metadata: authors: 0: author: Ravallion, Martin
count: World
docna: 0: docna: Price levels and economic growth : making
            sense of the PPP changes between ICP rounds
docty: Policy Research Working Paper
subtopic: Economic Theory & Research,Industrial Economics,Labor Markets,Economic Growth,Inflation,Macroeconomic Management,Inequality
teratopic: Private Sector Development,Macroeconomics and Economic Growth,Finance and Financial Sector Development
abstracts: cdata!: To the surprise of many observers, the
            2005 International Comparison Program (ICP) found
            substantially higher purchasing power parity (PPP) rates,
            relative to market exchange rates, in most developing
            countries. For example, Chinas price level index -- the
            ratio of its PPP to its exchange rate -- doubled between the
            1993 and 2005 rounds of the ICP. The paper tries to explain
            the observed changes in PPPs. Consistently with the
            Balassa-Samuelson model, evidence is found of a
            "dynamic Penn effect," whereby more rapidly
            growing economies experience steeper increases in their
            price level index. This effect has been even stronger for
            initially poorer countries. Thus the widely-observed static
            (cross-sectional) Penn effect has been attenuated over time.
            On also taking account of exchange rate changes and prior
            participation in the ICPs price surveys, 99 percent of the
            variance in the observed changes in PPPs is explicable.
            Using a nested test, the World Banks longstanding method of
            extrapolating PPPs between ICP rounds using inflation rates
            alone is out performed by the model proposed in this paper.
repnme: repnme: Price levels and economic growth : making
            sense of the PPP changes between ICP rounds
display_title: Price levels and economic growth :
            making sense of the PPP changes between ICP rounds
listing_relative_url: /research/2010/03/11966788/price-levels-economic-growth-making-sense-ppp-changes-between-icp-rounds
topicv3: Economic Growth m1326241 471,Poverty m1326687 695,Inflation m1326709 0870F4727ACED1CF8525815C00471347,Labor Productivity m1504060 2756,Price Surveys m1504546 3124
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Private Sector Development,Macroeconomics and Economic Growth,Finance and Financial Sector Development
no_of_pages: 29
model_extractions: WPS5229 Policy Research Working Paper 5229 Price Levels and Economic Growth Making Sense of the PPP Changes between ICP Rounds _Martin Ravallion_ The World Bank Development Research Group Director’s office March 2010
Policy Research Working Paper 5229

# **Abstract**

To the surprise of many observers, the 2005 International Comparison Program (ICP) found substantially higher purchasing power parity (PPP) rates, relative to market exchange rates, in most developing countries. For example, China’s price level index—the ratio of its PPP to its exchange rate—doubled between the 1993 and 2005 rounds of the ICP. The paper tries to explain the observed changes in PPPs. Consistently with the BalassaSamuelson model, evidence is found of a “dynamic Penn effect,” whereby more rapidly growing economies experience steeper increases in their price level index.

This effect has been even stronger for initially poorer countries. Thus the widely-observed static (crosssectional) Penn effect has been attenuated over time. On also taking account of exchange rate changes and prior participation in the ICP’s price surveys, 99 percent of the variance in the observed changes in PPPs is explicable. Using a nested test, the World Bank’s longstanding method of extrapolating PPPs between ICP rounds using inflation rates alone is out performed by the model proposed in this paper.

This paper—a product of the Director’s office, Development Research Group—is part of a larger effort in the department to understand and improve current macroeconomic data. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at mravallion@worldbank.org.

_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
# Price Levels and Economic Growth:

## Making Sense of the PPP Changes between ICP Rounds

### Martin Ravallion<sup>1</sup>

_Development Research Group, World Bank, 1818 H Street NW, Washington DC_ <u>mravallion@worldbank.org</u>

> 1 These are the author’s views and should not be attributed to the World Bank or any affiliated organization. The author is grateful to Erwin Diewert, Yuri Dikhanov, Branko Milanovic, Luis Servén and Eric Swanson for comments on an earlier draft and to Prem Sangraula for help in setting up the data set used here.
# **1. Introduction**

Purchasing Power Parity exchange rates (“PPPs” for short) have been mainly derived from the International Comparison Program (ICP), which collects data on prices across countries. The latest (2005) ICP survey round—thought to be the largest international statistical operation ever—collected prices for a great many goods and services, grouped under 155 “basic headings” (corresponding to the expenditure categories in the national accounts) for each of 146 countries in six regions (Africa, Asia-Pacific, Commonwealth of Independent States, South America, Western Asia and Eurosat-OECD). Region-specific product lists were developed and the regional PPPs were linked through a common set of global prices. The 2005 ICP’s governance structure entailed that each of the six regional ICP offices worked closely with government statistics offices in each country, while the World Bank provided global management and estimated the final PPPs. World Bank (2008a) provides estimates of the PPP for GDP and its main components for 2005. World Bank (2008b) compares the results to those based on the main prior ICP round, for 1993.

Some dramatic revisions to past PPPs are implied by the results of the 2005 ICP. Figure 1 compares the estimates of real (at PPP) GDP per capita for 2005 from the World Bank’s _World Development Indicators_ 2007 database—just prior to the release of the 2005 ICP results—with the estimates implied by the 2005 ICP.<sup>2</sup> Due to the changes in PPPs, real GDP was revised downwards for many low- and middle-income countries, and substantially so for some. In the Asia-Pacific region, real GDP for 2005 was revised down by 30% (World Bank, 2008b).

These large data revisions have been attributed to the changes in data and methods that were introduced in the 2005 ICP round, as described in World Bank (2008a,b). A potentially important difference is that (compared to prior ICP rounds) stricter quality standards were used in the 2005 price surveys, to assure that the ICP was obtaining prices for internationally comparable commodities. This is important given that one expects that lower quality goods are consumed in poorer countries, creating a risk that (without strict standards in defining the products to be priced) one will underestimate the cost of living in poor countries by confusing quality differences with price differences. With better funding of the ICP in 2005, clearer product descriptions were developed.

