metadata: authors: 0: author: Deng, Haiyan
1: author: Feenstra,Robert C.
2: author: Heston,Alan Wiley
3: author: Timmer,Marcel Peter
count: World
docna: 0: docna: Estimating real production and expenditures
            across nations : a proposal for improving the Penn World Tables
docty: Policy Research Working Paper
subtopic: Labor Markets,International Trade and Trade Rules,Macroeconomic Management,Transport Services
teratopic: Macroeconomics and Economic Growth,International Economics and Trade
abstracts: cdata!: From its inception, the Penn World
            Tables (PWT), building on the International Comparisons
            Program (ICP) of the United Nations, has sought to compare
            the standard of living of individuals in different
            countries. That is, the term "real GDP per capita"
            as reported in the PWT is intended to represent the ability
            to purchase goods and services by a representative agent in
            the economy. The same is true of benchmark comparisons as
            published by the United Nations, Eurostat, or OECD. But this
            expenditure-side interpretation of real GDP is quite
            different from the uses to which benchmark ICP and PWT data
            are frequently applied, such as in growth regressions, where
            "real GDP" is intended to reflect the production
            side of the economy. In this paper the authors propose a new
            approach to international comparisons of real GDP measured
            from the output side. They modify the traditional
            Gary-Khamis system, which measures real GDP from the
            expenditure side using real domestic expenditure, to include
            differences in the terms of trade between countries. The
            analysis shows that this system has a strictly positive
            solution under mild assumptions. On the basis of a set of
            domestic final output, import, and export prices and values
            for 151 countries in 1996, differences between real GDP
            measured from the expenditure and output side can be
            substantial, especially for small open economies.
repnme: repnme: Estimating real production and expenditures
            across nations : a proposal for improving the Penn World Tables
display_title: Estimating real production and
            expenditures across nations : a proposal for improving the
            Penn World Tables
listing_relative_url: /research/2007/03/7451133/estimating-real-production-expenditures-across-nations-proposal-improving-penn-world-tables
topicv3: Transport m1326661 135,Trade m1326924 698,Trade Balance m1327679 1136,Labor Productivity m1504060 2756,Deflation m1505334 3102
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Macroeconomics and Economic Growth,International Economics and Trade
no_of_pages: 28
author_keys: 0: author_key: 664692
1: author_key: 165910
2: author_key: 1168139
model_extractions: # WPS4166

## **Estimating Real Production** **_and_ Expenditures across Nations: A Proposal for Improving the Penn World Tables**

Robert C. Feenstra University of California, Davis, and NBER Alan Heston University of Pennsylvania Marcel P. Timmer University of Groningen Haiyan Deng Conference Board, New York World Bank Policy Research Working Paper 4166, March 2007 _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 view of the World Bank, its Executive Directors, or the countries they represent. Policy Research Working Papers are available online at http://econ.worldbank.org._

* We thank Bettina Aten, Brian Easton, Erwin Diewert, Peter Neary, Prasada Rao, Marshall Reinsdorf, Bart van Ark and seminar participants at Dartmouth College, the NBER, and the IARIW meeting in Cork, Ireland for helpful comments, along with Chang Hong, Edwin Stuivenwold and Gerard Ypma for exceptional research assistance. Financial support was provided by the National Science Foundation and the World Bank (research grant P094655).
# **Abstract**

From its inception, the Penn World Tables (PWT), building on the International Comparisons Program (ICP) of the United Nations, has sought to compare the _standard of living_ of individuals in different countries. That is, the term “real GDP per capita” as reported in the PWT is intended to represent the ability to purchase goods and services by a representative agent in the economy. The same is true of benchmark comparisons as published by the United Nations, Eurostat or OECD. But this expenditure side interpretation of real GDP is quite different from the uses to which benchmark ICP and PWT data are frequently applied, such as in growth regressions where “real GDP” is intended to reflect the production side of the economy.

In this paper we propose a new approach to international comparisons of real GDP measured from the output side. We modify the traditional Gary-Khamis system, which measures real GDP from the expenditure side using real domestic expenditure, to include differences in the terms of trade between countries. The analysis shows that this system has a strictly positive solution under mild assumptions. On the basis of a set of domestic final output, import, and export prices and values for 151 countries in 1996, differences between real GDP measured from the expenditure and output side can be substantial, especially for small open economies.

