metadata: authors: 0: author: Majumder,Amita
1: author: Ray,Ranjan
2: author: Santra,Sattwik
count: World
docna: 0: docna: Preferences, purchasing power parity, and
            inequality : analytical framework, propositions, and
            empirical evidence
docty: Policy Research Working Paper
subtopic: Economic Theory & Research,Industrial Economics,International Trade and Trade Rules,Economic Growth,Inflation,Inequality,Transport Services
teratopic: Poverty Reduction
abstracts: cdata!: This paper makes analytical,
            methodological and empirical contributions to the literature
            on purchasing power parity. Purchasing power parities are
            required in a host of cross-country welfare comparisons,
            such as poverty rates and gross domestic product. The
            subject has recently generated much interest in the wake of
            the release of the final results of the 2011 International
            Comparison Program. This paper introduces a preference-based
            analytical framework that departs from the conventional
            Balassa-Samuelson framework in deriving empirically
            verifiable propositions on the link between purchasing power
            parity and exchange rates, and between purchasing power
            parity and inequality. The paper also provides an
            alternative methodology for calculating purchasing power
            parities that are benchmarked against the 2011 International
            Comparison Program purchasing power parities. As this study
            shows, the alternative methodology is capable of easy
            implementation on readily available data sets. The
            benchmarking exercise suggests that the 2011 International
            Comparison Program generally understates purchasing power
            parity and overstates gross domestic product, and that the
            purchasing power parities vary across expenditure
            percentiles. The study reports regional variation in the
            direction of the difference between the two purchasing power
            parities. The empirical evidence is supportive of the
            positive association between inequality and purchasing power
            parity derived in the paper.
repnme: repnme: Preferences, purchasing power parity, and
            inequality : analytical framework, propositions, and
            empirical evidence
display_title: Preferences, purchasing power
            parity, and inequality : analytical framework, propositions,
            and empirical evidence
listing_relative_url: /research/2015/08/24921639/preferences-purchasing-power-parity-inequality-analytical-framework-propositions-empirical-evidence
topicv3: Economic Growth m1326241 471,Transport m1326661 135,Poverty m1326687 695,Inflation m1326709 0870F4727ACED1CF8525815C00471347,Trade m1326924 698
publishtoextweb_dt: 2015-08-18T00:00:00Z
historic_topic: Poverty Reduction
no_of_pages: 57
author_keys: 0: author_key: 871101
model_extractions: WPS7395 Policy Research Working Paper 7395 Preferences, Purchasing Power Parity, and Inequality Analytical Framework, Propositions, and Empirical Evidence _Amita Majumder Ranjan Ray Sattwik Santra_ Development Economics Vice Presidency Office of the Chief Economist August 2015
Policy Research Working Paper 7395

# **Abstract**

This paper makes analytical, methodological and empirical contributions to the literature on purchasing power parity. Purchasing power parities are required in a host of cross-country welfare comparisons, such as poverty rates and gross domestic product. The subject has recently generated much interest in the wake of the release of the final results of the 2011 International Comparison Program. This paper introduces a preference-based analytical framework that departs from the conventional Balassa-Samuelson framework in deriving empirically verifiable propositions on the link between purchasing power parity and exchange rates, and between purchasing power parity and inequality. The paper also provides an alternative methodology for calculating purchasing power parities that are benchmarked against the 2011 International Comparison Program purchasing power parities. As this study shows, the alternative methodology is capable of easy implementation on readily available data sets. The benchmarking exercise suggests that the 2011 International Comparison Program generally understates purchasing power parity and overstates gross domestic product, and that the purchasing power parities vary across expenditure percentiles. The study reports regional variation in the direction of the difference between the two purchasing power parities. The empirical evidence is supportive of the positive association between inequality and purchasing power parity derived in the paper.

This paper is a product of the Office of the Chief Economist, Development Economics Vice Presidency. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at amita@isical.ac.in, ranjan.ray@monash.edu, and sattwiks@gmail.com.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
Preferences, Purchasing Power Parity, and Inequality: Analytical Framework, Propositions, and Empirical Evidence Amita Majumder<sup>a</sup> Ranjan Ray<sup>b</sup> Sattwik Santra<sup>c</sup>

**Keywords:** Non-homothetic Preferences, Tradeable Items, Penn Effect, Counterfactual PPP. **JEL Classification** : D11, D63, E31, F01, I31.

# Acknowledgements:

The work on this paper started when Ranjan Ray visited the World Bank in June 2015. The authors thank seminar participants at The Centre for Studies in Social Sciences, Calcutta, and at the World Bank, Washington D.C., for helpful comments and, especially, Kaushik Basu, Francisco Ferreira, Nada Hamadeh, Dean Jolliffe, Sugata Marjit and Abhirup Sarkar for useful discussions. The disclaimer applies and the authors retain full responsibility for the contents of this paper.

> a Professor, Economic Research Unit, Indian Statistical Institute, Kolkata, India. amita@isical.ac.in

> b Professor, Department of Economics, Monash University, Melbourne, Australia. ranjan.ray@monash.edu; corresponding author

> c Assistant Professor of Economics, Centre for Studies in Social Sciences, Calcutta. sattwiks@gmail.com
# **Preferences, Purchasing Power Parity, and Inequality: Analytical Framework, Propositions, and Empirical Evidence**

## **1. Introduction**

## **Background**

The recent release of the final report of the 2011 International Comparison Program (ICP)<sup>1</sup> has generated renewed interest in the subject of Purchasing Power Parity (PPP). PPPs are required in a range of cross-country comparisons that include real expenditure, inequality and poverty comparisons. For example, the implementation of the international poverty line (IPL), typically denominated in US dollars, requires the use of PPPs to convert the IPL to local currencies. The manner of implementation of the PPPs in specifying country specific poverty lines by the World Bank has, however, been criticized by Reddy and Pogge (2007) on the grounds that it (a) “uses an arbitrary international poverty line that is not adequately anchored in any specification of the real requirements of human beings” and (b) “employs a concept of ‘purchasing power equivalence’ that is neither well defined nor appropriate for poverty assessment”. Reddy and Pogge’s (2007) view is at odds with the result of Deaton and Dupriez (2011) who have sought to justify the conventional use of PPPs in defining IPL by finding that that PPPs for the global poor are not much different from the economywide PPPs obtained from national accounts statistics.

The International Comparison Program (ICP) that is centrally directed from the global office of the World Bank is, by any measure, truly impressive in the scale of the exercise and highly ambitious in what it claims to achieve. As the volume [World Bank (2013)] that describes the objectives, methodology and the data sets of the ICP 2005 exercise states in its title, it seeks to measure the ‘real size’ of the world economy, even though it is not clear what the term ‘real’ really means. It does so by calculating ‘purchasing power parity’ (PPP) rates between the various countries’ currencies and using the PPPs rather than the market exchange rates in converting the national accounts of various countries and their components, denominated in local currencies, into a common currency, typically, the US dollar. As is well known, market

> 1 See World Bank (2015). The preliminary results were published in World Bank (2014).  See, also, Hamadeh and Mouyelo-Katoula (2014) for a lucid summary of the ICP, 2011 findings, and Diewert (2010) for a description of the new methodological developments in the earlier ICP, 2005 round.

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exchange rates are inappropriate for currency conversions since they do not measure the ‘true’ purchasing power of a currency. For example, on market exchange rates, the price of a haircut in India seems incredibly cheap to an American visiting India or, conversely, a taxi ride in Australia will be almost as expensive as plane travel between two cities in India. PPP provides the adjustments required to market exchange rates such that the price of an item in two countries is identical if expressed in a common currency. A working definition of the PPP is provided in World Bank (2013, p. 19), namely, that ‘ _it represents the number of currency units required to purchase the amount of goods and services equivalent to what can be bought with one unit of currency unit of the base or reference or numeraire country’_ .

There are several reasons for the divergence between the market exchange rates and the PPP rates (however measured). The short term factors include the capital movements between countries, interest rate movements, speculation in foreign exchange markets, etc. The longer term factors include the fact that the exchange rates are almost exclusively dependent on the relative prices of tradeable items, while standard of living comparisons between countries should include both tradeable and non-tradeable items, especially in the context of developing countries. Consequently, the PPP rates are based on a much wider selection of items than market exchange rates including both tradeable and non-tradeable items. It is not surprising, therefore, that the PPP rates deviate from exchange rates much more for developing countries than the developed ones. The use of PPPs has provided some comfort to authorities in developing countries who have used them to argue that the ’real size’ of their economies is much higher than shown by the exchange rate converted figures.

