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The World Technology Frontier

By FRANCESCO CASELLI AND WILBUR JOHN COLEMAN II*

We study cross-country differences in the aggregate production function whenskilled and unskilled labor are imperfect substitutes. We find that there is a skill biasin cross-country technology differences. Higher-income countries use skilled labormore efficiently than lower-income countries, while they use unskilled labor rela-tively and, possibly, absolutely less efficiently. We also propose a simple explana-tion for our findings: rich countries, which are skilled-labor abundant, choosetechnologies that are best suited to skilled workers; poor countries, which areunskilled-labor abundant, choose technologies more appropriate to unskilled work-ers. We discuss alternative explanations, such as capital-skill complementarity anddifferences in schooling quality. (JEL E13, E23, J31, O14)

An important question in macroeconomics ishow to accurately describe the relationship be-tween aggregate inputs and aggregate output—the aggregate production function—and howthis relationship varies across countries. Cur-rently, most research focuses on the model

(1) y � k��Ah�1 � �,

where y, k, and h are, respectively, output, phys-ical capital, and human capital per worker. Thisaggregate production function is generally al-lowed to vary across countries via the totalfactor productivity (TFP) term A1��. The typ-ical finding is that TFP is higher in high-incomecountries.1

In constructing h, most of the work usingproduction function (1) assumes that workerswith different educational achievement (hence-forth, skill level) are perfect substitutes inproduction. This assumption clashes with con-siderable evidence to the contrary. In particular,the empirical labor literature consistently docu-ments elasticities of substitution betweenskilled and unskilled workers between 1 and 2,i.e., well short of infinity.2 In addition, currentpractice tends to use only data on output andinput quantities. But such variables do not ex-haust the available sources of evidence that maybe relevant in characterizing how the produc-tion function varies across countries: factorprices may also be informative.

In this paper we investigate the implicationsof relaxing the assumption of perfect substitut-ability of different types of labor, as well as ofbringing to bear cross-country evidence on fac-tor prices—particularly skill premia. This isachieved by generalizing (1) to a productionfunction of the form:

(2) y � k��Au Lu �� As Ls ��1 � ��/�,

where Lu is unskilled labor and Ls is skilledlabor. Here, the labor input into productioncan be thought of as a constant-elasticity-of-

* Caselli: Department of Economics, London School ofEconomics, London WC2A, United Kingdom (e-mail:[email protected]); Coleman: Fuqua School of Business,Duke University, Box 90120, Durham, NC 27708 (e-mail:[email protected]). We are grateful to Daron Acemoglu,Ravi Bansal, Chris Foote, Jess Gaspar, Chad Jones, PeteKlenow, Sam Kortum, Aart Kraay, Per Krusell, Greg Man-kiw, Philippe Martin, Pietro Peretto, Richard Rogerson, LeeOhanian, James Schmitz, Nikola Spatafora, Silvana Ten-reyro, Jaume Ventura, and Gianluca Violante for usefuldiscussions and suggestions. We also thank Robert Barroand Jong-Wha-Lee for sharing their data on duration ofschooling. Caselli thanks the University of Chicago Grad-uate School of Business, and Coleman thanks the Center forInternational Business and Economic Research, for finan-cial support.

1 The literature based on (1) is vast. Caselli (2005) pre-sents a partial survey.

2 See, among many others, the surveys of Daniel S.Hamermesh (1993) and Lawrence F. Katz and David H.Autor (1999).

499

substitution (CES) aggregate of unskilled andskilled labor in which the elasticity of substitutionbetween skilled and unskilled labor is 1/(1 � �).The two types of labor are imperfect substitutesas long as � � 1 (the perfect-substitutabilitycase is the special case where � � 1). Theparameters Au and As convert raw quantities ofthe two labor types into efficiency units. Inanalogy to the standard practice of allowing A tovary across countries in (1), we allow Au and Asto vary across countries in (2). And in analogyto the practice of backing out A from (1), wepresent a simple methodology to back out eachcountry’s efficiency pair (Au, As) when the pro-duction function is (2). The methodology usesdata on output, factor inputs, and factor prices.All the results presented in this paper are basedon the CES aggregate of labor types just de-scribed, but we also argue that our results arenot driven by functional form assumptions.

In order to interpret cross-country differencesin Au and As, it is first useful to recall what suchdifferences mean in a cross-time context. WhenAs (Au) increases over time, technical change issaid to be skilled-labor (unskilled-labor) aug-menting: the economy is becoming more effi-cient at using skilled (unskilled) workers. Whenthe ratio As/Au is constant over time, technicalchange is defined as skill neutral. Finally, whenAs/Au increases (decreases) over time, technicalchange is skilled (unskilled) biased, and theeconomy is becoming relatively more efficientat using skilled (unskilled) labor.3 In order toadapt this time-series terminology to a cross-section of countries, we can replace the timeindex with an index of per capita income. Wecan then say that cross-country technology dif-ferences are skilled-labor (unskilled-labor)augmenting if As (Au) tends to be higher in

higher-GDP countries, i.e., if richer countriesuse skilled labor (unskilled labor) more effi-ciently than poor countries. Further, cross-coun-try technology differences are skill neutral if allcountries are characterized by the same ratioAs/Au, and skilled biased (unskilled biased) ifAs/Au tends to be higher (lower) in higher-GDPcountries.

The central finding of this paper is that Asand Au do not move in lockstep across coun-tries. While As rises steeply with y, the relation-ship between Au and y is much weaker. Hence,the ratio As/Au is systematically higher in richcountries, implying skilled-biased cross-country technology differences. This pattern ofskill bias is an extremely robust result acrossdefinitions of “skilled,” choices of calibratedparameter values, and alternative functionalforms. Under our preferred set of assumptions,however, we also find some suggestion of astronger form of bias: not only are As/Au and Ashigher in rich countries, but Au is actually ab-solutely lower in these countries. To distinguishbetween the weaker and the stronger version ofthe result, we refer to the tendency of As/Au tobe higher in rich countries as relative skill bias,and to the tendency of As to be higher and Au tobe lower in rich countries as absolute skill bias.

Our finding of skill bias suggests that cross-country differences in technology are notmerely a matter of some countries having anoverall higher level of technical efficiency thanothers, as assumed in most of the theories thataim to explain cross-country income differ-ences. Rather, these theories may need to beenriched to account for the fact that poor coun-tries seem to use certain factors relatively, andperhaps even absolutely more efficiently thanrich ones. With that goal in mind, while uncov-ering the evidence of skill bias in cross-countrytechnology differences is the main objectiveand contribution of the paper, we also sketch apossible theoretical explanation for our empiri-cal finding.

Our suggested explanation for the cross-country pattern is best motivated by a simpleexample. Suppose that there exist two methodsto produce output. One is with an assembly linewhere unskilled workers, supervised by a fewskilled workers, wield hand tools; the other iswith a computer-controlled and -operated facil-ity that is mainly run by skilled workers and

3 More precisely, technical change is skilled biased if itincreases the marginal productivity of skilled labor relativeto unskilled labor. Under (2), the relative marginal produc-tivity of skilled labor increases in As/Au if � � 0, i.e., if theelasticity of substitution is greater than one, and decreases inAs/Au if � � 0. As we already mentioned, and as we furtherargue below, the range � � 0 is the empirically relevantcase. The definitions of factor augmenting, neutral, andbiased technical change go back to John R. Hicks (1939).Their application to skilled and unskilled labor in the con-text of (2) is discussed, among others, by Autor et al.(1998), Katz and Autor (1999), and Daron Acemoglu(2002).

500 THE AMERICAN ECONOMIC REVIEW JUNE 2006

where unskilled workers play the role of jani-tors. Since the first method makes the most ofunskilled workers, it seems fairly plausiblethat—faced with this choice—firms in un-skilled-labor-abundant countries (which happento be low-GDP countries) will tend to chooseassembly-line production. Since the secondmethod uses skilled workers more efficiently,firms in skilled-labor-abundant countries (i.e.,high-income countries) will tend to choose thecomputerized facility.

To see how this example relates to our em-pirical findings, notice that firms are choosingbetween two possible production functions, sayf1(K, Lu, Ls) and f2(K, Lu, Ls). Suppose that bothf1 and f2 are as in (2), and what makes them twodifferent production functions is that they havedifferent parameters (Au, As). In particular, theassembly-line production function, which usesunskilled labor relatively more efficiently, haslow As/Au, while the IT-based production func-tion, which makes the most of skilled labor, hashigh As/Au. Since poor countries choose theformer and rich countries choose the latter, wetherefore observe skill bias in cross-countrytechnology differences.4 We present a simplemodel of endogenous technology choice thatgeneralizes this example, checks the conditionsunder which this intuition works, and estab-lishes when we should observe relative, andwhen absolute, skill bias. The model also showshow our evidence can be reconciled with theidea that some countries face barriers to tech-nology adoption, and links our results to theliterature on development accounting.

Having advanced one possible explanationfor our empirical findings, we also consideralternative ones. We first discuss alternativefunctional forms of the production function,most notably ones allowing for capital-skillcomplementarity, which is not featured in ourbaseline specification. We argue that our re-sults are not driven by functional-form as-sumptions. We then tackle the possibility thatour results are driven by cross-country differ-ences in the quality of schooling. We arguethat our model of endogenous technology

choice provides a more plausible interpreta-tion of the evidence.