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# **1. Introduction**

From its inception, the Penn World Tables (PWT), building on the International Comparisons Program (ICP) of the United Nations, has sought to compare the _standard of living_ of individuals in different countries. That is, the term “real GDP per capita” as reported in the PWT is intended to represent the ability to purchase goods and services by a representative agent in the economy. The same is true of benchmark comparisons as published by the United Nations, Eurostat or OECD. But this expenditure-side interpretation of real GDP is quite different from the uses to which benchmark ICP and PWT data are frequently applied, such as in the “millions” of growth regressions (Sala-i-Martin, 1997) where “real GDP” is intended to reflect the production side of the economy.<sup>1</sup> The goal of this paper is to carefully distinguish the production or output-side measure of real GDP, denoted _real GDP_<sup>_o_</sup> , from the expenditure-side measure, denoted _real GDP_<sup>_e_</sup> . Real GDP<sup>o</sup> reflects the production possibilities of an economy, whereas real GDP<sup>e</sup> measures real expenditures which includes an adjustment for the trade balance. The reason these concepts were not distinguished in the ICP and PWT is that these projects treat the net foreign balance in an unsatisfactory way. While there may have been some data justifications for that treatment in benchmark studies of the 1970s, this is no longer the case. The treatment of exports and imports proposed in this paper will not only remove the ambiguity presently surrounding real GDP<sup>e</sup> and real GDP<sup>o</sup> in the ICP and PWT, but provides a rich new international measure, namely the difference between them. Essentially, these two concepts differ by the _terms of trade_ in the economy, i.e. the prices at which goods are exported and imported.

In section 2, the distinction between real GDP on the output-side and expenditure-side is set out conceptually, followed by a discussion of how they can be separately measured in time series data. In order to incorporate these concepts into the PWT, however, we need to have a _cross-country_ measure of their difference. To achieve this, we propose a measure of the purchasing power parity for outputs (PPP<sup>o</sup> ) rather than expenditures (PPP<sup>e</sup> ). Currently the cornerstone of the ICP and PWT is the PPP for final expenditures (PPP<sup>e</sup> ), used to deflate nominal national income to obtain real GDP<sup>e</sup> . If instead we want to deflate nominal GDP to

> 1  There are many other applications where expenditure-side real GDP is used when output-side real GDP is really needed. Recent examples are Bernard and Jones (1996), Jones and Hall (1999) and Acemoglu and Ventura (2002).
obtain _real GDP_<sup>o</sup> _,_ then we need to use PPP<sup>o</sup> , which incorporates prices for exports and imports including both final goods and intermediate inputs.

In section 3 we show how PPP<sup>o</sup> can be computed using the Geary (1958)-Khamis (1970,1972) (GK) system, and further broken down into separate PPP’s for final expenditures, exports and imports. It should be emphasized that by working at the level of entire economies, rather than sectors, some of the difficulties with measuring output-based PPP’s are avoided. In particular, we find that while the international prices of intermediate inputs are used, the corresponding domestic prices of intermediates are not needed at all. In this sense, our use of trade data provides a _short cut_ to obtain output-based deflators for the entire economy.<sup>2</sup> In section 4, we provide an empirical application of our techniques. The data used for this illustration are from the 1996 ICP-PWT benchmark comparison, using 4-digit SITC export and import unit-values for 151 countries. With the normalization that world real GDP<sup>e</sup> equals world real GDP<sup>o</sup> , we find that one-third of the countries have real GDP<sup>e</sup> exceeding real GDP<sup>o</sup> , which means that they are less productive than indicated by the PWT and instead benefit from high terms of trade. Included in this group are Australia, New Zealand, Japan, North America and most countries in Europe, but also a set of developing countries that happen to benefit from high unit-values on selected export products. The remaining two-thirds of countries have real GDP<sup>e</sup> below real GDP<sup>o</sup> , which means that they are more productive than indicated by the PWT but have low terms of trade. That group has lower GDP per capita on average than the former group, but still includes some wealthy countries such as Australia, Hong Kong and Norway.

When we split our sample between oil and non-oil exporters, we find that the relationship between GDP and the terms of trade differs for the two sets of countries. Generally, there is a positive relationship for non-oil exporters: countries with higher per-capita GDP also have higher terms of trade. This terms-of-trade effect is driven mainly by an increase in export price levels, as import price levels are relatively stable. In contrast, we find no significant relationship between GDP per capita and the terms of trade for our set of 25 oil exporters. This appears to be

> 2  The International Comparisons of Output and Productivity (ICOP) project at the University of Groningen constructs real GDP by sector from the output side using the industry-of-origin approach. This requires comparison of sectoral output prices across countries (see van Ark and Timmer, 2001, for example). Sectoral real output can be aggregated to obtain real output GDP , but his has only been done for a limited number of countries so far. The short-cut proposed here, which uses international rather than domestic prices of intermediates, is much easier to implement for a larger set of countries.