Though the concept of PPP can be traced back to the early work of Cassel (1916), its modern origin is due to Balassa (1964) and Samuelson (1964). The distinction between PPP and exchange rates is underpinned by the distinction between tradeable and non-tradeable items. While both PPP and exchange rates measure the ratio of prices of a basket of items in two countries, the former considers both tradeable and non-tradeable items, but the latter considers only tradeable items. Both Balassa (1964) and Samuelson (1964) base their distinction between PPP and exchange rates on productivity differences between the tradeable and the nontradeable sectors. As Balassa (1964) notes (p.585), “under the assumption of constant marginal rates of transformation, the relative price of the non- traded commodity will thus be higher in the country with the higher productivity levels than the other”. This leads him to conclude that (p. 586), “assuming that international productivity differences are greater in the production of 3
traded goods than in the production of non-traded goods, the currency of the country with higher productivity will appear to be overvalued in terms of purchasing power parity”. Since developing countries have lower productivity than developed countries, this argument leads to what Ravallion (2013a) terms the ‘static Penn effect’, where the ‘price level index’, defined as the ratio of the PPP to the exchange rate is higher in the developed countries. Ravallion (2013a) extends this argument to claim that with economic growth, the developing countries witness productivity gains in the traded goods sector leading to the ‘dynamic Penn effect’ whereby there is a positive association between changes in economic growth and that in the ‘price level index’. The Balassa Samuelson analysis is reinforced by Bhagwati (1984) who argues that services, a typical non-tradeable item, are cheaper in developing countries. Though the distinction is not always emphasized in the literature, Balassa (1964) draws a distinction between the ‘absolute’ and ‘relative’ interpretations of the PPP doctrine that views the PPP as ‘equilibrium exchange rates.’<sup>2</sup> While, according to the first interpretation, PPP tends to approximate the equilibrium rates of exchange, according to the second interpretation, ‘changes in relative prices would indicate the necessary adjustments in exchange rates’ (Balassa (1964, p. 584)). Though the equivalence is not exact, the ‘static Penn effect’ corresponds to the absolute interpretation of the PPP doctrine while the relative interpretation corresponds to the ‘dynamic Penn effect’. As we report later, while the present study finds no evidence in favor of the ‘static Penn effect’, which involves cross sectional PPP comparisons between countries in a given year, it does find robust evidence in favor of a ‘dynamic Penn effect’ which relates to the same country over time. The latter has, recently, been the subject of controversy between Ravallion (2013a, 2013b) and Inklaar (2013) with the former claiming robust evidence in favor of a ‘dynamic Penn effect’, and the latter denying such an effect.

# **Motivation**

This paper revisits this debate using an extended analytical framework and presents evidence that suggests that both the protagonists are missing the role of within-country inequality movements in affecting the temporal changes in PPP. The importance of inequality movements in studying PPP changes becomes paramount in the context of non-homothetic consumer preferences on which we provide supporting evidence in this study. The examination of the

> 2 This view has however been challenged by Rogoff (1996) who points to the ‘PPP puzzle’, namely, the need to ‘reconcile the extremely high short term volatility of real exchange rates with the glacial rate... at which deviations from PPP seem to die out” (p.664). In a rare departure from the Balassa Samuelson framework, Rogoff (1996) points to the role of transportation costs and tariffs in explaining the ‘PPP puzzle’.

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effect of inequality on PPP, that is one of the principal motivations of this paper, requires an analytical framework that makes an explicit attempt to link consumer preferences with PPP movements.<sup>3</sup> One of the contributions of this paper is to provide such a framework.

The need to get a valid and reasonably general PPP specification stems from the fact that the ICP PPPs or, PPPs from other sources, are available only after discrete time intervals due to resource costs and administrative complexities in conducting PPP exercises, and that such time intervals between ICP exercises have been increasing. Yet, PPPs are required much more frequently, typically annually or even quarterly, as the international community and global agencies need to make cross-country poverty and real expenditure comparisons on a regular scale. This calls for a satisfactory PPP forecasting mechanism that generates PPPs between the ICP benchmark years. Examples of attempts to provide dynamic PPP mechanisms include Rambaldi, Rao and Ganegodage (2010), Rao, Rambaldi and Doran (2010), McCarthy (2013), Pelagatti (2010), Ravallion (2013a, 2013b) and Inklaar (2013).<sup>4</sup> The result of this study on the need to link inequality movements with PPP changes over time thus acquires considerable significance.

Another key motivation of this study is to subject the recently released 2011 ICP PPPs to robustness checks by comparing them with a set of counterfactual PPPs for 2011 that is obtained using an alternative methodology that is based on consumer preferences and using a data set that is similar to that used in the 2011 ICP study. In concentrating exclusively on the 2011 ICP, we depart from counterfactual exercises such as Jolliffe and Prydz (2015) and Inklaar and Rao (2015) that attempt to reconcile the 2005 and 2011 ICP results. A related motivation is the test of the underlying assumption in the ICP PPPs, and in their use in crosscountry welfare comparisons, that a single PPP number is valid for all the expenditure classes, namely, the poor, middle income and affluent households. While there is now widespread appreciation of the importance of constructing ‘subnational PPPs’, this study is motivated by the need to draw attention to the importance of constructing ‘subclass PPPs’ as well.

> 3 See Majumder, Ray and Sinha (2012, 2015a, 2015b) for recent attempts at estimating sub-national PPPs in India and Vietnam based on preference consistent demand systems.

> 4 See, also, Chakrabarty, Majumder and Ray (2015) for an attempt to move from the cross country framework of forecasting national PPPs to the intra-country framework of forecasting subnational PPPs using a dynamic stochastic specification.

5
# **Distinctive Features**

The existing attempts at forecasting PPP between benchmark years can be divided into two broad approaches. The first is largely an accounting exercise that adjusts PPPs for changes in the relative purchasing power of currencies by using inflation differentials between countries. The second, typified by Ravallion (2013a), links the PPP changes to changes in the real GDP of the countries.<sup>5</sup> The present study deviates from these approaches by attempting to link the PPP changes with that in consumer preferences over time. In doing so, the paper deviates from the Balassa Samuelson framework that has dominated the PPP literature and has given primacy, almost exclusively, to the role of productivity differences in driving differences between PPP and exchange rates. As this paper shows, extending the Balassa Samuelson framework to explicitly bring in consumer preferences allows the introduction of distributional variables such as intra-country Gini inequality in studying PPP changes. While in some cases changing consumer preferences can add to the Balassa-Samuelson effects on PPP, in others they can ameliorate such effects. As the empirical evidence presented later shows, one of the consistently robust results of this study is the significant effect of inequality changes on PPP movements in the case of low income countries. These results acquire significance in the context of the recent contribution of Piketty (2015) that has put distribution back at the center of international policy debates.

As indicated above in ‘Motivation’, another key feature of this study is that it provides counterfactual PPPs, along with a proposed methodology for calculating an alternative set of PPPs, which allow comparison with the 2011 ICP PPPs that have come out only very recently. The need for such counterfactual PPPs has recently been emphasized by, for example, Inklaar and Rao (2015) in the context of findings that suggest that while the 2005 ICP PPPs made the developing countries suddenly look a lot ‘poorer’ than they did previously [Chen and Ravallion (2010)], the 2011 ICP PPPs did the very reverse leading to the Inklaar and Rao (2015) conclusion that ‘the (previous) international income inequality had been overstated’. Against a background of continuing controversy on the accuracy of the price information used in the 2005 and the 2011 ICPs, with one group arguing that the 2005 prices were ‘too high’, and the

> 5 Though neither  Ravallion (2013a, 2013b) nor Inklaar (2013) draws a distinction between the cross sectional/ cross country base of the ‘static Penn effect’ and the temporal context of the ‘dynamic Penn effect’, the present study does and provides separate estimates of the two quite  different types of ‘Penn effects’.

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other side arguing that the 2011 prices were ‘too low,’<sup>6</sup> the results of the comparison of the 2011 ICP PPPs with the counterfactual PPPs acquires considerable interest. Since a key distinctive feature of the alternative methodology proposed here to calculate PPP is that it dispenses with the need for price information, the present results acquire significance in the context of this debate on the quality of the price information used in the ICP PPPs. Moreover, it addresses a significant practical issue, namely, that in the case of most developing countries the required price information is missing or is of suspect quality.

Another distinctive feature of this exercise is the use of the Indian rupee as the numeraire currency instead of the US dollar. This is much more than a simple change of the base country, from USA to India, since while interest in all the existing PPP applications in ‘real expenditure comparisons’ centers on the question of whether the world is ‘richer’ or ‘poorer’ in relation to the USA, the counterfactual PPPs and their implied real expenditure comparisons presented here are with respect to India. While the 2011 ICP PPPs suggest that the world has suddenly become a lot ‘richer’, or more accurately ‘less poor’, with respect to the USA when compared with the 2005 ICP PPPs, a distinctive finding of this study is that the 2011 ICP PPPs make much of the developing world look ‘richer’ or ‘less poor’ with respect to India as well, but the comparison here is with the alternative set of 2011 non ICP PPPs, not with a previous set of ICP PPPs. The move to India is justified by the fact that India occupies a unique position in sharing the features of a developing economy in terms of its poverty rates and per capita expenditure, yet it offers a market and the size of its aggregate economy that dwarf many of the developed economies. If the often made comparisons between the 2005 and 2011 ICP PPPs suggest a downward bias in the 2011 ICP PPPs, vis a vis the US dollar, the counterfactual exercise of the present study extends that finding vis a vis the Indian rupee.

