Christian Morrisson
email: christian.morrisson@wanadoo.fr

Fabrice Murtin
email: fabrice.murtin@oecd.org

Philippe Aghion

Tony Atkinson

Franc ¸ois Robert J Barro

Matthias Bourguignon

Oded Doepke

Avner Galor

Marc Greif

Pierre-Cyrille Gurgand

Francis Hautcoeur

Steve Kramarz

Steve Machin

Hugh Pischke

Halsey Rockoff

John Rogers

Romain Van Reenen

David Wacziarg

Gavin Weil

Wright

The century of education

Keywords: D31, E27, F02, N00, O40 Education, economic history, database

This paper presents a historical database on educational attainment in 74 countries for the period 1870-2010, using perpetual inventory methods before 1960 and then the Cohen and Soto (2007) database. The correlation between the two sets of average years of schooling in 1960 is equal to 0.96. We use a measurement error framework to merge the two databases, while correcting for a systematic measurement bias in Cohen and Soto (2007) linked to differential mortality across educational groups. Descriptive statistics show a continuous spread of education that has accelerated in the second half of the twentieth century. We find evidence of fast convergence in years of schooling for a sub-sample of advanced countries during the 1870-1914 globalization period, and of modest convergence since 1980. Less advanced countries have been excluded from the convergence club in both cases.

Introduction

Global economic transformations have never been as dramatic as in the twentieth century. Most countries have experienced radical changes in the standards of income per capita, technology, fertility, mortality, income inequality and the extent of democracy in the course of the past century. It is the goal of many disciplines -economics, history, demography, sociology, political science -to comment these transformations, assess their causes and describe their consequences. But one major obstacle hinders the analysis of such long term processes: the lack of data. In particular, there does not exist any data spanning over the whole century that describes one fundamental aspect of economic development: education, the knowledge of nations.

In this paper, we make a contribution by building consistent series of average years of schooling in 74 countries for the period 1870-2010. This has never been achieved before probably because of the huge amount of data that needed to be treated adequately to ensure comparability across countries and time. This involves about 30 000 figures.

Our series derive from two data sets. The first one spans over 1870-1960 and is original, the second describes the period 1960-2010 and has been constructed by Cohen and Soto (2007), quoted hereafter as Cohen-Soto. This source has been chosen because it provides the most reliable estimates of average years of schooling as they take into account differential mortality across age groups, and as most of their figures rely on national censuses. For the pre-1960 period, the main source is Mitchell (2003 a-b-c), who provides, among much other information, long series of total enrolment in primary, secondary and higher education as well as age pyramids. These two sets of variables are combined to derive an estimate of average years of schooling for each cohort of age from 1870. This perpetual inventory method enables us to estimate average schooling in the population aged 15-64 years or that older than 15 years. As average years of schooling depend on past enrolment in school, one needs series of enrolment going back as far as the eve of the nineteenth century in order to start our series in 1870.

Early enrolment data were taken from Lindert (2004) for many European countries.

Several assumptions were needed to complete a consistent data set describing educational attainment over such a long period. Thus, it is important to gauge to what extent our series are influenced by these assumptions. A large part of this paper is devoted to a discussion of this issue. In particular, we find that missing data can generate sizeable measurement errors at the beginning of the period, especially for less advanced countries. We show that in most European countries schooling is estimated accurately as soon as 1870, and that 1900 constitutes a good start date for other countries. Also, comparing our figures with Cohen-Soto in 1960, we find a high correlation of 0.96. As the two methodologies are completely different, one relying on perpetual inventory of enrolment at school, the other mainly on surveys, this proves to be an excellent result.

Besides, the comparison between the two databases in 1960 motivates a statistical framework that corrects time-persistent measurement errors in our historical data set, as well as systematic ones in Cohen-Soto. Indeed, a third of their data relies on surveys conducted in the 1990s, which were used to infer average schooling in 1960. However, the latter authors neglected differential mortality across educational groups. As a result, they overestimated average schooling in 1960, or equivalently, underestimated the growth of schooling between 1960 and 1970.

As a result, the data reflects an unprecedented global development of education that has accelerated after the Second World War. From that perspective, the twentieth century has clearly been the "Century of Education". Importantly, we show that our global distribution of years of schooling has widened since 1870. We also find that the two globalization periods have witnessed a convergence in average years of schooling for all countries with average schooling above a minimal threshold of 2 years -about 30% of literate people. This convergence has been rapid during the former globalization era and much more modest since 1980.

Section 2 explains the building of the historical database, while section 3 describes the data. A robustness analysis follows, then we explain how we merged the two data sets in section 5. Section 6 provides elementary descriptive results and the last section concludes.

2 The Building of a Historical Data Set 1870-1960 In this section, we explain why we focus on average schooling rather than on enrolment rates. This is because the data we observe offers robust estimates of the former, but none of the latter. Then we expose the assumptions used in the perpetual inventory procedure.

A Statistical Trade-off Between Quantity and Quality of Pupils

The fundamental challenge is the following. One is interested into the knowledge of the distribution of education, namely a vector n = (n 0 , n 1 , ..., n P , ..., n S , ..., n H )

describing the number of people in the population having completed respectively e = (0, 1, ...P, ...S, ...H)

years of schooling, where P represents the last year of primary schooling, S the last year of secondary and H that of higher education. Often the available data sum up this information into a reduced number of educational groups: for instance, Cohen-Soto consider 7 groups, people without schooling, people with incomplete and completed primary schooling, and similarly for secondary and tertiary. In Mitchell's data, we have access to a vector of total enrolments in the three stages of education, but not to their distribution within each stage. For instance, we observe the total number of pupils in primary n 1 + ... + n P , but not their distribution (n 1 , ..., n P ). The fundamental challenge stems from the impossibility of infering the share of pupils that have given up school at some point, in other words, to derive the distributional vector n. If one had some historical information on the durations P , S and H as well as on the dropout rates in any country, then it would be possible to recover the latter distribution. Such information is obviously not available on the long term.