Related Literature.—As is clear from the dis-cussion above, our empirical result of a relativeskill bias in cross-country technology differ-ences has a time-series analog in a large body ofevidence of skilled-bias technical change. Thisliterature is comprehensively reviewed in, e.g.,Katz and Autor (1999). A particularly strongconnection exists with the paper by Katz andKevin M. Murphy (1992), who use equation (3)below to estimate the time trend of As/Au in theUnited States. To back out As/Au, however, wefollow a calibration approach, so that we do notneed to impose structure on its pattern of vari-ation across countries (i.e., we do not need toimpose the analog of a time trend, such as a“GDP trend”). More important, with our meth-odology we go one step further and back out theactual levels of As and Au. This allows us toinvestigate the possibility of absolute skill bias.5

Our proposed model of endogenous technol-ogy choice belongs primarily in the appropriate-technology literature, which goes back at leastto Anthony B. Atkinson and Joseph E. Stiglitz(1969) (who called it “localized technology”),and has recently been further explored theoret-ically by Ishac Diwan and Dani Rodrik (1991),Susanto Basu and David N. Weil (1998), andAcemoglu and Fabrizio Zilibotti (2001). Thekey idea in this literature that is shared by ourmodel is that countries with different factorendowments should choose different technolo-gies. The Acemoglu and Zilibotti paper is par-ticularly closely related in that it focuses onskilled and unskilled labor, as ours, in order tointerpret patterns in cross-country data. How-ever, a central result of their model is that As/Auis constant across countries, which our evidencedirectly contradicts. On the empirical side,supportive evidence for appropriate technologyhas recently been developed by Caselli andColeman (2001a) and Caselli and Daniel J. Wil-son (2004), who found that cross-country diffu-sion of R&D-intensive technologies is stronglyinfluenced by factor endowments.

4 Needless to say, our example is chosen to once againevoke the parallel with the skilled-biased technical-changeliterature. The adoption of IT-based production methods isthe canonical source of increases in As/Au over time.

5 Absolute skill biased in the U.S. time series has re-cently been documented by Marta Ruiz-Arranz (2002). Seealso Caselli and Coleman (2002).

501VOL. 96 NO. 3 CASELLI AND COLEMAN: THE WORLD TECHNOLOGY FRONTIER

Like all appropriate technology models,ours is also related to the literature on inducedinnovation/directed technical change, whichstudies the analogous problem of how factorendowments determine whether technicalchange will be biased toward certain factorsrather than others. Important contributions inthis tradition are Hicks (1932), CharlesKennedy (1964), Paul A. Samuelson (1965,1966), Acemoglu (1998, 2002), and Charles I.Jones (2005). Formally, our model is closestto Samuelson’s. Our argument that the cross-country skill bias we document is driven byendogenous technology choice dictated byskilled-labor endowments parallels Acemo-glu’s (1998) idea that skilled-biased technicalchange in recent years is driven by endoge-nous responses of R&D to changes in therelative supply of skilled labor.6

I. The Skill Bias in Cross-CountryTechnology Differences

When working with equation (1), one typi-cally needs only solve for the unknown A. Ourversion of the exercise is slightly more compli-cated because equation (2) has two unknowns,Au and As. We solve this problem by noting that,if factors of production are paid their marginalproductivity, the skill premium is

(3)ws

wu� �As

Au��Ls

Lu�� 1

.

The idea, then, is that (3) can be used as asecond equation to combine with (2) to solve forthe two unknowns.7 Hence, we back out eachcountry’s technology pair (Au, As) so that mea-sured inputs to production are exactly consistent

with measured output and skill premia.8 In or-der to execute this plan we need data on y, k, Lu,Ls, and ws/wu, as well as calibrated values for �and �.9

A. The Data

Due to limitations in the availability of skill-premium data over time, we focus on a singlecross-section of countries. Data for y and k forthe year 1988 are obtained from Hall and Jones(1999); y is GDP per worker in internationaldollars (i.e., PPP adjusted); and k is an estimateof the real per-worker capital stock, obtainedthrough a version of the perpetual-inventorymethod. The underlying data for both seriescome from Robert Summers and Alan Heston(1991).

Central to our exercise is the construction ofthe labor aggregates Lu and Ls, and the skillpremia ws/wu. We build these variables up fromthree underlying datasets. The first dataset, from

6 As mentioned, the model also makes contact with theliterature on barriers to technology adoption. It is impossi-ble to cite all, or even most, of the contributions in this vein.Some recent examples include Robert S. Barro and XavierSala-i-Martin (1997), Robert E. Hall and Jones (1999), PeterHowitt (2000), Stephen L. Parente and Edward C. Prescott(2000), Jonathan Eaton and Samuel S. Kortum (2001),Douglas Gollin et al. (2001), Philippe Aghion et al. (2005),Caselli and Nicola Gennaioli (2003), and Peter J. Klenowand Andres Rodrıguez-Clare (2006).

7 The closed-form solution is:

Au �y1/�1 � ��k��/�1 � ��

Lu� wu Lu

wu Lu � ws Ls� 1/�

,

As �y1/�1 � ��k��/�1 � ��

Ls� ws Ls

wu Lu � ws Ls� 1/�

.8 It is important for our methodology that relative wages

are informative about relative marginal productivities. Ifdeveloping countries had more egalitarian labor marketinstitutions, the observed skill premium in these countrieswould underestimate the difference between the marginalproductivity of skilled and unskilled labor, potentially lead-ing to a spurious evidence of skill bias. Of course, however,it is well known that—if anything—social and politicalpressures for containing wage dispersion are much moresevere in rich than in poor countries (with the possibleexception of the United States), so, if anything, this type ofmeasurement error biases the results against our finding ofskill bias.

9 Our methodology is to allow Au and As to vary acrosscountries, while � is constant, much as in the skilled-biasedtechnical change literature. Needless to say, there is a cer-tain amount of arbitrariness in the choice of which param-eters vary, and which don’t, across countries. Thisarbitrariness is inescapable: changes in � cannot be sepa-rately identified from changes in As and Au, as shown in theclassic paper by Peter Diamond et al. (1978). It would,however, be possible to fix Au, or As, or Au/As, and let � varyacross countries. One would again be solving two equationsin two unknowns, but one of the unknowns would now be�. We leave the exploration of this alternative exercise forfuture work. See also John Duffy and Chris Papageorgiou(2000).


Barro and Jong-Wha Lee (2001), reports foreach country the share of the labor force intoeach of seven categories of educational achieve-ment: no education, some primary, completedprimary, some secondary, completed secondary,some higher, and completed higher education.The second dataset, from Mark Bils and Kle-now (2000), reports each country’s Minceriancoefficient, i.e., the coefficient on the number ofyears of education in a log-wage regression.The third dataset is an unpublished dataset byBarro and Lee which, for each country, reportsthe duration in years of primary and secondaryschooling. Barro and Lee report attainment dataat five-year intervals, so we pick 1985 to matchthe data on output and capital as close aspossible.

In order to construct Lu and Ls, we must firstdecide which of the seven attainment subgroups toclassify as “unskilled” and which as “skilled.” Forreasons discussed below, our preferred classifi-cation is that everyone who has completed aprimary cycle of schooling is skilled, and thosewho have not are unskilled. Hence, Lu is aweighted sum of the first two subgroups, noeducation and some primary, while Ls is aweighted sum of the other five subgroups, fromprimary completed to completed higher educa-tion and above.

In order to identify the appropriate weight foreach subgroup, we follow the standard conven-tion according to which relative wages equalrelative efficiency units. In particular, for eachof the two aggregates, we choose the subgroupwith least education as the “base” subgroup, andthen weight all other subgroups by their wagesrelative to the base subgroup. Hence, for exam-ple, defining Lu,0 as the share of the labor forcewith no education, Lu,1 as the share of the laborforce with only some primary education, andwu,1 as the ratio of the wage of workers withsome primary education to the wage of workerswith no education, Lu is constructed as Lu,0 wu,1Lu,1. Thus, Lu is measured in “no schoolingequivalents.” Similarly Ls is measured in “pri-mary completed equivalents.”10

In order to estimate the wages of the various

subgroups relative to the base subgroup in eachof the two labor aggregates, we use the Mince-rian coefficients and the duration in years of thevarious schooling levels. From the duration ofprimary and secondary schooling we estimatethe difference in years of schooling betweendifferent subgroups. For example, if secondaryschooling takes five years, the difference inschooling years between workers who havecompleted secondary education (and not gonebeyond) and workers who have completed pri-mary schooling is five. Now the Mincerian co-efficient is the percentage wage gain associatedwith an extra year spent in school, so that if � isthe Mincerian rate of return, and n is the differ-ence in schooling years between two workers,the ratio of their wages is exp(�n).11

After completing the steps above, we have Luand Ls in units of “no education” and “primarycompleted” equivalents. An additional correc-tion is required, however, because in the datathere is some (albeit minimal) cross-countryvariation in the duration of primary schooling.Hence, Ls is not fully comparable across coun-tries, as the base worker may have differentyears of schooling (typically either four or five).In order to make Ls comparable across coun-tries, therefore, we apply an additional rescalingthat converts all workers in Ls into “four-years-of-schooling equivalents.” In particular, if np isthe duration of primary schooling, we multiplyLs in “primary completed equivalents” byexp[�(np � 4)].

