Hall and Jones - Why Do Some Produce So Much More Output Per Worker Than Others-1

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Why Do Some Countries Produce So Much More Output Per Worker ThanOthers?

Robert E. Hall; Charles I. Jones

The Quarterly Journal of Economics, Vol. 114, No. 1. (Feb., 1999), pp. 83-116.Stable URL:

http://links.jstor.org/sici?sici=0033-5533%28199902%29114%3A1%3C83%3AWDSCPS%3E2.0.CO%3B2-S

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QUARTERLY JOURNAL OF ECONOMICS

The breakdown suggested by the aggregate production func-tion is just the first step in understanding differences in outputper worker. Findings in the production function framework raisedeeper questions such as the following: why do some countriesinvest more than others in physical and human capital? And whyare some countries so much more productive than others? Theseare the questions that this paper tackles. When aggregatedthrough the production function, the answers to these questionsadd up to explain the differences in output per worker acrosscountries.

Our hypothesis is that differences in capital accumulation,productivity, and therefore output per worker are fundamentallyrelated to differences in social infrastructure across countries. Bysocial infrastructure we mean the institutions and governmentpolicies that determine the economic environment within whichindividuals accumulate skills, and firms accumulate capital andproduce output. A social infrastructure favorable to high levels ofoutput per worker provides an environment that supports produc-tive activities and encourages capital accumulation, skill acquisi-tion, invention, and technology transfer. Such a social infrastruc-

ture gets the prices right so that, in the language of North andThomas [19731, individuals capture the social returns to theiractions as private returns.

Social institutions to protect the output of individual produc-tive units from diversion are an essential component of a socialinfrastructure favorable to high levels of output per worker.Thievery, squatting, and Mafia protection are examples of diver-sion undertaken by private agents. Paradoxically, while thegovernment is potentially the most efficient provider of socialinfrastructure that protects against diversion, it is also in practicea primary agent of diversion throughout the world. Expropriation,confiscatory taxation, and corruption are examples of public

diversion. Regulations and laws may protect against diversion,but they all too often constitute the chief vehicle of diversion in aneconomy.

Across 127 countries we find a powerful and close associationbetween output per worker and measures of social infrastructure.Countries with long-standing policies favorable to productiveactivities-rather than diversion-produce much more output perworker. For example, our analysis suggests that the observeddifference in social infrastructure between Niger and the United


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variation in long-run economic performance by studying directlythe cross-section relation in levels2

The purpose of this paper is to call attention to the strongrelation between social infrastructure and output per worker.Countries with corrupt government officials, severe impedimentsto trade, poor contract enforcement, and government interferencein production will be unable to achieve levels of output per workeranywhere near the norms of western Europe, northern America,and eastern Asia. Our contribution is to show, quantitatively, howimportant these effects are.

We can summarize our analysis of the determinants ofdifferences in economic performance among countries as

Output per Worker

(Inputs, Productivity)

Social Infrastructure.

This framework serves several purposes. First, it allows us todistinguish between the proximate causes of economic success-capital accumulation and productivity-and the more fundamen-tal determinant. Second, the framework clarifies the contributionof our work. We concentrate on the relation between socialinfrastructure and differences in economic performance. Theproduction function-productivity analysis allows us to trace thisrelation through capital accumulation and productivity.

We are conscious that feedback may occur from output perworker back to social infrastructure. For example, it may be thatpoor countries lack the resources to build effective social infrastruc-tures. We control for this feedback by using the geographical and

linguistic characteristics of an economy as instrumental vari-ables. We view these characteristics as measures of the extent towhich an economy is influenced by western Europe, the firstregion of the world to implement broadly a social infrastructurefavorable to production. Controlling for endogeneity, we still find

2. Chari, Kehoe, and McGrattan [I9971 also analyze levels of economicperformance. In cross-country growth regressions that include the initial levelofincome and emphasize the transition dynamics interpretation, one can map thegrowth regression coefficients into effects on the long-run level of income. However,we know of only one attempt to do this mapping, the prepublication version of

Sachs and Warner [19971.


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additional year of schooling raises a worker's efficiency proportion-ally by +'(EL3Note that if +(E) = 0 for all E this is a standardproduction function with undifferentiated labor.

With data on output, capital, and schooling, and knowledge ofa and c$ (.), one can calculate the level of productivity directly fromthe production function. It turns out to be convenient to rewritethe production function in terms of output per worker, y = YIL, as

where h =HIL is human capital per worker.

This equation allows us to decompose differences in outputper worker across countries into differences in the capital-outputratio, differences in educational attainment, and differences inproductivity. We follow David [19771; Mankiw, Romer, and Weil[19921; and Klenow and Rodriguez [I9971 in writing the decompo-sition in terms of the capital-output ratio rather than the capital-labor ratio, for two reasons. First, along a balanced growth path,the capital-output ratio is proportional to the investment rate, sothat this form of the decomposition also has a natural interpreta-tion. Second, consider a country that experiences an exogenous

increase in productivity, holding its investment rate constant.Over time, the country's capital-labor ratio will rise as a result ofthe increase in productivity. Therefore, some of the increase inoutput that is fundamentally due to the increase in productivitywould be attributed to capital accumulation in a framework basedon the capital-labor ratio.

To measure productivity and decompose differences in outputper worker into differences in capital intensity, human capital perworker, and productivity, we use data on output, labor input,average educational attainment, and physical capital for the year1988.

Our basic measure of economic performance is the level ofoutput per worker. National income and product account data andlabor force data are taken from the Penn World Tables Mark 5.6revision of Summers and Heston [19911. We do not have data onhours per worker for most countries, so we use the number ofworkers instead of hours to measure labor input. Our calculationsof productivity also incorporate a correction for natural resources

3. Bils and Klenow [I9961 suggest that this is the appropriate way toincorporate years of schooling into an aggregate production function.