However, there exists a way to exploit the information given by Mitchell's data. If the distribution of schooling cannot be identified, stocks of schooling can. The intuition is as follows: there is a trade-off between average duration at school and enrolment in the first year of schooling, given total observed enrolment. The lower the average duration the higher the initial enrolment rate, given that a total number of pupils has to be matched in the data. In particular, two unknown factors affect average duration at school: the maximal durations P , S and H, as well as the dropout rates. When these factors vary, average duration and initial enrolment rate vary inversely to each other.

Their product, roughly equal to the stock of average years of schooling, is likely to vary little with maximal duration and the dropout rate. At least, this is an empirical question that can be adressed.

Are Average Years of Schooling a Robust Statistics?

The computations of stocks of schooling are similar to those completed in Cohen-Soto.

We take here the example of primary schooling. Let P i, t be the population of age i at time t, N t be the number of intakes -those attending their first year of school in year t. Given a cohort of age i at time t, the probability to have been an intake at the age of 6 is simply

pr = N t-i+6 P 6, t-i+6 (3)
Similarly to Cohen-Soto, a pupil can repeat a maximum of three years during primary schooling, which lasts P years. Let d and r be the dropout and repeating rates, and g the growth rate of intakes. The expression linking total enrollment E t to first-year enrollment N t and a factor capturing the relative proportion of intakes 1 µ (d, r, g, P ) is

E t = N t µ (d, r, g, P ) (4)
This formula simply decomposes each grade at school between students who have repeated 0, 1, 2 or 3 times before. Besides, a cohort i at time t has an average number of years of schooling equal to

H i, t = N t-i+6 P 6, t-i+6 λ (d, P ) (5)
In this equation λ (d, P ) is the mean duration of primary 2 , held constant over time, and not taking into account repeated years. From ( 4) and ( 5), the average stock of years of schooling H i, t for cohort i at time t is given by

H i, t = E t-i+6 P 6, t-i+6 λ (d, P ) µ (d, r, g, P ) (6)
In the case where d = r = g = 0, one simply has H i, t = E t-i+6 /P 6, t-i+6 since λ (d, P ) = µ (d, r, g, P ) = P. In that case, the stock of schooling does not depend on P , and there is a perfect trade-off between average duration (λ) and initial enrolment rates (E/µ) given the observed total number of pupils E.

In other cases, stocks will have to be adjusted by the factor λ/µ that depends on the underlying parameters (d, r, g, P ). Figure (1) displays the value of the adjustment factor λ/µ for g = 0, as well as g = 7% corresponding to a doubling of enrolment 1 as in Cohen-Soto one has formally:

µ (d, r, g, P ) = P -1 j=0 (1 -d -r) j [ 1 (1+g) j + r j+1 1 (1+g) j+1 + r 2 j+1 2 (1+g) j+2 + r 3 j+1 3 (1+g) j+3 ] 2 equal to P -1 j=1 j (1 -d) j .d + P (1 -d) P
rate every 10 years -the most rapid growth historically observed. It calculates the ratio λ/µ for different values of r and for P = 6 -it has been checked that other values of P were changing results only marginally. As expected, over periods of constant flows of intakes -upper graph -, the dropout and repeating rates have a reasonably low influence on stocks of schooling. Let us stress that an annual dropout rate of 20% is enormous: it means that only 25% of enrolled pupils have completed 6 years of primary schooling, a situation only experienced by some African countries according to Cohen-Soto statistics in 1960 [START_REF] Bourguignon | Inequality among world citizens: 1820-1992[END_REF] . As an illustration, a dropout rate around 3% could suit to Western countries, meaning that about 83% of a cohort will complete 6 years of primary school, while intermediate countries might be around 5-7.5%. In those cases, the estimated stocks of average years of schooling will not differ by more than 10% as shown by Figure (1). During phases of fast enrolment growth -lower graph -, the adjustment factor is smaller than one as intake cohorts are relatively more numerous to a situation without growth in intakes. Overall, stocks of average schooling do not vary by more than 15% when the dropout rate varies from 0 to 0.10. In contrast, average enrolment rates will be dramatically affected by the dropout rate. For instance, a 10%

(respectively 0.15) annual dropout rate during 6 years will have the average enrolment rate established at 70% (resp. 59%) of its initial value.

As a sum, Mitchell's data offers access to the quantity of years of schooling, a statistics in which economists have been much interested in. However, the distribution of schooling itself remains unidentified. The use of other data such as illiteracy rates could partly alleviate this constraint, but this is beyond the scope of this paper. We explain hereafter how we derived statistics of average schooling for the whole population.

A Perpetual Inventory Method

First, we derived stocks of schooling for each cohort of age in each country at each point in time since 1870. Dropout and repetition rates were chosen from Unesco data (2007). The annual repeating rate was comprised between 2% and 5% in Europe and North America all over the period, and between 5% and 10% elsewhere. The annual dropout rate was calibrated so that the share of pupils completing primary school was equal to 90% in most advanced Western countries, was comprised between 70% and 85% in less advanced Western, South American and Asian countries, and 50% in the least advanced countries4 . As underlined above, these figures do not entail a distribution of schooling that can be trusted, but do entail stocks of schooling in which one can have confidence.