The previous paragraphs describe the con-struction of labor aggregates based on a“primary-completed” definition of skilled. Wealso report results based on two alternativethresholds: completed secondary schooling andcompleted college. The construction of the la-bor aggregates and the skill premia for thesealternative thresholds follows the same criteriaas above. Hence, when we report results for the

10 In other words Lu and Ls would sum to 100 (percent)if these two groups were constituted exclusively by workersat the respective “base” level of education (no education andprimary completed, respectively).

11 For subgroups with only partial completion of a cer-tain education level (partial primary, partial secondary, orpartial tertiary), we assume that they have completed ex-actly half of the overall duration of that course of study. Soif primary schooling takes four years, workers with partialprimary schooling have two years more schooling than theirbase group (no education). We do not have cross-countrydata on the duration in years of “higher education andabove,” so we assume that it lasts five years everywhere.


second definition of “skilled,” Ls is in “nine-years-of-schooling equivalents” (since acrosscountries the modal number of years to com-plete secondary education is nine), and when wereport results for the third threshold it is in“fourteen-years-of-schooling equivalents.” Lu isalways in “no-schooling equivalents.”

Clearly there is no obvious way to establish apriori which of the three splits is the most em-pirically relevant. Workers within each of thetwo subaggregates are assumed to be perfectsubstitutes (though of course with different ef-ficiency units), while workers across subaggre-gates are assumed to be imperfect substitutes.Heuristically, differences within groups are“quantitative”—some workers are more pro-ductive than others—but differences betweengroups are “qualitative”: some workers are fun-damentally different. Reality is obviously muchmore nuanced, and drawing an arbitrary line toclassify workers in these two categories is asubjective judgment. Having said that, our ownintuition is that the definition of “skilled” basedon primary schooling completed is the one thatmost closely captures this distinction. This def-inition roughly separates out the completely il-literate and innumerate from those who can atleast read a simple text (e.g., a simple set ofinstructions or a newspaper article) and performsome basic arithmetic operations. We perceivethis difference as qualitative: there are manytasks that no number of completely illiterateagents will be able to perform. Beyond theliteracy threshold, most increases in educationseem to us to have more of an incremental effecton skills, in the sense that most (though admit-tedly not all) production-relevant tasks that re-quire literacy are accessible to all literateworkers—though the less educated will needmore time to perform them. Hence, the assump-tion that all workers who are at least literate areperfect substitutes is possibly more defensiblethan the assumption that the completely illiter-ate are perfectly substitutable with, say, thosewith some high-school education (but not withcollege).

The construction of the skill premia ws/wu isconsistent with the construction of the laboraggregates. Hence, when defining skill as pri-mary completed, the skill premium ws/wu isexp(�4). When skill is defined as secondarycompleted, the skill premium is exp(�9). And

when skill is defined by the completion of col-lege, the skill premium is exp(�14).

There are 52 countries with complete data fory, k, Lu, Ls, and ws/wu (this dataset is reproducedin Appendix Table A.1). Table 1 reports somebasic statistics from the dataset. For Ls, Lu, andws/wu we report only the values correspondingto our preferred definition of skilled (alternativevalues are available on request). Output perworker in the richest country is 19 times higherthan that in the poorest country. The supplies ofskilled and unskilled workers also vary widelyacross countries (the implied ratio between Lsand Lu ranges from 0.32 to 36.11). The skilledwage premium ranges from 10 percent to 300percent. Output is strongly positively correlatedwith both capital and the supply of skilled labor,while it is strongly negatively correlated withthe supply of unskilled labor. As Bils and Kle-now have documented, output is also negativelycorrelated with the skilled wage premium. Notsurprisingly, then, the relative supply of skilledlabor is negatively correlated with the skilledwage premium.

B. Calibration

In order to solve (2) and (3) for As and Au weneed to calibrate two parameters, � and �. Theparameter � measures, of course, the capital

TABLE 1—SUMMARY STATISTICS OF THE DATA

Variable Mean Std. dev. Minimum Maximum

y 13,506 9,717 1,854 35,439k 32,271 28,991 1,218 107,870Ls 89 41 30 229Lu 61 28 6 115ws/wu 1.50 .33 1.10 3.16

Correlation matrix

log(y) log(k) log(Ls) log(Lu) log�ws

wu�

log(y) 1log(k) 0.96 1log(Ls) 0.62 0.66 1log(Lu) �0.74 �0.74 �0.66 1log(ws/wu) �0.38 �0.32 0.06 0.67 1

Notes: y and k are per-worker levels of real GDP andcapital; Ls and Lu are supplies of skilled and unskilled labor;ws/wu is the skilled/unskilled wage premium.


share in GDP. For ease of comparability withprevious results in the literature, we stick to thestandard convention of setting � � 1⁄3 , whichmatches the U.S. historical value for thisvariable.12

The parameter � is related to the elasticity ofsubstitution between skilled and unskilled labor,1/(1 � �). This elasticity is the object of con-siderable focus in the labor-economics litera-ture. After conducting their own review of theevidence, Autor et al. (1998) conclude that theelasticity of substitution is very unlikely to falloutside of the interval between 1 and 2. Hence,we experiment with a variety of values withinthis range.13

In the (1, 2) interval, the most popular esti-mate appears to be that of Katz and Murphy(1992), who set 1/(1 � �) at 1.4. They arrive atthis value by estimating equation (3) on U.S.time-series data between 1963 and 1997, with atime trend to control for changes in As/Au. Ifdeviations of As/Au from the trend are not sys-tematically related to changes in Ls/Lu, thisseems a plausible approach to generating anestimate of �. Accordingly, Katz and Murphy’s1.4 will be our “preferred” value for 1/(1 � �).14

C. The Result

For each choice of labor aggregates and eachchoice of the parameter �, we solve equations(2) and (3) for the two unknowns As and Au.Table 2 reports the coefficients of regressions oflog(As) on log(y) (first entry) and of log(Au) onlog(y) (second entry), implied by differentchoices of � and different placements of theunskilled-skilled boundary. A “*” on the “diff”column indicates that the two slope coefficientsare statistically significantly different from eachother (at the 5-percent level). As is readily seen,in all cases the relation between As and y isstronger than the relation between Au and y, inthe sense that a 1-percent increase in y is typi-cally accompanied by a larger percent increasein As than in Au. This is our relative skill biasresult. In 10 cases (out of 12), the differencebetween coefficients is economically huge. Innine cases it is also statistically significant.

In four cases, Au actually declines with in-come, or we get absolute skill bias. As alreadynoted, one of the cases in which we get absoluteskill bias is our preferred case, where the skillthreshold is literacy (or primary completed) andthe elasticity of substitution is 1.4. Figures 1 and2 show scatterplots against log(y) of log(As)and log(Au), respectively, in this benchmarkcase. The negative association between Au and ydepicted in Figure 2 is statistically significant(P-value 0.012), and becomes more so if wedrop the two seeming outliers, USA andJamaica (P-value 0.007). If we omit the fourrichest and poorest countries, however, the re-

12 Recent cross-country estimates of the capital share byGollin (2002) and Ben S. Bernanke and Refet S. Gurkaynak(2002) actually do show considerable cross-country varia-tion, but this variation is not systematically related to in-come. It is unlikely, therefore, that setting a common valuefor this parameter will bias our results in any particulardirection.

13 An ingenious recent addition to this literature is An-tonio Ciccone and Giovanni Peri (2005), whose estimates of1/(1 � �) are well within the consensus bounds.

14 An important caveat is that the existing estimates of1/(1 � �) are based on datasets where skilled workers areidentified with the college educated, which leads to a slightmismatch between some of our definitions of skilled and the

calibrated parameters. This is why we report results for abroad range of possible elasticities.

TABLE 2—REGRESSION COEFFICIENTS OF As AND Au ON y

1/(1 � �)

Literacy High school College

As Au diff As Au diff As Au diff

1.1 3.45 �5.26 8.71* 4.62 �1.13 5.75* 3.90 0.55 3.35*1.4 1.41 �0.70 2.11* 1.62 0.33 1.29* 1.35 0.75 0.601.7 1.12 �0.05 1.17* 1.19 0.54 0.65* 0.99 0.78 0.212 1.00 0.21 0.79* 1.02 0.62 0.40* 0.84 0.78 0.06

Notes: The As column reports the coefficient of a regression of log(As) on log(y). The Au column reports the coefficient ofa regression of log(Au) on log(y). The “diff” column reports the difference between the two coefficients. The symbol *indicates that this difference is statistically significantly different from zero.


lationship becomes bortherline insignificant (P-value 0.10). Because of this fragility, moreconclusive support for the absolute bias prop-erty will have to await further work.