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ITA

NER

MRT

Coeff = 0.600

TGO

CHN

BRlir

StdErr= 0.028

COM

I I1000

I I2000 4000 8000 16000Output per Worker, 1988 (in 1985 U.S. Dollars)I32000IFIGUREIProductivity and Output per Worker

in productivity are very similar to differences in output perworker; the correlation between the two series (in logs) is 0.89.Apart from Puerto Rice,$ the countries with the highest levels ofproductivity are Italy, France, Hong Kong, Spain, and Luxem-

bourg. Those with the lowest levels are Zambia, Comoros, BurkinaFaso, Malawi, and China. U. S, productivity ranks thirteenth outof 127 countries.

Table I decomposes output per worker in each country intothe three multiplicative terms in equation (3): the contribution

8. Puerto Rico deserves special mention as it is-by far-the most productivecountry according to our calculation. Its output per worker is similar to that in theUnited Kingdom but measured inputs are much lower. The result is a high level ofproductivity. Baumol and Wolff [I9961 comment on Puerto Rico's extraordinary

recent growth in output per worker. In addition, there is good reason to believethat Puerto Rico's national income accounts overstate output. Many U. S. firmshave located production facilities there because of low tax rates. To take maximumadvantage of those low rates and to avoid higher U. S. rates, they may reportexaggerated internal transfer prices when the products are moved within the firmfrom Puerto Rico back to the United States. When these exaggerated nonmarketprices are used in the Puerto Rican output calculations, they result in an


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overstatement of real output.


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OUTPUT PER WORKER ACROSS COUNTRIES

TABLE IPRODUCTMTY RATIOS

CALCULATIONS: TO U. S. VALUES

Contribution from

Country YIL (KIy)d[~-d HIL A

United States

CanadaItalyWest GermanyFranceUnited Kingdom

Hong KongSingaporeJapan

MexicoArgentina

U.S.S.R.IndiaChinaKenyaZaire

Average, 127 countries:Standard deviation:Correlation with YIL (logs)Correlation with A (logs)

The elements of this table are the empirical counterparts to the components of equation (31, all measuredas ratios to the U. S. values. That is, the first column of data is the productof the other three columns.

from physical capital intensity, the contribution from humancapital per worker, and the contribution from productivity. It isimportant to note that this productivity level is calculated as aresidual, just as in the growth accounting literature.

To make the comparisons easier, all terms are expressed asratios to U. S. value^.^ For example, according to this table, output

per worker in Canada is about 94 percent of that in the UnitedStates. Canada has about the same capital intensity as the UnitedStates, but only 91 percent of U. S. human capital per worker.Differences in inputs explain lower Canadian output per worker,so Canadian productivity is about the same as U. S. productivity.Other OECD economies such as the United Kingdom also have

9. A complete set of results is available from the web site listed in theacknowledgment footnote.


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productivity levels close to U. S. productivity. Italy and France areslightly higher; Germany is slightly lower.1

Consistent with conventional wisdom, the U.S.S.R. has ex-tremely high capital intensity and relatively high human capitalbut a rather low productivity level. For the developing countries inthe table, differences in productivity are the most important factorin explaining differences in output per worker. For example,Chinese output per worker is about 6 percent of that in the UnitedStates, and the bulk of this difference is due to lower productivity:without the difference in productivity, Chinese output per workerwould be more than 50 percent of U. S, output per worker.

The bottom half of Table I reports the average and standarddeviation of the contribution of inputs and productivity to differ-ences in output per worker. According to either statistic, differ-ences in productivity across countries are substantial. A simplecalculation emphasizes this point. Output per worker in the fivecountries in 1988 with the highest levels of output per worker was

31.7 times higher than output per worker in the five lowest

countries (based on a geometric average). Relatively little of thisdifference was due to physical and human capital: differences incapital intensity and human capital per worker contributedfactors of 1.8 and 2.2, respectively, to the difference in output perworker. Productivity, however, contributed a factor of 8.3 to thisdifference: with no differences in productivity, output per workerin the five richest countries would have been only about four timeslarger than in the five poorest countries. In this sense, differencesin physical capital and educational attainment explain only amodest amount of the difference in output per worker acrosscountries.The reason for the lesser importance of capital accumulationis that most of the variation in capital-output ratios arises from

variation in investment rates. Average investment rates in thefive richest countries are only 2.9 times larger than averageinvestment rates in the five poorest countries. Moreover, thisdifference gets raised to the power a/(l -a)which for a neoclassi-cal production function with a = 1/3 is only %--so it is the squareroot of the difference in investment rates that matters for outputper worker. Similarly, average educational attainment in the fiverichest countries is about 8.1 years greater than average educa-

10. Hours per worker are higher in the United States than in France andItaly, making their productivity levels more surprising.


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tional attainment in the five poorest countries, and this differencealso gets reduced when converted into an effect on output: eachyear of schooling contributes only something like 10 percent (theMincerian return to schooling) to differences in output per worker.Given the relatively small variation in inputs across countries andthe small elasticities implied by neoclassical assumptions, it ishard to escape the conclusion that differences in productivity -theresidual-play a key role in generating the wide variation inoutput per worker across countries.

B. DiscussionOur earlier paper [Hall and Jones 19961 compared resultsbased on the Cobb-Douglas formulation with alternative resultsbased on the application of Solow's method with a spatial ratherthan temporal ordering of observations.ll In this latter approach,the production function is not restricted to Cobb-Doublas, andfactor shares are allowed to differ across countries. The resultswere very similar. We do not think that the simple Cobb-Douglasapproach introduces any important biases into any of the resultspresented in this paper.

Our calculation of productivity across countries is related to acalculation performed by Mankiw, Romer, and Weil [1992]. Twoimportant differences are worth noting. First, they estimate theelasticities of the production function econometrically. Theiridentifying assumption is that differences in productivity acrosscountries are uncorrelated with physical and human capitalaccumulation. This assumption seems questionable, as countriesthat provide incentives for high rates of physical and humancapital accumulation are likely to be those that use their inputsproductively, particularly if our hypothesis that social infrastruc-ture influences all three components has any merit. Our empiricalresults also call this identifying assumption into question since,as shown in Table I, our measure of productivity is highly

correlated with human capital accumulation and moderately

11. More specifically, assume that the index for observations in a standardgrowth accounting framework with Y = &'(KJf) refers to countries rather thantime. The standard accounting formula still applies: the difference in outputbetween two countries is equal to a weighted average of the differences in inputsplus the difference in productivity, where the weights are the factor shares. AsinSolow [19571, the weights will generally vary across observations. The onlysubtlety in this calculation is that time has a natural order, whereas countriesdonot. In our calculations, we found that the productivity results were robust to

different orderings (in order of output per worker or of total factor input, forexample).