> 2 The least squares regression line has an intercept of -0.580 (While s.e.=0.236) and slope of 1.057 (s.e.=0.025); R<sup>2</sup> =0.938; n=136. One can reject the null hypothesis that the original estimate is an unbiased predictor of the revised estimate (i.e., intercept=0, slope=1); the F-test is 4.491 with prob 0.013.

2
Methodological changes between ICP rounds cast doubt on the comparability of the resulting PPPs over time. This is one reason why users often avoid mixing PPPs between ICP rounds, letting national price data override the ICP data for inter-temporal comparisons. In other words, the PPP conversion is done at the ICP benchmark year. It has been argued that this is the most reasonable practice, given the changes in methodology (Dalgaard and Sørensen, 2002; World Bank, 2008b; Chen and Ravallion, 2010a). Theoretical arguments have been made both for and against this practice. Nuxoll (1994) argues that the real growth rates measured using local deflators better reflect the trade-offs facing decision makers at the country level, and thus have a firmer foundation in the economic theory of index numbers. Of course, this means that the economic aggregates may well lose purchasing power comparability as one goes further back in time from the ICP benchmark year. In the context of studies of economic growth using PWT, Johnson et al. (2009) argue instead that comparisons should only be made between ICP rounds, since only then can one be sure that the economic aggregates are consistently evaluated at purchasing power parity.

All this begs a neglected question: _Can we make sense of the changes in PPPs?_ This paper tries to answer that question by comparing the latest (2005) PPPs with those for 1993 and 1985. Unlike most past empirical studies of PPPs, which have focused on the cross-sectional differences, this paper is concerned with explaining the observed changes over time. I focus on the price level index, defined as the PPP for GDP divided by the exchange rate (US=100%);<sup>3</sup> the inverse of this index is sometimes also called the real exchange rate. For the same reason that one uses PPPs rather than exchange rates for international comparisons, it can be hypothesized here that the PPP will tend to rise relative to the market exchange rate in a growing economy. In the models of Balassa (1964) and Samuelson (1964) this happens if economic growth comes with higher labor productivity in the traded-goods sector (relative to non-traded goods). This can be thought of as a dynamic Penn effect (DPE), corresponding to the widely-observed static Penn effect in which the price level index tends to be higher in richer countries.<sup>4</sup>

> 3 While the term “price level index” is widely used in the literature, it is potentially confusing, since the index is a relative price—the ratio of two nominal prices. But I will stick to common usage.

> 4 The term “Penn effect” appears to be due to Samuelson (1994) and stems from Penn World Tables (PWT) (Summers and Heston, 1991), which provided the data that were used to establish this effect empirically. Evidence of a static Penn effect in data from various rounds of the ICP is reported in Balassa (1964), Rogoff (1996), World Bank (2008), and Deaton and Heston (2010), amongst others. The

3
Whether one would see the DPE in a growing developing country is a moot point. It can be argued that such economies are characterized by factor-market imperfections and surplus labor, dulling the Balassa-Samuelson mechanism. Productivity increases for non-traded goods could also dull the effect. In addition to the possibility of a DPE, one can also expect that there will be measurement errors confounding the PPP comparisons.

A better understanding of the economics of PPPs changes should help in estimating PPPs for the (many) years for which there is no ICP round, with implications for the extent of the data revisions needed at each new ICP. There are two distinct problems of missing data in estimating PPPs; the first is that some countries chose not to participate in the ICP’s price surveys, while the second is that there are long gaps between those surveys. Existing data compilations (such as the World Bank’s _World Development Indicators_ ) use extrapolations based on non-ICP data to fill in these missing PPPs, but very different types of data are used. The extrapolations to deal with the first problem are based on GDP per capita at market exchange rates, exploiting the static Penn effect. By contrast, in addressing the second problem, the PPPs for non-benchmark years are estimated by re-scaling the PPP from the most recent ICP round according to the inflation rate (GDP deflator for the GDP PPP, and Consumer Price Index for the consumption PPP) in the country in question relative to the US inflation rate. The reliability of this method is unclear. While in theory, a suitable inter-temporal price index could deliver reliable extrapolations, it is far from obvious how well the methods used in practice perform, notably in reflecting the changes in the relative price of non-traded goods in growing economies.<sup>5</sup> However, as this paper will show, there is another possible method for the inter-temporal extrapolations, consistent with how the first problem of missing data is dealt with. If the relationship between price levels and mean income—the static Penn effect that is used to deal with the cross-sectional missing data—also holds over time then this could be exploited in the dynamic extrapolation methods between ICP rounds, thus offering scope for reducing the need for the large data revisions often implied by each new round of ICP data.<sup>6</sup>

> most common parametric test entails regressing the log of the price level index on the log of GDP per capita in $US at market exchange rates.

> 5 Neither the underlying prices nor the aggregation methods are typically the same between the national deflators and the PPPs constructed by the ICP.

> 6 In the only precedent to this alternative approach I know of, Prados de la Escosura (2000) fills in the missing data on GDP at PPP both cross-sectionally and over time using a single model of the price level index, estimated on pooled data for OECD countries.

4
To see how well the changes over time in price levels can be explained, I have assembled a data file of the price level index (PPP for GDP over exchange rate) and GDP per capita at PPP for the 2005 and 1993 ICP rounds for all countries (developed or developing). These are the World Bank’s estimates, rather than Penn World Tables (PWT).<sup>7</sup> I will also study the changes in PPPs between 1985 (using PWT) and 2005.

The following section summarizes the arguments as to why one might expect the PPP changes to be predictable. Section 3 describes the empirical models to be estimated while section 4 presents the results. Section 5 tests for whether the 2005 PPP for China—the country that has clearly received the most attention in the debates surrounding the release of the results of the 2005 ICP—is consistent with the pattern seen across countries. Section 6 looks at the implications for extrapolating PPPs between ICP rounds. Section 7 concludes by summarizing the paper’s findings and drawing some implications for future analyses of ICP data.

