Technical Paper Series 

Congressional Budget Office 

Washington, DC

FACTOR ACCUMULATION WITHOUT 

DIMINISHING RETURNS: THE CASE OF EAST ASIA

Peter Debaere 

University of Texas at Austin 

Austin, Texas 

E-mail: debaere@eco.utexas.edu

Ufuk Demiroglu 

Congressional Budget Office 

Washington, DC 

E-mail: ufuk.demiroglu@cbo.gov

December, 2003 

2003-11 

Technical papers in this series are preliminary and are circulated to stimulate 

discussion and critical comment. These papers are not subject to CBO’s formal 

review and editing processes. The analysis and conclusions expressed in them are 

those of the authors and should not be interpreted as those of the Congressional 

Budget Office. References in publications should be cleared with the authors. 

Papers in this series can be obtained at www.cbo.gov (select Publications and then 

Technical Papers). 
2

Abstract: We investigate the similarity of the country endowments of the newly 

industrialized East Asian countries and their major developed trading partners since the 

1960s. In particular, we analyze their factor endowments in years 1965, 1977 and 1990, 

using the lens condition of Deardorff (1994). Because of the similarity of endowments of 

the NICs and their developed-country trading partners, we cannot reject the hypothesis 

that these countries were able to produce the same set of goods since the 1960s. This 

empirical evidence supports the theoretical analyses of the East Asian growth miracle of 

Mankiw (1995) and Ventura (1997) in an environment in which factor accumulation did 

not imply decreasing returns to capital. 

Acknowledgements: The authors thank Li Gan,Wolfgang Keller, Keith Maskus and Jim 

Rauch for helpful suggestions. We also thank Bob Barsky, Alan Deardorff, Stefan 

Oppers for their comments on an earlier version of the paper. The authors are solely 

responsible for the paper’s content. 
3

Introduction: 

The distribution of world output has been at the forefront of recent debates in 

international economics. In particular, researchers have wondered about the extent to 

which there is production specialization across countries. From Schott (2001), Debaere 

and Demiroglu (2003) and Cunat (2000), we know that country endowments in the world 

are so different that it is unlikely that all countries of the world can produce a similar set 

of goods. Within the framework of the Heckscher-Ohlin model, still one of the major 

models used in trade analysis, this observation has important implications. Because of the 

very different factor endowments between developed and developing countries, it implies 

that trade cannot equalize factor prices (even not in productivity equivalents). As 

emphasized by Leamer (1996), the latter has important consequences. Whether or not 

developed and developing countries lie in the same cone has very different implications 

for the trade and wages debate. 

In this paper, we revisit that debate. We explicitly study the condition that is critical for 

production specialization over time; the existing studies mainly focus on a cross section. 

In particular, we study this condition for the newly industrialized East Asian economies 

and their trading partners. This group of countries is of particular interest for a number of 

reasons. The rapid, yet sustained growth between 1960 and the first half of the 1990s of 

Hong Kong, Singapore, Taiwan and South Korea has been at the center of the debate in 

the growth literature. The condition for production specialization is especially critical for 

this part of the research that has tried to integrate Hechscher-Ohlin type trade into the 

discussion about the role of trade in the East Asian growth miracle. 

In the growth literature, there is a consequential difference between Solow’s one-sector, 

closed-economy model and its two-sector, open-economy counterpart by Stiglitz (1970) 

in which countries produce the same products. In Solow's world, capital accumulation 

leads to decreasing capital returns and hence to lower growth rates. When countries 

produce the same products and are allowed to trade, however, the familiar Rybczynski 

effect takes place and production shifts in the accumulating country towards capitalintensive sector. Moreover, there is no drop in the return to capital as countries grow, 

since factor prices are set at the world level instead of at the country level.1

 In recent 

years, this distinction between a one-sector world with complete specialization and a 

multiple-sector, diversified economy has gained attention. This interest is due in part to 

the “neoclassical revival" (Klenow and Rodriguez-Clare, 1997) in growth with its reevaluation of the Solow model and the role of factor accumulation. Mankiw (1995) and 

Ventura (1997) pointed out that the rapid, yet sustained growth between 1960 and the 

1990’s in Hong Kong, Singapore, Taiwan and South Korea was accompanied by the 

gradual shift in production towards more capital-intensive sectors without incurring 

diminishing returns, and argued that this might be due to the Rybczynski effect. It is no 

coincidence that the East Asian countries are relatively open economies, characterized by 

 

1

 If countries are small, prices for goods do not change and the return to capital in the world as a whole 

does not change. If countries are big, prices for goods may change due to capital accumulation in one 

country, yet the change in the return to capital will be a function of the marginal change in the factor 

endowments at the world level. 
4

massive capital accumulation and a drastic expansion of their (increasingly capitalintensive) manufacturing production and exports since the 1960s. 