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due to the fact that export prices in these countries are driven by movements in the global oil market that are common to all. Conclusions and directions for further research are discussed in section 5. The most important task for future work is to correct trade unit-values for quality, after which the calculation of real GDP<sup>e</sup> and real GDP<sup>o</sup> can be done over multiple years and incorporated into the PWT.

# **2. Concepts of Real GDP**

The distinction between real GDP on the output and expenditure-side can be illustrated by a simple diagram in a two-good economy, shown in Figure 1. We suppose that the production possibilities frontier shifts out due to technological change. At unchanged prices, production would increase from point A to point B. Suppose, however, that the relative price of good 1 falls due to its increased supply, so that the new prices are shown by the slope of the line P3P3. Production now occurs at B' rather than B. We have drawn the case where the budget lines P1P1 and P3P3 are both tangent to an indifference curve U, at points C and D, indicating that the utility of the representative consumer is unchanged.

In the case we have illustrated, the production points A and B' lie on the same ray from the origin so that the _relative outputs_ of the two goods are unchanged. This means that any index of real output would be identical, and would simply equal 0B'/0A > 1, which is the proportional increase in both outputs. This is the increase in real GDP<sup>o</sup> as measured on the output-side.

Now suppose we pose a different question, and ask what has happened to the welfare of the representative consumer, with indifference curve shown by U in Figure 1. An exact measure of consumer welfare, or real GDP<sup>e</sup> measured on the expenditure-side, would be _unchanged_ since the consumer has the same utility at the two prices. This occurs because there has been a fall in the price of the exportable good 1. The change in real GDP<sup>e</sup> could be measured by the change in nominal expenditure deflated by an _exact consumer price index,_ constructed with the same prices as real GDP<sup>o</sup> but using _consumption quantities_ rather than _production quantities_ in the index. The difference between these is exports and imports, of course, but for production quantities we also need to include the imports and exports of all _intermediate inputs,_ as well as their prices. These data are not currently used by the ICP, which restricts its attention to final goods.

5
This distinction between real GDP on the expenditure and output-side is recognized by the United Nations 1993 System of National Accounts (SNA). The former is called real Gross Domestic Income (GDI), while the latter is real GDP. One definition<sup>3</sup> of real GDI is: Real GDI = (Nominal GDP)/(Domestic absorption price index), (1) as compared to, Real GDP = (Nominal GDP)/(GDP price index). (2) Nominal GDP, of course, is domestic absorption (C+I+G) adjusted for the trade balance (X–M). The “domestic absorption price index” in (1) is constructed over the components of (C+I+G). By _excluding_ export and import prices from this price index, changes in the terms of trade (which affect nominal GDP) are then reflected in real GDI, as demonstrated by Diewert and Morrison (1986). An improvement in the terms of trade, for example, would cause real GDI to grow faster than real GDP. Kohli (2004) has shown that this pattern holds for Switzerland, due to its terms of trade improvement. We shall avoid the term “real GDI,” because it is suggestive of the incomeapproach to measuring GDP (through adding up the earnings of factors) which we do not use. Instead, we use real GDP<sup>e</sup> to reflect the expenditure-side concept like (1). This is essentially the same as “real expenditure”, except that by using nominal GDP rather than nominal expenditures in the numerator of (1) we are adjusting for the net foreign balance.

Now we come to the key question motivating this paper: which concept does the PWT use as “real GDP” – the output-side measure real GDP<sup>o</sup> , or the expenditure-side measure real GDP<sup>e</sup> ? It turns out that the answer is unclear: the ICP constructs real GDP<sup>e</sup> in _benchmark years_ , but then to interpolate between these years, the PWT must reconcile these changes in real GDP<sup>e</sup> with the national accounts data reports on countries real GDP growth. Since national accounts real GDP growth is closer to real GDP<sup>o</sup> , which is being compared to benchmark estimates of real GDP<sup>e</sup> , the distinction between these becomes lost in the reconciliation.<sup>4</sup> In other words, the

> 3  See <u>http://unstats.un.org/unsd/sna1993/introduction.asp</u> , paragraph 16.154.  The other definitions of real GDI depend on the deflator used for (X-M).  Other than the domestic absorption price index, we might use the import price index, export price index, or an average of these, as recommended by Geary; see Neary (1997).

> 4  The process of reconciling the initial PWT estimates (in benchmark years) and the national accounts data for each country is described in Summers and Heston (1991, pp. 339-341).

