PPPs using equation (4). 17 Statistic d i is then a measure of the forecasting bias, RMSD is a measure of forecasting uncertainty 18 and b i an indication whether the bias varies systematically with GDP or consumption per capita. 19 Given the challenge of comparing prices of more than a thousand individual products across almost 200 countries, it is not surprising that measurement error is present, which would lead to RMSD being non-zero. 20 Indeed, this can be a rationale for conducting regular benchmark price comparisons: since the PPP of a given country in a given year will be measured with error, it is good to have measurements in multiple years to avoid relying too heavily on a single (possibly error-prone) observation. 21 That said, RMSD is still a useful measure since a method of extrapolating PPPs that would lead to a lower value of RMSD would be preferable. The average bias d i and the systematic variation in the bias measured by b i are arguably the most worrisome measures as they imply a shift in the world income distribution. This is most obvious for b i, as this measures whether lower-income countries show systematically larger (or smaller) differences. But a non-zero d i is also worrisome because PPPs are given relative to the United States and this thus implies an average shift in prices and thus expenditure levels relative to US. Table 1 shows summary statistics corresponding to the two panels in Figure 1. The average country has expenditure levels in ICP that are about 25 percent higher than those based on extrapolations from ICP Put differently, the average country is 24 percent richer relative to the US than estimated previously, implying a sizeable decline in cross-country income inequality. The root mean squared difference is also comparable between the GDP 17 An exception was Ravallion (2013, 2014), who has argued for a so-called dynamic Penn effect. However, Inklaar (2013) showed that the forecasting performance of the dynamic Penn effect was inferior to the standard inflation-based extrapolation. 18 In the terminology of the forecasting literature, this would be the root mean squared prediction error, RMSPE, see West (2006). 19 Note that the average difference and root mean squared difference are not independent of the numeraire country. However, since typical comparisons are almost exclusively made with the US as the numeraire this is not a major drawback. However, see Diewert (2009) for alternative measures. 20 See Deaton and Heston (2010) for a discussion of the conceptual and practical challenges of cross-country price comparisons. Note also that measurement errors may not just be a problem for measuring PPPs but also for tracking inflation at the national level. The errors in inflation measurement should typically be smaller since it is more likely that a particular product can be priced from one period to the next than in to (potentially) disparate) countries, though information on spending patterns are not regularly updated, measured inflation could well start to substantially deviate from true inflation. 21 See also e.g., Deaton (2012) and Rao and Hajargasht (2014) on the estimation of PPP standard errors from the variation of individual product prices around the overall GDP or consumption PPP. 8

12 and consumption, at percent. The main difference between the GDP and consumption extrapolation errors is that the coefficient on expenditure per capita is much larger for consumption that for GDP, though both are significant. As was apparent from Figure 1, the differences tend to be smaller for non-oil-producing countries and the mean difference is even larger for developing economies than for the sample as a whole. Table 1, Differences between ICP 2011 and extrapolation from ICP 2005 summary statistics Non-oil countries Developing economies All countries GDP Mean difference 0.237*** 0.199*** 0.278*** Root mean squared difference Coefficient on log(expenditure/capita) * *** (0.012) (0.010) (0.019) Consumption Mean difference 0.254*** 0.218*** 0.308*** Root mean squared difference Coefficient on log(expenditure/capita) *** *** (0.011) (0.009) (0.019) Notes: summary statistics based on differences in Figure 1 for 142 countries. Countries where fuel exports contribute more than 10 percent of real GDP are labeled as oil countries (source: Penn World Table, version 8.0). Developing economies are the set of low-income and middle-income countries as defined by the World Bank, so with a GNI/capita level less than $12,746. Robust standard errors of the regression coefficients are shown in parentheses below the coefficients. * denotes a variable significantly different from zero at a 10%- level, ** at 5%-level, *** at a 1%-level. In the remainder of this paper, the results in 1 will serve as a baseline for comparison with statistics based on counterfactual versions of ICP 2005 that harmonize methodology and resolving sampling biases. Ideally, those adjustments will lead to a closer alignment between the extrapolated (counterfactual) ICP 2005 results and ICP 2011 thus providing a clue as to whether the developing world has indeed suddenly become richer. In the following section, we describe the main methodological improvements introduced in 2011 ICP, drawing on World Bank (2014) and explain how the counterfactual versions of ICP 2005 are constructed. 3. Methodological innovations in ICP 2011 and the counterfactuals for ICP 2005 The International Comparison Program (ICP) is a major international statistical initiative in which prices and national accounts data are collected and processed to compile PPPs and 9