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correlated with the capital-output ratio. Second, they give littleemphasis to differences in productivity, which are econometricresiduals in their framework; they emphasize the explanatorypower of differences in factor inputs for differences in outputacross countries. In contrast, we emphasize our finding of substan-tial differences in productivity levels across countries. Our produc-tivity differences are larger in part because of our more standardtreatment of human capital and in part because we do not imposeorthogonality between productivity and the other factorsof production.12

Finally, a question arises as to why we find a large Solowresidual in levels. What do the measured differences in productiv-ity across countries actually reflect? First, from an accountingstandpoint, differences in physical capital intensity and differ-ences in educational attainment explain only a small fraction ofthe differences in output per worker across countries. One interpre-tation of this result is that we must turn to other differences, suchas the quality of human capital, on-the-job training, or vintageeffects. That is, we could add to the inputs included in theproduction function. A second and complementary interpretation

of the result suggests that a theory of productivity differences isneeded. Differences in technologies may be important: for ex-ample, Parente and Prescott [I9961 construct a theory in whichinsiders may prevent new technologies from being adopted. Inaddition, in economies with social infrastructures not conducive toefficient production, some resources may be used to protectagainst diversion rather than to produce output: capital couldconsist of security systems and fences rather than factories andmachinery. Accounting for the differences in productivity acrosscountries is a promising area of future research.

At an accounting level, differences in output per worker aredue to differences in physical and human capital per worker and

12. In helping us to think about the differences, David Romer suggested thatthe treatment of human capital in MRW implies that human capital per workervaries by a factor of more than 1200 in their sample, which may be much higherthan is reasonable. Klenow and Rodriguez [I9971 explore the differences betweenthese two approaches in more detail. Extending the MRW analysis, Islam [I9951reports large differences in productivity levels, but his results, led by econometricestimates, neglect differences in human capital in computing the levels.


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to differences in productivity. But why do capital and productivitydiffer so much across countries? The central hypothesis of thispaper is that the primary, fundamental determinant of a country'slong-run economic performance is its social infrastructure. Bysocial infrastructure we mean the institutions and governmentpolicies that provide the incentives for individuals and firms in aneconomy. Those incentives can encourage productive activitiessuch as the accumulation of skills or the development of newgoods and production techniques, or those incentives can encour-age predatory behavior such as rent-seeking, corruption, andtheft.

Productive activities are vulnerable to predation. If a farmcannot be protected from theft, then thievery will be an attractivealternative to farming. A fraction of the labor force will beemployed as thieves, making no contribution to output. Farmerswill spend more of their time protecting their farms from thievesand consequently grow fewer crops per hour of effort.

Social control of diversion has two benefits. First, in a societyfree of diversion, productive units are rewarded by the full

amount of their production: where there is diversion, on the otherhand, it acts like a tax on output. Second, where social control ofdiversion is effective, individual units do not need to investresources in avoiding diversion. In many cases, social control ismuch cheaper than private avoidance. Where there is no effectivesocial control of burglary, for example, property owners must hireguards and put up fences. Social control of burglary involves twoelements. First is the teaching that stealing is wrong. Second isthe threat of punishment. The threat itself is free: the onlyresources required are those needed to make the threat credible.The value of social infrastructure goes far beyond the notion thatcollective action can take advantage of returns to scale in avoid-ance. It is not that the city can put up fences more cheaply than

can individuals: in a city run well, no fences are needed at all.

Social action-typically through the government-is a primedeterminant of output per worker in almost any view. Theliterature in this area is far too voluminous to summarizeadequately here. Important contributions are Olson [1965, 19821,Baumol [19901, North [19901, Greif and Kandel [19951, andWeingast [19951.

A number of authors have developed theoretical models of


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equilibrium when protection against predation is incomplete.l3Workers choose between production and diversion. There may bemore than one equilibrium: for example, there may be a poorequilibrium where production pays little because diversion is socommon, and diversion has a high payoff because enforcement isineffective when diversion is common. There is also a goodequilibrium with little diversion, because production has a highpayoff and the high probability of punishment deters almost alldiversion. Rapaczynski [I9871 gives IIobbes credit for originatingthis idea. Even if there is only a single equilibrium in thesemodels, it may be highly sensitive to its determinants because ofnear-indeterminacy.

Thus, the suppression of diversion is a central element of afavorable social infrastructure. The government enters the pic-ture in two ways. First, the suppression of diversion appears to bemost efficient if it is carried out collectively, so the government isthe natural instrument of antidiversion efforts. Second, the powerto make and enforce rules makes the government itself a veryeffective agent of diversion. A government supports productiveactivity by deterring private diversion and by refraining from

diverting itself. Of course, governments need revenue in order tocarry out deterrence, which requires at least a little diversionthrough taxation.

Diversion takes the form of rent-seeking in countries of all

types, and is probably the main form of diversion in moreadvanced economies [Krueger 19741. Potentially productive indi-viduals spend their efforts influencing the government. At highlevels, they lobby legislatures and agencies to provide benefits totheir clients. At lower levels, they spend time and resourcesseeking government employment. They use litigation to extractvalue from private business. They take advantage of ambiguities

in property rights.

Successful economies limit the scope of rent-seeking. Consti-tutional provisions restricting government intervention, such asthe provisions in the U. S. Constitution prohibiting interferencewith interstate commerce, reduce opportunities for rent-seeking.A good social infrastructure will plug as many holes as it canwhere otherwise people could spend time bettering themselveseconomically by methods other than production. In addition to its

13. See, for example, Murphy, Shleifer, and Vishny [19911; Acemoglu [19951;Schrag and Scotchmer [1993]; Ljungqist and Sargent [19951; and Grossman andKim [1996].


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direct effects on production, a good social infrastructure may haveimportant indirect effects by encouraging the adoption of newideas and new technologies as they are invented throughout theworld.