6
differences between real GDP<sup>e</sup> (using ICP data) and real GDP<sup>o</sup> (using national accounts data) is eliminated, and the year-to-year growth of real GDP from the national accounts is used to impute real GDP in the PWT for all years in-between the benchmark years. The fact that the distinction between real GDP<sup>e</sup> and GDP<sup>o</sup> is not clearly made is a limitation of previous versions of the PWT that future revisions intend to improve upon.<sup>5</sup>

# **3. Measurement of Real GDP**

Suppose there are i =1,...,M final goods, such as the categories of goods currently collected by the ICP, of which the first M0 are non-traded. These final goods may also be used as intermediate inputs, and there are another i =M+1,...,M+N goods that are exclusively intermediate inputs; for convenience we treat these all as traded internationally. To treat domestic demand, trade and production in a consistent framework, an input-output analysis must be used. In this framework the fundamental equality is between total demand and total supply of each good. For each country j = 1,...,C, denote final demand by qij, intermediate demand by zij, output by yij, exports by xij and imports by mij, for i = 1,...,M+N. We assume that all of these quantities are _nonnegative,_ but many can be zero: in particular, the intermediate inputs i = M+1,...,M+N have qij = 0, and the non-traded goods = 1,...,M0 have xij = mij = 0. Total demand in country j is given by qij + xij + zij, and total supply by yij + mij. Hence the equality between demand and supply is: Re-arranging terms, we obtain: where we refer to yij – zij as “net output” of each good, i.e. gross output minus intermediate demand.

Multiplying by prices and summing over goods i = 1,...,M+N, nominal GDP can be measured either from the expenditure side (left-hand side of (4)) or from the production side

> 5  For example the title of the Phase III report of the ICP was _World Product and Income_ (Kravis, Heston and Summers, 1982). This clearly implied a treatment of GDP converted at PPPs of countries as interchangeable with what is termed _output_ and _expenditure_ in this paper. Further the provision of output per worker figures in PWT, though provided because users were taking per capita real GDP as a labor productivity measure, clearly implies that

7
(right-hand side), where the units are the national currency. We presume that for a particular product, the prices of exports and imports can differ from domestic output and consumption. Such price differences always occur in practice, which is why we incorporate them here, without considering why the price differences arise. We distinguish the prices pij > 0 for domestic output and consumption, used to multiply qij, i = 1,...,M+N, from those for exports and imports, pij<sup>x></sup> 0 and pij<sup>m></sup> 0 respectively.<sup>6</sup> Consistent with the System of National Accounts (SNA), the export prices are measured _net of tariffs and freight, including any subsidy to the buyer but not to the seller_ , i.e. as the f.o.b. (free on board) price in the exporting country.<sup>7</sup> Likewise, the import prices are measured _net of tariffs._<sup>_8_</sup> m x M + N x M + N m With these conventions for p and ij pij _,_ let X j = ∑ i = M0 + 1pij x ij and M j = ∑ i = M0 + 1pij mij denote the value of exports and imports at tariff-free prices, so that nominal GDP measured on the expenditure side is: Using (4), we can re-write (5) as: where the first line is obtained by using qij = (yij – zij) – (xij – mij) for the final goods i=1,...,M, whereas the intermediates have qij = 0, so that [(yij – zij) – (xij – mij)] = 0 for i=M+1,...,M+N. Then the second line follows because xij = mij = 0 for the non-traded goods i=1,...,M0. We can interpret (pij<sup>−</sup> pijm ) as import tariffs (subsidies if negative), and (pij<sup>−</sup> pijx ) as exports subsidies (taxes if negative). So the final summation on the second line is interpreted as import revenue

> the real GDP number is an output measure.

> 6  In principle we should also distinguish producer from consumer prices, which can differ due to taxes and retail margins, but do not incorporate that distinction here.

> 7  See <u>http://unstats.un.org/unsd/sna1993/introduction.asp, paragraphs 6.235, 6.237 and 15.35.</u>

> 8  The SNA recommends that transport costs also be removed from import prices, but that is not possible using the unit-values from UN data, where imports are measured c.i.f. (cost, insurance, freight).

8
M + N less export subsidies. Adding this to the value of net output ∑ i = 1 pij (yij − z ij ) as in (6) gives us nominal GDP measured on the production or output side: which clearly equals nominal GDP measured on the expenditure side, from (6).

The real counterpart to GDP measured on the expenditure-side in the PWT is obtained by using data for many countries, and computing average “reference price” for goods according to the Geary-Khamis (GK) system. The reference prices<sup>π</sup> ei<sup>for final goods and the purchasing</sup> power parities PPP for each country are obtained from the simultaneous equations: je and, In (8), the nominal prices pij of final goods are deflated by the PPP’s, and then averaged across countries. The PPP’s are obtained from (9), as the ratio of nominal to real final expenditure, where real expenditure is evaluated using the reference prices. The fact that q ij ≥ 0 in (8)-(9), along with ∑ Nj = 1q ij > 0 , ensures a positive solution for<sup>π</sup> ei<sup>and</sup> PPP (Prasada Rao, 1971, je Diewert, 1999). Then a normalization can be used to obtain a unique solution.