In this paper, we show that the condition for specialization is not violated for the East 

Asian countries and their major developed trading partners since the 1960s. This 

condition is essential to make the factor accumulation and growth without diminishing 

returns that Mankiw and Ventura consider possible, since it ensures that East Asia’s 

factor prices are not determined at the country level. Instead, factor prices are set for the 

entire group of countries as a whole. Our finding links the growth debate with the recent 

empirical literature in international trade. There is a growing consensus in that literature 

that because of the substantial differences in the factor proportions across the countries of 

the world, all countries cannot produce the same goods. Some countries have to 

specialize in goods that are completely different from the ones others produce and trade 

will not be the critical integrating factor of their factor markets.2 However, within such a 

world, it is perfectly possible that a more limited set of countries are diversified and are 

able to produce the same set of goods. 

To check the necessary conditions for specialized production empirically, we use 

Deardorff’s lens condition (Deardorff, 1994) that relates the factor intensities of multiple 

sectors to the cross-country distribution of the endowments. The intuition behind this 

condition is fairly straightforward. Countries whose endowments are too different can 

never produce the same set of goods at the same factor prices. A very poor country with 

little capital per worker cannot produce highly capital-intensive goods competitively, 

because its scarce capital will be too expensive. Therefore, countries with very different 

factor endowments should specialize and produce different goods. Alternatively, the 

countries with similar endowments will be able to produce goods with similar factor 

intensities. We check the lens condition for 1965, 1977 and 1990 for the East Asian 

countries and their major trading partners. For each year, we allow for factor-augmenting 

productivity differences between countries as in Trefler (1993), so that factor returns 

across countries can differ. With Deardorff's condition, we study the (changing) 

international environment within which East Asian sustained growth and capital 

accumulation took place. This study highlights an aspect of interdependence that is not 

easily captured by cross-country growth regressions or by studies of the sectoral shifts 

within individual countries since it hinges on the changing distribution of endowments of 

multiple countries in conjunction with the changing factor intensities of multiple 

production sectors. 

The paper proceeds as follows. Section one presents Deardorff’s lens condition. In 

section two, we discuss the empirical implementation of the condition and the data. The 

third section discusses the results. 

 

2

 There is ample evidence that factor prices are not the same (see Leamer and Levinsohn, 1995). Debaere 

and Demiroglu (2003), Schott (2001), Cunat (2000) and others all argue that there are multiple 

diversification cones. 
5

1. Deardorff's Lens Condition 

In the standard 2 x 2 x 2 Heckscher-Ohlin (HO) model, countries produce the same set of 

goods with factor price equalization if and only if their capital-labor ratios lie inside the 

diversification cone. The condition that + 

Deardorff develops is a higher dimensional version of this cone of diversification and 

builds on the standard HO assumptions. In higher dimensions, the condition is perhaps 

most easily understood by example. In the example given in Figure 1 there are three 

countries and five sectors. The graph shows two lenses; the one in dashed lines is called 

the ‘country lens’ and the other one in solid lines the ‘goods lens’. To draw the country 

lens, countries' capital Kc and labor Lc endowment vectors vc = (Lc ,Kc) are first ranked 

according to capital-labor ratio. Next, these vectors are concatenated, first in increasing 

and then in decreasing order of their capital-labor ratios, both times starting from the 

origin. The goods lens is constructed in a similar fashion. This time we concatenate the 

sectoral factor use vectors zi = (Ki , Li) whose coordinates are respectively the total 

amount of capital and labor used in sector i in all the countries for which the lenses are 

drawn. 

In the example of Figure 1, Deardorff’s lens condition is satisfied: the country lens lies 

inside the goods lens. In this case the endowments are similar enough so that all 

countries can produce the same set of goods. Because of this, countries are said to be 

diversified in production. The factor prices are set at the world level and the same for all 

countries.3

 Figure 2 shows a violation of the lens condition. Endowments are not similar 

enough and it is impossible that the same set of goods is made everywhere. 

Consider the violation of the lens condition in Figure 2 in which the country lens does not 

entirely lie in the goods lens. Country 1 has too much capital. Even if the country only 

produced the most capital-intensive products (z1 and z2), it could never employ all its 

resources for a given set of factor prices. Consequently, countries will produce different 

sets of goods at different factor prices in the world. Figure 2 shows that one can obtain a 

violation of the diversification condition even if the range of the capital-labor ratios of 

the goods is wider than that of the endowments. In other words, the absolute size of 

sectors also matters in a setting that has more than two goods and more than two 

countries. 

In the implementation, we adjust Deardorff's condition for factor-augmenting 

technological differences between countries as in Trefler (1993) to relax the all-too-strict 

assumption of identical technology across countries.4

 We express each country’s 

 

3

 Trading countries with immobile factors are said to replicate the integrated world economy (IWE), i.e. the 

hypothetical world equilibrium that would be obtained if all factors were perfectly mobile. See Dixit and 

Norman (1980). 

4

 Introducing factor-augmenting differences is important to reconcile the model with some stylized 

observations. Factor augmenting differences allow for differences in factor prices across countries (see 

Leamer and Levinsohn, 1995), they are consistent with differences in sectoral capital-labor ratios across 

countries. Also, with factor-augmenting differences the capital shares in faster growing countries do not 

necessarily increase more rapidly. 
6

production factors in terms of the US productivity equivalents. (We multiply country c’s 

factors f by πcf , where πcf is the productivity of country c in factor f relative to the US.) 