IV. ESTIMATINGTHE EFFECTOF SOCIALINFRASTRUCTURETwo important preliminary issues are the measurement ofsocial infrastructure and the econometric identification of ourmodel.

A. MeasurementThe ideal measure of social infrastructure would quantify thewedge between the private return to productive activities and thesocial return to such activities. A good social infrastructureensures that these returns are kept closely in line across the rangeof activities in an economy, from working in a factory to investingin physical or human capital to creating new ideas or transferringtechnologies from abroad, on the positive side, and from theft tocorruption on the negative side.

In practice, however, there does not exist a usable quantifica-

tion of wedges between private and social returns, either for singlecountries or for the large group of countries considered in thisstudy. As a result, we must rely on proxies for social infrastructureand recognize the potential for measurement error.

We form our measure of social infrastructure by combiningtwo indexes. The first is an index of government antidiversionpolicies (GADP) created from data assembled by a firm thatspecializes in providing assessments of risk to internationalinvestors, Political Risk Services.14 Their International CountryRisk Guide rates 130 countries according to 24 categories. Wefollow Knack and Keefer [I9951 in using the average of five ofthese categories for the years 1986-1995. Two of the categories

relate to the government's role in protecting against privatediversion: (i) law and order, and (ii) bureaucratic quality. Threecategories relate to the government's possible role as a diverter: (i)corruption, (ii) risk of expropriation, and (iii) government repudia-

14. See Coplin, O'Leary, and Sealy [I9961 and Knack and Keefer [19951. Barro[I9971 considers a measure from the same source in regressions with the growth ofGDP per capita. Mauro [I9951 uses a similar variable to examine the relationbetween investment and growth of income per capita, on the one hand, andmeasures of corruption and other failures of protection, on the other hand.


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tion of contracts. Our GADP variable is an equal-weightedaverage of these five variables, each of which has higher values forgovernments with more effective policies for supporting produc-tion. The index is measured on a scale from zero to one.

The second element of our measure of social infrastructurecaptures the extent to which a country is open to internationaltrade. Policies toward international trade are a sensitive index ofsocial infrastructure. Not only does the imposition of tariffs divertresources to the government, but tariffs, quotas, and other tradebarriers create lucrative opportunities for private diversion. Inaddition, policies favoring free trade yield benefits associated withthe trade itself. Trade with other countries yields benefits fromspecialization and facilitates the adoption of ideas and technolo-gies from those countries. Our work does not attempt to distin-guish between trade policies as measures of a country's generalinfrastructure and the specific benefits that come from free tradeitself.

Sachs and Warner [I9951 have compiled an index that focuseson the openness of a country to trade with other countries. An

important advantage of their variable is that it considers the timesince a country adopted a more favorable social infrastructure.The Sachs-Warner index measures the fraction of years duringthe period 1950 to 1994 that the economy has been open and ismeasured on a [0,11 scale. A country is open if it satisfies all of thefollowing criteria: (i) nontariff barriers cover less than 40 percentof trade, (ii) average tariff rates are less than 40 percent, (iii) anyblack market premium was less than 20 percent during the 1970sand 1980s, (iv) the country is not classified as socialist by Kornai[1992], and (v) the government does not monopolize major exports.

In most of the results that we present, we will impose (aftertesting) the restriction that the coefficients for these two proxies

for social infrastructure are the same. Hence, we focus primarilyon a single index of social infrastructure formed as the average ofthe GADP and openness measures.

B. IdentificationTo examine the quantitative importance of differences insocial infrastructure as determinants of incomes across countries,we hypothesize the following structural model:

log YIL = a + ps + E,


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and

(5) S = y + 6 log YIL + X0 + 9,where S denotes social infrastructure andX is a collection of othervariables.

Several features of this framework deserve comment. First,we recognize explicitly that social infrastructure is an endogenousvariable. Economies are not exogenously endowed with the insti-tutions and incentives that make up their economic environ-ments, but rather social infrastructure is determined endoge-nously, perhaps depending itself on the level of output per workerin an economy. Such a concern arises not only because of thegeneral possibility of feedback from the unexplained component ofoutput per worker to social infrastructure, but also from particu-lar features of our measure of social infrastructure. For example,poor countries may have limited ability to collect taxes and maytherefore be forced to interfere with international trade. Alterna-tively, one might be concerned that the experts at Political RiskServices who constructed the components of the GADP index wereswayed in part by knowledge of income levels.

Second, our specification for the determination of incomes inequation (4)is parsimonious, reflecting our hypothesis that socialinfrastructure is the primary and fundamental determinant ofoutput per worker. We allow for a rich determination of socialinfrastructure through the variables in the X matrix. Indeed, wewill not even attempt to describe all of the potential determinantsof social infrastructure; we will not estimate equation (5) of thestructural model. The heart of our identifying assumptions is therestriction that the determinants of social infrastructure affectoutput per worker only through social infrastructure and notdirectly. We test the exclusion below.

Our identifying scheme includes the assumption that EX' =

0. Under this assumption, any subset of the determinants of socialinfrastructure constitute valid instruments for estimation of theparameters in equation (4). Consequently, we do not require acomplete specification of that equation. We will return to thispoint in greater detail shortly.Finally, we augment our specification by recognizing, asdiscussed in the previous section, that we do not observe socialinfrastructure directly. Instead, we observe a proxy variablecomputed as the sum of GADP and the openness variable,normalized to a [0,1] scale. This proxy for social infrastructure is


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related to true social infrastructure through random measure-ment error:

where v is the measurement error, taken to be uncorrelated with Sand X. Without loss of generality, we normalize $ = 1; this is anarbitrary choice of units since S is unobserved. Therefore,

Using this measurement equation, we rewrite equation (4)as

(7) log YIL= cr + p8 + Z,where

Z = E -pv.

The coefficient P will be identified by the orthogonalityconditions EX'Z = 0. Therefore, both measurement error andendogeneity concerns are addressed. The remaining issue todiscuss is how we obtain valid instruments for GADP and ouropenness measure.