Then, we average all stocks of schooling across the relevant cohorts of age at each point in time. This provides us with average years of schooling among the people aged between 15 and 64 since 1870 and among people older than 15. One can also split the latter statistics across stages of education, and derive the average years of primary, secondary and tertiary schooling among the population older than 15, given by

H t = i H i,t P i,t i P i,t (7)
As the stock of education depends on previous enrolment rates in the population, some problems are likely to arise from this perpetual inventory method. In particular, the population structure in year t is not necessarily the outcome of year t -T given a mortality rule between those two periods, because migrations can affect a substantial proportion of the population. Between the 19th and the 20th century, countries from the Commonwealth, Latin America, North-America, and some of Europe have had intense periods of migrations. Depending on the relative amount of human capital of migrants and natives, the net impact of migration can be positive or negative. In particular, the US have absorbed about 60% of total migrations from Europe to the Americas between 1820 and 1920. The impact of mass migrations on US average schooling is examined in Murtin and Viarengo (2009), and we retain their original series in the historical database.

Data Description

We present hereafter the data available in Mitchell: series of total enrolment from which enrolment rates can be derived for illustrative purposes, as well as age pyramids.

We introduce the problem of missing data for those two sets of variables.

Implicit Series of Enrolment Rates

A difficulty arises with the definition of primary and secondary schooling in Mitchell's data. It is not clear which grades primary and secondary respectively encompass, and occasionally some breaks in the series have been mentioned with the report of some secondary schools to primary and vice-versa [START_REF] Blundell | Initial Conditions and Moment Restrictions in Dynamic Panel Data Models[END_REF] . Similarly, definition for primary may vary across countries. In order to ensure comparability across countries and across time, it is necessary to provide a unique definition for primary schooling: let it be the stage of education composed of the first six years of schooling. Hence, statistics from a country displaying 8 years of primary schooling have to be adapted to this definition, and the last two years of primary in this country are reclassified as secondary schooling.

In the data, the number of grades that primary and secondary encompass in each country is unknown, and can hardly be recovered from other sources. Even if it could, it would not reveal what definition Mitchell has adopted when building his series. So we have to guess from the data itself the number of years of schooling that primary schooling encompasses in Mitchell's statistics. This can be done relatively easily for the most advanced countries. Indeed, for countries that have reached full enrolment in primary school before 1960, the enrolment rate profile flattens at some point in time and remains constant. This constant is logically equal to one when full enrolment is completed in the country. Hence, for each country we test several assumptions on the maximal duration of primary and select those ensuring an enrolment close to one at the end of the period [START_REF] Chesnais | La Transition Demographique[END_REF] .

For less developed countries, this procedure is limited since enrolment rates never reach 100%. So we had to make ad-hoc assumptions, typically that primary was lasting 6, 7 or 8 years in those countries. As stressed above, enrolment rates are sensitive to the latter assumptions, so that those enrolment profiles might not be taken at their face value for those countries. In contrast, average schooling is only marginaly modified by assumptions made on maximal duration of primary -see below. These series of enrolment also have the advantage of revealing for each country and for each stage of education the relative proportion of observed and interpolated data. They make transparent the treatment of series linked to border changes7 .

Missing Data on Schooling Enrolment

A major difficulty is missing data on total enrolment. Series start often but not systematically before 1870 for European countries, US, Canada and Australia. In Latin America, Eastern Europe and in some Asian countries, series often begin around 1870 or 1880. Moreover, for African countries and other Asian countries, Mitchell gives no data before 1930 or even 1950.

In order to treat this problem, we used data given by Lindert (2004) on total enrolments in primary and secondary for most advanced countries before 1850. The latter author uses specific historical studies and has also corrected unplausible series of total enrolment in Mitchell (2003a-b-c), most notably that of England and Wales. For other countries, we assumed ad-hoc and very low values for enrolment rates in primary schools in 1820 -0.01% in Asia, South America, Africa -and a constant rate of increase between 1820 and the first observed year in Mitchell's series. As the first observed enrolment rate is typically low, the entailed measurement error is expected to be low. Figure 2 plots the first observed average years of schooling in primary by year of first observation. Countries with initial average schooling greater than 4 years are the most problematic because unobserved enrolment of some cohorts can be very high, potentially entailing large measurement errors in the data. This will be investigated in the robustness analysis section.

Age Pyramids

The demographic data depict the structure of the population by age group. The number of countries for which age pyramids are available in 1820 is scarce. For other countries, we postulate that the distribution of mortality F is Weibull (a, b) , with parameters calibrated on life expectancy of the corresponding population -available from Bourguignon-Morrisson (2002) -and on the survival rate after 60 taken equal to 10% in 1820. Life expectancy is corrected for child mortality, taken equal to m 0 = 20% at birth and to m 1 = 7% the following 4 years. Formally, life expectancy LE is given by

LE = m 0 + m 1 (2 + 3 + 4 + 5) + (1 -m 0 )(1 -m 1 ) 4 k≥6 p k k, p k Weibull (a, b) = ν (m 0 , m 1 , a, b) (8)
Once calibrated, the survival function 1 -F provides the relative weight of each cohort of age inside each age group

p(Age = i) p(Age = j) = 1 -F (Death ≤ i) 1 -F (Death ≤ j) (9)
For early years, age pyramids are interpolated with the first observation for the country.

Also, for a significant proportion of countries -20 in total -no age pyramid was reported in Mitchell. These countries were imputed a rescaled age pyramid derived from a neighbour country. In the robustness analysis section, we show that this imputation has little impact. The reason is simple: age pyramids have not been very different across countries over that period, at least in comparison to how different they are by now.

Let us give a quick overview of the data on age pyramids over the last two centuries.