What is now required is that the surface or lens spanned by the productivity-adjusted 

country vectors lies inside the surface spanned by productivity adjusted goods vectors. 

The equations (1) are for the vectors with which we can draw both lenses (the i's refer to 

sectors, the c's to countries). 

zi = [Li Ki] and vc = [Lc Kc], where 

Ki = Σc πck Kic Kc = Σi πck Kic (1) 

Li = Σc πcl Lic Lc = Σi πcl Lic 

A note of caution is in order. If the productivity-adjusted lens condition holds, countries 

are able to produce the same set of goods (at productivity-equivalent factor prices). One 

should note an important difference between the productivity-adjusted case and the case 

with no factor augmenting productivity adjustments, however. In the latter case, the 

(immobile) factors would have no incentive to move even if they had the ability, because 

factor prices are the same everywhere. With adjustments, however, this absence of 

incentive may no longer be the case. In particular, if factor-augmenting productivity 

differences are not completely inherent to factors, but are, at least in part, due to 

institutional differences, factors in less-paying countries would be eager to move abroad 

in order to earn a higher return. To avoid any confusion, we will talk about integrated 

economies only in the first case (without factor-augmenting productivity differences) and 

use diversified economies (referring to the fact that countries can produce the same set of 

goods) as the more general term in both cases -- that is independent of whether these 

adjustments are made or not. 

Note that one can specifically implement the lens condition for a world with non-traded 

goods. As implied by the work of Helpman and Krugman (1985) and Courant and 

Deardorff (1990), one should in that case only consider the total factors used in the 

production of traded goods to construct the lens condition. This is the route that we take 

in the empirical implementation. 

2. The Empirical Implementation of the Lens Condition 

Deardorff (1994) develops his lens condition for the world economy as a whole. Debaere 

and Demiroglu (1998) show that this condition can be used for any group of countries 

that does not encompass the entire world. The latter clears the way for an empirical 

analysis of the production factors of various groups of countries. In this paper, we study 

Deardorff’s condition for Hong Kong, South Korea, Singapore and their major developed 

country trading partners. 

There is a specific rationale for choosing this particular set of developed countries. As 

argued, diminishing returns to capital accumulation are not just a function of one 

country’s individual capital accumulation. Factor prices are set for the entire group of 

countries. What matters is the factor accumulation among the group of diversified 

economies. Therefore, for an explanation of East Asian growth along the lines of Mankiw 
7

(1995) and Ventura (1997) to make sense, there has to be a set of countries beyond the 

East Asian economies that fulfill two conditions. First, the countries (other than the East 

Asian economies) have to be relatively big and they must have accumulated capital at a 

slower rate than NICs, so that the total capital stock for the entire group (including the 

East Asian countries) grows at a moderate rate. Second, these countries should produce a 

similar set of goods as the East Asian economies. Suppose this were not the case. For 

example, assume that the East Asian countries were specialized among themselves. In 

that case, as they accumulated capital rapidly, the East Asian Tigers would have 

experienced diminishing returns to capital as a group, which would make it difficult for 

them to sustain such high rates of capital accumulation and growth. 

In this study we investigate whether the NICs and their major trading partners (the US, 

the UK, Germany, Japan and Canada) are diversified economies. These countries fulfill 

the conditions mentioned above. The size of the NIC economies is only a fraction of the 

combined size of these developed countries, which constitute more than fifty percent of 

the world economy. Moreover, the trading partners of the NICs did not grow (and 

accumulate capital) at the same pace as the NICs did over the period 1965-1990. (Even 

Japan grew at a slower pace.) Note that there is a degree of discretion as to how we 

delineate the group of countries we choose to analyze. For our purpose, what matters is 

that the group is sufficiently large. It is not necessary that the set of countries includes all 

trading partners. This discretion does not mean, however, that countries are chosen 

arbitrarily. The rich OECD countries are particularly appropriate because their 

endowments have been found to be similar enough to allow them to produce the same set 

of goods (see Debaere and Demiroglu (2003)). Therefore, we could easily extend the 

study to other developed countries such as Belgium or Holland, without any impact. 

Other big countries such as India and China, if their data were available, could also be 

included, yet their inclusion is not necessary once we establish that the NICs and the 

developed country group are diversified economies that are able to produce the same set 

of goods.5

 Moreover, the OECD countries and the NICs are relatively open economies, 

whereas many developing countries are not. Consequently, to make a credible argument 

that hinges on openness, the group of countries must be chosen carefully. 

The aim is to check Deardorff’s condition empirically for the 1965-1990 period. This 

requires data on sector-level capital and labor as well as measures of factor augmenting 

productivity differences between countries in order to obtain the vectors in (1). In this 

section we discuss the sources of the capital and labor data that we use. We also 

introduce human capital measures and factor price data to proxy for factor-augmenting 

technological differences between countries. 