D. Deconstructing the Result

Before we move to a theoretical explanationfor our finding of skill bias, it is worth digginga little deeper and assess what are the features ofthe data that drive our result. A glance at thetwo equations we are solving, equations (2) and

(3), immediately reveals that for each countrythe relative efficiency As/Au is entirely pinneddown by equation (3). In other words, As/Au ischosen to fit the theoretical relationship be-tween observed relative wages and observedrelative labor supplies. We plot this theoreticalrelationship as the line “Model” in Figure 3 fora fixed choice of As/Au. Clearly the relationshipis negative, as an increase in relative employ-ment of skilled labor leads to a fall in relativemarginal productivities. Changes in As/Au causethe line to shift: for example, a lower As/Auimplies lower skill premia for each value of

FIGURE 1. EFFICIENCY OF SKILLED LABOR

FIGURE 2. EFFICIENCY OF UNSKILLED LABOR


Ls/Lu, as skilled labor becomes relatively lessproductive. Changes in �, i.e., changes in theelasticity of substitution, cause the line to tilt:for example, a higher elasticity of substitutionimplies that relative wages are less sensitive tochanges in Ls/Lu.

Our main result is driven by the fact that—given empirically plausible values of �—therelationship between ws/wu and Ls/Lu in the datais flatter than the theoretical relation, as sum-marized in the figure by the line “Data.” Inorder to reconcile the data with (3), then, lowLs/Lu countries must have lower As/Au, as de-picted by the line “Model’.” Recalling now thatlow Ls/Lu countries are also low-income coun-tries, we have uncovered the sources of ourrelative skill bias result.

This discussion also allows us to under-stand why in Table 2 the skill bias becomesless pronounced when we increase the elas-ticity of substitution. As mentioned, as weincrease the elasticity of substitution the the-oretical relationship between Ls/Lu and ws/wubecomes flatter (the wage premium becomesless responsive to changes in relative em-ployment), and hence closer to the empiricalone. Hence, less of a shift (less of a differencein As/Au) is required to match facts withtheory.

So much for the relative bias. As for theabsolute bias, it should be clear that—onceequation (3) has dictated the value of As/Au—the absolute levels are those necessary to fit theoutput equation, i.e., equation (2). In particular,note that we can rewrite equation (2) as

(4) y � k�Au1 � ��Lu

� � �As

Au��

Ls�� 1 � ��/�

,

which pins down Au for given As/Au. As we justdiscussed, the wage and employment data callfor a positive relation between As/Au and Ls/Lu(and hence y), the more so the lower the elas-ticity of substitution, �. The steeper the profileof As/Au against y, the flatter the profile of Aurequired to match the output data, y. When theAs/Au profile is at its steepest, as in our preferredcase, matching the output data actually requiresa declining profile for Au.15

II. Explaining Our Findings: A Simple Model ofTechnology Choice

The previous subsection explains mechanicallywhat features of the data give rise to the differentpatterns, vis-a-vis income per worker, in the ob-served efficiency units of skilled and unskilledlabor. As such, the previous section does notprovide an economic explanation for these pat-terns. The goal of this section is to sketch onepossible explanation. Our explanation has itsroots in the “appropriate-technology” tradition,which stresses that technology choice dependson factor endowment. To fully account for thepatterns in the data, however, the idea of appro-priate technology needs to be combined with the

15 While on the topic of reparametrizations of (2), wealso note that our production function can be rewritten as:

y � A1 � �k��Lu �� 1 � ��Ls ��1 � ��/�,

where � is what is usually (mis)named a share parameter.Clearly, then, As � (1 � �)A and Au � �A. In principle,therefore, one could read our evidence as indicating that“TFP” (A) is higher in rich countries, but that � is muchhigher in poor countries, and the latter effect swamps theformer, so that �A ends up being no higher in rich countries.It should be clear that this reinterpretation makes no sub-stantive difference. In particular, one would still require thebasic ingredients of the model in the next section to ratio-nalize these findings: the higher A in rich countries wouldhave to be explained by barriers to technology adoption(akin to the B term in the model below), while the higher �in poor countries would continue to call for an appropriate-technology explanation. Similar observations would applyto any other reparametrization of (2).

FIGURE 3. RELATION BETWEEN RELATIVE WAGE AND

RELATIVE EMPLOYMENT


idea of “barriers to technology adoption,” i.e.,with cross-country differences in the overallability of countries to absorb and implementtechnological improvements.

A. The Idea

As mentioned in the introduction, our pro-posed explanation is partly motivated by therecent literature on skilled-biased technicalchange. This literature has documented sub-stantial increases in As/Au over the last fewdecades in the United States and in a fewother industrialized countries. A canonicalexample of skilled-biased technical change isthe transition from an assembly line mannedby unskilled workers, and supervised by a fewskilled workers, to a computer-controlled fa-cility operated by skilled workers, and whereunskilled workers are at best retained as jan-itors (if not entirely displaced). In particular,the widely held view is that the shift fromassembly-line-type methods to computer-based methods is strongly skilled-labor aug-menting, i.e., it leads to a big increase in As.At the same time, since unskilled workers aredemoted to janitorial roles, if not entirelydisplaced (to resurface elsewhere in menialjobs), it is plausible that the same shift leadsto a decline in Au. A decline in Au over timeis documented in Ruiz-Arranz (2002), and isconsistent with the fact that absolute wages inthe lower half of the wage distribution haveactually declined in the United States overmuch of the last few decades.

Now the switch to the computer-controlledplant is of course a choice by the firm, sinceit could have decided to stick to the assemblyline. But the fact that rich-country producersseem largely to have embraced the switch tocomputer-controlled production does notmean that firms in poor countries should nec-essarily make the same choice. In a countrythat is skilled-labor abundant, such as theUnited States, it makes sense to expect firmsto adopt more skilled-biased technologies.But in countries abundant in unskilled labor,we may expect firms to stick to the old tech-nology, and avoid the loss in the efficient useof the abundant factor. In this case, we willobserve the cross-country skill bias we docu-ment: the skilled-abundant country will have

high As, and low Au, relative to the unskilled-abundant country.

Our model generalizes this example simplyby allowing a choice from a large number oftechnologies, instead of just the two of the ex-ample. The basic idea is that in each countryfirms choose from a menu of different produc-tion methods that differ in the use they make ofskilled and unskilled labor. Each of these meth-ods is a different production function. To cap-ture the idea that different production functionsuse different inputs more or less efficiently, weassume that all production functions are of theform (2), but they differ in the parameters Auand As. Hence, we can represent the menu ofpossible choices of production function by a setof possible (Au, As) pairs. Clearly, no countrywill use a production function characterized bya certain pair (Au, As) when another productionfunction exists such that both Au and As arehigher, so only nondominated (Au, As) pairs arerelevant. We call this set of nondominated (Au,As) pairs a “technology frontier.” We illustrate apossible frontier in Figure 4, where the axesmeasure the efficiencies of skilled labor andunskilled labor. The locus labelled A is thetechnology frontier for country A.16

16 Clearly, this reasoning relies on cross-country tech-nology differences as being entirely characterized by differ-

FIGURE 4. TECHNOLOGY CHOICE AND BARRIERS TO

ADOPTION

Notes: A (B) is the technology frontier of country A (B). Aa

and Ba (Ab and Bb) are appropriate choices of technologyfor unskilled-labor (skilled-labor) rich countries.


The profit-maximizing choice of productionfunction depends of course on factor prices. Sincefactor prices depend on factor endowments, firmsin countries with different endowments will oper-ate different production functions. If country A isunskilled-labor abundant, skilled labor will be rel-atively expensive, so we might expect firms in thiscountry to choose a technology such as the onerepresented by point Aa, i.e., a relatively unskilled-complementary technology. If, instead, thiscountry is skill abundant, firms may choose atechnology such as Ab. In terms of the existingliterature, Aa is an appropriate technology for anunskilled-labor-abundant country, while Ab is anappropriate technology for a skilled-labor-abundant country.17

Aside from the example we opened this sub-section with, another way to motivate the ideaof a technology frontier is suggested in a recentpaper by Jones (2004). Jones argues that a newinvention is essentially a draw from the distri-bution of possible (but yet uninvented) pro-duction functions. Suppose that productionfunctions all have the functional form (2), butdiffer in the parameters Au and As. Then a newidea—a newly invented production function—can be represented as a point in (Au, As) space.Hence, technical change is nothing but the pro-gressive “filling up” of the (Au, As) space withnewly available technologies. At any givenpoint in time, firms will choose their productionfunction from this set of feasible possibilities.Clearly, again, no country will choose a domi-nated technology, so only the subset of non-dominated production functions will berelevant. Such a set may look like a downwardsloping curve in (Au, As) space: a technologyfrontier.

An important question is how this appropriate-technology idea can be reconciled with the(more mainstream) view that poor countriesface barriers to technology adoption. This is

important because the evidence on TFP differ-ences is so compelling that one would not wantto abandon the latter in order to embrace theformer. In order to combine our appropriate-technology model with the “barriers” view oftechnology differences, we let the technologyfrontiers be country specific. The idea is thatcountries with more severe barriers face amore limited set of choices. In Figure 4 weillustrate this by drawing a separate frontierfor country B. Since country B’s frontier ishigher than country A’s, country B has fewerbarriers to technology adoption. On its fron-tier, country B will choose Ba if it is un-skilled-labor abundant, and Bb if it is skilled-labor abundant.