In order to illustrate the demographic transition, we computed the share of population aged 6-20 in total population for each available age pyramid. the peak in the natural increase of population, which is the difference between death and birth rates [START_REF] Ehrlich | The Evolution of Income and Fertility Inequalities over the Course of Economic Development: A Human Capital Perspective[END_REF] .

Robustness Analysis

In this section we test whether missing data and unobserved distributions of schooling can affect substantially the schooling estimates.

Missing Data on Schooling Enrolment

Assumptions made to supplement missing enrolment data might bias schooling estimates in early years. In order to gauge this measurement problem, we run the following counterfactual experiment: in one simulation, all past unobserved enrolment rates are equal to the first observed enrolment rates in primary, secondary and higher education -this clearly overestimates the actual stocks of schooling since an increase in average enrolment has been a common rule for all countries at any time with only a few exceptions occurring during World Wars and the Great Depression. In a second simulation, past enrolment rates are reconstructed backward by assuming a fast enrolment process starting in the immediate past of the first observation. The pace of such a process is calibrated as an increase in 20% percentage points of enrolment every 10 years before the first observation. For primary schooling, this has been observed historically in only a few countries such as Finland after its 1917 independance or African countries after the Second World War. This scenario is clearly an underestimation of stocks of schooling, as older generations receive less education than they might have had in reality.

The two latter simulations provide us with upper and lower bounds for average years of schooling. We are almost certain that for any country at any time, the true value of schooling lies within this interval. Hence, we can build a dispersion statistics, a pseudo-standard error equal to the width of this interval divided by (2x1.96). This echoes the well-known fact that regression estimates have an asymptotic normal distribution with a confidence interval width equal to (2x1.96) times the standard error. As we will see below, assuming a normal distribution for the measurement error affecting average schooling is empirically supported.

The distribution of this pseudo-standard error is reported on Figure 4 for 1870, 1900, 1930 and 1960. In 1870, missing data can generate sizeable but still reasonable measurement errors, as the average pseudo-standard error equals 0.23. This is equivalent to 4 percentage points of enrolment rate in primary assuming 6 completed years.

There are twelve outliers for which this standard error is over 0.5 [START_REF] Krueger | Education for Growth: Why and for Whom?[END_REF] . Thirty years later, pseudo-standard errors have been reduced. Their average value is 0.14, or 2.3 percentage points of enrolment rate. There are only seven countries above 0.5 [START_REF] Lindert | Growing Public[END_REF] . In 1930, the measurement error linked to missing initial data has almost completely shrinked as it averages 0.06 -1 percentage point of enrolment rate -and is greater than 0.5 only in Czechoslovaquia and Poland with identical value 0.6.

A complementary analysis focuses on the relative size of measurement error and schooling attainment. In less developed countries, it could be that even small measurement errors are comparable in size with average schooling. In fact, it is the case for a large number of countries in 1870. Figure 5 depicts a pseudo-coefficient of variationthe pseudo-standard error divided by the estimated level of schooling -with respect to average years of schooling. Exactly half of the countries have a coefficient of variation greater than 0.5, which means that "true" average schooling is comprised between 0 and twice the estimated value. All of these countries are obviously among the less developed ones, with average schooling smaller than 2 years. However, only 4 countries fall in this category in 1900: Cambodia, Benin, Ethiopia and Senegal. The average coefficient of variation has been dramatically reduced from 0.48 in 1870 to 0.22 in 1900.

Summing up, missing data generate measurement errors that are significant in 1870, both in absolute and relative terms. In particular cross-country comparisons are not appropriate for less developed countries at the beginning of the period as measurement errors are large compared to estimates. However, 1900 appears to be a satisfying start date for the whole sample.

Dropouts

The second robustness experiment addresses the sensitivity of data with respect to the underlying distribution, in other words, to the unobserved dropout rate. We adopt the same strategy as before and compute average schooling for two opposite counterfactuals: one stating that the dropout rate is equal to 0 in any country at any time, while the other assumes that only half of initially enrolled children complete 6 years of primary schooling. Although the latter scenario might well be realistic in some African and Asian countries -unfortunately even today -, it clearly constitutes a lower bound of achievement in other countries. The pseudo-standard error is reported in Figure 6. It turns out that the underlying distribution has a negligeable impact on average schooling in 1870. However, its influence increases with educational development. The average pseudo-standard error amounts to 0.09 in 1960 -1.5 percentage points of enrolment rate with the former convention. This remains a somewhat modest influence, that will anyhow be tackled by the comparison with survey-based figures in a subsequent section.

Maximal Duration of Primary and Unknown Age Pyramids

A further source of mis-measurement is the maximal duration [START_REF] Lipset | Political Man: The Social Bases of Politics[END_REF] of primary schooling that had to be chosen on an ad-hoc basis for developing countries, in which the enrolment rate never attained 100% before 1960. We simulate average years of schooling while selecting either P = 6 or 8 and compute the corresponding pseudo-standard error. For the sake of caution, we include all countries in this experiment. As before a pseudo-standard error is computed and reported in Figure 7. Measurement errors linked to unknown duration turn out to be negligeable for any country at any date.

Last, we tackle the issue of age pyramids, which were unobserved for 33 countries.

We consider the following two extreme age pyramids: the United States in 1950 and Kenya at the same date. The shares of people aged 6-20 years in total population are respectively 0.27 and 0.39. The former is ranked among the smallest share ever observed over the period 1870-1960 -excluding developed European countries -, the latter is the highest share ever measured in Africa before 1960. It is almost certain that shares of young people in any country will be comprised between those two bounds.

Then we make the radical assumption that age pyramids are constant over time in the two counterfactual simulations in order to keep a constant "confidence interval". We rule out most advanced countries [START_REF] Lleras-Muney | The Relationship Between Education and Adult Mortality in the US[END_REF] from the analysis as we have a good knowledge of age pyramids for all of these countries in the nineteenth century. Figure 8 reports the distribution of pseudo-standard errors, which are found to be low in 1900 with an average of 0.06, or about 1 percentage points of enrolment rate in primary school.