 

5

 Furthermore, from Debaere and Demiroglu (2003), we know that developed and developing countries 

have too dissimilar endowments in order to be able to produce the same set of goods. It is unlikely that the 

lens condition for the NICs and India or China would hold. 
8

2.1. The Capital and Labor Data 

a. UNIDO and Penn World Data: For our group of countries United Nations Industrial 

Statistics (UNIDO) provide at the manufacturing level employment figures and 

investment flows with which we can construct capital stocks. Hence, the relevant country 

endowments (with non-tradable goods) amount to the sum of the factors used in 

manufacturing. We use the UNIDO data to determine the distribution of factor use across 

the industries within a country. To ensure that the magnitudes of the endowments are 

internationally comparable, we link the UNIDO data with the Penn World Tables. 

Specifically, we want to infer the capital-labor ratio of a country's manufacturing sector 

kMc from the strong correlation that is found in the Penn World Tables between kc, a 

country's overall capital per worker ratio, and yc, its real GDP per worker ratio.6 

First, we run the cross-country regression (2) merely for predictive purposes with the 

Penn World Data for 62 countries. 7 The period is 1965-1990. 

ln kct = αc + αt +trendc +β lnyct + εct (2)

 

The high R2 of 0.97 is no surprise, since the regression includes year effects and also 

country specific time trends and fixed effect. Moreover, there is a fairly strong 

correlation between lnkct and lnyct in the Penn data.8

 The β -coefficient takes the value of 

1.1 and is significant at the 95 percent level. All variables are in 1985 international 

prices. 

In order to predict kMc , we plug a country's per worker GDP in manufacturing yMc in 

regression (2). We take yMc from the UN National Accounts and use the Yearbook of

Labour Statistics to adjust the data for differences in hours worked. Table 1 provides yM

and the predicted kM. We report the predicted kMc in levels instead of logs and correct for 

the bias arising from the logarithmic transformation in the usual way.9,10 

 

6

 We presume that the UNIDO employment data can be more easily compared internationally than the 

UNIDO investment data. The methodology is similar to Debaere and Demiroglu (2003). 

7

 The countries are: Switzerland, Luxembourg, Germany, Norway, Finland, Canada, Sweden, Australia, 

Belgium, Canada, Sweden, Australia, Belgium, Japan, France, USA, Austria, Denmark, New Zealand, 

Netherlands, Italy, Spain, Taiwan, Greece, Iceland, Ireland, Israel, United Kingdom, Venezuela, SouthKorea, Ecuador, Iran, Syria, Panama, Mexico, Hong Kong, Colombia, Poland, Portugal, Argentina, Chile, 

Sri Lanka, Peru, Yugoslavia, Turkey, Dominican Republic, Bolivia, Botswana, Thailand, Honduras, 

Mauritius, Zimbabwe, Philippines, Guatemala, Swaziland, Jamaica, Morocco, India, Madagascar, Zambia, 

Ivory Coast, Paraguay, Kenya, Nigeria, Malawi and Sierra Leone. 

8

 If one relates the regression to a Cobb-Douglas production function, one notices that the time trend and 

the country effects allow for technological differences between countries. 

9 exp β = exp (b - var(b)/2), where b is an estimate of the true β. The latter implies the assumption that b, in 

our case lnkc, is distributed normally. 
9

To construct capital stocks for the UNIDO data with the perpetual inventory method, we 

need 15 years of investment flows. To construct the 1977 and 1990 capital stocks, we use 

investment flows from 1976-1990 and 1963-1977. The initial capital in a sector is based 

on the investment flow of the first year of the period the following fashion: I / (d+g),

where I is the investment flow of the first year considered in a sector, d the depreciation 

rate and g the growth of investment. We always assume that the depreciation rate is 13.3 

percent. We deflate a country's investment data into 1985 prices by its investment 

deflator taken from the IMF World Economic Outlook and the UN National Accounts. To 

construct the 1965 stock requires, due to data limitations a somewhat different procedure. 

We take the initial capital stock of 1963 to which we add the real investment flows of 

1963, 1964 and 1965, with the appropriate depreciation. 

 

Once we have the UNIDO capital stocks and the predicted kMc's we construct 

internationally comparable capital stocks as follows. We take the total labor force of the 

UNIDO data, Lc, and multiply it by the predicted capital-labor ratio in manufacturing, 

kMc, to obtain the capital stock of manufacturing in country c, Kc as in the first equation. 

We then use the sectoral distribution of the UNIDO capital stocks (KUNic/KUnc -- i stands

for sector) to determine the sectoral capital stock in a country as in the second equation. 

And finally, the total stock of capital in a particular sector for the set of countries that we 

consider is obtained by adding all sectoral stocks across countries as in the third equation. 

Note that all labor data are adjusted for differences in hours worked versus the United 

States. 

Kc = kMc x Lc

 Kic = KUNic/KUNc x Kc (3) 

Ki= ΣcKic 

In theory, the capital-labor ratio of a sector should be the same in all countries that lie in 

the same cone. It is well known that this is not the case. A country's share in the total 

capital stock of a sector, Kic/Ki, is usually not equal to its share in the total labor 

employed in that sector, Lic/Li, even though they should be the same in theory. There are 

various reasons why (productivity adjusted) sectoral capital to labor ratios can vary. One 

reason, of course, is that countries may lie in different cones. Aggregation also matters. 