Subtracting from real expenditure the trade balance deflated by the PPP exchange rate, e we obtain what is called real GDP in the PWT, and what we shall call real GDP : j 9
Notice that the trade balance (Xj – Mj) is deflated by the PPP for domestic final goods, to evaluate real GDP on the expenditure side. In contrast to (10), suppose that we have reference je prices for final goods,<sup>π</sup> ei<sup>, i=1,...,M as well as for the traded exports and imports,</sup> π ix and<sup>π</sup> im<sup>,</sup> for i=M0+1,...,M+N. The consider the following definition of real GDP on the output side: jo where the second line follows from (4) using (yij – zij) = qij for non-traded final goods i=1,...,M0, while the intermediate inputs have qij = 0 so that (yij – zij) = (xij – mij), i=M+1,...,M+N.

The first line of (11) is similar to nominal GDP measured on the production side in (6), but using reference prices in (11) rather than nominal prices. In principle, the first line of (11) relies on domestic reference prices for intermediate inputs (that is,<sup>π</sup> io<sup>for i=M0+1,...,M+N). But</sup> the second line of (11), where we re-write real GDP using the trade balance evaluated with jo reference prices, shows that the domestic reference prices for intermediate inputs are not need after all! Essentially, the use of the international reference prices π ix and<sup>π</sup> im<sup>gives us a short-cut</sup> method for evaluating real GDP on the output side. jo To evaluate the reference prices used in (11), consider the augmented-GK system: and, 10
In (12) we construct domestic reference prices for the final goods, and in (13) and (14) we construct reference prices for exports and imports. These are used to construct purchasing-powerparity PPP in (15), which is the ratio of nominal GDP and real jo GDPjo . In order for these definitions to make sense, we assume:

# **<u>Assumption 1</u>**

Summing up, we have shown that the augmented-GK system (12)- (15) can be used to obtain a cross-country measure of the GDP price deflator on the output-side, which is PPPjo . We have therefore achieved our goal of demonstrating that final goods data, in conjunction with export or import data, can be used to construct real GDP on the output side. However, it jo remains to be shown that this system has a solution. This task is complicated by the fact that real GDPjo , appearing in (11) and the denominator of (15), is not guaranteed to be positive for all possible reference prices. This can be ruled out by some additional assumptions, as follows.

First, define the _budget shares_ for each final, export and import goods as: where i=1,...,M for v = q; i= M0+1,...,M+N for v = x, m; and j=1,...,C. Notice that these budget shares are measured relative to nominal GDP. In addition, define the _market shares_ for each good as: where i=1,...,M for v = q; and i=M0+1,...,M+N for v = x, m. The market shares are measured relative to the world quantity of final demand, exports or imports for each good. Denote the column vectors of budget and market shares by θ vj and μ vj for v = q, x, m and country j. Then our second assumption is: 11
# **<u>Assumption 2</u>**

Clearly, this assumption limits the size of the import shares θ ijm and μ ijm . It is appropriate C to think of wjk as “weights” because it is readily shown that ∑ k = 1 w jk = 1. While is it easy to construct examples where Assumption 2 is violated for some countries j and k, it is also true that for many values of the import budget and market shares, Assumption 2 will hold. Then we have:

# **<u>Theorem</u>**

Under Assumptions 1 and 2, the system (12)- (15) has a strictly positive solution for π io , π ix , π im , real GDP and jo PPPjo .

It is worth emphasizing that Assumption 2 is a sufficient condition to obtain this result, but is not necessary. In particular, we show in the Appendix that the vector of real GDP across jo countries is a row eigenvector of the matrix W = [wij], corresponding to an eigenvalue of unity. Under Assumption 2, this is the Frobenius root of W and its corresponding eigenvector is strictly positive, so that real GDP is strictly positive along with jo PPP and all the references prices, as jo stated in the Theorem. However, it is quite possible to obtain a strictly positive eigenvector and therefore a positive solution for real GDP even without having all the elements of W positive.jo<sup>9</sup> By rewriting real GDPjo , it is possible to give a clear interpretation about the difference between it and real GDPje . Notice that real GDP in (11) can be decomposed as: jo W can define the three ratios appearing in (18) as the inverse of the PPP’s for final expenditure, exports and imports:

> 9  Assumption 2 did not hold over our entire sample of 152 countries, because initially we obtained some negative prices. As a result we dropped Nigeria, resulting in positive prices for all other 151 countries.