# **Organization**

The rest of the paper is organized as follows. Section 2 proposes a non-homothetic preference based analytical framework that yields propositions on the relationship between (a) PPP and exchange rates, (b) PPP and consumption patterns, (c) PPP and factor endowments, and (d) PPP and inequality. Section 3 presents the empirical evidence on non-homothetic preferences

> 6 See Ravallion (2014) and Jolliffe and Prydz (2015) for alternative, indeed contradictory, comparative assessments of the price information collected in ICP 2005 and ICP 2011. While Ravallion (2014) finds issues with ICP 2011, Jolliffe and Prydz (2015) are critical of the price information collected in ICP 2005. Inklaar and Rao (2015) attempt at reconciling the PPPs from ICP 2005 and ICP 2011, and argue that “relying on a single benchmark for country figures is hazardous”.

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that allow the link between PPP and inequality. Section 4 provides robust evidence that confirms the effect of inequality on PPP and of a stable ‘dynamic Penn effect’. While the empirical results in Sections 3 and 4 are based on a time series of the ICP PPPs to date, Section 5 widens the study by proposing an alternative preference-based methodology for estimating PPPs and then using it to calculate counterfactual PPPs that provide a useful comparison with the ICP PPPs. Section 6 concludes the paper with a summary of the principal results and a discussion of issues that could feature in the future agenda of the ICP.

# **2. Analytical Framework and the Link Between PPP and Inequality**

We model a system of two economies that are linked by trade. The consumption basket of the representative individual of either of these economies is composed of three goods<sup>7</sup> and the economies are allowed to engage in bilateral trade in two of these goods. Thus, the market for commodities of any economy is constituted by the domestically produced non-tradable good as well as by the tradable goods produced either domestically or imported from abroad. Note that although each of these economies is endowed with the technology to produce all the commodities, whether a particular tradable good is produced in an economy is determined by the nature of product specialization as directed by the terms of trade. Trade between the economies is assumed to be free<sup>8</sup> and balanced. The productions of the goods in the economies are organized by constant returns to scale production technologies that utilizes a single factor of production. We shall refer to this factor of production as capital. The factor of production is perfectly mobile within an economy but is immobile across the economies. There is perfect competition in both the product and factor markets.

Given this overview of the nature of the economies, we first detail their production structures. Henceforth, we refer to the economies as ‘ _home_ ’ ( _h_ ) and ‘ _foreign_ ’ ( _f_ ) and use as subscripts the letters _h_ and _f_ to distinguish the various exogenous and endogenous variables of the respective economies. Given the assumptions of our model, the production of non-tradable and tradable goods denoted by _X_ , _Y1_ and _Y2_ in that order, are given by:

> 7   In a perfectly competitive setting (as assumption that we invoke subsequently), three is the minimal number of commodities that ensures bilateral trade as also the presence of at least one non-tradable.

> 8   Defined as trade that does not involve any transaction costs in the form of tariffs/subsidies or transportation costs.

8
In the above relations, _α_ , _β1_ and _β2_ represent the productivity parameters of the subscripted ‘ _i_<sup>_th_</sup> ’ economy and _k_ denotes the amounts of capital employed in the particular production activity. Since perfect competition prevails in both the commodity and factor markets, profit maximization on the part of the firms equates the prices of the goods to their marginal costs of production. Or, in terms of notations: In the above relations, _p_ represents the price of the subscripted good and _r_ represents the rental rate of capital: our sole factor of production. In the case where a particular traded good is not produced in a particular economy, the above equations depict the relationship between the price and the rental rate that would have prevailed had that good been manufactured by the competitive firms of the said economy.

In order to model the demand side of the economies, we assume that the individuals of both economies share identical tastes and preferences. As of now, we will assume a very general form of preferences of a typical individual of an economy and introduce the variables: ���, ����and ����∀�∈��, �� to represent the fraction of total income, the ‘ _i_<sup>_th_</sup> ’ economy spends to consume the subscripted goods. Obviously, for each of the economies, these income shares add up to unity. Additionally, apart from being functionally linked to the parameters of the utility function, these variables are functionally dependent on the market prices of the goods and the income distributions of the respective economies for general utility formulations. If the preferences are homothetic, then these income shares are homogenous of degree zero in the market prices and are not functions of the distributions of income in the respective economies.

With this very abstract form of individuals’ preferences, we move on to analytically solve for the equilibrium that prevails at trade. For our model, given the assumptions so far, it is evident that the only way the countries might engage in gainful trade is when the relative productivity parameters of the traded goods vary across the countries; leading to a Ricardian type of 9
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appP! 1 a; apppi 1 <u>a0</u> xi. e ~~FRe~~ x ~~H~~ Ej, a ~~,~~ aj ~~30,~~ xj p **i** ~~kigK~~ ,,oxi 29 —B + ~~ay;~~ j j aj ~~aPLi; 1 OPPPi aPLii 1 OPPP} 7O..~~ i ~~Kj~~ a i ~~Ki ap.~~ i ~~Ki~~ = <u>Ti</u> ~~99.~~ i ~~ki~~ 00x; Ey <u>Oxi</u> Ej OO xj Ej <u>K</u> Oxi 00x; Ej <u>K pOxi</u> Ej 00x; Ej <u>K</u> pOxt

| = =1

PPP} > E} PLI;i PPP;i_= E;pi PPP; PLI; PPP;i < £;i PPP; — PLI; PPP}
spent on the consumption of the good produced in the non-traded sector of the concerned economy. The rest of the result follows from proposition 4.

Note that in course of the above argument, the prices of the commodities (which depend on the productivity parameters only) remain unaltered. Under the altered assumption where the relatively poor consume the nontraded good proportionately less than the relatively rich, the previous propositions get completely reversed.

# **3. The Evidence in Favor of Non-Homothetic Preferences**

In order for the income distribution to affect aggregate demand and, hence, the ‘reference basket’, thereby opening up the link between consumption pattern, inequality and PPP that is central to this exercise, preferences need to be non-homothetic. In other words, the item-wise budget shares must vary with aggregate household expenditure. To provide evidence on this issue, we ran cross-country regressions of mean budget shares on aggregate per capita expenditure, inflation (as measured by the GDP deflator), and country dummies reflecting the country’s status as a ‘low’, ‘middle’ or ‘rich’ income country. Taking the high income OECD and non OECD countries as the default category, the country dummies 2, 3, and 4 refer to, respectively, ‘middle high income’ countries, ‘middle low income’ countries and ‘low income’ countries.<sup>10</sup> These cross-country regressions were run on the pooled cross-country consumption data collected in the ICP 2005 and ICP 2011 exercises [World Bank (2008, 2015)]. The local currency–denominated aggregate expenditures were converted to US $ using the PPP for that year.

# [Table 1 about here]

The results of the regressions on a five broad item breakdown of aggregate expenditure have been reported in Table 1. Relative to the default country group consisting of the rich countries, the ‘middle low’ and ‘low income’ countries spend a greater share of the household budget on items of necessity such as food and clothing, and significantly less on education and health. Four of the five item groups reject homotheticity quite convincingly. Consistent with Engel’s law, the budget share of the first group of items, which is heavily dominated by the necessities

> 10 These are defined in Appendix A.

18
<!-- Start of picture text --> In (—"«) PPPit-1 PPP; =atB,lInBs (+) Pit-1 Pj + B eo In (=) Yit-1 Yi + B sz ln (=+) Eit-1 Ej + Bs B,ln () INit-1 Inj + €;it<br><!-- End of picture text -->
po Bs In (PPP;,) = & + B, In (Pe) + Bo ln (Ye) + Baln (E,) + Bi ln (Ini) + € it Bo Bs = 1.
<!-- Start of picture text --> B, B=<br><!-- End of picture text -->

|Din(PPP;,) = Trend + a,Dln(GDPDeflator;,) + a,DIn(GDP;,) + a3DIn(E<br>jz)+BDZit + €ix<br>Dx, =X — Xprevious t<br>t € {1993, 1996, 2005,2011}<br>Zit<br>B|
|---|
# [Table 3 about here]

Table 3 presents the estimates of equation (22) without the inequality variables. Since the information on inequality is available for only a subset of the countries, Table 2 allowed estimation on the maximum number of observations available in the pooled sample. Note that the evidence in favor of a ‘Dynamic Penn effect’ is quite strong (for both with and without the ‘Trend’ variable) with the highly significant positive estimates of the coefficients of per capita GDP variable and exchange rate variable and non-rejection of the hypothesis of �� �1. The coefficient of the GDP deflator variable is positive, but non-significant. The strong positive relationship between PPP and exchange rate corroborates the prediction of Proposition 2. The inclusion or omission of the Trend variable has little or no effect on the estimates.