# **2. What might account for the observed changes in PPPs between ICP rounds?**

Some of the country-specific factors that influence price levels (or, equivalently, real exchange rates) can be treated as time–invariant between ICP rounds.<sup>8</sup> By focusing instead on the changes in PPPs, the following analysis will eliminate the influence of all additivelyseparable error components stemming from such country-specific factors.

An important clue to why PPPs change over time can be found in the very same reason PPPs were developed. It has long been recognized that international comparisons of GDP at market exchange rates are deceptive about the differences in real income, given that some commodities are not internationally traded, notably most services. Without trade, there is no mechanism for assuring price parity across borders. The most common economic explanation of why the PPP would differ systematically from the nominal exchange rate is the BalassaSamuelson model (outlined independently by Balassa, 1964, and Samuelson, 1964).<sup>9</sup> This assumes a competitive market economy in which all factors of production are fully employed

> 7 There are methodological differences between the World Bank’s PPPs and those in PWT; see Deaton and Heston (2010) for a useful overview of those differences.

> 8 For example, Clague (1985) shows that natural resource endowments will influence the price level index at a given level of GDP per capita. However, such endowments can be treated as country-level fixed effects for the present purposes.

> 9 An alternative explanation was proposed by Bhagwati (1984) based on factor endowments, leading (labor-intensive) services to be cheaper in poor countries.

5
and are freely mobile between the traded and non-traded-goods sectors. The relative price of traded goods is then given by the labor productivity differential between traded and non-traded goods. To see this more formally, let _MP_ T denote the marginal (physical) product of labor in the traded goods sector and let _MP_ N denote the corresponding marginal product in the production of non-traded goods. Also let _P_ T and _P_ N denote the prices of traded and non-traded goods while _W_ T and _W_ N are the corresponding wage rates. Under standard assumptions (including competitive, profit-maximizing, producers) we have _W_ T= _P_ T _MP_ T and _W_ N= _P_ N. _MP_ N. With perfect labor mobility, we have _W_ T= _W_ N in equilibrium. The key relationship generating the BalassaSamuelson effect is then immediate, namely that _P_ T/ _P_ N= _MP_ N/ _MP_ T.

In using the Balassa-Samuelson model to explain why PPPs tend to be lower (relative to market exchange rates) in poorer countries, it is assumed that the more developed the country the higher its labor productivity in traded goods, but that productivity for non-traded goods does not vary systematically with level of development. A higher marginal product of labor in traded goods production comes with a higher wage rate, which is also binding on the non-traded goods sector (given that labor is freely mobile), implying a higher price of non-traded goods in more developed countries and thus a higher overall price level. By the same reasoning, low real wages in poor countries entail that non-traded goods tend to be cheaper. The ratio of the purchasing power parity rate to the market exchange rate will thus be an increasing function of income.

This argument helped reinforce the (considerable) international statistical effort that has gone into the development of purchasing power parity exchange rates, led by the _International Comparison Program_ (although PPPs existed before Balassa-Samuelson). The PPP rate expresses a currency’s value in terms of its purchasing power over commodities, both traded and non-traded, relative to the numeraire currency (almost invariably the $US). The PPP is based on the prices actually paid for goods; the exchange rate does not directly enter into its calculation (though of course it will matter indirectly, via domestic prices and spending patterns).

The Balassa-Samuelson model offers a theoretical explanation for the Penn effect. Balassa (1964) found evidence that richer countries tend to have higher price levels in data for 12 countries. Since then most empirical tests of the Penn effect have used cross-sectional data from the ICP. Every round of the ICP appears to have confirmed the Penn effect.<sup>10</sup> Based on such

> 10 Amongst others, see Summers and Heston (1991), Heston, Nuxoll and Summers (1994), Rogoff (1996), World Bank (2008a) and Deaton and Heston (2010).

6
evidence, the Wikipedia entry on the Penn effect describes it as “a consistent econometric result for at least fifty years.” The economic mechanism postulated by the Balassa-Samuelson model should also hold over time, as long as the data are in reasonable accord with the assumptions of the model. As a poor country develops, its productivity in the traded goods sector will then rise, as will the real wage rate, and so its PPP will move closer to its exchange rate. There is some supportive evidence in time series data for specific developed countries, notably Japan, but not others (Rogoff, 1996). Past tests of whether the implications of the Balassa-Samuelson model (including the Penn effect) hold over time have been largely confined to developed countries.<sup>11</sup> Arguments can be made for and against the Balassa-Samuelson assumptions. A key assumption is that richer countries have higher relative productivity in traded goods. Balassa (1964) presented (influential) evidence supporting that assumption. But technology has changed considerably since 1964, entailing greater potential for productivity growth in the services sector. Take, for example, India’s booming business services sector. This sector has seen very high growth since the early 1990s, facilitated by the availability of skilled labor and changes in information technology.<sup>12</sup> Superficially this does not sound much like the Balassa-Samuelson model. However, it should be noted that this change has also come with a transformation of many business services into internationally traded commodities. So it can be argued that India’s rising productivity in services is in fact consistent with Balassa-Samuelson. By this view, it is the presumption that services are non-traded that is now questionable, given technological change.

However, even if growth does come with rising productivity for traded goods, the way labor markets work in reality may not pass this effect fully onto wage rates in the non-traded goods sector. This could happen if there are impediments to labor mobility. For example, labor hiring in the traded-goods sector may be subject to (explicit or implicit) contracts favoring incumbents, leaving the services sector as a residual employer. Or there may be specialized skill requirements, which effectively restrict entry to the traded-goods sector in poor countries with limited human capital. A wedge between wage rates in the two sectors could also arise if the traded-goods sector is the “formal” sector, which is taxed, while services are informal, and untaxed. Then we may find a persistent wage gap (with _W_ T> _W_ N), creating a potential disconnect

> 11 The only exception I know of is Choudhri and Khan (2005) who find evidence consistent with Balassa-Samuelson effects in panel data for 16 developing countries.