Measurement errors increase with educational development to reach an average of 0.24 in 1960, or 4 percentage points [START_REF] Lutz | Reconstruction of Population by Age, Sex and Level of Educational Attainment of 120 Countries for 1970-2000[END_REF] . But mismeasurements at the end of the period are unlikely to be large because age pyramids have been often available for decades prior to 1960.

Overall, this counterfactual simulation shows that unknown age pyramids are not likely to affect our estimates in a significant way. The main reason for this is that observed age pyramids were much more similar from one country to another than they are now. In 2000 the share of the 5-19 population was still around 0.39 in Kenya, but it was equal to 0.15 in Italy and it fell to 0.22 in the United States (US Census online statistics). So differences are much sharper today than they used to be before 1960.

As a sum, missing data on initial enrolment affect schooling estimates at the beginning of the period, while unknown distribution of dropouts within each degree, as well as unknown age pyramids, may have an impact around 1960. All effects remain somewhat modest in absolute terms. In relative terms, they can definitely be viewed as large for less developed countries. Typically, estimates of schooling below 2 average years might be subject to much caution when used for comparative purposes.

A Unified Database 1870-2010

In this section, we explain how we merged the former historical data set with Cohen-Soto data in order to build unified series for the period 1870-2010. Once again, we relied on Cohen-Soto rather than extending our permanent-inventory methods beyond 1960 because we believe that Cohen-Soto data set, drawing heavily on surveys, does perform a better job than any inventory procedure weakened for instance by migration phenomenoms that have prevailed from 1960.

Comparison with Cohen-Soto in 1960

We consider average years of schooling among the population aged between 15 and 64, as well as among the population older than 15. The latter stock can be decomposed by degree: Cohen-Soto also provide average years of primary, secondary and tertiary schooling among the population older than 15, which also includes pupils [START_REF] Mitchell | International Historical Statistics: the Americas 1750-1993[END_REF] . So far, this leaves us with 5 series for 82 countries common to our data set and Cohen-Soto.

The comparison is meaningful because the way the data were constructed was fundamentally different. As depicted above, our figures are built with an inventory method, while Cohen-Soto base a large majority of their data upon surveys. In fact, they use surveys for 62 countries over 82 and similar inventory methods for the remaining 20.

Figures (9) to (12) and Barro-Lee (2001) when data are taken in levels, but much less when they are taken in differences. So there is a need for a closer investigation of the differences between both samples, in order to see whether systematic -though modest in magnitude -differences emerge in one or another data set. This is the purpose of what follows.

A Measurement Problem: Differential Mortality Across Educational Groups

Sources of mistakes are likely to differ across the two samples, and we aim at exploiting this difference [START_REF] Mitchell | International Historical Statistics: Europe 1750-1993[END_REF] .

What are the problems likely to occur with the Cohen-Soto data set? Among the 68 remaining countries, 11 were surveyed in the 60s, 10 in the 70s, 7 in the 80s, 22 in the 90s and inventory methods were used for the remaining 18. As an example, Germany was surveyed in 1991; the percentage of German people with primary schooling aged between 60 and 65 in 1960 is estimated as the percentage of German people with primary schooling aged between 60+31=91 and 96 in 1991, and similarly for secondary and tertiary Education. A large majority of the data uses this backward computation.

Two problems are likely to happen: one is linked to migrations. Whether lowskilled or high-skilled migrants have entered or left Germany between 1960 and 1991, the 1991 figure will imperfectly reflect the 1960 reality. The magnitude of the bias will depend on both the intensity of migration flows and the skill composition of these flows [START_REF] Mitchell | International Historical Statistics: Africa, Asia and Oceania 1750-1993[END_REF] .

The second problem is linked to differential mortality across educational groups.

If education has an effect on life expectancy, then the education distributions in 1960 and 1991 will not be similar because highly educated people will have a higher probability of survival than people with lower education over the 1960-1991 period. If this differential effect is not likely to be sizeable over a 10 year time span, it could be significant over a 30 year time span. We expect that educational attainment in 1960 will be overestimated when inferred from 1990s surveys.

A simple model rationalizes that. Without loss of generality consider two groups of population, one with education level h in proportion λ, the other with zero education.

At initial time, the first group has a survival function S h (t) that determines the probability that its members survive t years. The second group has survival function S 0 (t).

Then the average education in the population is initially h(0) = hλ. After t years, it becomes (10) It is easy to show that for α(t) to be increasing with time, the hazard rate of the educated population must be smaller that that of the non-educated population [START_REF] Morrisson | Women's Discrimination in Developing Countries: a New Data Set for Better Policies[END_REF] . This overestimation of educational attainment has to be taken into account in Cohen-Soto data.

h(t) = hλS h (t) λS h (t) + (1 -λ)S 0 (t) = h(0) + hλ(1 -λ) S h (t) -S 0 (t) λS h (t) + (1 -λ)S 0 (t) α(t)
Regarding the historical data set, the former robustness analysis section mentions several sources of bias: missing enrolment data, unobserved dropouts, and unknown age pyramids. They turned out to be of modest magnitude, albeit not negligeable.

Importantly, we tend to think that measurement errors in a given country are highly correlated across time. This is because of the nature of data we are examining, stocks.

As data spans over 10-year intervals, the population at stake in two subsequent observations will likely be the same to a large extent: the population aged over 15 in 1900 will be that over 25 in 1910, that over 35 in 1920 and so on. If measurement errors affect the estimation in 1900, they will automatically contaminate the estimates for subsequent years. This serial correlation is likely to be very high and has to be taken into account.