# [Table 4 about here]

Table 4 presents a more complete picture by reporting the estimates of equation (22) with the inequality. Proposition 5 predicts that the nature of the effect of inequality on PPP will vary between countries (mostly developing) with PPP less than exchange rates, and those with PPP equal to or greater than exchange rates (mostly affluent developed countries). Table 4 presents robust evidence of a positive relationship between PPP and intra-country inequality as predicted by Proposition 5 for countries with PPP less than the exchange rate.<sup>16</sup> Note from the table that the inclusion or omission of the Trend variable has little effect on the strong statistical significance of the inequality coefficient estimate in case of the low income countries. A comparison between the first two columns of estimates of Table 4 shows that the enforcement of the restriction that the exchange rate coefficient, �� =1, which means that we are estimating the changes in the price level index (PLI) rather than in the PPP, increases quite sharply the magnitude of the estimated inequality effect. Note, also, from the first and third columns of estimates, that the existence of the DPE (�� > 0, �� =1) is robust to the inclusion of the inequality variable and, as in Table 3, the Trend variable has no visible effect on the estimates.

# **5. Counterfactual PPPs : Methodology and Comparison with the ICP PPPs**

# **The Methodology**

> 16 In the ‘low income group’ in 98% cases PPP is less than the Exchange rate.

22
The procedure used here for calculating the alternative set of PPPs to bench mark against those implied by the ICP PPPs is due to Coondoo, Majumder and Chattopdhyay (2011). The present study extends the Coondoo et al. (2011) study by using their suggested procedure proposed in the single country context of India to provide evidence on sub-national PPPs to the current cross country context to estimate an alternate set of PPPs that provide a useful comparison with the recently released ICP PPPs from the 2011 round.

The Coondoo, Majumder and Chattopadhyay (2011) procedure is based on the estimation of Engel curves on a single cross section data. The attractiveness of their procedure has been described by the authors as follows: “The novelty of the procedure is that it overcomes the problem of data inadequacy, a problem that is shared by most of the developing countries. The procedure does not require item-specific price/unit value data and price index numbers can be calculated from consumer expenditure data grouped by per capita income/total consumer expenditure class in a situation where unit level data are not available.” (p. 138) In the current context, this offers a significant advantage for benchmarking the ICP PPPs, since much of the controversy over the accuracy of the ICP PPPs has centered around questions over the accuracy of the price information used in the ICP 2005 and ICP 2011 rounds. The counterfactual PPPs presented here allow a clean comparison since the procedure does not need to use the controversial price information collected in the ICP 2011 round. Moreover, as this study illustrates, the published World Bank data does contain the disaggregated expenditure information (by items and by expenditure classes) at country level required to implement the procedure to calculate the alternative set of PPPs.

The use of estimated Engel curves to construct price indices has a rich history. The idea can be traced back to Costa (2001) and Hamilton (2001) who used it to investigate and correct the ‘biases’ in official consumer price indices. Recent applications include Almas (2012) to estimate the consequence of ‘PPP bias’ on real income comparisons between countries, Almas, Kjelsrud and Somanathan (2013) to examine the bias in calculating poverty rates in India, and Beatty and Larsen (2005), Gibson, Stillman and Le (2008), Barrett and Brozozwoski (2010) to estimate the bias in CPI in Canada, the Russian Federation and Australia, respectively. The procedure rests on the underlying assumption of Costa (2001) and Hamilton (2001) that (a) 23
<!-- Start of picture text --> b(p)<br><!-- End of picture text --> _ a(p) b(p) (p)

> w, = a4(p) + bi(p) In ~~(2)~~ + ~~*®hi~~ ( ~~in)~~ 2

x p p° InP(p1,p°,u ) [lna(p*) — Ina(p®)] + ~~reb(p?)~~ _ ~~=b(p°)~~ p' = 6p° 6 >0 a(p') = 8a(p°) 9
1= 9 S09 bp = b(p) (p') = (p°) wij = af + bi lnxf + cj,-(Inx})* + €f; j ‘i Qj, bi, cp a(p"), bY — B® = Ina(p°)(2é9) — Ina(p")(227) ee? ; or = 1,2,..,, RB.

ej aj,bi,c; —_p® b(p®) = Alp) = 1, uy x; (= C(ufp’)) ~~Td~~ 1 = ~~a~~ 1 +1. " <u>al?)</u> (p") (p") a(p") a(p°)
To estimate (29) we take _j_ as decile (percentile) group so that the data are comparable across countries. The PPPs are then estimated as TCLIs from equation (25) for a given reference level of utility u<sup>∗</sup> (taken to be the one corresponding to the median level income of the base country, India). It may be emphasized that ���<sup>�</sup> �, ���<sup>�</sup> �and ���<sup>�</sup> � are estimated as composite variables and no explicit algebraic forms for these functions are assumed. This confers the advantage that the estimated PPPs are not dependent on a priori specified particular functional forms such as, for example, the specification proposed by Banks, Blundell and Lewbel (1997).

# **Comparison with the ICP PPPs**

# [Table 5 about here]

Table 5 presents the counterfactual PPPs based on World Bank data on broad item groups by income categories for rural and urban sectors,<sup>22</sup> with India as base. The table also presents the 2011 ICP Consumption PPPs, where the base country has been shifted from the US to India by dividing all the PPPs (with respect to US $) by the PPP of India with US as base. In case of a few countries, for example, Chad, Ethiopia and Ghana, the two PPPs are nearly identical, but this is not always the case. The bias in the 2011 ICP PPPs in relation to the counterfactual PPP is not unidirectional. In general, the 2011 ICP PPPs in the African region exceed the counterfactual PPPs, and the reverse is the case in the Asia/Pacific region. While in case of several countries, for example, South Africa, China and Indonesia, there is a large difference between the 2011 ICP PPP and its 2011 counterfactual, overall, there is a positive correlation between the two. The overall correlation coefficient, over all countries taken together, turns out to be 0.9134. The region specific correlations are 0.9189, 0.9996, 0.9985 and 0.9706, respectively, for the ‘African region’, the ‘Asia and Pacific region’, the ‘Commonwealth of Independent States and Eurostat-OECD’ region and the remaining region consisting of Latin America, Western Asia and the Caribbean.<sup>23</sup>

[Figures 4, 5 and 6 about here]

> 22 See Appendix A for description of income category level.

> 23 All the correlations are significant at less than 1% level.

26
Figure 4 presents a graph of these counterfactual PPPs against the 2011 ICP PPPs in logarithmic scale. The 45 degree broken line through the origin represents the benchmark case of equality between the two PPPs for each country. It can be clearly observed that for most part the 2011 ICP PPPs are lower than the counterfactual PPPs. From the table it is evident that almost the entire non-African region and some African countries constitute this part with the ICP PPPs lower than the corresponding counterfactuals. This result is analogous to the observation made in, for example, Ravallion (2014) that the 2011 ICP PPPs were lower than their counterpart in the 2005 ICP PPP. This feature translates into the PPP deflated GDP values, presented in Figures 5 and 6. While Figure 5 plots the per capita GDP values using counterfactual PPP deflator against those using the 2011 ICP PPP deflator, Figure 6 plots the corresponding aggregate GDP values. On superimposition of the line of equality between the two axes Figure 5 shows that for most part the per capita GDPs deflated by 2011 ICP PPPs lie above those deflated by the counterfactual PPPs. Figure 6 shows the overstatement of GDP by the 2011 ICP PPP in relation to the counterfactual PPP more clearly since the 45 degree line of equality between the two GDP values lies uniformly above the fitted line. This is analogous to the result noted in Ravallion (2014), Inklaar and Rao (2015), Jolliffe and Prydz (2015) on the overstatement of the 2011 PPP deflated real GDP in relation to the 2005 PPP deflated real GDP. While the temporal comparison between the 2005 and 2011 PPP and real GDP values in the above cited studies is with respect to the US dollar and the US economy, the comparison here relates to the same year (2011) and is with respect to the Indian Rupee and the size of the Indian economy. If one considers the present results in conjunction with the earlier ones, then we have robust evidence of understatement of the PPPs and overstatement of the PPP deflated GDP values in the 2011 ICP.

<mark>[Tables 6a and 6b about here]</mark> Table 6a presents the per capita annual <mark>GDP evaluated at 2011 ICP Consumption PPP and at counterfactual PPP with India as base and Table 6b presents the corresponding values for per capita aggregate consumption.</mark><sup>24</sup> <mark>The qualitative pictures portrayed by these tables are quite similar and mirror the comparative PPP estimates reported in Table 5. The revisions to the 2011 ICP PPP deflated GDP and consumption figures implied by the corresponding counterfactual</mark>

> 24 Tables B6a and B6b, in Appendix B, present the results in logarithmic scale.