> 12 See Kotwal et al. (2009) for evidence on this point.

7
between relative prices and relative labor productivities between the two sectors, thus breaking the Balassa-Samuelson effect. Whether that actually happens depends on how the relative wage rate ( _W_ T/ _W_ N) is in fact determined. However, the key point is that with market imperfections it is an open question whether the PPP will start to approach the exchange rate in poor but growing economies, or whether it continues to lag. Given market frictions, one might also conjecture that the DPE only starts to emerge when the growth rate is sufficiently high.

There are also measurement errors in the PPPs. While these are largely unobservable, one observable clue is that not all of the countries that participated in the 2005 round had participated in 1993. Most of the PPPs for these non-benchmark countries were estimated econometrically by the ICP team using regressors observed for both sets of countries.<sup>13</sup> Any bias in those estimates will be reflected in the subsequent changes observed when the country participates properly in the ICP’s price surveys. This too could dull the effect of economic growth on price levels.

# **3. Modeling the changes in PPPs**

Let _PPPri_ denote the PPP rate for country _i_ in year _r_ using ICP round _r_ and let _Eri_ be the corresponding market exchange rate. By definition, the price level index is _Pri_  _PPPri / Eri_ (which is of course a relative price, interpretable as the inverse real exchange rate). Also let _Yri_ denote GDP per capita in $US at the market exchange rate, while _YriPPP_ is GDP per capita at PPP. Thus _Yri_  _GDPri_ / _Eri_ where _GDPri_ is GDP in local currency units and _YriPPP_  _GDPri_ / _PPPri_ . The basic empirical model for changes in the price level index is as follows: ln( _P_ 05 _i_ / _P_ 93 _i_ )     ln( _Y_ 05 _i_ / _Y_ 93 _i_ )   _i_ (1) A number of remarks will help motivate and interpret this model. First, equation (1) can be interpreted as the time-differenced version of the widely used double-log model in the crosscountry literature on the Penn effect, incorporating a year effect but common slope (though this will be relaxed later).<sup>14</sup> Second, unlike the cross-sectional specification, the parameter estimates

> 13 See World Bank (2008a). The log GDP per capita in 1993 PPP was regressed on log GDP per capita at market exchange rates and the log of the secondary school enrollment rate This is equivalent to regressing the log of the price level index on these same two variables (though with different parameters of course). (China’s PPP for 1993 was estimated by a different method, as noted later).

> 14 The most common specification for the Penn effect in the literature expresses the log of the price level index as a linear function of the log of GDP per capita at exchange rates. Note that this is equivalent

8
in (1) will be robust to any (time-invariant) country characteristics that jointly influence the level of prices and GDP. Third, if   0 then there is evidence of a DPE. Fourth, if   0 (<0) then the 2005 ICP schedule of price levels is higher (lower) than that for 1993 at given GDP per capita. Finally, note that equation (1) can be written equivalently in terms of GDP at PPP: I will treat the growth rate as exogenous in equation (1). This can be questioned. It has been argued by Rodrik (2008) and Korinek and Servén (2010) that policies promoting a high real exchange rate—implying a lower price level index—can promote longer-term economic growth by stimulating exports. To some extent, these can be thought of as long-run policies that would be within the country fixed effect for the level of the price index, and so be swept away in the time-differenced specification in (1). However, any changes in exchange rate policy that impact on growth would still leave a bias. If a higher real exchange rate does in fact promote growth then the OLS estimate of (1) will under-estimate the true value of  .<sup>15</sup> Correcting for this bias would yield even stronger evidence in favor of the existence of the DPE.

The basic specification in (1) will be augmented in three ways. First, one can think of equations (1) and (2) as restricted forms of the following equation: ln( _PPP_ 05 _i_ / _PPP_ 93 _i_ )     ln( _Y_ 05 _i_ / _Y_ 93 _i_ )  ln( _E_ 05 _i_ / _E_ 93 _i_ )   _i_ (3) It is of interest to see if the restriction that   1 cannot be rejected. One can, however, question a causal interpretation of equation (3); indeed, the “law of one price” implies the market exchange rate is determined by the _PPP_ , although the fact that price level indices are less than unity for many countries discredits this as a model of exchange rate determination, at least in the short term.<sup>16</sup> Nonetheless, it would clearly be worrying if one could reject the null that   1 .

Second, I will allow the DPE parameter to vary with initial GDP. I expect a negative interaction effect, on the grounds that it is the initially poorer countries where higher growth should come with the type of structural change that would put upward pressure on the price level

> to the alternative specification sometimes found in which the log of GDP at PPP is a linear function of the log of GDP at exchange rates; the slope parameters in these two specifications sum to unity.

> 15 Similarly, the existence of the DPE implies a bias in OLS growth regressions using the real exchange rate as a regressor (as in Rodrik, 2008).

> 16 Rogoff (1996) reviews the literature.

9
index. I will also test whether the 1993 PPP was derived from actual price surveys—in which case we refer to the country as a 1993 “benchmark country” (following common practice).

The third variation entails testing a nested model encompassing the above specification and the inflation-adjustment method used by the World Bank’s _World Development Indicators_ to update PPPs over time between ICP rounds. By this method, the extrapolated PPP for GDP for date _t_ (>1993), using the 1993 ICP round (say) as the benchmark, is given by: where _DEFti_ is the GDP deflator (or CPI when updating the consumption PPP) for country _i_ at date _t_ (where _i=US_ denotes the US deflator). The encompassing test entails adding a term in ln( _DEF_ 05 _i_ /<sup>_DEF_</sup> 93 _i_ ) to equation (3). If one cannot reject the joint null that the coefficient on this extra variable is unity, while    0 , then the inflation-adjustment method is supported.