A Measurement Error Framework

Denote by h cs i , the estimate of years of schooling for country i in 1960 taken from

Cohen-Soto, h mm i that deriving from the historical data set, and h 0 i the true value.

From what precedes a natural measurement error framework arises:

h cs i = h 0 i + α i(t) h mm i = 1 γ h 0 i + µ + i (11)
where α i(t) are dummies for the time period t in which the survey was conducted in country i, γ and µ two constant terms capturing systematic structural biases in the historical data set and i idiosyncratic measurement errors with zero-mean. Three time dummies capture the fact that in Cohen-Soto database, surveys have been run between 1970 and 1979, 1980 and 1989, or after 1990. The coefficient in front of these time dummies are expected to be positive and increasing with the time period as described in the former subsection. We introduced two constant terms γ and µ as there could be systematic measurement errors in our historical data. In constrast, Cohen-Soto data are assumed to be exact estimates of the true data once taken into account the differential mortality effect. Then one has

h cs i = γh mm i + α i(t) -γµ -γ i ( 12
)
This equation is estimated for the following variables: average schooling among 15-64 and among 15+; average primary, secondary and tertiary schooling among 15+. It provides us with the bias in Cohen-Soto linked to differential mortality, with measurement errors in the historical sample due to data construction, as well as with a direct test of whether the two data sets are consistent through testing the null hypothesis γ = 1 and µ = 0 [START_REF] Morrisson | Education Inequalities and the Kuznets Curves 1870-2000[END_REF] .

Table 1 presents the results for total years of schooling among 15-64 and 15+. Two major conclusions arise: historical data and Cohen-Soto are most of the time consistent with each other; the differential mortality effect is significant for countries surveyed after 1990, but not for those surveyed before. The first conclusion comes from the fact that after including all regressors in the equations (columns II), the estimated coefficient γ is very close to 1 and the intercept is not significant. In other words, no systematic distortion affects the historical sample, although the intercept is significant in column I for the population 15+.

On the other hand, in all cases we find that the dummy for countries surveyed after 1990 has a large and significant coefficient roughly equal to 0.5. The following simplified example shows that the order of magnitude is reasonnable: indeed, take a country -approximatively the UK in 1960 -where half of the population has some primary schooling (5 years) and the other half has secondary schooling (10 years). Then average years of schooling is 0.5x5+0.5x10=7.5 years. Three decades later, it is realistic to assume that 50% of the population with primary schooling has passed away, versus 20% for the population with secondary schooling. This is equivalent to assuming that 5 extra years of schooling decreases the mortality rate by 50-20=30% percentage points over 3 decades, or equivalently that one additional year of schooling decrease the mortality rate by 2% per decade. This is realistic because Lleras-Muney (2005) assesses this effect of education on decennial mortality and finds OLS estimates equal to 1.7% and IV estimates of 3.6% in the US. Hence, three decades later, the population is composed of 0.5x0.5/(0.5*0.5+0.8*0.5)=40% of people with primary schooling and 60% with secondary schooling. This translates into average years of schooling equal to 0.4x5+0.6x10=8 years of schooling in 1990, namely an over-estimation of 0.5 years of schooling. This is exactly what Table 1 suggests.

Of course, one could not assess the validity of the former measurement-error framework simply on the basis of the two variables that this framework is intended to link, as several different framework structures could lead to the same equation ( 12). So we need to rely on an external source of information to ensure identification of the latter framework. We use another suggestive evidence, independant from our data, that supports our view. Unesco (1957) reports worldwide illiteracy rates in the first half of the twentieth century, and most particularly in 1950. Similarly Cohen-Soto reports the percentage of individuals who have not attended school in 1960. There is no equivalence between being illiterate and not attending school, as literacy could be acquired outside school and pupils with few years of schooling could be classified as illiterate.

However, there is plausibly a high correlation between those two variables, even with a 10-year time span. Regressing Ill cs the percentage of individuals without schooling

given by Cohen-Soto on Unesco illiteracy rates Ill 0 and dummies for dates of surveys in 51 countries, [START_REF] Murtin | American Economic Development or the Virtues of Education 1840-2000[END_REF]

α i(1970) + u i
The significant and negative coefficient in front of the 1990s survey dummy suggests the same conclusion: differential mortality has lead to an under-estimation of true illiteracy levels in 1960 in the Cohen-Soto data set, conversely, to an overestimation 21 of [START_REF] Murtin | American Economic Development or the Virtues of Education 1840-2000[END_REF] Countries having achieved mass education for a long time (illiteracy rates smaller than 5%) are excluded from the sample -hence, we avoid the oversampling of low illiteracy levels. The sample of illiteracy rates has therefore 5% as a mimimum, 99% as a maximum, and 62% as an average. 39% (respectively 9% and 13%) of included countries are surveyed in the 1990s (resp. the 1980s and the 1970s). [START_REF] Murtin | Assessing the Demographic Transition[END_REF] This also means that computing reliability ratios between our historical schooling variable and the one from Cohen-Soto in 1960 would not make sense, as the above results show that measurement-errors affecting average schooling in 1960 [START_REF] Murtin | Convergence of Compulsory Schooling in Western Europe: 1950-2000[END_REF] .