The following metaphor may be helpful inthinking about our framework. Suppose that ineach country there is a library, containing blue-prints, or recipes to turn inputs into output. Eachblueprint is associated with a different realiza-tion of the efficiency vector. For example, thereis a blueprint entitled “computer-controlled pro-cessing,” which leads to high skilled-labor effi-ciency and low unskilled-labor efficiency; andone called “assembly line” which is associatedwith an opposite pattern of efficiencies. Thedifferent country-specific frontiers can furtherbe interpreted as library sizes. Some countrieshave just a handful of blueprints that fit on ashort shelf, while some others have roomfuls ofthem.

It should be clear now how combining the“appropriate-technology” and the “barrier-to-adoption” ideas can rationalize our basic find-ings. Consider again the world of Figure4, and imagine that country A is unskilled-labor abundant (and hence uses Aa) and coun-try B is skill-labor abundant (uses Bb). If thefrontiers are relatively close to each other, theappropriate-technology effect will dominate,and we will observe absolutely higher As incountry B (the rich country), and absolutelyhigher Au in country A (the poor country). Inother words we will find absolute skill bias.This is the case depicted in the figure. If,instead, the frontiers are relatively far apart,the barriers effect will dominate, and As andAu will be both higher in the rich country. Ineither case, however, the ratio of As to Au ishigher in the rich country, i.e., we alwayshave relative skill bias.

ences in (Au, As). If we considered additional sources ofheterogeneity in aggregate production functions, it wouldno longer be the case that the technology frontier had to bedownward sloping in (Au, As) space.

17 Also, as mentioned in the introduction, this reasoningis analogous to models of induced innovation/directed tech-nical change, where an increase in the relative supply ofskilled labor induces a skill bias in R&D activities (Ace-moglu, 1998).


We conclude this discussion by noting thatour framework implicitly defines a world tech-nology frontier. This can be thought of as the“highest” frontier, or the frontier of a countrythat faces no barriers. It represents the set ofnondominated (Au, As) combinations dreamedup to date by scientists and management gurus,i.e., it reflects the current state of human tech-nical knowledge. By introducing new technol-ogies that dominate a subset of the pre-existingones on the frontier, technological progressshifts this locus (locally) up.18

B. The Model

The following simple model formalizes theideas set out in the previous subsection andestablishes the conditions under which the intu-ition that countries will choose technologiesthat augment the abundant factor go through.We will see that the key parameter is the elas-ticity of substitution between skilled and un-skilled labor.

We consider an economy with a large numberof competitive firms. Each firm generates outputusing a production function of the form (2),which we reproduce here for convenience asequation (5):

(5) y � k��Au Lu �� As Ls ��1 � ��/�.

Firms hire the two labor types and capital, tak-ing as given the rental rates wu, ws, and r. Thenovel element is that—besides optimallychoosing factor inputs—firms also optimallychoose the production function. In particular,they can choose from a menu of productionfunctions that differ by the parameters Au andAs. The menu of feasible technology choices isgiven by:

(6) �As �� Au �� B,

where �, , and B, all strictly positive, areexogenous parameters. This says that, on theboundary of the feasible menu—on the technol-ogy frontier—changing production function in-volves a trade-off between the efficiency ofunskilled labor, on the one hand, and the effi-ciency of skilled labor, on the other. The pa-rameters and � govern the trade-off; theparameter B determines the “height” of the tech-nology frontier. The particular functional formof equation (6) is dictated by technical conve-nience, but it is rather flexible, and it does get atthe central idea that there are trade-offs associ-ated with technology choice.

In sum, in each country the representativefirm maximizes profits ( y � wuLu � wsLs �rk) with respect to Lu, Ls, k, and Au and As,subject to (5) and (6), the latter with equality.Here r is the firms’ cost of capital. We closethe model by assuming that the economy’sendowments of k, Lu, and Ls are all inelasti-cally supplied.19 An equilibrium is a situationwhere all firms maximize profits and all in-puts are fully employed.

In the Appendix, we prove the following.

PROPOSITION: An equilibrium exists and isunique. If � � �/(1 � �) the equilibrium issymmetric, in the sense that all firms choose thesame technology (Au, As), and the same factorratios, Ls/k and Lu/k. If � � �/(1 � �) the equi-librium is asymmetric, with some firms settingAu � 0 and employing only skilled labor, andsome others setting As � 0 and employing onlyunskilled labor.

The proposition says that condition � ��/(1 � �) is what is needed to rule out devia-tions from the symmetric equilibrium, devia-tions in which a firm chooses a corner witheither As � 0 or Au � 0.20 Its meaning is rather

18 We do not take a stand (because we don’t need to) ontwo questions that are implicit in the foregoing discussion.First, we are agnostic about the determinants of the positionof the world technology frontier in (Au, As) space. Acemo-glu and Zilibotti (2001) and Jones (2004) present two pos-sible approaches to this question. Second, we are alsoagnostic on the sources of country-specific barriers to tech-nology adoption. The literature exploring the possible cul-prits is huge, and growing, and we eschew a laundry listhere. See footnote 6 for some citations.

19 None of the results we care about would change if weassumed that capital freely flows in and out of the countryat some given world cost of capital r.

20 Note that a symmetric equilibrium is always interior,in the sense that it features As � 0, Au � 0. To see this,notice that a firm choosing As � 0 (Au � 0) would alsoalways choose Ls � 0 (Lu � 0). But then there must be someother firm making a different technology choice.


intuitive. When � is low the two inputs are poorsubstitutes, and firms will want to operate pro-duction functions with positive quantities ofboth Ls and Lu. But if one is going to employboth inputs, it better be the case that the respec-tive efficiency units As and Au are strictly pos-itive. As � becomes larger, however, and Ls andLu become better and better substitutes, it makesmore and more sense to use only one of theinputs, and then maximize the efficiency of thatinput. For example a firm may choose to setLu � 0 and then maximize As by also settingAu � 0. The condition says that this will happenwhen � becomes sufficiently large relative to �;� regulates the concavity of the technologyfrontier—a higher � pushes the frontier furtheraway from the origin, i.e., it makes interiortechnology choices more attractive relative tothe corners. Hence, it makes firms more reluc-tant to move to the corners. Notice that thecondition for a symmetric equilibrium is alwayssatisfied if � � 0.

We now assume that the condition for exis-tence of a symmetric equilibrium is satisfied,and examine this equilibrium’s properties. Eachfirm’s first-order conditions include

(7) �Ls

Lu� 1 � �

� �As

Au��ws

wu,

(8) �As

Au��

� �Ls

Lu��

.

The first equation is of course just (3) rear-ranged. It combines the first-order conditionsfor Lu and Ls. It obviously says that the optimalchoice of Ls/Lu is decreasing in ws/wu. For � �0 (good substitutability between skilled laborand unskilled labor) it also says that the greaterthe relative efficiency of Ls, the greater thedesired relative employment of Ls. For � � 0(poor substitutability), Ls/Lu decreases in As/Au,as the firm tries to boost the input of the inef-ficient (and hence effectively scarce) input.

The second equation is the first-order condi-tion with respect to Au. It describes how tech-nology choice depends on the quantities ofinputs employed. For � � 0, the symmetric-equilibrium condition � � �/(1 � �) implies� � � � 0. Hence, equation (8) implies that

firms that employ a lot of skilled labor tend tochoose technologies that augment skilled laborrelative to unskilled labor. Conversely, if � � 0,firms tend to direct technology choice towardthe scarce input.21

Straightforward algebra combining the firsttwo conditions leads to the following solution tothe firm’s problem:

(9)As

Au� �ws

wu��/��

�1 � ��/��

(10)Ls

Lu� �ws

wu� �� /��

�/�� .

Of course the condition � � �/(1 � �) can berewritten as �� (� � �) � 0. Hence, if � �0 firms increase the relative efficiency of therelatively cheap factor, while for � � 0 firmsfocus on increasing the efficiency of the rela-tively expensive factor. Also, irrespective of �,relative demand for skilled labor decreases inthe relative skilled wage.22

It is straightforward now to move from thefirm’s problem to the general equilibrium of theeconomy. Since the equilibrium is symmetric,equation (8) holds for Ls/Lu equal to the econo-my’s endowment. Hence, with � � 0—i.e., wheninputs are relatively good substitutes—countrieswith abundant unskilled labor will choose rela-tively unskilled-labor-augmenting technologies,while with � � 0—or when inputs are poorsubstitutes—countries with abundant unskilled la-bor will try to boost the productivity of skilledlabor. In other words, when inputs are good sub-stitutes, countries make the most of the abundant

21 There is, of course, also a first-order condition withrespect to capital: r � �k��1[(AsLs)

� (AuLu)�](1��)/�;but it plays no role in our subsequent analysis.

22 An additional insight on the properties of the firm’soptimal technology choice is afforded by the equation:

wu Lu � ws Ls�Au

As� �

,

which is a direct implication of combining (7) with (8). Thisrelationship says that, in equilibrium, firms facing a rela-tively large skilled-labor share in output will tend to chooserelatively skill-complementary technologies, or that firmswill try to implement technologies that augment the factorsthat absorb a large share of income.


input, while when they are poor substitutes, it isoptimal to increase the effective supply of thescarce factor. Now recall that empirically the elas-ticity of substitution 1/(1 � �) is greater than 1,implying that � � 0. Hence equation (8)—to-gether with the fact that Lu/Ls is higher in poorcountries—is therefore the rationalization of ourbasic finding or relative skill bias.