12
Comparing (10) and (18), it is immediate that the difference between real GDP and real je GDP is due to the deflation of final expenditure, exports and imports: jo Real GDP – Real e GDPo j j We will find in practice that PPP and je PPP are very similar, since they are both computed jq from final expenditures, but with different reference prices. If these two deflators for final expenditure are equal, then either PPP > jx PPP or je PPP < jm PPP is needed to have real je GDP je exceed real GDPjo , and both inequalities holding is sufficient for this. To interpret these conditions, it is useful to first convert export and import prices to U.S. dollars using the nominal exchange rate. Then having export prices above their reference level and import prices below their reference level will contribute towards real GDP exceeding real je GDPjo . For example, proximity to markets that allow for higher export prices would work in this direction, but being distant from markets leading to high import prices would work in the opposite direction, raising m e o PPP and tending to make real j GDP less than real j GDPj .

We conclude this section with two warnings. First, the difference between our crosscountry measure of real GDP and real je GDP jo _does not_ measure the gains from trade as compared to autarky. Instead, the difference between real GDP and real je GDP is a measure of jo the gains from trade from having export or import prices that _differ_ from their reference prices<sup>π</sup> ix<sup>andπ</sup> im<sup>. Sinceπ</sup> ix<sup>andπ</sup> im<sup>are themselves</sup><sup>_averages_of countries’ actual export and import</sup> prices, it is impossible for all countries to be gaining (or losing) relative to these averages. What we can expect to find is that some countries – with high export prices or low import prices – will 13
gain in the sense that real GDP exceeds real je GDPjo , whereas other countries – with low export e o prices or high import prices – will have real GDP less than real j GDPj .

Second, in order for export prices to influence the measurement of real GDPjo , countries need to produce some goods in common. To see this, consider the opposite case where all countries are fully specialized in their own goods. Then the summations used in (13) to obtain reference prices for the export goods would actually be over a _single_ country, i.e. the unique country exporting that good. For convenience, suppose that each country exports just one good, x x o and re-order goods so that xij = 0 for i ≠ j and xjj > 0, so (13) becomes π j = p jj / PPPj . It follows from (19) that PPP =jx PPPjo , so with complete specialization, the PPP for exports is identical to the overall output PPP. This means that export prices will not contribute to any differences between real GDP and real je GDPjo ; only import prices matter. Countries with high import prices will still have real GDP less than real je GDPjo , due to their poor terms of trade.<sup>10</sup>

# **4. Application to UN Trade Data and Penn World Tables**

In this section we apply our formulas to a dataset for expenditure and trade in 1996 for a set of 151 countries. The source for the trade data in the NBER-UN dataset described in Feenstra _et al_ (2005), and we use only data for those countries that also appear in the PWT.<sup>11</sup> This database contains specific product data classified at the 4-digit SITC level, from which we obtain unit-values for exports and imports. The number of unit-values on the export side ranges from 10 for Chad to 1,020 in the United States, and on the import side from 29 in Israel to 776 in Egypt.

It is well-known that trade unit-values are measured with error, and so we applied a regression-based procedure to omit outliers. The procedure was to predict import and export unit values based on tariff rates, distance to trading partners and exporter wages.<sup>12</sup> Unit values which were greater than five or less than one-fifth times the predicted unit value were identified and

> 10 However, in a two-good, two-country Ricardian model, a unique country imports each good. Say country j export m m o m o good j and import good i ≠ j. Then (14) becomes π j = p ij / PPPj , for i =1,2, so that PPPj = PPPj from (19). Since x o e o e o PPPj = PPPj also, it follows by comparing (8)-(10) with (12)-(15) that PPPj = PPPj and so real GDPj = real GDPj . Thus,  the two concepts of real GDP do not differ in this case. We thank a referee for alerting us to explore it. 11 The only country excluded is Nigeria, because it resulted in some negative reference prices.

14
omitted. By this method, 11% of the 50,115 observations for export unit values were excluded and 8% of the import unit values. The resulting cleaned data set had on average about 294 export and 432 import price observations per country.<sup>13</sup> For measuring the expenditure price level, we used the PPP’s for three categories of final goods (private consumption, government consumption and investment) provided by the latest version of the PWT, so M = 3.<sup>14</sup> Denoting these aggregate prices from PWT by PPPij, we compute the “expenditure price levels” for each country, defined as: where Ej denotes the local currency price of US$ in each country j. Unlike the PPP’s, the price levels are unit free, and indicate how the US$ prices in each country compare to the reference prices, also in dollars. In column (1) of Tables 1 and 2, we report the expenditure price levels.