One step beyond, we decompose total years of schooling into years of primary, secondary and tertiary schooling. Columns II of Table 2 show that the differential mortality effect can be further decomposed: the stock of primary years of schooling appear to be the most overestimated, probably because of lower mortality among people with secondary and tertiary education relatively to those with only primary schooling. A further effect takes place within the tertiary group, plausibly reflecting disparities of educational attainment within this group. Moreover, the historical data turn out to be sometimes biased at this disaggregated level: there is a systematic mean difference of 0.22 for primary (column II), and some over-estimation of tertiary schooling for most developed countries as reflected by γ = 0.77 on column II. However, tertiary schooling plays a negligeable role in total stocks of education as shown, for instance, by Figure 12. So we will neglect this anomaly in the building of series [START_REF] Murtin | American Education in the Age of Mass Migrations 1870-1930[END_REF] .

Building Long Term Series

The last step consists in merging the two data sets while taking into account the former problems. We impose a coefficient equal to 1 for h mm in all regressions of Tables 1 and2. Then, we make the following two assumptions: first, Cohen-Soto provide exact estimates from 1970; second, the measurement error affecting our sample in 1960 has been the same before that date. The first assumption stems directly from the estimates of Tables 1 and2, as none of the dummies for 1970-1979 and 1980-1989 surveys are significant. The second assumption is a simplifying one.

In order to formalize this clearly, we notice hcs i,t and hmm i,t the average years of schooling in country i at time t given respectively by Cohen-Soto and the historical Cohen-Soto data are not idiosyncratic, hampering the validity of reliability ratios computation. [START_REF] Murtin | Convergence of Compulsory Schooling in Western Europe: 1950-2000[END_REF] Lutz et al. ( 2007) construct a database on education 1970-2000 with backward projection methods. They do take into account differential mortality across educational groups and find that this effect is significant. However, they do not use all of the information available in postwar surveys as Cohen-Soto do, which potentially magnifies measurement errors affecting their base-year survey (2000). [START_REF] Murtin | American Education in the Age of Mass Migrations 1870-1930[END_REF] As explained above 18 countries use constructed data in Cohen-Soto sample. Whether we include or exclude them from the analysis the estimates of γ remain almost the same. sample after the statistical corrections described above have been applied. They constitute the final data set. Modifications are thus the following

hcs i,1960 = h cs i,1960 -αi(1990) hcs i,t = h cs i,t for t ≥ 1970 hmm i,t = h mm i,t -μ -ˆ i for t ≤ 1960 ( 13
)
where αi(1990) are the estimated coefficients of 1990 surveys dummies, μ and ˆ i respectively the significant intercepts and error terms in columns (IV) of above regressions.

Hence, by construction hmm i,1960 = hcs i,1960 = h 0 i,1960 , so that the corrected samples match in 1960.

We applied this procedure using the constrained estimation (IV) in Table 1 for population aged 15-64, and the constrained estimations in columns (IV) of Table 2 for primary, secondary and tertiary schooling of population older than 15. The largest modification concerns Cohen-Soto OECD countries in 1960, in which primary schooling has been lowered by 0.36 average years -about 6 percentage points of average enrolment rate [START_REF] Murtin | The Democratic Transition[END_REF] .

It is interesting to look at the distribution of measurement errors, as Krueger-Lindhal (2001) have identified them as a cause of non-significance of education in growth equations. We consider for instance total years of schooling among 15-64 and we report a qq-plot of the measuremment error distribution against normal quantiles.

It turns out that the measurement error is well approximated by a normal distribution in Figure 13. The standard error of measurement errors amounts to 0.51, while 80% of the observations (54 countries out of 68) lie in the interval [-0.6, 0.6]. A maximum [START_REF] Murtin | The Democratic Transition[END_REF] The historical data have been corrected backwards. In order to avoid some negative stocks of schooling at some point in time due to the statistical correction, we imposed minimum levels of stocks: 0.02, 0.01 and 0.01 for respectively primary, secondary and tertiary years of schooling, which all correspond to a 0.25% enrolment rate in a 8-4-4 system. A small proportion of the total observations, around 6.5%, were consequently left-censored at these thresholds. These countries are India until 1900, Iraq until 1940, Myanmar until 1880, Paraguay until 1890, Philippines until 1910, Thailand until 1890, Tunisia until 1910, Turkey in 1870, Zimbabwe until 1920. gap of 0.6 represents 10% of enrolment rate in primary. Those latter 54 countries constitute the "core" data set, the final sample for which we have a reasonnably high level of confidence in the series at any date. Other countries are called the "outliers" and are treated individually -see below. For the core sample, the measurement error has a standard error of 0.32, which represents 5 percentage points of enrolment rate in primary on a 6 years basis. This ensures high accuracy in usual OLS estimates. Indeed, given that in 1960 the standard error of average years of schooling is equal to 2.66 for this sample, this can potentially lead to an underestimation of the schooling impact on growth by a factor equal to 1/(1 + 0.32 2 /2.66 2 ) = 0.986. In other words, measurement errors may not have any sizeable influence in this sample, and growth regressions derived from this unified sample are likely to offer robust estimates.

Treating the Outliers

Among the final sample of 74 countries, there are 74-54=20 countries excluded from the core sample that we would like to discuss briefly. Details of the manipulations are given in the appendix. The first and most important case is the United States, taken from Murtin-Viarengo (2009). US schooling estimates rely on IPUMS census surveys after 1940. For the 1870-1930 period, they estimate average years of schooling of US natives and US immigrants, using both our historical data on education in European countries, and a perpetual inventory of US immigrants by age and by country of origin.

Their serie for 1870-1930 is perfectly consistent with the first national estimate in 1940.

The US can then integrate the core sample, which brings its size to a final sample of 55 countries.

Then, France is the only country for which our estimate (8.61 average years in 1960) is more reliable than that of Cohen-Soto (6.73). This fact is confirmed by the examination of other data sources. Perhaps the latter authors have not taken into account the fact that primary schooling was lasting 8 years and not 5 until the 1960s. So we keep our estimate for 1960 and use different sources for 1960-2010 -see appendix.