Indeed, if all countries shared the same technol-ogy frontier, i.e., if B were the same in all coun-tries, it would follow directly from (8) and (6) thatwe should always find absolute skill bias: Aushould be absolutely higher in poor countries.However, the central message of the barriers-to-adoption literature is surely right: there are imped-iments to the diffusion of technology acrosscountries. As already mentioned, one can nest thisidea in the model by allowing the technologyfrontier in equation (6) to be country-specific. Inparticular, suppose that the height of the frontier,B, varies from country to country. It is straight-forward to show that in this case one gets therelative version of skill bias—it’s equation (8)!—without necessarily implying the absolute version.In particular, if B is much higher in rich countries,the absolute levels of both As and Au will be higherin those countries. This can be seen formally bycombining equations (8) and (6) to get:

As � � B

1 � �/�� Ls /Lu ��/�� 1/�

Au � � B/

1 � �/�� Ls /Lu ��/�� 1/�

.

Recalling that � � � is implied by our conditionfor an interior optimum, this says that As is in-creasing in both B and Ls/Lu, while Au is increas-ing in B and decreasing in Ls/Lu (as long as � �0). We will soon explore some quantitative impli-cations of our simple model. First, however, webriefly consider some alternative explanations.

III. Alternative Explanations

A. Alternative Functional Forms

The advantage of (2) is that it features only oneparameter, �, to capture the elasticity of substitu-

tion between skilled and unskilled labor. More-over, a broad consensus exists in the literature onthe likely magnitude (or at least a reasonably tightrange) of this parameter. Hence, as we have seen,equation (2) is relatively easy to calibrate. Never-theless, we also argue that our basic messagewould go through under alternative specificationsfor the aggregate production function.

Cobb-Douglas.—Since our stated aim wasto explore the implications of aggregate pro-duction functions where skilled and unskilledlabor are allowed to be imperfect substitutes,it would have been possible for us, insteadof working with (2), to study the productionfunction

(11) y � Ak�Lu�Ls

1 � � � �.

In particular, we could have allowed technol-ogy to vary across countries through variationin A and in � (with � always fixed at 0.33, asin our current exercise). Each country’s A and� would again be chosen to simultaneouslyfit the production function (11) and the ex-pression for the skill premium equivalentto (3).

The important observation to make about thispossible alternative exercise is that it is based ona counterfactual choice of the elasticity of sub-stitution between skilled and unskilled labor.Equation (11) imposes this elasticity to be 1. Asdiscussed above, empirical evidence puts it inthe neighborhood of 1.4. Our model (2) is thusconsistent with empirical evidence in a way that(11) is not.

With that caveat, when we perform the exer-cise described above, we find high � and low Ain poor countries, and low � and high A in richcountries.23 This is substantially the same resultthat obtained with our CES specification. No-tice, in particular, that it still involves exactlythe same trade-off between the contributions tooutput of unskilled and skilled labor: higher �gives more weight to unskilled labor and lessto skilled labor. Ultimately, then, one still ends

23 These patterns are very marked for the “primary” and“secondary” definition of skill, while the negative associa-tion between � and y is quite weak in the case of “college.”Note that in the case of college we are particularly confidentthat the elasticity of substitution is greater than 1.


up writing an endogenous technology-choicemodel where unskilled-abundant countrieschoose unskilled-complementary technologies(high �) and skilled-abundant countries chooseskilled-complementary technologies (low �).One cannot use the language of trading offefficiency units of skilled versus unskilled la-bor because by forcing the production functionto be Cobb-Douglas there is no such thing asa separate measure of efficiency units. Butthe economics of what is going on is the sameand there is no substantive difference inmessage.

Capital-Skill Complementarity.—Another al-ternative choice of functional form could havebeen the two-level CES

(12) y � �AuLu�� AsLs�� Akk��/��1/�.

As recently emphasized by Per Krusell et al.(2000), the potential advantage of this func-tional form is to allow for a version of capital-skill complementarity. In particular, if � ��, an increase in the supply of physical capitalincreases the skill premium. Readers ofKrusell et al. may wonder whether our findingthat As/Au is higher in high-income countriesis driven by not having taken into account thiscapital-skill complementarity effect.

We used (12) to perform an exercise simi-lar to that performed in this paper (resultsavailable upon request). In particular, webacked out not only Au and As, but also Ak.This required a third equation, besides theproduction function and the skill premium.We used an international no-arbitrage condi-tion on the return to capital. We experimentedwith a wide range of values for � and for �,finding overwhelming evidence of nonneu-trality and skill bias. For example, when usingthe Krusell et al. estimates of the parameterswe found that As and Ak are higher in richcountries, and Au is higher in poor countries.This is the same result we presented here.Note that the Krusell et al. parameters implycapital-skill complementarity, so it is clearly

not the case that our results are driven by theomission to account for capital-skill comple-mentarity. In sum, even accounting for possiblecapital-skill complementarity we obtain theskill bias result.

B. Quality of Schooling

Another potential concern is that As/Au ispicking up differences in the quality ofschooling across countries. This is best illus-trated by referring to the production functionas rewritten in (4). Since workers classified asunskilled are largely unschooled, it is plausi-ble to assume that they are homogeneousacross countries. Instead, workers included inLs, which is based on the quantity of school-ing, could still be heterogeneous if the qualityof schooling differed systematically acrosscountries. In this case, the term As/Au wouldpick up such quality differences, and the re-sult of a relative skill bias would really bereflecting higher quality of schooling in richcountries.

While we acknowledge this possibility, wethink it implausible that unmeasured school-ing quality explains more than a small frac-tion of the patterns we uncover. Caselli(2005) examines in detail the question ofhow much of the unexplained variation inincome can be attributed to schooling quality.He looks at data on pupil/teacher ratios,educational expenditures, test scores, etc.,and tries to calibrate how variations in thesemeasures can increase the cross-country vari-ance of human capital (and thereby reduce theunexplained component of the variance inGDP). The conclusion is that, to register evena small effect, one needs elasticities of humancapital to these measures of schooling qualitythat are vastly larger than those in the em-pirical labor literature. Admittedly, there maybe other dimensions of schooling quality notcaptured by these measures, but the differencein their impact would have to be enormous.Admittedly, also, Caselli’s calculations arebased on model (1). But given how littleimpact these corrections have on that versionof the production function, it is hard to imag-ine that similar corrections would do much to


flatten the upward sloping pattern of As/Auvis-a-vis y in model (4).

C. Exogenous Technology

In our model we took the skill distribution asgiven, and showed how (and when) high Ls/Lucountries choose high (As/Au) technologies. An-other view may be that some countries haveexogenously high (As/Au)—perhaps for Ricard-ian reasons—and the resulting higher skill pre-mia lead to greater human capital investment,thereby providing an alternative explanation forthe correlation between Ls/Lu and (As/Au). Theproblem with this alternative view is that, asimplied by Table 1, (Ls/Lu) and (ws/wu) arenegatively correlated: countries in which skilledworkers are relatively efficient generally have alow skilled-wage premium. This is clearly in-consistent with the alternative interpretation.Caselli and Coleman (2001b) exploit a similarobservation to interpret the interactions betweenrelative wages and relative labor supplies overthe last century in the United States.

IV. Some Quantitative Implicationsof the Model

If the interpretation of the data laid out in Sec-tion III is correct, we can use the model to extracta number of interesting quantitative implicationson the importance of appropriate technology, andon the size of barriers to technology adoption.How severe a trade-off (as dictated by and �) docountries face in their technology choice? Howlarge are the differences in the distance from theorigin (as captured by B) of different countries’frontiers?

In this section, we first show how one canparameterize our simple model to infer eachcountry’s frontier. That is, the additionalstructure generated by the model allows us togo beyond the simple backing out of Au andAs of the first part of the paper, and to quan-tify the parameters �, , and B with which wecan plot the family of equations (6) that ra-tionalizes each country’s choice. With thecountry-specific frontiers at hand, we thenassess the implications of both counterfactualmovements from appropriate to inappropriatetechnology along these frontiers, and counter-

factual removal of barriers that lift the fron-tiers themselves. We can also revisit theliterature on development accounting.

A. Backing out the Frontiers

Our approach to backing out each country’sfrontier is very simple. The first step is to relaxour assumption that all countries face the sametrade-off parameter , and allow each country’srealization of to be a random variable uncor-related with its endowments. With that assump-tion, we can rewrite (8) in logs as

(13) log �Asi

Aui� �

�

� � �log �Ls

i

Lui�

�1

� � �log i,

where we have now introduced country super-scripts to distinguish country-varying from invari-ant parameters or variables. Then, an estimate of�/(� � �) can be obtained by regressing ln(As

i /Au

i ) on ln(Lsi /Lu

i ). From this estimate (and ourcalibrated value of �), we can back out an estimateof �. Furthermore, each country’s trade-off coef-ficient i can be recovered from the regressionresidual. With i and � at hand, we can then backout each country’s Bi (and hence its technologyfrontier) from equation (6). In performing thisexercise, we use our preferred definition of skilledand our preferred calibration of � and � (and thevalues of As and Au that these choices imply). It isimportant to note that in our approach we do notneed to impose any restriction on the covariancebetween Ls /Lu and B. We do, however, have tomake the admittedly strong assumption that i isuncorrelated with (Ls

i /Lui ).