27
<mark>PPP deflated estimates are not unidirectional and vary across regions and between countries. However, the large downward revisions from the 2011 ICP PPP deflated to the counterfactual PPP deflated GDP and consumption figures occur more frequently than the reverse, especially in the larger and more populated countries such as South Africa, China, Mexico and Russia. Consequently, consistent with Figures 5 and 6, a comparison of the mean and median figures between the two PPP deflated values in either table establishes the result that the 2011 ICP overestimates the real size and consumption of the world at large. A result of particular interest is that the feature that China’s dominance over India on per capita GDP is sharply reduced from the ICP PPP to the counterfactual PPP deflated values.</mark>

# <mark>[Tables 7a and 7b about here]</mark>

The ratios of per capita annual GDP of the different countries to the per capita annual GDP of India, evaluated at the alternative PPPs, are presented in <mark>Table 7a and the corresponding ratios for per capita annual aggregate consumption are given in Table 7b. These tables mirror Tables 6a, 6b in showing that in most cases the dominance over India in the per capita GDP and consumption figures shrinks, and in few cases even gets reversed, when we use the counterfactual PPP in place of the 2011 ICP PPP. The widely made claim that the 2011 ICP made the poorer countries look lot ‘less poor’ vis a via the USA can be extended to the result that India looks ‘far poorer’ on the ICP PPP than on the counterfactual PPP.</mark> An underlying assumption in both sets of PPPs that we have compared in this study is that all the income groups face the same PPP, analogous to the assumption of a single economy-wide PPP for each country’s currency that holds true for all regions. While the latter assumption is now considered untenable as reflected in the increasing emphasis on the calculation of subnational PPPs, there is still not much awareness of the need for subclass PPPs. Table 8 provides evidence on the latter and, also, on the robustness of the comparison between the 2011 ICP PPP and its counterfactual, by presenting the counterfactual PPP by income quintile based on the publicly available disaggregated household level expenditure data of Iraq, Malawi and Tanzania supplemented by the unit records from India’s National Sample Survey and Vietnam’s Living Standard Survey- see Appendix A for details.

[Table 8 about here] 28
It is evident from Table 8 that except for Tanzania, the overall PPPs based on household level data are greater than the ICP PPPs. This is in line with the finding from Table 5, where for almost the entire non-African region and some African countries this feature is observed. There are variations in PPP values across income quintiles, the values of the coefficient of variation (CV) for Iraq, Malawi, Tanzania and Vietnam being 0.152, 0.085, 0.084 and 0.074, respectively. This complements the evidence in favor of subnational PPPs, and is consistent with the variation across expenditure percentiles in PPP between India and Vietnam reported in Majumder, Ray and Sinha (2015a). In other words, poverty level PPP s are quite different from the aggregate PPPs, and this should be recognized when drawing up international poverty lines. However, this variation in PPP has little effect on the overall inequality between households pooled over these four countries as evident from the values of the Gini coefficient presented in Table 9.

[Table 9 about here]

# **6. Concluding Remarks**

This paper is written in the wake of the recent release by the World Bank (2015) of the final results of the 2011 International Comparison Project (ICP) that provided estimates of the Purchasing Power Parities (PPP) between different countries’ currencies. PPPs play a central role in economic analysis because they are required in a host of international welfare comparisons, such as cross-country comparisons of poverty rates, real GDP and real consumption expenditures, and the calculation of the total number of people in poverty. The 2011 ICP exercise has generated renewed interest in the concept of PPP that can be traced back to the early work of Cassel, Balassa and Samuelson. PPPs are considered better measures of the ‘true’ purchasing power of a country’s currency and more relevant in comparisons of living standards than exchange rates, since PPPs are based on both tradeable and non-tradeable items unlike exchange rates, which reflect only the price differences of tradeable items. This distinction makes the PPP of particular importance for developing countries with a lower consumption share of tradeable items leading to a greater deviation of the PPPs from exchange rates in relation to the developed countries.

Since inaccurate PPP estimates are likely to distort the cross-country comparisons, much attention has been focused on the accuracy of the estimated PPPs yielded by the successive ICPs. If, as happened between 1993 and the 2005, the PPPs are revised upwards sharply, the 29
developing world suddenly looks lot ‘poorer’ than previously in relation to the USA, which is adopted as the base country. The reverse occurred between 2005 and 2011, with the downward revision not able to fully restore the PPPs to the 1993 level. With the poverty rates fluctuating wildly over time, it is not clear whether this is really due to changes in the poverty situation or is merely reflecting the PPP revisions between the ICP rounds. For example, are the 2011 ICP PPPs really ‘too low’ or are they merely correcting the ‘implausibly high’ estimates of the 2005 ICP? This raises the issue of benchmarking the 2011 ICP PPPs against those from using an alternative methodology on data for the same year. Since, given the large-scale nature of the ICP, such exercises cannot be undertaken frequently, and one needs the PPPs in intermediate years, much attention has also been paid recently to the econometric specification used to predict the PPPs in the intermediate years and beyond. This raises the issue of identifying the principal determinants of PPP changes between countries and over time. This paper investigates both sets of issues and provides empirical evidence that is likely to inform the World Bank on future directions for the ICP exercises.

The contribution of this study to the topic of PPP is analytical, methodological and empirical. On the analytical front, it provides a framework that deviates from the conventional Balassa Samuelson framework that is driven by productivity differences in the non-tradeable sector between the developed and developing countries. The proposed framework of this study focusses attention, instead, on the neglected link between consumer preferences and PPP, and derives propositions on the relation between PPP and exchange rate and, more significantly, between PPP and intra country inequality. The paper provides empirical evidence that provides support for several of the propositions. Taken in conjunction with the Balassa Samuelson predictions on PPP changes, this paper shows that the addition of inequality as a determinant of PPP changes helps to improve the estimating equation over the narrow specifications adopted previously that either considered only inflation differentials or differences in real GDP, dubbed the ‘Penn effect’, or both.

The role of the inequality variable in driving PPP changes, namely, a positive association between a country’s inequality and its PPP, is one of the most significant analytical results of this study. An increase in inequality leads to a shift in consumer preferences towards tradeable items, since the affluent are now able to access the international markets more readily than before. Easier credit availability to the new rich as the economy develops helps in making such access easier. This change in preferences spreads to the other households as the economy 30
witnesses greater availability of the tradeable goods and the lifestyles of the affluent influence those in the rest of the economy. A good example of this is the phenomenon witnessed in countries such as India with a move towards greater consumption of tastier food items that are imported and away from the domestically produced traditional food items. The ‘inequality effect’ supplements the ‘Penn effect’ in moving the PPP towards the exchange rates, i.e. increases the ‘Price Level Index’ towards unity.

This study proposes and applies an alternative methodology to that used in the ICP to present a set of PPPs that serve as a benchmark for comparing the 2011 ICP PPPs. The methodology is based on a utility theory consistent specification of consumer preferences and has quite modest data requirements. As the empirical exercise shows, the methodology can be readily implemented on easily available data sets published on the World Bank website. This is an attractive feature since it not only avoids the requirement of detailed price information, the quality of which has dogged successive ICPs, it is an easy procedure to use.

The empirical contribution of this paper includes the feature that this is the first attempt at benchmarking the 2011 ICP, indeed any ICP, not by reconciling the PPPs with those from a previous ICP, but with PPPs calculated on a similar data from the same year. Another distinguishing feature is the moving of the ‘base country’ from the USA to India. The latter country shares many of the features of a developing country including high poverty rates, but at the same time provides a market and an economy size that places it in the top tier of nations. The significant result here is the finding that, while there is remarkable closeness between the two PPPs for many countries, the overall picture is one of understatement by the ICP PPPs leading to an overstatement of the PPP deflated real GDP. The study does find, however, that there are large regional variations in the sign and size of the deviation of the two PPPs from one another. Another feature of this study is the use of expenditure percentile disaggregated data sets to show that the PPPs vary significantly between the expenditure percentiles. This has the important policy message that the aggregate data based PPPs may not be appropriate for use in poverty calculations.

This study takes place at a time when the ICP exercise is at a cross road with questions over its methodology, the quality of the price information used and accuracy of its PPP estimates. The results of this study point to the need to experiment with alternative methodologies that allow proper robustness check on the PPP estimates. The results also raise questions over the wisdom 31
of spending an enormous amount of time and resources to come up with a single number as the PPP for the whole country. In the wake of recent results on sharp regional variation in prices within large heterogeneous countries, the present results on PPP variation between expenditure percentiles point to a new research agenda on subnational and expenditure group varying PPPs that the ICP could explore in its future exercises.

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Ravallion, M. (2013a), “Price Levels and Economic Growth: Making Sense of Revisions to Data on Real Incomes”, _Review of Income and Wealth_ , 59(4), 593-613.

Ravallion, M. (2013b), “Reply to Robert Inklaar”, _Review of Income and Wealth_ , 59 (4), 623628.

Ravallion, M. (2014), “ _An Exploration of the International Comparison Program's New Global Economic Landscape_ ”, NBER Working Paper No. 20338, A copy of this paper is available on http://www.nber.org/papers/w20338.pdf.