C. Instruments

Our choice of instruments considers several centuries ofworld history. One of the key features of the sixteenth throughnineteenth centuries was the expansion of Western Europeaninfluence around the world. The extent of this influence was farfrom uniform, and thus provides us with identifying variationwhich we will take to be exogenous. Our instruments are variouscorrelates of the extent of Western European influence. These arecharacteristics of geography such as distance from the equatorand the extent to which the primary languages of WesternEurope-English, French, German, Portuguese, and Spanish-are spoken as first languages today.

Our instruments are positively correlated with social infra-

structure. Western Europe discovered the ideas of Adam Smith,the importance of property rights, and the system of checks andbalances in government, and the countries that were stronglyinfluenced by Western Europe were, other things equal, morelikely to adopt favorable infrastructure.

That the extent to which the languages of Western Europe arespoken as a mother tongue is correlated with the extent of


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Western European influence seems perfectly natural. However,one may wonder about the correlation of distance from theequator with Western European influence. We suggest this isplausible for two reasons. First, Western Europeans were morelikely to migrate to and settle regions of the world that weresparsely populated at the start of the fifteenth century. Regionssuch as the United States, Canada, Australia, New Zealand, andArgentina appear to satisfy this criterion. Second, it appears thatWestern Europeans were more likely to settle in areas that werebroadly similar in climate to Western Europe, which again pointsto regions far from the equator.15

The other important characteristic of an instrument is lack ofcorrelation with the disturbance E. To satisfy this criterion, wemust ask whether European influence was somehow more inten-sively targeted toward regions of the world that are more likely tohave high output per worker today. In fact, this does not seem tobe the case. On the one hand, Europeans did seek to conquer andexploit areas of the world that were rich in natural resources suchas gold and silver or that could provide valuable trade incommodities such as sugar and molasses. There is no tendency

today for these areas to have high output per worker.

On the other hand, European influence was much stronger inareas of the world that were sparsely settled at the beginning ofthe sixteenth century, such as the United States, Canada, Austra-lia, New Zealand, and Argentina. Presumably, these regions weresparsely settled at that time because the land was not especiallyproductive given the technologies of the fifteenth century. Forthese reasons, it seems reasonable to assume that our measures ofWestern European influence are uncorrelated with Z.

We measure distance from the equator as the absolute valueof latitude in degrees divided by 90 to place it on a 0 to 1scale.16 It

is widely known that economies farther from the equator are moresuccessful in terms of per capita income. For example, Nordhaus

15. Engerman and Sokoloff [I9971 provide a detailed historical analysiscomplementary to this story. They conclude that factor endowments such asgeography, climate, and soil conditions help explain why the social infrastructurethat developed in the United States and Canada was more conducive to long-runeconomic success than the social infrastructure that developed in Latin America.16. The latitude of each country was obtained from the Global DemographyProject at the University of California, Santa Barbara (http://www.ciesin.org/datasets/gpw/globldem.doc.html),discussed by Tobler et al. [19951. These locatio

ndata correspond to the center of the county or province within a country thatcontains the largest number of people. One implication of this choice is that thedata source places the center of the United States in Los Angeles, somewhat southof the median latitude of the country.


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[I9941 and Theil and Chen [I9951 examine closely the simplecorrelation of these variables. However, the explanation for thiscorrelation is far from agreed upon. Kamarck [I9761 emphasizes adirect relationship through the prevalence of disease and thepresence of a highly variable rainfall and inferior soil quality. Wewill postulate that the direct effect of such factors is small andimpose the hypothesis that the effect is zero: hence distance fromthe equator is not included in equation (4). Because of thepresence of overidentifying restrictions in our framework, how-ever, we are able to test this hypothesis, and we do not reject it,either statistically or economically, as discussed later in the paper.

Our data on languages come from two sources: Hunter [I9921and, to a lesser extent, Gunnemark [19911.l7 We use two languagevariables: the fraction of a country's population speaking one ofthe five primary Western European languages (including English)as a mother tongue, and the fraction speaking English as a mothertongue. We are, therefore, allowing English and the other lan-guages to have separate impacts.

Finally, we also use as an instrument the variable constructed

by Frankel and Romer [1996]: the (log) predicted tradeshare of an economy, based on a gravity model of internationaltrade that only uses a country's population and geographicalfeatures.

Our data set includes 127 countries for which we were able toconstruct measures of the physical capital stock using the Sum-mers and Heston data set. For these 127 countries we were alsoable to obtain data on the primary languages spoken, geographicinformation, and the Frankel-Romer predicted trade share. How-ever, missing data were a problem for four variables: 16 countriesin our sample were missing data on the openness variable, 17were missing data on the GADP variable, 27 were missing data on

educational attainment, and 15 were missing data on the miningshare of GDP. We imputed values for these missing data using the79 countries for which we have a complete set of data.18

17. The sources often disagree on exact numbers. Hunter El9921 is much moreprecise, containing detailed data on various dialects and citations to sources(typically surveys):18. For each country with missing data, we used a set of independentvariables to impute the missing data. Specifically, let C denote the set of 79countries with comolete data. Then. (i) for each countrv i not in C. let W be theindependent variables with data and V be the variables ihat are missing data. (ii)

Using the countries in C, regress V on W. (iii) Use the coefficients from theseregressions and the data W (i) to impute the values of V (i). The variables in VandW were indicator variables for type of economic organization, the fraction of years


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I 1 i I I I I JI0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Observed Index of Social InfrastructureFIGUREI1

Social Infrastructure and Output per Worker

Figure I1 plots output per worker against our measured indexof social infrastructure. The countries with the highest measuredlevels of social infrastructure are Switzerland, the United States,


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and Canada, and all three are among the countries with thehighest levels of output per worker. Three countries that are closeto the lowest in social infrastructure are Zaire, Haiti, andBangladesh, and all three have low levels of output per worker.

Consideration of this figure leads to two important questionsaddressed in this section. First, what is the impact on output perworker of a change in an exogenous variable that leads to aone-unit increase in social infrastructure? Second, what is therange of variation of true social infrastructure? We see in Figure I1that measured social infrastructure varies considerably along this

open, GADP, the fraction of population speaking English at home, the fraction ofpopulation speaking a European language at home, and a quadratic polynomial fordistance from the equator. In addition, total educational attainment and themining share of GDP were included in Vbut not in W; i.e., they were not treatedasindependent.