We use fairly aggregate sectoral data that may contain subsectors with different factor 

intensities. Whenever countries produce more or less capital intensively in these 

subsectors, the aggregate capital-labor ratios will vary. Finally there is also measurement 

error in the data. We will discuss these concerns in more detail below. 

b. Correcting for factor productivity differences and differences in human capital: It can 

be argued that there are differences in human capital across countries. We choose to 

adjust the data with proxies that should capture such differences. Our human capital 

measures are taken from Hall and Jones (1999). Hall and Jones used Psacharopoulos 

 10 To predict kMc for Singapore we use a slightly different procedure, since kc for Singapore is not part of 

the Penn World Tables. We run (2) with a common trend and dummy for the East Asian Economies and 

then plug in yMc of Singapore. 
10

(1994) cross-country survey evidence on the returns to schooling to construct human 

capital stocks. In their analysis, human capital augmenting labor is given by Hi = e φ(Ei)Li

where φ (Ei) reflects the efficiency of a unit of labor with E years of schooling relative to 

one with no schooling, φ (0) = 0. The derivative φ' (Ei) yields the return to schooling that 

can be estimated in a Mincerian wage regression. Based on Psacharopoulos' survey, Hall 

and Jones assume that φ(Ei) is piecewise linear with a return to education of 13.4 percent 

in the first four years of education, 10.1 for the next four years and 6.8 for the years 

beyond the 8th year. Hall and Jones provide for 1988 a human capital - labor ratios for all 

our countries with which we can upgrade the labor force. Note that, however imperfect 

these measures, the final outcome of our results hardly ever depends on them. The human 

capital corrections can be interpreted as a robustness check. 

To correct for factor-augmenting productivity differences between a country and the US, 

we also rely on relative factor prices. As in Trefler (1993), the wages are drawn from the 

Yearbook of Labour Statistics for the years 1965, 1977 and 1990. They are made 

internationally comparable with the consumption PPP from the Penn World Tables. Most 

data are hourly wages. In case the latter are not available (e.g. with monthly wages), we 

divide the wage number by the hours worked from the same Yearbook of Labour 

Statistics. We follow Trefler (1993) in choosing the 1990 PPP-adjusted investment price 

index from the Penn World Table. The values are reported in Table 1. From a theoretical 

point of view, differences in factor returns are the appropriate factor productivity 

correction when there is factor price equalization. If countries are not lying in the same 

cone, the relative factor returns are likely to overstate technological differences, however. 

While this is a concern, correcting factors in this way is not critical for the final outcome. 

The corrections function more like robustness checks in the absence of other, better 

measures for factor-specific productivity measures of the countries (and time-period) 

involved. 

3. The Empirical Results 

In this section, we discuss our empirical evidence and address the robustness of the 

presented results. We analyze the issues of measurement error and aggregation, and 

check the lens condition for various subgroups. In Debaere and Demiroglu (2003), we 

address other, more conceptual issues that are related to the methodology. There we show 

how the lenses we draw are likely to produce a violation of the lens condition when there 

is no factor price equalization and when countries are not able to produce the same set of 

goods because of too different factor endowments.11

 

Figures 3-5 present our main result. Figure 5 shows the 1990 country and goods lenses 

for Hong Kong, Singapore, South Korea and their main developed country trading 

 

11 In particular, we show how the way we draw the lenses generates a violation if countries produce 

different sets of goods (say, because their endowments are too different). This is true even if one only 

focuses on a subset of countries. Also, if there is factor intensity reversal (making FPE impossible) our 

methodology is likely to generate a violation since it will make the lens condition thinner (and hence more 

prone to violations.) Similarly, averaging factor intensities from countries that produce in different cones 

should lead to a violation of the lens condition when the lenses are drawn the way we propose. 
11

partners (the United States, Japan, Germany, the United Kingdom and Canada). For 1977 

and 1965 we consider the same group minus Hong Kong due to data limitations. The 

figures to the left show Deardorff's lenses without corrections for factor productivity 

differences. These figures are included merely for expositional purposes. They allow us 

to assess the impact of the factor productivity corrections that we introduce.12 The figures 

to the right show the impact of differences in factor-augmenting productivity. We use 

differences in factor returns in all cases but one; in Figure 5c for the year 1990 we make 

use of differences in the return to education instead. The NICs have lower capital-labor 

ratios than the developed countries in the group, their factor of production vectors are 

above the diagonal to the left of the upper right corner (and, under the diagonal to the 

right of the lower left corner). We normalize the total labor force and capital stock for 

this group of countries to one in the graphs, so that each side of the box has unit length. 