Reddy, S. and T. Pogge (2007), “How Not to Count the Poor,” in S. Anand and J. Stiglitz (eds.), _Measuring Global Poverty_ , Oxford University Press, Oxford, 2007.

Rogoff, K. (1996), “The Purchasing Power Parity Puzzle”, _Journal of Economic Literature_ , 34(2), 647-668.

Samuelson, P. (1964), “Theoretical Notes on Trade Problems”, _Review of Economics and Statistics_ , 46(2), 145-154.

World Bank (2008), _Global Purchasing Power Parities and Real Expenditures: 2005 International Comparison Program_ , World Bank, Washington DC.

World Bank (2013), _Measuring the Real Size of the World Economy: The Framework, Methodology, and Results of the International Comparison Program—ICP_ , World Bank, Washington DC.

35
World Bank (2014), _Purchasing Power Parities and Real Expenditures of World Economies:_ Summary of Results and Findings of the 2011 International Comparison Program, World Bank, Washington, DC.

World Bank (2015), _Purchasing Power Parities and the Real Size of World Economies_ : _A Comprehensive Report of the 2011 International Comparison Program_ , World Bank, Washington, DC.

36
# **Table 1: Results of the Regressions of Budget Shares: Evidence in Favor of**

# **Non-Homothetic Preferences**

||||**Item groups**<br>|**Recreation,**||
|---|---|---|---|---|---|
|**Explanatory**<br>**Variables**|**Food,**<br>**Clothing,**<br>**Fuel etc.**|**Education and**<br>**Health**|**Communication**<br>**and**<br>**Transport**|<br>**Culture,**<br>**Personal care**<br>**etc.**|**Miscellaneous**<br>**others**|
|**ln (total**|-0.070***|0.013**|0.022***|0.039***|-0.004|
|**expenditure)**<sup>**&**</sup>|(0.000)|(0.035)|(0.000)|(0.000)|(0.437)|
|**ln (GDP Deflator)**|0.005|0.002|0.002|-0.015***|0.006**|
||(0.272)|(0.518)|(0.410)|(0.000)|(0.017)|
|**Country group**<br>**Dummy**<sup>**$$**</sup>||||||
|**Middle high**<br>**income**|0.030*<br>(0.069)|-0.019**<br>(0.018)|0.026***<br>(0.001)|-0.036***<br>(0.002)|-0.001<br>(0.918)|
|**Middle low**|0.088***|- 0.038***|0.013|-0.057***|-0.006|
|**income**|(0.001)|(0.002)|(0.216)|(0.001)|(0.616)|
|**Low income**|0.077**|-0.043**|0.008|-0.035|-0.007|
||(0.038)|(0.027)|(0.605)|(0.161)|(0.667)|
|**Year dummy**<sup>**@**</sup><br>||||||
|**2011**|0.029***|-0.012**|-0.005|-0.011|-0.001|
||(0.007)|(0.029)|(0.322)|(0.114)|(0.848)|
|**Constant**|1.019***<br>(0.000)|0.067<br>(0.251)|-0.082*<br>(0.073)|-0.109<br>(0.160)|0.105*<br>(0.053)|
|**No. of**<br>**observations**|294|294|294|294|294|
|**No. of countries**|161|161|161|161|161|
|**R**<sup>**2**</sup>|0.6770|0.3347|0.3192|0.6494|0.0369|

Note: (1) Figures in parentheses are the p-values. *: significant at 10% level; **: significant at 5% level;

***: significant at 1% level.

- (2)<sup>&</sup> : These are PPP (consumption) adjusted expenditures.

- (3)<sup>$$</sup> : Default category: high income OECD and non OECD countries.

- (4)<sup>@</sup> : Default year: 2005.

37
**Table 2: Regression Results of Static Inequality augmented Inklaar Equations**

# **Dependent Variable: ln (PPP)**

||**Estimated P**<br>|**arameters**<br>|
|---|---|---|
|**Explanatory Variables**|**Year 2005**|**Year 2011**|
|**ln (GDP Deflator)**|0.405<br>(0.740)|Omitted due to<br>collinearity|
|**ln (GDPPC)**<br>|0.627***<br>(0.000)|0.227***<br>(0.000)|
|**ln (Exchange rate)**|0.357**<br>(0.016)|0.769***<br>(0.000)|
|**Inequality**|||
|**Low income countries**|4.200**<br>(0.045)|0.227<br>(0.577)|
|**Higher income countries**|1.709<br>(0.245)|-0.147<br>(0.619)|
|**Constant**<br>|- 6.607***<br>(0.000)|-2.373***<br>(0.000)|
|**R**<sup>**2**</sup>|0.9182|0.9856|
|**No. of observations**|107|101|
|**No. of countries**|107|101|
|**F-statistic for testing**��<br>��1|21.86***<br>(0.000)|38.59***<br>(0.000)|

Note: (1) Figures in parentheses are the p-values. **: significant at 5% level; ***: significant at 1% level.

- (2) **Low income countries** are those as specified by World Bank. **Higher income countries**

include lower middle, upper middle, high income non OECD and high income OECD countries.

38
**Table 3: Regression Results of Dynamic Inklaar Equation (22) without the Inequality Variable**

**Dependent Variable: D ln (PPP)**

|**Explanatory Variables**|**Estimated P**|**arameters**|
|---|---|---|
|**Trend**<br>|-0.000<br>(0.995)||
|**D ln (GDP Deflator)**|0.325<br>(0.278)|0.323<br>(0.153)|
|**D ln (GDPPC)**|0.555*<br>(0.074)|0.555**<br>(0.050)|
|**D ln (Exchange rate)**|0.749***<br>(0.003)|0.749***<br>(0.003)|
|**R**<sup>**2**</sup>|0.6846|0.6846|
|**No. of observations**|311|311|
|**No. of countries**|120|120|
|**F-statistic for testing**���1|1.25<br>(0.275)|1.26<br>(0.273)|

Note: (1) Figures in parentheses are the p-values. **: significant at 5% level; ***: significant at 1% level (2) The operator _D_ denotes difference over time.

39
**Table 4: Regression Results of Dynamic Inklaar Equation (22) with the Inequality Variable Dependent Variable: D ln (PPP)**

|**Explanatory**<br>**Variables**|**Parameter Esti**|**mates with Trend**|**Parameter**<br>**Estimates**<br>**without Trend**|
|---|---|---|---|
|**Trend**|-0.000<br>(0.990)|-0.023<br>(0.344)|-|
|**D ln (GDP Deflator)**|0.343<br>(0.182)|0.334*<br>(0.096)|0.338<br>(0.160)|
|**D l (GDPPC)**|0.563**|0.921|0.563**|
|**n**|(0.041)|(0.158)|(0.030)|
|**D ln (Exchange rate)**|0.756***<br>(0.003)|1<br>(constrained)|0.757***<br>(0.003)|
|**D Inequality**||||
|**Low income**<br>**countries**|3.980***<br>(0.004)|5.241***<br>(0.007)|3.980***<br>(0.005)|
|**Higher income**<br>**countries**|0.041<br>(0.941)|-0.444<br>(0.396)|0.041<br>(0.941)|
|**R**<sup>**2**</sup>|0.6898||0.6898|
|**No. of observations**|303|303|303|
|**No. of countries**|119|119|119|
|**F-statistic for testing**<br>���1|1.18<br>(0.288)||1.43<br>(0.245)|

Figures in parentheses are the p-values. *: significant at 10% level; **: significant at 5% level; ***: significant at 1% level.

40
**Table 5: 2011 ICP Consumption PPPs and Counterfactual PPPs (CPPP1) based on data by Income Categories (Base Country: India)**