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TABLE I1BASICRESULTSFOR OUTPUJ PER WORKERlogYIL=a+ ps+:

OverID test Coeff testSocial p-value p-valueSpecification infrastructure test result test result BE1. Main specification 5.1432 .256 ,812 ,840(508) Accept AcceptAlternative specifications to check robustness2. Instruments: 4.998 .208 ,155 321Distance, Frankel-Romer (567) Accept Accept3. No imputed data 5.323 .243 .905 ,88979 countries (.607) Accept Accept4. OLS 3.289 -,002 ,700(.a121 Reject

The coefficient on Social infrastructure reflects the change in log output per worker associated with aone-unit increase in measured social infrastructure. For example, the coefficient of 5.14 means than a

difference of .Ol in our measure of social infrastructure is associated with a 5.14 percent difference in outputper worker. Standard errors are computed using a bootstrap method, as describedin the text. The mainspecification uses distance from the equator, the Frankel-Romer instrument, thefraction of the populationspeaking English at birth, and the fraction of the population speaking a WesternEuropean language at birthas instruments. The OverID test column reports the result of testing the overidentifying restrictions, and theCoeff test reports the result of testing for the equality of the coefficients onthe GADPpolicy index variable andthe openness variable. The standard deviation of log YIL is 1.078.

zero-one scale. How much of this is measurement error, and howmuch variation is there across countries in true social infrastruc-ture? Combining the answers to these two general questionsallows us to quantify the overall importance of differences in socialinfrastructure across countries in explaining differences in long-run economic performance.

Table I1 reports the results for the estimation of the basicrelation between output per worker and social infrastructure.Standard errors are computed using a bootstrap method thattakes into account the fact that some of the data have beenimputed.lg

19. The bootstrap proceeds as follows with 10,000 replications. First, we drawuniformly 127 times from the set of 79 observations for which there are no missingdata. Second, we create missing data. For each "country," we draw from the samplejoint distribution of missing data to determine which variables, if any, are missing(any combination of GADP and years open). Third, we impute the missing data,using the method described in footnote 18. Finally, we use instrumental variable


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son the generated data to get a new estimate, P. The standard errors reportecin thetable are calculated as the standard deviation of the 10,000 observations of P.


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The main specification in Table I1 reports the results frominstrumental variables estimation of the effect of a change insocial infrastructure on the log of output per worker. Fourinstruments are used: distance from the equator, the Frankel-Romer predicted trade share, and the fractions of the populationspeaking English and a European language, respectively. Thepoint estimate indicates that a difference of .Ol in social infrastruc-ture is associated with a difference in output per worker of 5.14percent. With a standard error of .508, this coefficient is estimatedwith considerable precision.

The second column of numbers in the table reports the resultof testing the overidentifying restrictions of the model, such as theorthogonality of the error term and distance from the equator.These restrictions are not rejected. Similarly, we test for theequality of the coefficients on the two variables that make up oursocial infrastructure index, and this restriction is also not rejected.

The lower rows of the table show that our main result isrobust to the use of a more limited set of instruments and toestimation using only the 79 countries for which we have a

complete data set. In results not reported in the table, we havedropped one instrument at a time to ensure that no singleinstrument is driving the results. The smallest coefficient onsocial infrastructure obtained in this robustness check was 4.93.

Our estimate of p tells us the difference in log output perworker of a difference in some exogenous variable that leads to adifference in social infrastructure. The point estimate indicatesthat a difference of .Ol in social infrastructure, as we measure it, isassociated with a difference in output per worker of a little over 5percent. Because we believe that social infrastructure is mea-sured with error, we need to investigate the magnitude of theerrors in order to understand this number. We need to determine

how much variation there is in true, as opposed to measured,social infrastructure across countries.

Our discussion starts from the premise that true simultane-ity results in a positive correlation between the disturbance in ourstructural equation and social infrastructure. Recall that oursystem is

(8) log YIL = a + p8 + E -pv,


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The reduced-form equation for 8is

Correlation of 8 with E arises from two sources. One isfeedback controlled by the parameter 6. Provided that the systemsatisfies the stability condition 66 < 1,a positive value of S impliesthat E is positively correlated with 8.As we noted earlier, thenatural assumption is that S is nonnegative, since social infrastruc-ture requires some resources to build, and log YIL measures thoseresources.

The second source of correlation of 8with E is correlation of qwith E. Again, it would appear plausible that countries with socialinfrastructure above the level of the second structural equationwould tend to be the same countries that had output per workerabove the first structural equation. Thus, both sources of correla-tion appear to be nonnegative.

On the other hand, as the reduced-form equation for 8shows,measured social infrastructure is unambiguously positively corre-lated with the measurement error v. Hence there is a negativecorrelation between 8and the part of the disturbance in the first

structural equation arising from measurement error, -pv

Information about the net effect of the positive correlationarising from simultaneity and the negative correlation arisingfrom measurement error is provided by the difference between theinstrumental variables estimate of 6 and the ordinary leastsquares estimate. The last row of Table I1 reports the latter.Because the OLS estimate is substantially smaller than the IVestimate, measurement error is the more important of the twoinfluences.

Under the assumption that there is no true simultaneityproblem, that is, E is uncorrelated with 8,we can calculate the

standard deviation of true social infrastructure, us,from thedifference between the IV and OLS estimates. A standard result inthe econometrics of measurement error is that OLS is biasedtoward zero by a multiplicative factor equal to the ratio of thevariance of the true value of the right-hand variable to thevariance of the measured value. Thus,


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That is, we can estimate the standard deviation of true socialinfrastructure relative to the standard deviation of measuredsocial infrastructure as the square root of the ratio of the OLS andIV estimates. With our estimates, the ratio of the standarddeviations is 0.800.

If the correlation of 8and e is positive, so true simultaneity isa problem, additional information is required to pin down a,.Thepositive correlation from endogeneity permits a larger negativecorrelation from measurement error and therefore a larger stan-dard deviation of that measurement error. A simple calculationindicates that the ratio of standard deviations given in equation(11)is the correlation between measured and true social infrastruc-ture, which we will denote rS,s Therefore, a lower bound on thecorrelation between measured and true social infrastructureprovides a lower bound on us.It is our belief, based on comparingthe data in Figure I1 with our priors, that the R2 or squaredcorrelation between true and measured social infrastructure is nosmaller than 0.5. This implies a lower bound on rS,sof fi= ,707.