13 internationally comparable real expenditures. The early phases of the ICP, until 1985, were essentially world comparisons where data from all participating countries were treated as a single set. A major drawback of such a world comparison was that it proved hard to collect price data for the same products across such a wide range of countries and the requirements for global comparability stood in the way of comparability between the more similar countries in each region. A start was made to move away from a single world comparison with ICP 1993, but ICP 2005 was the first comparison with a fully-implemented regionalized approach. The regionalized approach involves compilation of PPPs in two stages. The first stage is at the regional level, where countries would collect and compile data according to regional product specifications, leading to more reliable relative prices within each region. In the second stage, the regional comparisons are linked to complete the global comparison. The methodology for linking regional comparisons was pioneered while data collection for ICP 2005 was in progress. So it was perhaps not surprising that after the release of ICP 2005, an assessment of the methods used in 2005 for linking regional comparisons indicated several deficiencies. These deficiencies are discussed in Rao (2013), on the methods for linking prices for product categories referred to as basic headings in ICP and in Diewert (2013b), for linking at the aggregate level. To remedy the signaled deficiencies, several methodological innovations have subsequently been implemented in ICP Major changes in methodology raise the question how the results from ICP 2005 and ICP 2011 can be compared. A direct comparison of ICP 2011 results with an extrapolation from ICP 2005 is like comparing apples and oranges in view of significant improvements in the methods used in the ICP 2011 round. In this paper, we offer a solution to this problem by constructing a counterfactual for ICP 2005 based on ICP 2011 methodology. We briefly describe the major methodological innovations in the ICP 2011 with further details available in World Bank (2014b). We then construct counterfactual 2005 PPPs based on data used in the ICP 2005 computations. The basic data used are the PPPs and national expenditure data at the basic heading level for all the 146 participating countries. In addition, productivity adjustment data for 2005, information on dwellings; 22 the 2005 ring product list 22 We thank Alan Heston and Nada Hamadeh for providing the data and the worksheets used in the computation of linking factors for dwellings. 10

14 and prices; the 2011 global core list products and their prices in all the participating countries have been obtained from the ICP Global Office at the World Bank Harmonization of methodology Aggregation at the regional level In ICP 2005, the African region employed the transitive and additively consistent aggregation method, the Iklé-Dikhanov-Balk (IDB) method, to compute aggregate PPPs within Africa, while all other regions used the Gini-Elteto-Koves-Szulc (GEKS) method. 24 Bringing all the regions to line, the GEKS method was implemented in all the regions in ICP The first step in the construction of the counterfactual is thus the replacement of the 2005 PPPs within the African region based on IDB method with PPPs computed using the GEKS method. Productivity adjustment to relative wages Government consumption, including spending on public administration, health and education, have always been considered comparison-resistant in ICP since market prices for the output of most of these services cannot be observed. So instead of relative output prices, ICP compares government consumption by comparing input prices, specifically wages and salaries. A drawback of using input prices is that relative productivity differences are not taken into account, which means that in lower-income countries, a simple measure of relative wages would understate relative output prices and overstate real expenditure under this category. In ICP 2005, the Asia-Pacific and African regions recognized the need to make a productivity adjustment to relative wage data, but no other regions implemented any adjustments. An implicit assumption in this limited use of productivity adjustment is that productivity of government employees in all the remaining economies is the same as that in the United States which is unlikely to be true. Consequently, a fully-fledged productivity adjustment for all the economies participating was implemented in ICP 2011, see World Bank (2014b) for details. Following the approach used in ICP 2011, we implement productivity adjustments based on the contribution in 2005 of differences in (physical) capital per worker to GDP. 25 We find a marginal increase in the share of Africa, Asia-Pacific and Eurostat/OECD countries when a 23 These data are routinely provided to all researchers upon request to the ICP Global Office. 24 See Diewert (2013a) for detailed descriptions of the IDB, GEKS and other aggregation methods. 25 See World Bank (2014b) for details on the methodology and the Penn World Table, version 8.0 for data on comparative capital stocks and the share of labor income in GDP. 11