|**Region**|**Country**|**2011 ICP**<br>**Consumption**|**Counter**<br>**factual**|**Region**|**Country**|**2011 ICP**<br>**Consumption**|**Counter**<br>**factual**|**Region**|**Country**|**2011 ICP**<br>**Consumption**|**Counter**<br>**factual**|
|---|---|---|---|---|---|---|---|---|---|---|---|
|||**PPP**|**PPP**|||**PPP**|**PPP**|||**PPP**|**PPP**|
||Benin|14.801|11.821||South Africa|0.340|0.571||Albania|3.400|1.486|
||Burkina Faso|14.552|8.171||Swaziland|0.273|0.169||Bosnia and<br>Herzegovina|0.055|0.398|
||Cameroon|15.253|12.418||Tanzania|38.494|21.820||Bulgaria|0.047|0.288|
||Chad|16.499|16.787|**AFRICA**|Togo|14.966|10.190||Latvia|0.025|0.127|
||Congo, Rep.|35.145|31.664||Uganda|61.989|48.688||Lithuania|0.112|0.491|
||Congo, Dem.<br>Rep.|19.711|13.335||Zambia|166.554|95.465|**EUROSTAT-**<br>**OECD**|Macedonia<br>(FYR)|1.392|6.807|
||Cote d'Ivoire|15.691|19.943||Bangladesh|1.628|1.786||Mi|0549|1126|
||Djibouti|6.727|11.370||Bhutan|1.119|1.906||exco|.|.|
||Egypt|0.115|0.252||Cambodia|96.712|120.760||Montenegro|0.028|0.175|
||Ethiopia|0.352|0.397||China|0.249|0.415||Romania|0.120|0.458|
||Gabon|23.877|59.136||Fiji|0.080|0.140||Russia|1.059|5.498|
|**AFRICA**|Gambia(The)|0.697|0.596||**India**|**1.000**|**1.000**||Serbia|2.802|13.968|
||Ghana|0.051|0.052||Indonesia|266.380|311.831||Turkey|0.072|0.059|
||Guinea|165.403|148.692||Lao PDR|181.329|222.421||Bolivia|0.200|0.409|
||Kenya|2.365|2.164||Maldives|0.677|1.250||Brazil|0.106|0.231|
||Lesotho|0.261|0.209|**ASIA AND**<br>|Mongolia|36.881|59.862||Colombia|81.836|173.525|
||Liberia|0.037|1.956|**THE**<br>**PACIFIC**|Nepal|1.698|2.114|**LATIN**<br>|ElSalvador|0.036|0.036|
||Madagascar|46.309|18.850||Pakistan|1.673|2.147|**AMERICA**|Guatemala|0.261|0.588|
||Mali|14.437|10.579||Philippines|1.261|1.552||Honduras|0.706|0.767|
||Mauritania|7.395|10.857||Sri Lanka|2.689|6.834||Nicaragua|0.613|0.310|
||Mauritius|1.181|2.826||Thailand|0.858|3.297||Peru|0.104|0.265|
||Morocco|0.276|0.605||Vietnam|479.060|569.544|**WESTERN**|Iraq|35.882|41.932|
||Mozambique|1.051|0.552||Armenia|10.880|22.195|**ASIA**|Jordan|0.021|0.093|
||Namibia|0.342|0.284||Azerbaijan|0.020|0.066||Yemen|5.319|14.339|
||Nigeria|5.184|4.483|**COMMON**|Belarus|109.735|414.875|**CARIBBEAN**|Jamaica|4.136|9.063|
|||||**WEALTH**|Kazakhstan|5.037|17.722|||||
||Republic of<br>Cabo Verde|3.164|8.940|**OF**<br>**INDEPEND**|Kyrgyz<br>Republic|1.037|1.852|||||
|||||**ENT**<br>|Moldova|0.328|0.840|||||
||Senegal|16.285|14.954|**STATES**|Tajikistan|0.106|0.215|||||
||Sierra Leone|114.179|146.402||Ukraine|0.204|0.811|||||

41
**Table 6a: Per Capita Annual GDP (PCGDP) in ’000** **<mark>local currencies converted to Indian Rupees unde</mark>** <mark>r</mark> **2011 ICP Consumption PPPs and Counterfactual PPPs of Table 5 (Base Country: India)**

|||**PCGDP e**<br>|**valuated at**<br>|||**PCGDP ev**<br>|**aluated at**<br>||**PCGDP**<br>|**evaluated at**<br>|
|---|---|---|---|---|---|---|---|---|---|---|
|**Region**|**Country**|**2011 ICP**<br>**PPP**|**Counter**<br>**factual**<br>**PPP**|**Region**|**Country**|**2011 ICP**<br>**PPP**|**Counter**<br>**factual**<br>**PPP**|**Region**|**Country**<br>**2011**<br>**ICP**<br>**PPP**|**Counter**<br>**factual**<br>**PPP**|
||Benin|25.54|31.98||South Africa|169.82|101.19||Albania<br>133.19|<br>394.24|
||Burkina Faso|19.72|35.11||Swaziland|90.49|146.00||Bosnia and Herzegovina<br>126.93|<br>17.52|
||Cameroon|41.06|50.44||Tanzania|21.10|37.22||Bulgaria<br>218.56|<br>35.57|
||Chad|30.11|29.59||Togo|18.88|27.73||Latvia<br>274.49|<br>54.54|
||Congo, Rep.|47.99|53.27|**AFRICA**|Uganda|21.48|27.34||Lithuania<br>314.48|<br>71.87|
||Congo, Dem. Rep.|17.33|25.62||Zambia|45.05|78.60||Macedonia(FYR)<br>160.43|<br>32.82|
||Cote d'Ivoire|38.82|30.54||Bangladesh|39.81|36.30|**EUROSTAT-**<br>**OECD**|<br>228.81|<br>111.60|
||Djibouti|33.70|19.94||Bhutan|108.43|63.68||Mexico||
||Egypt|150.21|68.24||Cambodia|37.85|30.31||Montenegro<br>187.72|<br>29.74|
||Ethiopia|16.96|15.05||China|141.35|84.93||Romania<br>216.86|<br>56.95|
||Gabon|219.64|88.68||Fiji|98.58|56.35||Russia<br>368.47|<br>70.99|
||Gambia(The)|21.48|25.13||**India**|71.54|71.54||Serbia<br>157.75|<br>31.65|
||Ghana|46.93|46.32||Indonesia|115.61|98.76||Turkey<br>244.05|<br>299.56|
|**AFRICA**|Guinea|19.59|21.80||Lao PDR|55.91|45.58||Bolivia<br>81.86|<br>40.04|
||Kenya|30.99|33.86|**ASIA AND**|Maldives|1.61|0.87||Brazil<br>202.89|<br>93.42|
||Lesotho|32.05|39.92|<br>**THE**|Mongolia|126.98|78.23||Colombia<br>161.30|<br>76.07|
||Liberia|7.50|0.14|**PACIFIC**|Nepal|32.22|25.88|**LATIN**<br>|El Salvador<br>103.63|<br>102.10|
||Madagascar|20.54|50.46||Pakistan|64.74|50.45|**AMERICA**|Guatemala<br>96.84|<br>43.00|
||Mali|21.97|29.99||Philippines|81.74|66.41||Honduras<br>61.09|<br>56.19|
||Mauritania|50.00|34.05||Sri Lanka|116.59|45.88||Nicaragua<br>59.84|<br>118.22|
||Mauritius|209.38|87.45||Thailand|191.63|49.90||Peru<br>160.15|<br>62.99|
||Morocco|90.26|41.10||Vietnam|66.06|55.57|**WESTERN**|Iraq<br>160.21|<br>137.09|
||Mozambique|14.51|27.63||Armenia|115.15|56.44|**ASIA**|Jordan<br>155.73|<br>35.15|
||Namibia|114.08|137.15||Azerbaijan|285.56|86.62||Yemen<br>52.97|<br>19.65|
||Nigeria|45.14|52.19|**COMMON**<br>|Belarus|285.86|75.61|**CARIBBEA**|Jamaica<br>109.00|<br>49.74|
||Republic of Cabo|94.07|33.29|**WEALTH**|Kazakhstan|330.60|93.97||||
||<br>Verde|||**OF**<br>**INDEPEND**|Kyrgyz<br>Republic|52.44|29.35||**MEAN 104.66**|**59.77**|
||Senegal|32.55|35.44|**ENT**<br>|Moldova|70.45|27.54||**MEDIAN 81.80**|**46.10**|
|||18.63|14.53|**STATES**|Tajikistan|36.82|18.11||||
||Sierra Leone||||Ukraine|139.91|35.11||||

42
**Table 6b: Per Capita Annual Aggregate Consumption (PCAgC) in ’000** **<mark>local currencies converted to Indian Rupees unde</mark>** <mark>r</mark> **<mark>2</mark> 011 ICP Consumption PPPs and Counterfactual PPPs of Table 5 (Base Country: India)**