With these numbers in mind we will consider the implications

of our estimate of bm = 5.14. Measured social infrastructureranges from a low value of 0.1127 in Zaire to a high value of 1.0000in Switzerland. Ignoring measurement error, the implied range ofvariation in output per worker would be a factor of 95, which isimplausibly high. We can apply the ratio rfi,~= os/og to get areasonable estimate of the range of variation of true socialinfrastru~ture.~~

The lower bound on this range implied by rS,s =.707 suggests that differences in social infrastructure can accountfor a 25.2-fold difference in output per worker across countries.Alternatively, if there is no true endogeneity so that r,gs = .800,differences in social infrastructure imply a 38.4-fold difference in

output per worker across countries. For comparison, recall thatoutput per worker in the richest country (the United States) andin the poorest country (Niger) in our data set differ by a factor of

35.1.We conclude that our results indicate that differences insocial infrastructure account for much of the difference in long-run economic performance throughout the world, as measured byoutput per worker. Countries most influenced by Europeans inpast centuries have social infrastructures conducive to high levelsof output per worker, as measured by our variables, and, in fact,

20. That is, we calculate exp (rs,SBN(~maxsmin)),

-


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have high levels of output per worker. Under our identifyingassumptions, this evidence means that infrastructure is a power-ful causal factor promoting higher output per worker.

A. Reduced-Form ResultsTable I11reports the two reduced-form regressions correspond-ing to our main econometric specification. These are OLS regres-sions of log output per worker and social infrastructure on the fourmain instruments. Interpreting these regressions calls for care:our framework does not require that these reduced forms becomplete in the sense that all exogenous variables are included.Rather, the equations are useful but potentially incompletereduced-form equations.

The reduced-form equations document the close relationshipbetween our instruments and actual social infrastructure. Dis-tance from the equator, the Frankel-Romer predicted trade share,and the fraction of the population speaking a European language(including English) combine to explain a substantial fraction ofthe variance of our index of social infrastructure. Similarly, theseinstruments are closely related to long-run economic performance

as measured by output per worker.

TABLE I11REDUCED-FORM

REGRESSIONS

Dependent variables

Social Log (outputRegressors infrastructure per worker)Distance from the equator, (0,l) scale 0.708(.110)

Log of Frankel-Romer predicted trade share 0.058(.031)Fraction of population speaking English 0.118(.076)Fraction of population speaking a Europeanlanguage 0.130(.050)R2 .41

N = 127. Standard errors are computed using a bootstrap method, as described inthe text. A constantterm is included but not reported.


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B. Results by ComponentTable IV examines in more detail the sources of differences inoutput per worker across countries by considering why somecountries have higher productivity or more physical or humancapital than others.

The dependent variables in this table use the contributions tooutput per worker (the log of the terms in equation (3)),so thatadding the coefficients across columns reproduces the coefficientin the main specification of Table 11. Broadly speaking, theexplanations are similar. Countries with a good social infrastruc-ture have high capital intensities, high human capital per worker,and high productivity. Each of these components contributes tohigh output per worker.

Along with this broad similarity, some interesting differencesare evident in Table IV. The residual in the equation for capitalintensity is particularly large, as measured by the estimatedstandard deviation of the error. This leads to an interestingobservation. The United States is an excellent example of acountry with good social infrastructure, but its stock of physical

capital per unit of output is not remarkable. While the UnitedStates ranks first in output per worker, second in educationalattainment, and thirteenth in productivity, its capital-outputratio ranks thirty-ninth among the 127 countries. The UnitedStates ranks much higher in capital per worker (seventh) becauseof its relatively high productivity level.

TABLE IVRESULTSFOR log KIY, log HIL, and log AComponent = a + PS + E

Dependent variable

a-log1-aKIYlog HIL log ASocial infrastructure 1.052 1.343 2.746(.164) (.I711 (.336)OverID test (p) ,784 ,034 .I51Test result Accept Reject AcceptA: ,310 ,243 .596oDepvar ,320 ,290 ,727

Estimation is carried out as in the main specification in Table 11. Standard err

ors are computed using abootstrap method, as described in the text.


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TABLE VFACTORS MAXIMUMIMINIMUM

OF VARIATION:

YIL (Klnd(l-a) HIL A

Observed factor of variation 35.1 4.5 3.1 19.9Ratio, 5 richest to 5 poorest countries 31.7 1.8 2.2 8.3Predicted variation, only measurement error 38.4 2.1 2.6 7.0Predicted variation, assuming ri,s = .5 25.2 1.9 2.3 5.6

The first two rows report actual factors of variat~on In the data, first for theseparate components and thenfor the geometric average of the five richest and five poorest countries (sortedaccord~ng to YIL).The last tworows report predicted factors of variation based on the-estimated-range of variation of true soc~alinfrastructure Specifically, these last two rows report exp (rpn(S,, -SmIn)),first w~th r = ,800 and secondwith r2 = .5.

Table V summarizes the extent to which differences in truesocial infrastructure can explain the observed variation in outputper worker and its components. The first row of the tabledocuments the observed factor of variation between the maximumand minimum values of output per worker, capital intensity, andother variables in our data set. The second row shows numbers wehave already reported in the interpretation of the productivityresults. Countries are sorted by output per worker, and then theratio of the geometric average of output per worker in the fiverichest countries to the five poorest countries is decomposed intothe product of a capital intensity term, a human capital term, andproductivity. The last two rows of the table use the basic coeffi-

cient estimates from Tables I1 and IV to decompose the predictedfactor of variation in output into its multiplicative components.

One sees from this table that differences in social infrastruc-ture are sufficient to account for the bulk of the observed range ofvariation in capital intensity, human capital per worker, andprod~ctivity.~~

Interpreted through an aggregate production func-tion, these differences are able to account for much of the variationin output per worker.