Our estimate of � is 0.41, with a standard errorof (0.01).24 To illustrate the implications of thisestimate, Figure 5 depicts the country frontiers for(from highest to lowest) Italy, Argentina, and In-dia, as well as every other country’s observed

24 These are backed out from a regression coefficient of2.280 and a regression standard error (0.086). Recall thatour preferred value for 1/(1 � �) is 1.4, which implies � �0.286. The R2 of the regression is 0.93.


technology choice (Au, As). Note that the poorcountry, India, is choosing from a frontier that isconsiderably inside the frontier of a rich countrysuch as Italy, and the middle-income country,Argentina, is somewhere in the middle. This is, ofcourse, consistent with the barriers-to-adoptioncomponent of our framework. Indeed, this obser-vation generalizes: the correlation between the logof the “intercept” parameter B and observed logper-worker income is 0.9. Poor countries are verysystematically on lower technology frontiers.

B. Counterfactual Calculations

With each country’s frontier at hand, we canidentify the World Technology Frontier as theouter envelope of the country-specific frontiers. Inother words, for each Au, we maximize over all ofthe country frontiers to find the maximum possiblevalue of As. As one of the authors is happy toreport, and as is already discernible from Figure5, this envelope coincides entirely with the frontierof Italy. As we have already seen, checking outeach country’s observed position relative to theworld technology frontier reveals that poor coun-tries are typically farther away from the worldfrontier than rich ones.

With the world technology frontier at hand,we can turn to the counterfactual calculations.In order to assess the quantitative importance ofappropriateness, we ask the following question:holding constant the technology frontier, by

how much would a country’s GDP change,should this country operate a technology (a pairof As) different from the appropriate one? Inother words, we assess the output consequencesof movements along a given technology fron-tier. For this experiment, we (counterfactually)assume that all countries have access to theworld technology frontier. We then compute thelevel of GDP associated with an optimal(appropriate) choice of technology on the worldtechnology frontier. Finally, we compare thisnumber with the level of GDP the same countrywould have if forced to use the technology thatis appropriate for the United States. In otherwords, for each country we compare two pointson the world technology frontier: the one cor-responding to that country’s optimal choice, andthe one corresponding to the optimal choice ofthe United States.

The result of this experiment is plotted in Fig-ure 6, where the vertical axis measures the ratio ofU.S.-appropriate-technology GDP to appropriate-technology (on the world frontier) GDP; and thehorizontal axis measures actual per capita output.As can be seen, the adoption of an inappropriatetechnology involves very large output losses—upto 50 percent of GDP—the more so the moredifferent the levels of development (and hencefactor endowments). We interpret this finding asindicating that appropriate-technology consider-ations could play an important role in determiningtechnology differences across countries.

FIGURE 5. TECHNOLOGY FRONTIERS OF ITALY (TOP), ARGENTINA (MIDDLE), AND INDIA (BOTTOM)


Next, we turn to a quantitative assessmentof the “barriers” to technology adoption. Ifthe role of appropriateness could be gleanedby movements along a constant frontier, look-ing at barriers involves some measure of the(economic) distance between different fron-tiers. Figure 7 compares each country’s ob-served level of GDP, with the level of GDPthe country would obtain if it had access tothe world technology frontier. Hence, we nowcompare two points on different technologyfrontiers: the one corresponding to that coun-try’s optimal choice on the world frontier, andthe one corresponding to its optimal choice onits own frontier. Both points are “appropri-ate,” but they are conditional on differentchoice sets. The Figure shows staggering ef-fects from barriers to technology adoption,with output increasing by up to a factor of 6.5if such barriers were removed.

C. Development Accounting

Several authors working with the skill neutralformulation in (1) have performed development-accounting exercises. Development accountingasks what fraction of the cross-country variance ofincome can be explained by observed factors of

production, and how much by the residual “TFP”term. The consensus view is that variation in TFPis roughly as important a source-of-income differ-ences as the combined effects of variation inobserved factor inputs, such as physical and hu-man capital. As an illustration, using (1) and ourdata, we find that variation in A accounts for 40percent of the variation in y.25, 26

In our framework based on (5) and (6), theanalogous to a higher TFP is a higher tech-nology frontier, i.e., a higher value of B. Thehigher the value of B, the higher the overalltechnological prowess of the country, whichis what the TFP term in standard accountingexercises is all about. The analogy betweenTFP and B is borne out quantitatively by ourdata: the correlation between log(B) as esti-

25 To perform this “standard” development accountingexercise, we constructed h from the average number ofyears of education in the working-age population, s, ascollected by Barro and Lee. We followed current practice indevelopment accounting and computed h � exp(0.10s),where 0.10 is roughly the world average Mincerian coeffi-cient on education in wage regressions.

26 Other studies tend to find an even larger role for A. Someof the papers in the development-accounting literature are N.Gregory Mankiw et al. (1992), Robert G. King and RossLevine (1994), Nazrul Islam (1995), Caselli et al. (1996),Klenow and Rodrıguez-Clare (1997), Hall and Jones (1997),Parente and Prescott (2000), and Caselli (2005).

FIGURE 6. RELATIVE OUTPUT FROM USING U.S.-APPROPRIATE TECHNOLOGY


mated in Section IVA and log( A) as esti-mated in the previous paragraph is 0.96!Hence, the same countries that are estimatedto have a low TFP in the skill-neutral ap-proach are estimated to have a low technologyfrontier in our framework. Hence, there isclearly strong support for the consensus viewthat poor countries are generally inside theworld technology frontier.

Indeed, adding appropriate-technologyconsiderations, as we have done, should de-liver an upwardly revised estimate of the roleof “barriers” (relative to factor endowments)in explaining cross-country income differ-ences. The reason is that the appropriatechoice of technology dampens the effects ofdifferences in factor endowments: countrieswith “poor” endowments can “remedy” bytailoring their technology choice to their fac-tor supplies, an option denied to them whenall differences are factor neutral.27

We therefore close the paper by adapting thedevelopment-accounting calculation for ourframework. In particular, we can compute thecross-country variation of per capita income thatwould be predicted by this model if all countrieshad access to the same set of potential technolo-gies. This is analogous to the exercise in the de-velopment-accounting literature, where it is askedhow GDP would vary if there were no differencesin TFP. In our model, if each country couldchoose the point on the world frontier that maxi-mizes its output—given its labor endowments—the standard deviation of the log of per capitaGDP would be 0.41. This compares to a value of0.8 in the data. Hence, differences in inputs ex-plain just about 50 percent of the observed dispar-ity of incomes, while the rest is explained bybarriers to technology adoption—i.e., by the factthat different countries have different frontiers. Aswe have seen above, a model in which technolog-ical choice is factor neutral leads to a roughly60–40 split of the responsibility for the variationof income between factor endowments and differ-ences in technology, so we confirm that marrying“barriers” with “appropriateness” makes theformer look even bigger.

27 Heuristically, in the appropriate-technology frame-work one asks what would income dispersion be if allcountries had pairs of Au and As chosen from the samefrontier, while in the factor-neutral approach one asks whatwould the dispersion of incomes be if all countries used thesame pair of Au and As. If this “TFP pair” is close to theoptimal choice of rich countries, the appropriate-technologyframework will assign less of a role to factor differencesthan the TFP framework; while if the TFP pair is close to

the optimal choice of poor countries, the role of factorendowments will be magnified in the appropriate-technology approach.

FIGURE 7. THE GAIN FROM ACCESSING THE WORLD TECHNOLOGY FRONTIER


V. Conclusions

A realistic generalization of the aggregateproduction function to allow for imperfect sub-stitutability among labor types, combined withcross-country data on skill premia, implies thatpoor countries are relatively—and possibly alsoabsolutely—better at using unskilled labor. Thesimple view that countries just differ in a mul-tiplicative TFP level, and that all that is neededis to transfer to them the technologies observedin rich countries, is overly simplistic. Instead,the data are better rationalized if one allows forthe possibility that at each point in time firmshave access to a whole menu of feasible tech-nologies, that some of these feasible technolo-gies are complementary with skilled labor andothers with unskilled labor, and that firms inpoor countries will choose to make the most oftheir abundant factor, unskilled labor. It turnsout, however, that accepting this appropriate-technology rationalization also implies thatpoor countries choose from a much narrowermenu of feasible technologies than rich coun-tries do, so in no way are our results inconsis-tent with the “barriers” view of technologydifferences.

Indeed, given that we find even larger bar-rier effects than previous contributions in de-velopment accounting, we hope that our paperwill provide further spur to ongoing efforts touncover the nature of these barriers. Givenour evidence that deviations from appropri-ateness entail large output losses, however,such efforts should be mindful that pushingpoor countries to adopt technologies used byrich countries may not be optimal, particu-larly if poor countries’ factor endowments aresignificantly different from those of rich na-tions. Removing barriers should be under-stood as widening poor countries’ choicesof technology, not passively copying richcountries’ production processes.