|||**PCAgC**|**evaluated**<br>|||**PCAgC**<br>|**evaluated**<br>|||**PCAgC**|**evaluated**<br>|
|---|---|---|---|---|---|---|---|---|---|---|---|
|**Region**|**Country**||**at**|**Region**|**Country**||**at**|**Region**|**Country**||**at**|
|||**2011**<br>**ICP**<br>**PPP**|**Counter**<br>**factual**<br>**PPP**|||**2011 ICP**<br>**PPP**|**Counter**<br>**factual**<br>**PPP**|||**2011**<br>**ICP**<br>**PPP**|**Counter**<br>**factual**<br>**PPP**|
||Benin|20.63|25.83||South Africa|115.97|69.10||Albania|113.67|336.47|
||Burkina Faso|13.34|23.76||Swaziland|81.54|131.56||Bosnia and Herzegovina|118.60|16.37|
||Cameroon|32.17|39.52||Tanzania|14.42|25.43||Bulgaria|153.65|25.01|
||Chad|20.68|20.32||Togo|16.71|24.55||Latvia|192.37|38.22|
||Congo, Rep.|11.89|13.19|**AFRICA**|Uganda|19.47|24.79||Lithuania|231.62|52.94|
||Congo,Dem. Rep.|11.15|16.49||Zambia|24.91|43.45||Macedonia(FYR)|132.81|27.17|
||Cote d'Ivoire|27.72|21.81||Bangladesh|29.95|27.31|**EUROSTAT-**||165.88|80.91|
||Djibouti|24.08|14.25||Bhutan|56.00|32.89|**OECD**|Mexico|||
||Egypt|119.46|54.28||Cambodia|31.89|25.54||Montenegro|172.48|27.33|
||Ethiopia|13.71|12.17||China|60.66|36.45||Romania|156.64|41.14|
||Gabon|83.71|33.80||Fiji|75.60|43.22||Russia|212.55|40.95|
||Gambia(The)|17.10|20.00||**India**|42.34|42.34||Serbia|141.57|28.40|
||Ghana|31.40|30.99||Indonesia|67.31|57.50||Turkey|192.33|236.08|
||Guinea|11.04|12.29||Lao PDR|32.79|26.73||Bolivia|51.27|25.08|
|**AFRICA**|Kenya|27.13|29.65|**ASIA AND**|Maldives|0.61|0.33||Brazil|138.75|63.88|
||Lesotho|35.36|44.04|**THE**|Mongolia|77.05|47.47||Colombia|109.75|51.76|
||Liberia|8.48|0.16|**PACIFIC**|Nepal|25.88|20.79|**LATIN**<br>|El Salvador|102.04|100.54|
||Madagascar|18.65|45.82||Pakistan|54.99|42.85|**AMERICA**|Guatemala|87.15|38.70|
||Mali|14.66|20.01||Philippines|62.89|51.09||Honduras|52.50|48.29|
||Mauritania|29.26|19.93||Sri Lanka|89.55|35.24||Nicaragua|50.23|99.24|
||Mauritius|165.44|69.10||Thailand|118.73|30.92||Peru|100.11|39.38|
||Morocco|60.35|27.48||Vietnam|41.89|35.24|**WESTERN**|Iraq|75.36|64.49|
||Mozambique|12.46|23.73||Armenia|102.30|50.15|**ASIA**|Jordan|124.21|28.03|
||Namibia|81.61|98.12|**COMMON**|Azerbaijan|117.17|35.54||Yemen|38.69|14.35|
||Nigeria|29.06|33.60|**WEALTH**|Belarus|162.14|42.89|**CARIBBEAN**|Jamaica|101.42|46.28|
||Republic of Cabo|66.49|23.54|**OF**|Kazakhstan|159.83|45.43|||||
||<br>Verde|||**INDEPEN**<br>|<br>Kyrgyz Rep.|<br>49.10|<br>27.48||**MEAN 73.30**||**43.21**|
||Senegal|26.94|29.34|**DENT**<br>|<br>Moldova|79.18|30.95|||||
||Sierra Leone|16.72|13.04|**STATES**|Tajikistan|42.37|20.84||**MEDIAN 58.17**||**31.94**|
||||||Ukraine|110.74|27.79|||||

43
**Table 7b: Ratio of Per Capita Annual Consumption evaluated at different PPPs to Per Capita Annual Consumption of India evaluated at the corresponding PPP**

|||**PCAgC ev**<br>|**aluated at**<br>|||**PCAgC ev**<br>|**aluated at**<br>|||**PCAgC**<br>|**evaluated at**<br>|
|---|---|---|---|---|---|---|---|---|---|---|---|
|**Region**|**Country**|**2011 ICP**<br>**consumption**<br>**PPP***|**Counter**<br>**factual**<br>**PPP***|**Region**|**Country**|**2011 ICP**<br>**consumption**<br>**PPP***|**Counter**<br>**factual**<br>**PPP***|**Region**|**Country**|**2011 ICP**<br>**consumptio**<br>**n PPP***|**Counter**<br>**factual**<br>**PPP***|
||Benin|0.487|0.610||South Africa|2.739|1.632||Albania|2.685|<br>7.947|
||Burkina Faso|0.315|0.561||Swaziland|1.926|3.107||Bosnia and H.|2.801|<br>0.387|
||Cameroon|0.760|0.933||Tanzania|0.341|0.601||Bulgaria|3.629|<br>0.591|
||Chad|0.488|0.480||Togo|0.395|0.580||Latvia|4.544|<br>0.903|
||Congo, Rep.|0.148|0.389|**AFRICA**|Uganda|0.460|0.586||Lithuania|5.471|<br>1.250|
||Congo,Dem. Rep.|0.501|0.312||Zambia|0.588|1.026||Macedonia(FYR)|3.137|<br>0.642|
||Cote d'Ivoire|0.655|0.515||Bangladesh|0.707|0.645|**EUROSTAT-**|||<br>|
||Djibouti|0.569|0.337||Bhutan|1.323|0.777|**OECD**|Mexico|3.918|<br>1.911|
||Egypt|2.822|1.282||Cambodia|0.753|0.603||Montenegro|4.074|<br>0.645|
||Ethiopia|0.324|0.287||China|1.433|0.861||Romania|3.700|<br>0.972|
||Gabon|1.977|0.798||Fiji|1.786|1.021||Russia|5.020|<br>0.967|
||Gambia(The)|0.404|0.472||**India**|1.000|1.000||Serbia|3.344|<br>0.671|
||Ghana|0.742|0.732||Indonesia|1.590|1.358||Turkey|4.543|<br>5.576|
||Guinea|0.261|0.290||Lao PDR|0.774|0.631||Bolivia|1.211|<br>0.592|
|**AFRICA**|Kenya|0.641|0.700|**ASIA AND**|Maldives|1.285|0.696||Brazil|3.277|<br>1.509|
||Lesotho|0.835|1.040|**THE**|Mongolia|1.820|1.121||Colombia|2.592|<br>1.223|
||Liberia|0.200|0.004|**PACIFIC**|Nepal|0.611|0.491|**LATIN**<br>|El Salvador|2.410|<br>2.375|
||Madagascar|0.441|1.082||Pakistan|1.299|1.012|**AMERICA**|Guatemala|2.058|<br>0.914|
||Mali|0.346|0.473||Philippines|1.486|1.207||Honduras|1.240|<br>1.141|
||Mauritania|0.691|0.471||Sri Lanka|2.115|0.832||Nicaragua|1.187|<br>2.344|
||Mauritius|3.908|1.632||Thailand|2.805|0.730||Peru|2.365|<br>0.930|
||Morocco|1.425|0.649||Vietnam|0.990|0.832||||<br>|
||Mozambique|0.294|0.560||Armenia|2.416|1.184||Iraq|1.780|<br>1.523|
||Namibia|1.928|2.318|**COMMON**|Azerbaijan|2.768|0.840||||<br>|
||Nigeria|0.686|0.794|**WEALTH**|Belarus|3.830|1.013|**WEST ASIA**|Jordan|2.934|<br>0.662|
||Republic of Cabo|||**OF**|Kazakhstan|3.775|1.073||||<br>|
||<br>Verde|1.571|0.556|**INDEPEND**<br>|Kyrgyz Rep.|1.160|0.649||Yemen|0.914|<br>0.339|
||Senegal|0.636|0.693|**ENT**<br>|<br>Moldova|1.870|0.731|**CARIBBEAN**||||
||Sierra Leone|0395|0308|**STATES**|Tajikistan|1.001|0.492||Jamaica|2.396|<br>1.093|
|||.|.||Ukraine|2.616|0.656|||||

*These columns are derived from Table 6b.

45
**Table 8: Counterfactual PPPs (CPPP2) based on Household level Data: (Base Country: India)**

|**Country**|**2011 ICP**<br>**PPP***|**Overall**|**Quintile 1**|**Quintile 2**|**Quintile 3**|**Quintile 4**|**Quintile 5**|
|---|---|---|---|---|---|---|---|
|Iraq|35.882|41.932|45.060|45.705|40.995|37.678|29.124|
|Malawi|5.195|7.166|5.718|7.244|7.116|7.461|6.811|
|Tanzania|38.494|30.080|23.887|29.605|29.047|31.053|30.117|
|Vietnam|479.060|639.906|562.399|663.861|635.605|628.115|542.026|

***** Base country: India

**Table 9: Gini Expenditure Inequality Index of households pooled over the 5 Countries at Different PPPs (Base Country: India)**

||**Gini Index (in**|**%) based on**||
|---|---|---|---|
|**2011 ICP PPP**|**CPPP1***|**CPPP2**|**Quintile wise**|
||||**PPPs**|
|38.634|38.585|38.541|38.572|

*Excluding Malawi

46
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<!-- Start of picture text --> GDP (in logs) evaluated at<br>counterfactual PPP against that evaluated at ICP 2011 PPP<br>2 +<br>oe<br>2 _ +.<br>ane +<br>« de® < Fg<br>cd tee * +<br>aor *<br>*<br>*<br>22 24 26 23 30 32<br>GDP_PPPCindiv<br>+ GDP_PPPecounter =§$——— Linear prediction<br>———-—- Y¥=X line<br><!-- End of picture text -->