In all but one of the cases, the country lens lies inside the goods lens. In other words, no 

violation of the diversification condition is obtained with and without factor productivity 

adjustments. The only violation that occurs is for the lens in 1965 when we do not correct 

for differences in productivity; this violation is easily undone with factor productivity 

adjustments.13

To compare the different results, we introduce as Debaere and Demiroglu (2003) a 

measure that should give an idea of how well the goods lens envelops the country lens, or 

how strong the violation of the lens condition is. This measure is especially useful when a 

(non-) violation is not so easily observed on the graph. The latter is the case for Figure 

3a; one can hardly see that Singapore violates the goods lens. A positive value indicates 

that the lens condition is not violated. When the measure is exactly 1, it implies that the 

country lens is identical to the diagonal. A very small positive number indicates that the 

two lenses are very close to one another. The measure is negative when there is a 

violation. The measure is derived as follows. Through any point x on the diagonal of the 

endowment box, we draw a line that is perpendicular to the diagonal. Call the point at 

which the perpendicular intersects the country lens point and the good lens point, 

respectively c(x) and g(x). Letting d(x,y) represent the distance between any two points x

and y, the measure is defined as 

 min ( , ( ))

( , ( )) x

dxcx

dxgx

1− 











Note that the advantage of the measure is that it works well at the corners of the lenses. 

The measures for the NICs and their trading partners are reported in Table 2. (In addition 

 

12 The uncorrected lenses are the theoretically correct measure to use only in case of factor-augmenting 

productivity differences that are the same across factors. Debaere and Demiroglu (1998) show that the uncorrected and the corrected lenses have the same shape in this case. 

13 Note that the disaggregation also undoes this violation, see below. 
12

to reporting the measure for the entire group of countries, we also report it for the 

subgroup of the trading partners and the NICs separately.) 

In what follows, we provide different ways to assess the robustness of the presented 

results.14 One may wonder whether measurement error would change our basic results. 

Especially the measurement error in our capital data may be a concern. We run Monte 

Carlo simulations to study its effect. For this exercise we use the cross-country variation 

in sectoral capital-labor ratios as a measure of the size of the measurement uncertainty. In 

theory, the capital-labor ratio for a sector must be the same across all countries with 

factor price equalization (in productivity equivalents), which is, as we pointed out, 

clearly not the case. As mentioned before, there are several reasons why these ratios may 

differ across countries: aggregation across different subsectors, a violation in the lens 

condition and measurement error in the data. In order to analyze the impact of 

measurement error, we temporarily make the generous assumption (that does not favor 

our analysis) that all the cross-country variation in sectoral capital-labor ratios is due to 

measurement error. This variation is substantial as one may note from Table 2 under 

Sigma, which is the average standard deviation of the log capital-labor ratio in a sector 

across countries. For example, a Sigma of 0.50 implies that one standard deviation of 

measurement error increases or decreases capital or labor by 35 percent.15

We run a Monte Carlo simulation with 2000 repetitions for each lens. We perturb the 

capital and labor data for a sector in a country by randomly drawn errors, distributed 

normally with the variance mentioned above. We count the number of times those 

generated data trigger a violation of the lens condition, and report the frequency as the 

probability of a violation.16 The results are presented in column two of Table 2. Except 

for the unadjusted lens for 1965, the violation probabilities are very low. 

As mentioned above, all of the variation in sectoral capital-labor ratios across countries is 

attributable to measurement error in that exercise. This most likely overstates the size of 

actual errors because part of that variation is certainly due to aggregation. Each sector 

 

14 We also used the data from the Michigan model that are described in Debaere and Demiroglu (2002) for 

the same set of countries (with Taiwan instead of Singapore) for 1990. Here also no violation was 

obtained. 

 

15 We compute the standard deviation of log capital-labor ratio for each sector across countries, and use the 

average of these standard deviations as the standard deviation of measurement error for all observations. 

The error may arise from either measurement of capital or labor, or both. (Attributing the error to one or 

the other does not make a substantial difference in the result.) For the reported numbers it is assumed that 

capital and labor are equally responsible for the overall measurement error. When the standard deviation of 

log Kic/Lic equals 0.5, the standard deviation of both ln(K) and ln(L) is 0.5/sqrt(2). We also correct for the 

bias that log-normal disturbance generates by dividing the new figures by exp(Var(error)/2). 

16 We precisely mean with “probability of violation” the following. If our capital stock and employment 

data were the true values and if new data were observed based on these values (but after being perturbed by 

errors with the assumed stochastic characteristics), the probability of violation would be the fraction of all 

cases in which the obtained lenses generated a violation. 
13

contains various subsectors with different capital-labor ratios, and variation in the withinsector composition across countries will result in unequal capital-labor. On the other 

hand, our analysis of measurement errors ignores the potential within-country correlation 

of measurement errors. 

Another concern is the aggregation issue mentioned above: Each sector in the UNIDO 

data consists of many subsectors. As we show in Debaere and Demiroglu (2003), sectoral 

aggregation makes the goods lens thinner. (If all sectors were aggregated, the goods lens 

would become the diagonal.) This means that aggregation can cause a spurious violation 

of the lens condition. At the same time, the presence of aggregation reinforces the 

significance of obtained non-violations of the lens condition. If there is a non-violation at 

the aggregate level, there will definitely be a non-violation when the goods lens is drawn 

with more accurate and disaggregated data that make the goods lens wider. To get a sense 

for how disaggregation may affect our results, we provide the results from a 

disaggregation exercise based on firm-level data from COMPUSTAT for the US. 