We next combine the three categories of final goods with i = 4,...,N+3 categories of export and import unit-values, and compute the extended-GK system in (12)-(15). In column (2) we report the relative output price level PLoj , computed as PPPjo / E j . The normalization used in column (2) is identical to that in column (1), i.e. the value of real GDP or real je GDPjo summed over all 151 countries equals the summed nominal value of GDP in US$. The difference between the output price levels PPP and expenditure price levels jo PPPje , and hence between real GDP measured either from the output or the expenditure side, varies highly across countries, as shown in column (9). In Table 1 we report the 51 countries with real GDPje > real GDPjo , and in Table 2 the 100 countries with real GDPje < real GDPjo ; the sample is also divided this way for the summary statistics reported in Table 3.

> 12  These regression results are available on request.

> 13 We also experimented with a looser criteria, omitting only unit values greater than 10 or less than one-tenth. In this case, the percentages omitted unit values drops to 5.4% for exports and 3.2% for imports, but the overall results are similar to those reported here.

> 14  An alternative to using just three categories of final goods (private consumption, government consumption and investment) is to use the benchmark ICP data for 1996, which gives 30 categories of final goods. However, that benchmark data is only available for about 50 countries (for which we also have trade data). By collapsing the 30 final goods into three aggregates, and using those PPP’s from PWT, we instead obtain data on 151 countries.

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Output price levels are decomposed into price levels for final goods, exports and imports: These price levels are reported in columns (3), (5) and (6) in Table 1. The ratio of PLxj / PL is mj reported as the terms of trade for each country in column (4): A number of observations can be made. First, the output price levels for final goods in column (3) are very close to the expenditure price levels in column (1), which is encouraging. It indicates that the use of a different set of reference prices for final goods does not influence the estimation of a PPP for final goods: PPP is almost equal to jq PPPje . The choice for output prices for final goods<sup>π</sup> iq<sup>or expenditure pricesπ</sup> ie<sup>, where the former is influenced by exports and</sup> imports via the simultaneous system (12)- (15), but the latter is not, is inconsequential.

Second, export price levels differ greatly across countries (see column 5). The highest export price levels are found for Switzerland, Ireland, Sweden and Bermuda, while low levels are found for countries such as Bangladesh, Cambodia, Guinea Bissau, Lao and Nepal. Several factors play an important role in explaining differences in export prices. It is well known that under imperfect competition, exporters can and do charge different prices in various destination markets. Such market segmentation can arise in response to changes in nominal exchange rates, or trade policies of the importer. In addition, it is becoming recognized that countries differ systematically in their qualities and bundles of export goods (Lipsey, 1994; Schott, 2004). This would also create differences in the relative unit-value of their exports.

To give one specific example, Bermuda has the highest terms of trade, which is explained by a high price level for exports as compared to imports. Ships and boats (SITC 7932) is by far the most important export product, with exports of $145 million in 1996, and a export unit-value 16
of $2,680 per metric ton. This is higher than its reference price of $1,910 per ton. So Bermuda’s exports of ships and boats are priced higher than the world average, and this product is primarily responsible for Bermuda’s high price level for exports. To the extent that the boats exported from Bermuda are of higher quality than other countries (which seems quite plausible to us), then the high price level of exports and high terms of trade is being driven by quality rather than a pure price difference with other countries. As we discuss in the conclusions, correcting the unit-values for quality is the most important direction for further research.

The third observation is that import price levels of countries, shown in column (6) of Table 1, are much closer together than export prices – the standard deviation of import price levels are less than two-thirds for exports, and less than half that for final goods, as shown in Table 3. This might be related to the fact that import baskets are much more similar across countries than export baskets. High import prices are found for countries like Japan, Korea, Switzerland and Scandinavian countries, whereas Benin, Gambia, Mexico, Niger and Sierra Leone are prominent examples of countries in which import price levels are low.

Dividing the export and import price level, we obtain the terms of trade for each country. These are especially low for countries like Cambodia, Guinea Bissau, India, Lao, Mongolia and Nepal. In these countries terms-of trade were lower than 60, indicating that their export PPPs are much lower than their import PPPs. In contrast, countries like Bermuda, Democratic Republic of Congo, Equatorial Guinea, Ireland, Malta, Niger and Switzerland benefit from high terms of trade (140 or higher). Those countries with high terms of trade also tend to have real GDPje > real GDPjo , but that is not guaranteed because the value of exports and imports also enter (20).