15 comprehensive productivity adjustment is implemented, see Appendix Table A1 for regional shares before and after comprehensive productivity adjustment. Linking dwellings using quantity indicator data 26 To compare relative rents of dwellings across regions, a procedure was followed for ICP 2005 and ICP 2011 that is different from other types of consumption, see Heston (2013) and World Bank (2014b). Ideally, information would be available on the actual (or imputed) rent paid on different types of dwellings, but data on the number of dwellings and some quality characteristics are more widely available. In ICP 2005, the available rental price data was used to link the relative rents for dwellings across regions, see Heston (2013). For ICP 2011, a similar approach was tried but the rental data supplied was judged to be of insufficient quality. Instead a method based on quantity indicators was applied. First, the number of dwellings per capita 27 is used to construct a regional quantity index for dwellings with OECD-Eurostat set at 100. The quantity index is then adjusted for quality differences using a quality index computed as the arithmetic average share of dwellings with electricity, inside water and private toilet. To harmonize this aspect of the methodology, we apply the ICP 2011 methodology on dwellings quantity and quality indicators data for 2005 supplied by the Global Office. We combine the per capita volume index with a per capita value index, computed as the ICP 2005 expenditure in the Actual and imputed rentals for housing basic heading category, converted to US dollars using the current exchange rate and divided by population. This gives a price level index for each region. The steps involved in implementing the 2011 linking methodology for dwellings on data from 2005 are shown in Appendix Table A2. In Africa, Asia-Pacific and Latin America, the prices according to the ICP 2011 methodology are lower than under the ICP 2005 methodology, suggesting an upward revision to income levels in countries from these regions. 26 We are grateful to Alan Heston who provided details of the approach used in 2005; Nada Hamadeh for providing data used in 2005 as well as in 2011; and to Paul Konijn for providing us with a copy of the document Linking the regions: the case of housing outlining the methodology used in linking dwellings data in 2011 ICP. The Konijn document describes the actual procedure implemented by the Computational Task Force for ICP Though data on usable surface in sq. meters was collected, it was not of sufficient quality for use in the linking process. Therefore, linking was essentially based on number of dwellings per capita data. 12

16 Aggregation above basic heading level In the implementation of the ICP, the very last step involves linking of regions at higher levels of aggregation, such as household consumption and GDP. The methodology used for linking at the GDP and component level used in 2005 was replaced by the country aggregation and redistribution (CAR) method in The starting point for linking above the basic heading level is data on national expenditure and PPPs for each of the 155 basic headings, usually with the US=1. The problem in aggregating these data for global comparisons of GDP is the additional requirement of fixity. The fixity requirement stipulates that the relative levels of consumption or GDP of countries within a region must be identical to the relative levels established at the regional level, thereby ruling out the standard aggregation methods. Diewert (2013b) summarizes a range of suggested methods for global comparisons that maintain fixity. The method used in ICP 2005 treats each region like a super-country 28 and requires regional quantity and aggregate price vectors. To construct these, first the implicit quantity for each basic heading in each country is derived by dividing national expenditure by the basic heading PPP. These basic heading quantities are then added across all the countries in each region, resulting in one quantity vector for each of the six regions for each basic heading. In the second step, the price of the basic heading for the region can be computed as total regional expenditure in the units of currency of regional reference country divided by the quantity measure. This yields a price and quantity vector for each of the regions, where prices are expressed in the currency units of the reference countries in each region. The GEKS method is then used to get relative regional prices at the aggregate level, which are combined with the within-region relative prices to compare prices across regions. As detailed in Diewert (2013b), though, it was later found that the method implemented in ICP 2005 was not invariant to the choice of the reference country in each region. For ICP 2011, the use of the Country Aggregation with Redistribution (CAR) method was recommended. This method starts with a global comparison of prices using the GEKS method and basic-heading-level data for all individual countries. The resulting relative prices are used to compute real, PPP-converted GDP for each country and these GDP levels are added to arrive at total regional real GDP. In the second step, the shares of each country in within-region GDP an outcome of the regional comparison is applied to total regional real 28 The term is from Deaton and Aten (2014). 13