# **4. Results**

I will use the PPPs for GDP for 2005, 1993 and 1985. The 1993 and 2005 PPPs are those estimated by the World Bank; the 1985 PPPs are from PWT (as 1993 was the first ICP round for which the Bank estimated global PPPs).<sup>17</sup> Figure 2 gives the empirical density functions (using normal kernels) for 1993 and 2005. The price level index is below 100% for the bulk of the data in both years. Even so, the index rose for 74% of countries. And it rose by 10 percentage points or more in almost half the countries (44% to be precise). For 2005, the (unweighted) mean price index across the 133 countries that participated in the 1993 ICP was 59% (median 49%) as compared to 53% in 1993 (median 41%). The mean ln( _P_ 05 _i_ /<sup>_P_</sup> 93 _i_ ) is 0.162, with a standard error of 0.026 (n=133).

So an upward revision to the price level is generally indicated. However, the bulk of this was for countries with initially low price levels. Indeed, the cumulative distribution functions implied by the densities in Figure 2 are virtually indistinguishable for price levels above 60%.

Regressing ln( _Pri_ ) on ln( _Yri_ ) , the data confirm the static (cross-sectional) Penn effect within each round, as widely reported in the literature; the regression coefficient of ln( _P_ 05 _i_ ) on

> 17 The 1993 PPPs for OECD countries were based on price surveys done in 1996, backcast to 1993. I will test robustness to excluding the OECD.

10
ln( _Y_ 05 _i_ )<sup>is 0.216, with a White standard error of 0.013 (n=144);18 Figure 3 plots the data from the</sup> 2005 ICP. For the 1993 round, the regression coefficient is 0.293 (s.e.=0.012; n=134), while for the 1985 round it is 0.275 (s.e.=0.024; n=56). The attenuation of the Penn effect between 1993 and 2005 is consistent with the fact that the proportionate increases tended to be larger in initially poorer countries, as can be seen in Figure 4.<sup>19</sup> Turning to the changes over time, let us begin by testing the homogeneity restriction that   1 . The estimate of the unrestricted model in equation (3) is (with White standard errors in parentheses):<sup>20</sup> The restriction clearly performs well. Given that this is a regression for changes rather than levels, it is also notable that almost 99% of the variance is accounted for.

On imposing   1 , the regression coefficient of ln( _P_ 05 _i_ /<sup>_P_</sup> 93 _i_ ) on ln( _Y_ 05 _i_ /<sup>_Y_</sup> 93 _i_ ) is <sup>ˆ</sup>  ˆ 0.283 (s.e.=0.054; n=132) with    .0019 (s.e.=0.043) and _R_<sup>2</sup> =0.212. This is close to the crosssectional estimate of the Penn effect, suggesting that latent country characteristics are not an important source of bias in past tests for the Penn effect using cross-sectional data.

Figure 5 plots the relationship between changes in price levels and growth rates. The price level does not start to rise until there is sufficient growth. The expected change in ln( _P_ 05 _i_ /<sup>_P_</sup> 93 _i_ ) is zero when ln( _Y_ 05 _i_ /<sup>_Y_</sup> 93 _i_ )  .0066, although the latter number is not significantly different from zero (s.e.=0.140). Thus one cannot reject the null hypothesis that the price level index conditional on GDP per capita is unchanged between the 1993 and 2005 ICP rounds.

Recall that this sample includes both developed and developing countries. The data suggest that the DPE is stronger in poorer countries, as can be seen from the following regression indicating a significant negative interaction effect: ln( _P_ 05 _i_ / _P_ 93 _i_ )  .0008  (.0604  .0049 ln _Y_ 93 _i_ ) ln( _Y_ 05 _i_ / _Y_ 93 _i_ )   ˆ _i R_ 2  .0246; _n_  132 (5) (.0046) (.0143) (.0020)

> 18 Using GDP at PPP instead, the regression coefficient of ln( _P_ 05 _i_ ) on ln( _Y_ 05 _PPPi_ )

> <sup>is 0.237</sup>

> (s.e.=0.020), while for the 1993 ICP it is 0.343 (s.e.=0.027). Note that White standard errors are used when relevant in this paper.

> 19 The slope of the regression line is -0.059 with a standard error of 0.014.

> 20 The regression was very similar for the non-OECD sample.

11
Note that this is not simply a difference between OECD and non-OECD countries. Indeed, the elasticity of the price level to economic growth is actually higher for the OECD subsample; the regression coefficient of ln( _P_ 05 _i_ /<sup>_P_</sup> 93 _i_ )<sup>on</sup> ln( _Y_ 05 _i_ /<sup>_Y_</sup> 93 _i_ ) is 0.511 for the OECD countries (s.e.=0.083; R<sup>2</sup> =0.661; n=24) while it is 0.272 (s.e.=0.055 (R<sup>2</sup> =0.200; n=108) for nonOECD countries. I will return to discuss this interaction effect further.

The DPE is not simply picking up an “Asia-Pacific effect.” The DPE is still evident if one adds a control for those countries for those countries for which the 2005 ICP was implemented by the Asian Development Bank.<sup>21</sup> (The regression coefficient on ln( _Y_ 05 _i_ /<sup>_Y_</sup> 93 _i_ ) changes little and the Asia dummy is not significantly different from zero.) The DPE is not in evidence if one re-writes the model in the form of equation (2). The regression coefficient of ln( _P_ 05 _i_ /<sup>_P_</sup> 93 _i_ ) on ln( _Y_ 05 _PPPi_ / _Y_ 93 _PPPi_ ) is -0.117, but this is not significantly different from zero (s.e.=0.073). Yet, the corresponding estimate for  of 0.283 using growth ˆ rates at market exchange rates implies  /(1 <sup>ˆ</sup> )  .0394 . The most likely explanation for this discrepancy appears to be that a large endogeneity bias emerges when one tests for the DPE using growth rates measured in PPP $s. Latent factors influencing the PPP will jointly affect both the price level index and the GDP growth rate, though in opposite directions (given that the PPP appears in the numerator of the price index, but the denominator of deflated GDP). Estimating the equation in the form of (1) avoids this problem. Alternatively, one can use a 2SLS estimate of (2), using ln( _Y_ 05 _i_ /<sup>_Y_</sup> 93 _i_ ) as the instrument for ln( _Y_ 05 _PPPi_ / _Y_ 93 _PPPi_ ) . Then one exactly retrieves the same estimate of  /(1   ) , namely 0.394 (s.e.=0.105), implied by the OLS estimate of (1).