From COMPUSTAT we take the average within-industry variation in firm-level log 

capital-labor ratios at the 3-digit level.17 We make the extreme assumption that this 

within-industry variation is only due to aggregation. We then investigate how the goods 

lens would look like if there were so much variation in each sector of every country in 

our datasets hidden behind the aggregate numbers. We break down all the factor use 

vectors of each country into 100 equal parts, as if there were 100 firms.18 We perturb the 

capital-labor ratios so that they are distributed randomly around the industry's original 

capital-labor ratio with a cross-firm variance that equals the value from the 

COMPUSTAT data. (We normalize the new firm-level vectors to make sure that they add 

up to a country's original factor use vectors.) We finally re-draw the lenses for the 

hypothetical "disaggregate" goods lens. (See Table 2, the column under “Measure after 

Disaggregation.”) Overall, disaggregation does not have a big impact on our measure. 

The disaggregation effect is strong enough, however, to overturn the only violation that 

we had. 

Conclusion 

In this paper, we link the debate about factor accumulation and growth in East Asia to the 

recent empirical literature in international trade. Mankiw (1995) and Ventura (1997) have 

conjectured that East Asian countries could sustain rapid capital accumulation over long 

periods of time without incurring diminishing returns because factor prices were a 

function of the world factor endowments and were set for the world as a whole. An 

important necessary condition that has to be satisfied for Mankiw and Ventura’s 

conjecture is Deardorff's (1994) lens condition. We investigate whether that condition 

holds, which involves comparing the factor endowments of the NICs and of their main 

 

17 The average standard deviation of log Kif/Lif of firms f within their respective 3-digit industry i is 0.47, 

which is quite substantial. 

18 The result is not sensitive to the magnitude of the number, as long as it is larger than 30. 
14

developed-country trading partners with the sectoral factor use at different points in time. 

To account for productivity differences across countries, we adjust factor endowments 

and factor use data for factor-augmenting productivity differences. We study the years 

1965, 1977 and 1990. We find that Deardorff’s lens condition is satisfied for those three 

years. 

Bibliography 

Courant, Paul and Alan Deardorff (1990), “On the Likelihood of Factor Price 

Equalization with Non-traded Goods,” Review of International Economics, Vol. 31, 

No.3, pp. 589-596. 

Cunat, Alejandro (2000), “Can Trade Equalize Factor Prices?,” mimeo, Harvard 

University. 

Deardorff, Alan (1994), “The Possibility of Factor Price Equalization Revisited,” Journal 

of International Economics, Vol. 36, pp. 167-175. 

Deardorff, Alan and Robert Stern (1990), Computational Analysis of Global Trading 

Arrangements, The University of Michigan Press, Ann Arbor. 

Debaere, Peter and Ufuk Demiroglu (1998), “On the Similarity of Country 

Endowments,” Journal of International Economics, mimeo, University of Michigan. 

Debaere, Peter and Ufuk Demiroglu (2003), “On the Similarity of Country 

Endowments,” Journal of International Economics, Vol. 59, No. 1, pp. 101-136. 

Debaere, Peter (2003), “Does Lumpiness Matter in an Open Economy? Studying 

International Economics with Regional Data,” forthcoming, Journal of International 

Economics. 

Demiroglu, Ufuk and Kwan Koo Yun (1999), “The Lens Condition for Factor Price 

Equalization,”Journal of International Economics, Vol. 47, No. 2, pp. 449-456. 

Dixit, A.K. and V. Norman (1980), The Theory of International Trade, Cambridge 

University Press. 

Hall, R. and C. Jones (1999), “Why do Some Countries Produce So Much More Output 

Per Worker Than Others?”, Quarterly Journal of Economics, Vol. 114, No. 1, pp. 83-

116. 

Helpman, E. and P. Krugman (1985), Market Structure and Foreign Trade, MIT Press, 

Cambridge, MA. 
15

Klenow, P. and Andres Rodriguez-Clare (1997), The Neoclassical Revival in Growth 

Economics: Has It Gone Too Far?” In B. Bernanke and J. Rotemberg (eds.), NBER 

Macroeconomics Annual 1997, MIT Press, Cambridge, MA, pp. 73-103. 

Leamer, E. (1996), “In Search of Stolper-Samuelson Effects on US-wages,” NBER 

Working Paper, No. 5427. 

Leamer, E. and J. Levinsohn (1995), “International Trade Theory: The Evidence” in G. 

Grossman and K. Rogoff, eds., Handbook of International Economics, vol. III, Elsevier, 

New York. 

Mankiw, N. Gregory (1995), “The Growth of Nations,” Brookings Papers on Economic 

Activity, Vol. 25, pp. 275-310. 