17 GDP. In constructing the counterfactual comparisons for 2005, we implement the CAR approach with the basic heading PPPs and national expenditures obtained after using the linking procedures detailed above. Effect of harmonized methodology on ICP 2005 The first step in our approach to construct a counterfactual for ICP 2005 prices is to harmonize the methodology that used in ICP In Table 2, we show how the original ICP 2005 and the different counterfactuals compare to ICP Comparing the first and last column, it is clear that harmonizing the methodology results in lower mean differences and a lower RMSD for both GDP and consumption. Though the mean difference for the fully harmonized counterfactual is still sizeable at 17 to 18 percent, this is 26 percent smaller for GDP and 31 percent smaller for consumption than the original. Similarly, the RMSD has gone down by 15 (GDP) to 18 (consumption) percent. Going through the various stages of the harmonization, the most substantive change results from harmonizing the within-africa PPPs, while implementing the CAR method, productivity adjustment and dwellings adjustment matter relatively less. Table 2, Differences between ICP 2011 and extrapolations from ICP 2005 counterfactuals based on harmonized methodology Original CAR method + Within-Africa harmonization + Productivity adjustment + Dwellings adjustment GDP Mean difference 0.237*** 0.216*** 0.175*** 0.192*** 0.184*** Root mean squared difference Coefficient on * *** * log(expenditure/capita) (0.012) (0.013) (0.010) (0.010) (0.010) Consumption Mean difference 0.254*** 0.254*** 0.187*** 0.187*** 0.174*** Root mean squared difference Coefficient on *** *** *** *** *** log(expenditure/capita) (0.011) (0.017) (0.010) (0.010) (0.010) Note: column labeled Original is from Table 1. CAR method uses the regional linking methodology of ICP 2011, + Within-Africa harmonization uses the GEKS method rather than the IDB method to compare prices within the African region; + Productivity adjustment also implements the productivity adjustment for public wages for the Eurostat/OECD region and Latin America and + Dwellings adjustment also implements the ICP 2011 method for comparing the (rental) price of dwellings across regions. This column corresponds to a set of PPPs where the methodology has been harmonized to the extent possible. Robust standard error of the regression coefficients shown in parentheses below the coefficients. * denotes a variable significantly different from zero at a 10%-level, ** at 5%-level, *** at a 1%-level. 14

18 In addition to the methodological innovations in 2011 discussed here, ICP 2011 also introduced a new method for measuring relative prices in construction. ICP 2005 used the basket of construction components (BOCC) method was see McCarthy (2013a) for details but it was replaced in ICP 2011 by a simpler method based on the prices of basic construction materials, different types of labor, and the hire of machinery and equipment. However, the information required to implement the ICP 2011 construction methodology was not available from the 2005 data sources. 3.2 Accounting for price sampling biases due to ring country linking methodology in ICP 2005 This section outlines the adjustments made to 2005 ICP in the process of constructing a counterfactual that incorporates the main improvements to methodology introduced in ICP World Bank (2014b) emphasizes changes to linking methodology as a major innovation in ICP Linking regional comparisons to arrive at the overall global comparison is a critical step in ICP. ICP 2011 introduced a global core list (GCL) of products and pricing of GCL products by all 177 participating countries in ICP 29 in the process of linking PPPs. In contrast, the linking procedure in ICP 2005 was based on data for only 18 countries, the so-called ring countries, 30 which were deemed to be representative for the full set of countries in their respective regions. The ring countries collected prices for items on the global ring product list and those prices were then used to link PPPs from different regions; see also Deaton and Heston (2010) and Vogel (2013). 31 After the completion of ICP 2005, several issues were identified with the linking procedure based on ring countries and the ring products. The first is whether the particular selection of 18 ring countries would induce a bias compared to the use of data for all the participating countries. We term this bias the ring country selection bias. The second issue relates to the items included in the ring product list. A close examination of the products included in the ring list and the product specifications used for pricing purposes revealed a strong rich country bias in the products. The list included items like Uncle Toby oats; a bottle of Heineken beer, Bordeaux wine; and a Peugeot 408, which is suggestive of a rich country bias 29 Though ICP 2011 covered 199 countries, only 177 countries participated fully and the remaining are Pacific Island countries whose participation was limited to comparisons of household consumption. 30 The ring countries are Comoros, Egypt, Kenya, Senegal, South Africa and Zambia in Africa; Hong Kong, Malaysia, Philippines and Sri Lanka in Asia-Pacific; Brazil and Chile in Latin America; Jordan and Oman in Western Asia; and Estonia, Japan, Slovenia and the United Kingdom in Eurostat/OECD. 31 See Rao (2013) on the linking methodology at the basic heading level and Diewert (2013b) on linking at the aggregate level. 15