Overall, we find that one-third of the countries (51) have real GDP exceeding real je GDPjo , which means that they are less productive than indicated by the PWT and instead benefit from high terms of trade. Included in this group are Australia, New Zealand, Japan, North America and most countries in Europe, but also a set of developing countries that happen to benefit from high unit-values on selected export products. The most extreme case in this group is Bermuda, which has real GDP twice as high as real je GDPjo , which is explained by its high export unit-value for sailboats. The remaining two-thirds of countries (100) have real GDP je 17
below real GDPjo , which means that they are more productive than indicated by the PWT and have low terms of trade. That group has lower GDP per capita on average than the former group, but still includes some wealthy countries such as Hong Kong, for which real GDP is two-thirds je that of real GDPjo , due to low export prices from Hong Kong.<sup>15</sup> An alternative way to split our sample is by oil and non-oil exporters, since we expect the relationships for the two sets of countries may be different.<sup>16</sup> In Figure 2 we plot the terms-oftrade and GDP per capita levels for the set of 126 non-oil exporting countries, together with the regression line. Generally, there is a positive relationship: countries with higher per-capita GDP also have higher terms of trade. The slope coefficient on GDP per capita is significantly positive (at the 5% level). This terms-of-trade increase is driven mainly by an increase in export price levels, as import price levels are relatively stable (see Table 3). However, GDP per capita explains only 5% of the variation in the term of trade. In contrast, we find no significant relationship for our set of 25 oil exporters (see Figure 3). This appears to be due to the fact that export prices in these countries are driven by movements in the global oil market that are common to all.

The pattern shown in Figure 2, whereby countries with higher per-capita GDP have higher terms of trade, carries over to the comparison of real GDP<sup>e</sup> and real GDP<sup>o</sup> . In Figure 4, a comparison of the two is given for the full set of countries, together with the 45 degree line. In o column (9) of Table 1 the difference between the two is given as a percentage over real GDPj . The magnitude of this difference depends on the openness of a country and its terms-of-trade. For example, although India had a particularly low terms-of-trade in 1996, the difference between real GDP and real je GDP is only 4%, due to its low share of exports and imports in jo GDP. Alternatively, big differences can be found for small open economies such as Bermuda, Ireland, Israel, Malta and Singapore in which real GDP was at least 30% than real je GDP due jo to advantageous terms-of-trade. Countries such as the Bahamas, Hong Kong, Moldova, Macao,

> 15   An number of electronic products exported from Hong Kong have lower unit-values than those exports from other countries. An example is electronic microcircuits (SITC 7764), which sell for $1.09 from Hong Kong, but $1.43 from Japan and $1.74 from the U.S.

> 16 Oil-exporters are defined as those having export shares of mineral fuels of at least 25%. Data on mineral fuel exports is taken from the World Bank, _World Development Indicators_ .

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Mongolia and Norway are prominent examples of the opposite, with real GDP<sup>e</sup> at least 19% lower than real GDP<sup>o</sup> due to disadvantageous terms-of-trade.

# **5. Conclusions**

In this paper, it has been shown that there is a fundamental difference between real GDP measured from the output side or from the expenditure side in international comparisons. The difference between the two concepts is in the treatment of the terms of trade. Real GDP from the expenditure side represents the ability to purchase goods and services while real GDP from the output side measures the production possibilities of the economy. It is the latter concept of real GDP which is of interest to many studies of growth and convergence in the world economy. However, available data from the Penn World Tables are based on a mix of cross-country expenditure-side measures of real GDP for benchmark years, with national growth rates of real GDP based on output-side measures.

In this paper a clear-cut distinction between the two measures is made. It is shown that real GDP<sup>e</sup> can overstate real GDP<sup>o</sup> by as much as 100% (for Bermuda) and understate it by as much as 33% (for Hong Kong). In these two extremes and other cases, we would want to closely examine the export unit-values before treating the estimates of real GDP as reliable. For jo Bermuda, its exported sailboats may well be of higher quality than the world average, which indicates that we are overstating its high terms of trade. Conversely, the low export unit-values for Hong Kong may reflect it status as an entrepôt economy, processing and shipping goods from China and elsewhere in Asia. It is impossible to avoid using these trade unit-values as measures of prices, however, since no dataset exists for comparing actual trade prices across countries. So it is essential that we should attempt to correct the unit-values for differences in quality across countries. Recent papers along these lines include: Choi, Hummels and Xiang (2006), Feenstra and Romalis (2006), Hallak (2006), Hallak and Schott (2006), Hummels and Klenow (2005), and Timmer and Richter (2006); and we can hope that enough progress will being made on these methods to allow implementation over a wide set of countries, products and years. In our view, that is the key theoretical and empirical issue that must be resolved before applying the techniques described herein to obtain separate measures of real GDP on the output side, and the expenditure side, in the Penn World Tables.

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