There is also evidence of an “ICP participation effect,” whereby the relationship between the price level changes and growth rates differs between the benchmark ( _D_ 93 _i_<sup></sup> 1 ) and nonbenchmark ( _D_ 93 _i_<sup></sup> 0 ) countries from the 1993 ICP, as is evident in the following regression:<sup>22</sup>

> 21 Essentially this excludes OECD countries in Asia but includes the Pacific Islands. 22

> As a further check on the restriction that   1 , on re-estimating in the form of (3), the augmented ˆ

> specification corresponding to (6), gave   .1003 with s.e.=0.011 with _R_<sup>2</sup> =0.991.

12
An F-test rejects the restricted form in which the model is the same when _D_ 93 _i_<sup></sup> 1 as _D_ 93 _i_<sup></sup> 0 ; F(2,128)=23.516; prob.<0.001. Differentiating the DPE between the 1993 benchmark and nonbenchmark countries doubles the share of the variance in ln( _P_ 05 _i_ /<sup>_P_</sup> 93 _i_ ) that is explained. The DPE is stronger for benchmark countries; Figure 6 plots the relationship. We now find that the estimated expected value of ln( _P_ 05 _i_ /<sup>_P_</sup> 93 _i_ ) is positive when ln( _Y_ 05 _i_ /<sup>_Y_</sup> 93 _i_ )  .0443, and this switch point is significantly different from zero (s.e.=0.058). Only when the growth rate (annualized log difference) exceeds 3.7% do we find upward pressure on the price level.

So, amongst the 1993 ICP participants one finds that the 2005 price levels are actually <u>lower</u> at given GDP per capita than those of 1993. To put the point another way, these results suggest that it is economic growth in developing countries that explains the upward shift in price levels implied by the 2005 ICP, rather than statistical factors such as the stricter quality standards in the 2005 ICP’s price surveys. The statistical-comparability problem appears to stem largely from the subset of 2005 ICP countries that had not participated in the 1993 ICP round.

Why is the Penn effect so much weaker for non-benchmark countries? Some explanations can be suggested. First, it might be conjectured that the ICP participation effect reflects the fact that the above model does not include all regressors used to predict the 1993 PPP for the non-benchmark countries.<sup>23</sup> The simplest way to check this is to see if the results change when one controls fully for the econometrically-estimated price level indices for the nonbenchmark countries in 1993, by re-estimating (6) in the following form:<sup>24</sup> The Penn effect is still weaker for the non-benchmark countries. So this is not the explanation. Second, possibly the ICP participation effect stems from non-linearities in the Penn effect, given that the non-benchmark countries tended to be poorer.<sup>25</sup> The following regression encompasses both the ICP participation effect and the negative interaction with initial GDP:

> 23 The missing variable is the secondary school enrollment rate.

> 24 Note that when _D_ 93 _i_<sup></sup> 0 , _P_ 93 _i_ is predicted based on the observed covariates used by the ICP.

> 25 The non-benchmark countries in the 1993 ICP had an (unweighted) mean GDP per capita of $2,268, as compared to $6,923 for benchmark countries.

13
The negative interaction effect is still evident, though less precisely estimated (which is not too surprising given the tendency for ICP non-participants to be poorer). A significant difference between the benchmark and non-benchmark models is still evident.<sup>26</sup> The mystery remains. The non-benchmark countries are quite heterogeneous.<sup>27</sup> It appears that all countries were invited to participate in the 1993 ICP, but the (unknown) process determining why some countries chose not too was based on variables that are correlated with the strength of DPE. When interpreted in terms of the Balassa-Samuelson model, it appears that the countries that chose not to participate had latent characteristics that made their productivity differences for tradable goods less responsive to the differences in their GDP per capita.

One can speculate on one possible explanation. Some countries undoubtedly chose not to participate in the 1993 ICP for idiosyncratic, possibly political, reasons. But it can be expected that many non-participants lacked the public-institutional capacity for implementing the ICP’s surveys. Furthermore, it can be conjectured that weak statistical capacity is probably correlated with weak institutions more generally, including weak states. Suppose now that institutional capacity is cooperant with labor in the production of traded goods—such that the marginal product of that labor is lower when institutions are weaker. Then we can see that nonparticipation in the ICP could signify a weaker relationship between GDP and the relative productivity of labor in the traded-goods sector, and (hence) a weaker Penn effect in the data.

The ICP participation effect helps explain why the increases in the price level index tended to be higher in countries with lower GDP per capita in 1993, as seen in Figure 3. Simply adding a control for benchmark countries brings the slope of the regression line in Figure 3 down from -0.059 (s.e.=0.014) to -0.037 (s.e.=0.014). Adding the 1993 GDP to equation (6) gives:<sup>28</sup>

> 26 The difference also persisted when I allowed for non-linearity in the underlying cross-sectional double log model for the Penn effect, by adding ln( _Y_ 05 _i_ ) 2  ln( _Y_ 93 _i_ ) 2 to the differenced model in (1).

> 27 The specific countries are Albania, Angola, Bhutan, Bosnia and Herzegovina, Brunei, Burkina Faso, Burundi, Cambodia, Cape Verde, Central African Republic, Chad, China, Colombia, Comoros, Democratic Republic of the Congo, Cote d'Ivoire, Cyprus, Djibouti, Equatorial Guinea, Ethiopia, Gambia, Ghana, Guinea-Bissau, India, Israel, Lesotho, Macao China, Macedonia, Malta, Mauritania, Mozambique, Niger, Paraguay, Rwanda, South Africa, Sudan, Togo, and Uganda.

> 28 The weighted mean coefficient on GDP in 1993 is -0.039 (s.e.=0.002), as compared to a regression coefficient without controls of -0.059 (s.e.=0.014).