19 in the ring list. Deaton (2010) presented further suggestive evidence that the use of the ring product list led to relatively high price levels (and thus lower real incomes) in low-income ring countries. We refer to this as the ring product selection bias. In addition, we also consider the widely discussed urban bias in prices of household consumption goods in China in ICP In this section we describe how we quantify these biases and use them in constructing a counterfactual for ICP Urban bias in consumption prices from China It is well documented that consumption prices provided by China to the Asia-Pacific regional comparison in 2005 were collected from only 11 capital cities and their surrounding areas (see ADB, 2007 and Word Bank, 2008). 32 The general consensus from Deaton and Heston (2010), Chen and Ravallion (2010a,b) and Feenstra, Ma, Neary and Rao (2013) is that the Chinese consumption prices used in ICP 2005 were biased upwards relative to national average prices by 20 percent or more. 33 In contrast, the Chinese price survey for ICP 2011 was much more comprehensive, covering urban and rural areas in each of the country s provinces (see ADB, 2014). In constructing the counterfactual for 2005, we make a 20 percent upward adjustment to consumption prices for China. Ring country selection bias We cannot use data for 2005 to establish whether there was any bias from the specific selection of ring countries. However, given the price data for all 177 countries in 2011, we can examine if selecting the 18 ring countries from 2005 would have introduced any systematic bias in the (2011) linking factors at the basic heading level. The assumption here is that the ring country bias we find in 2011 would have been present to the same degree in 2005 as well. To measure this bias, we exploit the basic structure of the country-product-dummy (CPD) model used in the ICP. 34 We specify a simple regression model that explains log prices P of product i in country j located in region r using dummies for each product, Di, each region, Dr, 32 The Global Office of the ICP at the World Bank and the regional coordinating agency, Asian Development Bank, devised a mechanism to derive national average prices for China based on price data from the 11 cities. However, the method employed failed to account for rural-urban and regional price differentials. 33 PWT 7.1 and 8.0 implemented a downward adjustment in the preparation of their PPP and real expenditure extrapolations. A similar adjustment was used in Chen and Ravallion (2010a,b) in estimating absolute poverty in China. 34 Details of the CPD model and its use in the ICP can be found in Rao (2013). 16

20 a ring country dummy R (which takes value 1 if the country is one of the 18 ring countries) and interactions between the regional dummies and the ring country dummy: logp ijr D i r D r R r D r R ijr (6) i i r Following the linking procedure used at the basic heading level (see Rao, 2013 for details), prices are first converted into regional numeraire currencies using within-region basic heading PPPs. This model, without the ring country dummy and interaction terms, is used in ICP to derive the linking factors for each basic heading, see Vogel (2013). The r parameters are of main interest since a significant coefficient would indicate that pricing in the ring countries in that region are significantly different from pricing in the other countries in the region. Table 3, Estimating the difference in 2011 pricing of global core list products in ring countries versus other countries Region coefficient Region x ring country coefficient r Africa *** Africa x ring country (0.0288) (0.0117) Asia-Pacific *** Asia-Pacific x ring country *** (0.0309) (0.0202) Latin America *** Latin America x ring country (0.0288) (0.0209) Western Asia *** Western Asia x ring country (0.0294) (0.0152) Ring country dummy (0.0079) Number of observations 57,415 Note: table shows regression results where the log of consumption item prices for 2011, converted to the regional base country s currency, are explained by dummies for each region, whether a country was a ring country in ICP 2005, interactions between this ring country dummy and the regional dummies, and dummies for each of the 1192 items (not shown), see also equation (6). Items are weighted by their importance, see main text for discussion. The Eurostat/OECD region is taken as the base region and hence the coefficients should be interpreted as price differences relative to the Eurostat/OECD. Robust standard errors of the regression coefficients shown in parentheses below the coefficients. * denotes a variable significantly different from zero at a 10%-level, ** at 5%-level, *** at a 1%-level. r r 17