VI. ROBUSTNESS

OF THE RESULTS

The central equation estimated in this paper has only a singlefundamental determinant of a country's output per worker, social

21. One must be careful in interpreting these results since social infrastruc-ture is potentially endogenous. What this statement really means is that differ-ences in exogenous variables that lead to the observed range of variation in social


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infrastructure would imply the factors of variation reported in the table.


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infrastructure. Our maintained hypothesis (already tested in partusing the test of overidentifying restrictions) is that this relationdoes not omit other fundamental determinants of output perworker. For example, characteristics of an economy such as thesize of government, the rate of inflation, or the share of high-techgoods in international trade are all best thought of in our opinionas outcomes rather than determinants. Just as investment inskills, capital, and technologies, these variables are determinedprimarily by a country's social infrastructure.

To examine the robustness of our specification, we selected aset of candidates to be additional fundamental determinants andconsider a range of specifications. These alternative specificationsare reported in Table VI.

The first two specifications redefine measured social infra-structure to be either the GADP variable or the Sachs-Warneropenness variable, rather than the average of the two. The results

TABLE VIROBUSTNESS

RESULTSlog YIL = a +PS +X Added Variable +Z

OverID testSocial Additional p-valueSpecification infrastructure variable test result 6:

1.s =GADP 5.410 ... ,006 ,769(.394) Reject2. s =years open 4.442 ... ,131 1.126(371) Accept3. Distance from equator 5.079 0.062 .I29 ,835

(2.61) (2.062) Accept4. Ethnolinguistic fractionalization 5.006 -0.223 ,212 ,816(N = 113) (.745) (.386) Accept5. Religions affiliation (N = 121) 4.980 See ,478 .771(.670) Note Accept6. Log (population) 5.173 0.047 .412 ,845(513) (.060) Accept7. Log (C-H density) 5.195 -0.546 ,272 ,850(539) (1.11) Accept8. Capitalist system indicator 6.354 -1.057 ,828 ,899variable (1.14) (.432) Accept9. Instruments: main set plus 4.929 ... ,026 ,812continent dummies (.388) Reject

See notes to Table I1 Instruments are the same as in Table 11, except where noted Additional variablesare discussed in the text The coefficients on the religious variables in line 5,followed by standard errors, areCatholic (0 992,.354), Muslim (0.877,.412),Protestant (0.150,.431),and Hindu (0.839,1.48).


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are similar to those in our main specification. When socialinfrastructure is measured by GADP alone, the overidentifyingrestrictions are rejected; some of the instruments appear to belongin the equation.

In the third specification we treat distance from the equatoras an included exogenous variable. The result, consistent withprevious overidentifying tests, is little change in the coefficient onsocial infrastructure and a small and insignificant coefficient ondistance from the equator.22 This supports our contention that thebulk of the high simple correlation between distance from theequator and economic performance occurs because historicalcircumstances lead this variable to proxy well for socialinfrastructure.

The fourth specification examines the ethnolinguistic fraction-alization (ELF) index computed by Taylor and Hudson [I9721 andused by Mauro [19951. ELF measures the probability that any twopeople chosen at random from within a country will belong todifferent ethnic or linguistic groups. While the simple associationof this variable with output per worker is quite strong, the partial

regression coefficient is small in magnitude (the variable ismeasured on a [0,11 scale) and statistically insignificant.

The fifth specification adds religious affiliation variables tothe specification. Specifically, these variables measure the frac-tion (on a [0,11 scale) of a country's population affiliated with theCatholic, Muslim, Protestant, and Hindu religions.23 The pointestimate on social infrastructure is changed little when thesevariables are included in the specification. Both Catholic andMuslim affiliation variables enter significantly into the regres-sion, while the Protestant and Hindu variables do not.

The sixth specification adds the log of population to the

regression. A number of recent growth models in the tradition ofRomer [19901 emphasize that nonrivalry of ideas should lead toincreasing returns to scale. Our simple attempt to measure scalewith population does not find evidence of this effect. One explana-

22. The large standard error on social infrastructure is somewhat misleading.The associated p-value testing the hypothesis of a zero coefficient on socialinfrastructure (computed from the bootstrap distribution of coefficients) is only0.008. The large standard error-the standard deviation of the bootstrap coeffi-cients-occurs because the distribution of coefficients is skewed heavily towardtheright, i.e., toward positive values. In contrast, the distribution of the bootst

rapcoefficients for distance from the equator is skewed heavily toward the left.23. These data were provided by Robert Barro and are discussed in Barro[19971.


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tion is that national boundaries do not limit the areas where ideasare applied.

The seventh specification considers a measure of the densityof economic activity, computed following the methods of Cicconeand Hall [19961.24 The density measure is constructed to have atheoretical coefficient of one: it would have precisely this value inCiccone and Hall's cross section of states. Here, however, in a crosssection of countries, the variation in other determinants of outputper worker is so large that it is difficult to measure the effects ofdensity with much precision.

The results for the eighth specification are unexpected. Thisspecification adds an indicator variable taking the value of one forcountries that are categorized as capitalist or mixed-capitalist bythe Freedom House [Finn 19941. The odd result is that theregression coefficient implies that capitalist countries producesubstantially less output per worker than otherwise similarnoncapitalist countries. In part, this reflects the particular defini-tion of capitalism employed by the Freedom House. According totheir classification, a number of sub-Saharan African economies

are classified as capitalist.

The final specification of Table VI adds a list of continentdummies to the instrument set.25 As with the other specifications,the coefficient on social infrastructure is unchanged by theaddition of the continents to the instrument list. However, theoveridentification test now rejects the restrictions, in part becauseAfrican economies have lower output per worker than otherwisesimilar economies on other continents.

VII. CONCLUSIONCountries produce high levels of output per worker in the longrun because they achieve high rates of investment in physical

capital and human capital and because they use these inputs with

24. The Ciccone-Hall measure for country i is given bywhere N, is the population of country i, Si is the set of all provinces in country i, n,is the population of provinces, and a,is the area of provinces. We use a value of y =1.058, as estimated by Ciccone and Hall. This value implies that doubling densityincreases D, by about 6 percent.

25. The continents are North America (including Central America), SouthAmerica, Africa, Asia (plus Oceania), and Europe.


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Hall and Jones - Why Do Some Produce So Much More Output Per Worker Than Others-1

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