14
(Estimating in the form of equation (3), the coefficient on the log difference in the exchange rate ˆ is again not significantly different from unity;   .0995 with s.e.=0.010 and the R<sup>2</sup> rises to 0.991.) It is also of interest to see how well one can explain the changes between the 1985 and 2005 PPPs. Here there are further comparability problems, stemming from the differences between the World Bank’s methods and those of PWT.<sup>29</sup> Even so, the corresponding estimate of equation (3) has similar explanatory power (in obvious notation):<sup>30</sup> ˆ ln( _PPP_ 05 _i_ / _PPP_ 85 _i_ )   .0168  .0417 ln( _Y_ 05 _i_ / _Y_ 85 _i_ )  .0991 ln( _E_ 05 _i_ / _E_ 85 _i_ )   _i_ (.0111) (.0079 ) (.0025 ) (10) 2 _R_  .0981; _n_  54 Using instead the period 1985-1993, one obtains: Imposing the restriction that   1 the regression coefficient of ln( _P_ 05 _i_ /<sup>_P_</sup> 85 _i_ ) on ln( _Y_ 05 _i_ /<sup>_Y_</sup> 85 _i_ ) is ˆ <sup>ˆ</sup>  0.431 (s.e.=0.075; n=55; _R_<sup>2</sup> =0.488) and    .0194 (s.e.=0.104). So it appears that the DPE is even stronger over 1985-2005, despite the methodological differences between PWT and the World Bank’s methods. Figure 7 plots the data for this longer period (with fewer observations, and confined to 1985 benchmark countries). The switch point (at which _E_ ln( _P_ 05 _i_ /<sup>_P_</sup> 85 _i_ )  0) is at ln( _P_ 05 _i_ /<sup>_P_</sup> 85 _i_ ) =0.451 (s.e.=0.168), corresponding to an annual growth rate of 2.3%.

# **5. China’s controversial PPP revisited**

The new PPP for China from the 2005 ICP attracted much attention, given that it implies that the country’s GDP per capita at PPP for 2005 is 40% lower than we thought, at $4,091 rather than the prior estimate for 2005 of $6,760 (World Bank, 2008b). Just before the release of the 2005 ICP’s results, China’s price level index for 2005 was deemed to be 25%, up from 19% in 1993. The price surveys from the 2005 ICP implied a price index of 42%.

> 29 See Deaton and Heston (2010) for a description of the differences in methods.

> 30 The negative interaction effect with the initial (log) GDP was also evident using the 1985 PPPs, but for brevity this discussion is confined to the simpler version of the DPE.

15
Some observers have questioned whether China’s new PPP is credible. Bhalla (2008) argues that, when combined with the official growth rates, the new PPP implies that China was too poor to be believed in (say) 1950; in Bhalla’s words, the World Bank’s numbers imply that “most Asians (were) dead in 1950.” Maddison and Wu (2008) and Deaton and Heston (2010) raise similar objections, leading Maddison and Wu to claim that the new PPP for China is “weird” and “implausible.” It is far from clear whether these extrapolations back in time constitute a sound basis for validating the new PPP for China. Ravallion (2010) points out that the new PPP only implies that China was as poor (in terms of GDP per capita) in 1950 as the Democratic Republic of the Congo is today, and that about 400 million people in the world (40 million of them in China) currently live below that income level; they survive, albeit at very meager levels of consumption. Nonetheless, given the size of this data revision, the subsequent controversy, and the importance of the global importance of the Chinese economy, it is of interest to look more closely at the data for China.

How much of the observed change in China’s price level index implied by the 2005 ICP is accountable to the dynamic Penn effect? If one adds a dummy variable for China to equation (6) or (8) the coefficient is 0.278 (s.e.=0.077), while it is 0.239 (s.e.=0.083) when added to (7). Yet the observed change in the log of China’s price level index is 0.795. So the model can account for 65-70% of the change in China’s price level between 1993 and 2005.

This assessment is affected little by allowing for over-estimation of China’s growth rate. Maddison (2007) has claimed that China’s long-run growth rate is over-estimated by possibly two percentage points per year (though also see Holz’s, 2006, comments on Maddison’s assumptions). However, even cutting two percentage points off China’s annual growth rate and re-estimating the regressions,<sup>31</sup> the China coefficient is still 0.320 (s.e.=0.066) in equation (6) and 0.282 (s.e.=0.071) in equation (7).

The rest of the change in China’s price level could well stem from the sampling bias in the 2005 ICP’s price surveys for China. The 2005 round of the ICP was the first time that China had officially participated in the ICP; priors had been based on an estimate of the country’s PPP for 1993 that was not based on a 1993 price survey, but rather was an updated version of an older

> 31 Given that the 2% is annual, the term in ln( _Y_ 05 _i_ /<sup>_Y_</sup> 93 _i_ ) for non-benchmark countries was replaced by ln( _Y_ 05 _i_ / _Y_ 93 _i_ )  .024 _China_<sup>where</sup><sup>_China_is a dummy variable for China, which also appears as a</sup> separate regressor for the purpose of this test.

16
PPP for China from non-ICP price data.<sup>32</sup> On looking more closely at how China’s price surveys were done for the 2005 ICP, Chen and Ravallion (2010b) point to sampling biases that would lead to an overestimation of the level of prices. However, their proposed correction still implies a large increase in China’s price level between 1993 and 2005.<sup>33</sup> The correction for that bias proposed by Chen and Ravallion (2010b), using non-ICP data on rural prices, brought China’s (expenditure-weighted) price index for consumption (rather than GDP as a whole) down from 52% to about 45%, though still considerably higher than the prior estimates of around 25% based on the 1993 ICP (19% for GDP). Assuming a similar correction for the GDP price index, the combined effect with the DPE (given China’s high growth rate), leaves the doubling of China’s price index almost fully explained.