21 Table 3 reports the results of a pooled regression across all basic headings, based on 57,415 price observations 35 and using the importance weights that are also used in ICP The regional coefficients in the left panel provide the average regional linking factors r. For example, the table shows that 6.15 Hong Kong dollars (exponential of , the coefficient for the Asia-Pacific) for one US dollar is the linking factor when all the countries are used in linking the regions. We also observe that the coefficient of ring country dummy is numerically very small and statistically insignificant. This means that the selection of ring countries on average has no influence on the linking factors. Turning to the r parameters, we find insignificant coefficients for ring countries in all the regions with the exception of the Asia-Pacific region. The significant interaction term for the Asia-Pacific ring countries indicates that prices in the ring countries (Hong Kong, Malaysia, Philippines and Sri Lanka) from this region are, on average, 6.95 percent lower than in other Asia-Pacific countries. In our counterfactual ICP 2005, we divide prices by the exponent of this coefficient to counteract this ring country selection bias. Ring product selection bias In ICP 2005, the 18 ring countries priced items from the ring product list and ideally, this list should contain products that are part of a representative consumption bundle in every country of their respective region. In practice, this is much harder, as discussed in more detail by Deaton and Heston (2010). For instance, a bottle of Heineken beer was on the ring product list, but if this is a premium brand in poor countries, while a standard choice of beer in rich countries, beer prices in the poor country will be relatively higher than would be the case for beer in general. Deaton (2010) presented suggestive evidence that points to a rich country bias in the ring product list. Given this potential for bias, a global core list (GCL) of products was developed for ICP 2011 which is representative of goods and services that are consumed in all regions of the world. The ICP 2011 GCL product approach seems to have been fairly successful as the GCL had significant overlap with the regional product lists. Of the 692 consumption products on the GCL, 610 matched with the regional list in Africa; 412 with Asia; 394 with OECD- 35 The regressions includes data from 148 countries. If these had priced all the 692 GCL products, we would have 102,416 observations, so not all products were priced in all countries. 36 A product that is deemed important in a particular country gets a weight of 3 and other products get a weight of 1. 18

22 Eurostat; 489 with Latin America and the Caribbean and 606 with the list used in Western Asia. To explicitly test whether the product selection in drawing up the ring product list was a source of bias, we exploit the fact that there were multiple ICP 2005 ring countries in each region and that these ring countries participated in two sets of price comparisons: one based on the regional product list as a part of the regional comparisons and the other based on the ring product list for the purpose of computing linking factors. As the regional lists were drawn up to be representative of products in each region, it seems reasonable to assume that the results based on the regional price comparison are a more accurate measure of relative prices between the ring countries within the region than the relative price differences implied by the ring product list. Indeed, in the compilation of ICP 2005 the ring product list prices are only used for linking prices between regions, not for price comparisons within the region. So if we find that the relative prices within each region based on the ring product list prices differ systematically from the relative prices implied by the regional product prices, we take this as evidence of a bias from the particular selection of the products on the ring product list. We use the following variant of the CPD model to test for the presence of product selection bias: logp ijr i D i r B r i ijr (7) where P represents item price (converted using the basic heading PPP), i refers to item, j refers to country and r represents region. The new dummy variable B r, the base country of region r. Importantly, P ijr measures the price of item i in country j which is part of region r relative to the basic heading PPP for the product group of which item i is a part. The basic heading PPPs are expressed relative to the base country of each region. The base countries in different regions in ICP 2005 tended to be the highest-income countries of the set of ring countries in the region: South Africa in Africa, Hong Kong in Asia-Pacific, United Kingdom in Eurostat/OECD, and Oman in Western Asia. The exception was Latin America, where Brazil was the base country but Chile had a higher income level. If there were no ring product selection bias, we would expect the estimate of r not to differ significantly from zero. However, based on the arguments of Deaton (2010) and Deaton and Heston (2010) that the ring product list was a rich-country product list, we would expect 19