The framework developed in this paper couldbe extended in a number of directions. First, itwould be interesting to explore the relation be-tween skilled-labor endowments and the locationin space of each country’s technology frontier.The interaction between barriers and skill accu-mulation is a potentially important one, and itcould shed light on the nature of the barriersthemselves. Second, it would be interesting to

bring in a dynamic dimension and try to identifyhow the world and the country-specific frontiershave evolved over time. Again, this would shedfurther light on the nature of barriers. Further-more, it would uncover potential factor-biases intechnological change over time.

Third, one could attempt to unpack the ag-gregate data we used and look at cross-countrybarriers and appropriateness at the industrylevel. A potentially fruitful way to interpret thefrontier we identify is not that countries arefaced with different ways of producing the samegood, but rather that goods may differ in therelative efficiency of different factors. Thiswould provide our model of appropriate tech-nology with roots in the Heckscher-Ohlin tradi-tion. Repeating our estimates at the industrylevel would allow us to distinguish between thetwo interpretations. It would also link our workto the work of Trefler (1993), who has arguedthat country-specific augmentation of factorsupplies (which can be interpreted as countryand factor-specific efficiency levels, just as inour analysis) helps explain jointly the pattern oftrade in factor services and cross-country dif-ferences in factor prices.

APPENDIX: EXISTENCE AND UNIQUENESS OF

SYMMETRIC EQUILIBRIUM

Consider first the optimal choice of inputs fora firm that faces given factor prices ws, wu, andr, and has a given technology, Au, As. Thesolution to the cost-minimization problem canbe shown to give rise to the following costfunction:

Cost�wu , ws , r; y�

� �r��wu

Au��/�� 1�

� �ws

As��/�� 1�� 1�/��1 � ��

y,

where � � 1/[��(1 � �)1��]. Note that this costfunction also accurately describes minimizedcosts when Au or As is zero. Now it is obvious thateven if Au and As are chosen by the firm, thechoice of factors must still be cost-minimizing inthe sense above. Furthermore, since the cost func-tion is linear in output the optimal choice of tech-nology must itself be cost minimizing. Hence, thechoice of an optimal technology is a choice of (Au,


TABLE A.1—DATA

Country Code y k LuP Ls

P �ws

wu�P

LuS Ls

S �ws

wu�S

LuH Ls

H �ws

wu�H

Argentina ARG 14,805 33,151 60 106 1.51 148 29 2.53 192 7 4.23Australia AUS 29,858 88,076 17 129 1.24 85 56 1.63 146 15 2.13Bolivia BOL 4,953 9,076 75 51 1.33 105 20 1.89 125 6 2.70Botswana BWA 3,316 9,885 115 41 2.15 174 5 5.58 190 1 14.50Brazil BRA 11,297 21,227 100 62 1.80 129 22 3.75 159 7 7.83Canada CAN 33,337 82,443 7 134 1.23 83 56 1.60 159 6 2.07Chile CHL 9,323 22,452 73 108 1.62 143 35 2.94 203 8 5.37China CHN 2,124 4,156 65 50 1.22 105 13 1.57 124 1 2.01Colombia COL 9,360 15,434 83 76 1.75 138 22 3.53 180 5 7.10Costa Rica CRI 9,118 16,695 83 77 1.55 126 28 2.67 156 10 4.60Cyprus CYP 15,805 37,046 48 144 1.55 125 54 2.69 211 13 4.66Dom. Rep. DOM 7,314 12,232 85 49 1.46 116 17 2.33 134 6 3.73Ecuador ECU 8,388 21,190 69 107 1.60 126 39 2.89 171 13 5.22El Salvador SLV 5,548 5,617 92 38 1.47 123 10 2.39 136 3 3.89France FRA 28,972 84,929 46 112 1.49 130 33 2.46 183 7 4.06Ghana GHA 1,854 1,218 84 35 1.40 123 5 2.15 130 1 3.29Greece GRC 16,607 42,802 27 85 1.11 88 26 1.28 109 9 1.46Guatemala GTM 7,431 7,773 98 43 1.81 133 11 3.82 151 3 8.05Honduras HND 4,597 6,175 102 75 2.02 152 21 4.87 217 3 11.75Hong Kong HKG 21,532 29,128 38 99 1.28 97 39 1.73 151 6 2.35Hungary HUN 10,869 33,857 37 89 1.19 111 22 1.47 128 8 1.83India IND 3,046 3,775 79 34 1.22 102 12 1.55 115 3 1.99Indonesia IDN 3,914 8,084 85 72 1.97 177 11 4.62 222 0 10.80Israel ISR 23,362 51,768 37 119 1.29 87 58 1.78 156 14 2.45Italy ITA 29,552 82,318 43 66 1.10 91 20 1.23 110 4 1.38Jamaica JAM 4,596 12,831 96 185 3.16 294 29 13.36 490 3 56.37Japan JPN 20,807 64,181 28 119 1.30 106 43 1.79 152 12 2.48Kenya KEN 1,998 2,748 109 34 1.93 159 4 4.38 166 1 9.93Malaysia MYS 9,472 23,543 59 82 1.46 127 22 2.33 169 2 3.73Mexico MEX 15,330 28,449 81 92 1.76 144 28 3.56 196 7 7.20Netherlands NLD 28,550 79,069 24 128 1.34 119 40 1.95 169 10 2.82Nicaragua NIC 4,453 8,762 91 40 1.47 114 15 2.39 126 6 3.89Pakistan PAK 4,552 3,793 85 30 1.47 107 9 2.39 120 2 3.89Panama PAN 7,898 19,794 63 139 1.73 142 47 3.43 227 11 6.81Paraguay PRY 6,015 9,689 88 68 1.58 141 19 2.82 170 5 5.00Peru PER 8,387 18,075 65 75 1.38 106 30 2.07 139 10 3.11Philippines PHL 4,473 8,042 46 97 1.38 103 37 2.05 141 13 3.06Poland POL 8,439 33,949 19 98 1.12 98 24 1.30 119 7 1.50Portugal PRT 12,960 29,437 64 59 1.49 118 14 2.46 142 3 4.06S. Korea KOR 13,483 24,651 28 159 1.53 114 61 2.60 219 12 4.41Singapore SGP 21,470 56,218 71 89 1.71 150 22 3.34 196 4 6.53Sri Lanka LKA 5,476 5,919 51 76 1.32 117 18 1.88 149 1 2.66Sweden SWE 27,886 72,777 28 133 1.31 78 67 1.83 170 13 2.55Switzerland CHE 30,965 107,870 22 142 1.37 87 64 2.04 192 8 3.02Taiwan OAN 15,787 26,240 36 97 1.27 95 37 1.72 143 7 2.32Thailand THA 5,558 7,477 87 65 1.52 143 16 2.55 152 8 4.29Tunisia TUN 7,696 10,823 82 36 1.38 104 14 2.05 122 3 3.06UK GBR 25,775 50,409 36 115 1.31 121 36 1.84 163 9 2.59USA USA 35,439 87,330 6 229 1.48 65 116 2.42 237 27 3.94Uruguay URY 12,036 23,398 62 97 1.47 139 28 2.39 176 7 3.89Venezuela VEN 17,529 42,713 69 71 1.40 111 27 2.13 142 8 3.24W. Germany DEU 28,992 89,368 41 94 1.22 122 22 1.55 145 5 1.99

Note: Superscripts “P” (“S”, “H”) identify variables computed under the “primary completed” (“secondary completed,”“college completed”) definition of skill.


As) on a country’s technology frontier that mini-mizes this cost function.

Make the change of variables Du � (Au)� andDs � (As)

�. To simplify the notation, also write� � �/[�(1 � �)]. We can then write the firm’sproblem as

MinDs ,Du�Cost�wu , ws , r; y�

� �r��wu��/�� 1��Du��

� �ws��/�� 1��Ds�

�� 1�/��1 � ��y�.

Subject to: Ds � Du � B.

Consider first the case where � � 1, or � ��/(1 � �). It is clear in this case that the firm’sproblem has a unique interior solution. Hence, ifthis condition is satisfied, all firms choose thesame interior technology. The particular technol-ogy choice depends on factor prices. From thefirst-order conditions for an interior optimum, wehave (10)—which shows that if firms are in asymmetric equilibrium, there is a unique equilib-rium wage ratio for given Ls/Lu. Hence, we haveexistence and uniqueness in the � � 1 case.

For the � � 1 case, it is immediate that the firmcost-minimization problem requires firms to be ata corner, with either As � Ls � 0 or Au � Lu � 0.The zero-profit condition for firms choosing theformer strategy is r�(wu/(B/)1/�)1�� 1, wherethe left-side term is the unit production cost andthe right side is the unit revenue. Similarly, forfirms choosing the latter strategy we have r�(ws/B1/�)1�� 1. Finally, the marginal product ofcapital must equal the interest rate, or �k��1(Ls/B1/�)1�� r. These three conditions identifyunique equilibrium values of wu, ws, and r. Notethat at these factor prices, firms are indifferentbetween hiring only skilled workers or onlyunskilled workers. This indifference guaranteesfull employment.

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