# **6. Implications for estimating PPPs for non-benchmark years**

As noted in the introduction, the most widely-used method for extrapolating and updating PPPs relies solely on the inflation rate in the country in question, relative to the US. I find that the inflation rate is a strong predictor of the proportionate changes in PPPs; the regression coefficient of ln( _PPP_ 05 _i_ /<sup>_PPP_</sup> 93 _i_ ) on ln( _DEF_ 05 _i_ /<sup>_DEF_</sup> 93 _i_ ) is 0.981 (s.e.=0.044), with R<sup>2</sup> =0.958. (Note that the US inflation rate is a constant and so drops out.) However, in a nested test, the inflation-adjustment method is clearly outperformed by a model incorporating the DPE. This is evident is one adds a term in ln( _DEF_ 05 _i_ /<sup>_DEF_</sup> 93 _i_ )<sup>to equation (4); its coefficient is 0.094, with a</sup> standard error of 0.102, while other coefficients and their standard errors change little. So one cannot reject the null hypothesis that the inflation rate has no effect, once one controls for the DPE and the change in market exchange rates.

Another way to assess these methods is to compare their errors in predicting the 2005 PPP. Figure 8 plots the empirical (normal kernel) density functions of those errors (log of PPP minus its predicted value). One density in Figure 8 is for the errors obtained using the inflationadjustment method (based on the GDP deflator) while another is for the residuals from a regression of ln _PPP_ 05 _i_<sup>on</sup> ln _PPP_ 93 _i_ , ln( _Y_ 05 _i_ /<sup>_Y_</sup> 93 _i_ ) and ln( _E_ 05 _i_ /<sup>_E_</sup> 93 _i_ )<sup>(which naturally have zero</sup>

> 32 More precisely, the previous PPPs were derived using a bilateral comparison of 1986 prices between the United States and China as documented in Ruoen and Kai (1995).

> 33 The ICP aims to collect prices from a representative sample of outlets in each country. However, this was not possible in China and the ICP only covered 11 cities.

17
mean); these are very close to the errors in predicting ln _PPP_ 05 _i_ by simply adding ln _PPP_ 93 _i_ to (4). It can be seen that the density function of the errors implied by the inflation-adjustment method has thicker tails (large errors in both directions, but more so in the upper tail) and is not centered on zero, with underestimation at the mean; the mean error is 0.071, or roughly a 7% underestimation of the PPP (or 7% overestimation of GDP at PPP).

It can be argued that this comparison is biased against the inflation-adjustment method, since the proposed alternative is calibrated using data that include the 2005 PPPs from the ICP, which would not (of course) be available when updating the 1993 PPPs prior to release of the 2005 ICP. However, virtually identical results are obtained if one simply assumes that the PPP has an elasticity of unity to the market exchange rate and that the DPE coefficient is 0.293— based on the cross-sectional value estimated above using the 1993 PPPs. I also give the density function for this simple and feasible estimator in Figure 8. This does not yield zero-mean error, but the mean error is much smaller than the inflation-adjustment method (-0.017 versus 0.071), and it also trims the large errors in the tails generated by the latter method.

# **7. Conclusions**

The substantial downward revisions to the estimates of the real GDP of developing countries implied by the 2005 ICP have surprised many observers. Some have questioned the data. Concerns about the comparability of ICP data across survey rounds have loomed large, and have reinforced past practices of not mixing PPPs across ICP rounds.

This paper has tried to make sense of the PPP changes between ICP rounds. The paper reports new evidence consistent with the existence of a Balassa-Samuelson effect over time such that the PPP rises relative to the exchange rate in a growing economy. There are signs that this only starts to happen with a sufficiently high growth rate. The paper finds that this “dynamic Penn effect” is even stronger in initially poorer countries. Thus the widely-observed static Penn effect (whereby the price level index is lower in poorer countries) has been attenuated over time.

The higher price levels (lower real exchange rates) for many developing countries implied by the 2005 ICP are accountable in part to their economic growth. On its own, the dynamic Penn effect accounts for about one fifth of the variance in the proportionate changes in the price levels over 1993-2005, rising to one half over 1985-2005. An augmented version of the 18
basic model allowing for measurement error in the PPPs not based on price surveys can explain almost half the variance in the proportionate changes in price levels.

This degree of explanatory power certainly does not eliminate concerns about the comparability of PPPs between ICP rounds. The dynamic Penn effect alone still leaves almost 80% of the variance in the proportionate changes in the price level index between 1993 and 2005 unexplained, although this drops to 60% or less once one allows for the measurement errors associated with the need to estimate PPPs econometrically for the countries that did not participate in the 1993 ICP. However, the results of this paper do cast doubt on the extreme view of “PPP non-comparability” in which past ICP rounds are essentially ignored at each update.

The results of this paper do not suggest that China’s new PPP is as “weird” or “implausible” as some observers have claimed. Given China’s high growth rate, it is not too surprising that the country’s price level index rose appreciably between the 1993 and 2005. This paper’s calculations suggest that about two thirds of that increase is accountable to the dynamic Penn effect. The bulk of the remainder may well reflect an upward bias in China’s PPP due to the 2005 ICP’s weak coverage of China’s rural areas.

What light do these findings throw on the substantial data revisions implied by the 2005 ICP, such as illustrated by Figure 1 for real GDP? The current methods used to update PPPs between ICP rounds do not allow for the dynamic Penn effect identified here (yet the extrapolations used to fill in missing PPPs in a given benchmark year are explicitly based on the static Penn effect). The results of this paper suggest an alternative approach in which the dynamic Penn effect would be brought explicitly into the inter-temporal extrapolations for the price-level index, using market exchange rates to back out the implied PPPs for non-benchmark years. This method yields more reliable estimates than the widely-used inflation-adjustment method for updating PPPs between ICP rounds.

The upshot of all this is that many of the large revisions to real GDP data in Figure 1 could have been avoided by exploiting some simple but neglected insights from the original Balassa-Samuelson model—ironically, the same model that had helped motivate the considerable international statistical effort since the 1960s to collect price data for measuring PPPs—so as to better understand how price levels evolve over time in developing countries.

19