Psacharopoulos, George (1994), “Returns to Investment in Education: A Global Update,” 

World Development, Vol. 22, No. 9, pp. 1325-1343. 

Schott, Peter (2001), “One Size Fits All?”, mimeo, Yale University. 

Stiglitz, Joseph (1970), “Factor Price Equalization in a Dynamic Economy,” Journal of 

Political Economy, Vol. 78, No. 3, pp. 456-488. 

Trefler, Daniel (1993), “International Factor Price Differences: Leontief Was Right!”, 

Journal of Political Economy, Vol. 101, pp. 961-987. 

Ventura, Jaume (1997), “Growth and Interdependence,” Quarterly Journal of Economics, 

Vol. 112, No. 1, pp. 57-84. 

Yearbook of Labour Statistics, various years, United Nations.
16

Table 1. Per Worker Capital and Income and the Factor Returns Relative to the US 

 1965 1977 1990 

 yc kMc wc rc yc kMc wc rc yc kMc wc rc

Canada 22,245 7,744 0.80 1.26 28,779 10,300 0.99 1.32 34,380 14,168 1.14 1.05

Germany 17,282 8,774 0.49 0.85 25,406 15,065 0.71 1.16 29,509 19,023 0.96 1.48

Japan 7,333 3,017 0.41 0.88 14,436 8,408 0.70 1.15 22,624 16,246 1.02 1.50

Korea 3,055 1,335 0.09 0.57 7,358 2,622 0.19 0.70 16,022 5,958 0.58 0.91

Hong 

Konga 22,827 3,287 0.64 1.40

Singapore 5,476 886 0.13 1.11 13,764 4,066 0.15 1.20 24,369 6,028 0.50 1.34

UK 16,645 2,970 0.54 0.98 20,654 7,914 0.63 0.94 26,755 10,384 1.16 1.42

US 28,051 6,653 1.00 1.00 31,869 10,857 1.00 1.00 36,771 12,856 1.00 1.00

 

yc

per capita income in country 

c 

kMc capital per worker in manufacturing in country c 

wc wage in country c relative to the US 

rc return to capital in country c relative to the US 

 

a Data for Hong Kong is available for 1990 only 
17

Table 2. The Measure, Probability of Violation, and the Measure after 

Disaggregation 

Country Year Adjustment Measure Probability Measure after Sigma 

Group of violation Disaggregation 

 (%) 

All Unadjusted 0.20 5.55 0.26 0.64 

Countriesa Adjusted 1990 0.26 3.85 0.35 0.56 

Human-cap 0.27 2.60 0.32 0.58 

 Unadjusted 0.19 10.25 0.21 0.71 

 

1977 

Adjusted 0.44 0.30 0.46 0.63 

 Unadjusted -0.04 40.70 0.09 0.94 

 

1965 

Adjusted 0.45 0.45 0.47 0.69 

Asian Unadjusted 0.54 0.00 0.58 0.51 

Countries Adjusted 0.60 0.15 0.62 0.57 

 

1990 

Human-cap 0.36 0.30 0.43 0.56 

 Unadjusted 0.64 0.55 0.68 0.58 

 

1977 

Adjusted 0.19 14.75 0.29 0.74 

 Unadjusted 0.55 1.50 0.64 0.87 

 

1965 

Adjusted 0.72 0.55 0.79 0.80 

Trading Unadjusted 0.59 0.10 0.65 0.46 

Partners Adjusted 0.28 2.45 0.37 0.49 

 

1990 

Human-cap 0.39 1.00 0.46 0.40 

 Unadjusted 0.59 0.00 0.63 0.46 

 

1977 

Adjusted 0.44 0.05 0.47 0.50 

 Unadjusted 0.24 2.40 0.34 0.58 

 

1965 

Adjusted 0.45 0.05 0.48 0.52 

a The countries are the United Kingdom, the United States, Canada, Japan, Germany, Korea, 

Singapore and, only for 1990, Hong Kong. 
18

Figure 2. The goods and country lenses violating the lens condition

Figure 1. The goods and country lenses satisfying Deardorff's (1994) lens condition

Goods lens (z's are sectoral factor use vectors)

Country lens (v's are factor endowment vectors of countries)

Goods lens (z's are sectoral factor use vectors)

Country lens (v's are factor endowment vectors of countries)
19

Figure 3. Lenses in 1965 

 a. Unadjusted Capital and Labor b. Productivity Adjusted Capital and Labor 

0

1

0 1

Goods Lens

Country Lens

0

1

0 1

Goods Lens

Country Lens

Figure 4. Lenses in 1977 

 a. Unadjusted Capital and Labor b. Productivity Adjusted Capital and Labor 

0

1

0 1

Goods Lens

Country Lens

0

1

0 1

Goods Lens

Country Lens
20

Figure 5. Lenses in 1990 

 a. Unadjusted Capital and Labor b. Productivity Adjusted Capital and Labor 

0

1

0 1

Goods Lens

Country Lens

0

1

0 1

Goods Lens

Country Lens

 c. Capital and Human Capital 

0

1

0 1

Goods Lens

Country Lens