Four advanced countries were excluded from the statistical framework because they were clearly outliers: these are Australia, Canada, New-Zealand and Switzerland. For those countries, the discrepancy in 1960 comes from an ill-measured enrolment in secondary schools. It is well known that the "high school movement" happened in the 1920s in the most advanced country, the United States. So we make the assumption that estimates taken from the historical data set are all correct until 1930 [START_REF] Nehru | A New Data Base on Human Capital Stocks in Developing and Industrial Countries: Sources, Methodology and Results[END_REF] . Then, we interpolate [START_REF] Portela | Measurement Error in Education and Growth Regressions[END_REF] to reach the 1960 levels of Cohen-Soto, corrected for the differential mortality bias. This is a tentative solution and one recommends to pay some caution when using these four series.

Fourteen countries have been excluded from the core sample because they had a measurement error larger than 0.6 in absolute value. These countries and the corresponding measurement error are: Belgium (-0.61), Bulgaria (+0.83), Denmark (-0.71), Finland (+0.89), Greece (-1.17), Hungary (+1.16), Ireland (-1.19), Italy (+1.18), Norway (-1.00), Costa Rica (-0.71), Egypt (-1.18), Paraguay (-1.12), Philippines (-0.71) and Sudan (+0.61). Nine of these countries are European, so that the bulk of the 1960 statistical error may again come from mis-measurement of average years of secondary schooling. Hence, we apply the same rule and select the figures from the historical data set until 1930 and interpolate between 1930 and 1960. This procedure avoids unplausible results for 1870 figures if large measurement errors were applied to the 1870-1960 series, leading to sizeable over-estimation or under-estimation of initial levels. Similarly, we tend to think that measurement errors affecting the remaining 5 developing countries may have occurred in the immediate postwar period, when schooling enrolment accelerates. So we keep the historical series until 1940 [START_REF]World Illiteracy at Mid-Century[END_REF] and interpolate them with the corrected figures of Cohen-Soto in 1960.

Results

A Global Overview

In this section we describe the global evolution of education since 1870. For the sake of completeness, we have added two large countries in our sample, China and Russia. Although there does not exist any satisfactory historical statistics for the latter countries, we have relied on historical studies. However the data for the latter two countries serves only an illustrative purpose specific to this section and shall be taken with caution.

Figure 14 provides an overview of education in 9 large geographical areas [START_REF]Statistical Yearbook[END_REF] covering between 80 and 87% of the world population all over the period. It is the first comprehensive overview over 130 years, as the attempt by Baier et al. (2006) to estimate similar curves spans over a much shorter period: for several regions information is provided only from 1940 or later.

In 1870, world education seems to be a quasi-monopoly of high-income countries in which educational attainment reaches more than 4.5 years, versus 2 years or less in all other regions. However, there is a significant gap between South-East Asia, India, MENA and Sub-Saharan Africa with less than 0.5 years on the one hand, and on the other hand Southern Europe, Latin America, Japan and China 29 where average years of schooling vary between 1 and 2. In Southern European countries as well as in Latin America, this is because a minority of persons was educated as in Western Europe. In China and Japan, the context for literacy is different as reading requires the knowledge of thousands of characters. In order to read or write a simple text, people must know around 2000-3000 characters. In those two countries, historians estimate that in 1870 more than 40% of men and more than 10% of women had reached this level after 3 or 4 years of schooling.

Educational attainment rapidly increased in Western countries until the First World

War, but slightly slowed down in the interwar period, and dramatically accelerated in the postwar period as a consequence of the Baby-Boom and mass enrolment in sec- It is clear that the most successful story has been that of Japan, a consequence of the priority granted to education since the Meiji revolution. But the performances of other East Asia countries are also satisfactory. In South-East Asia (Indonesia, Malaysia, Philippines and Thailand), schooling has exceeded 7 years in 2000 whereas these countries were ranked at the bottom of the distribution in 1870. China is slightly below this level at the same date. MENA is also a success story. This region was ranked at the bottom distribution in 1870 and little progress has been made until 1960, but then average education has been multiplied by 6.

As a sum, only Sub-Saharan Africa and India are now lagging behind other countries, a result which is partly linked to the discrimination against women in these societies, and to the large gap between enrolment rates of boys and girls in primary schools.

On the contrary, the educational take-off within other Asian and African countries has closed the gender gap, with some notable exceptions.

Finally, it is clear from Figure 14 that the polarization of education between Western countries and the rest of the world has been largely reduced since 1870. But it is also worth stressing that the absolute differences in years of education between the most and the least educated countries increased over the last 130 years. We let the reader refer to Morrisson-Murtin (2008), who use a preliminar version of this database, for a full description of global education inequality.

With some more detailed information given by country-level statistics, we can complement the former overview. As it will be assessed in the next section, there is a convergence process taking place among Western countries since 1870, making this group much more homogeneous by now. In 1870, differences among the latter group of countries were relatively large: average education equalled only 2.1 years in Australia, 4.2 years in Belgium and in France, 6.2 years in Switzerland and 5.7 years in Norway. These differences were linked to heterogeneous educational policies since the 18th century, with a school set up in each village of most advanced countries at that time, whereas in other countries this obligation appeared much later, as in France around 1840. But we observe that the United States, Canada and Switzerland took rapidly the lead among Western countries.

As for South America in 1900, Argentina and Chile are more comparable with Southern European countries. There is a large gap between these two countries and the other Latin American countries: in 1930 as in 1960, average schooling in Argentina or Chile was double of that in Brazil and Mexico. The evolution of the latter two large countries was comparable but a few other countries such as Guatemala or Nicaragua were far below.

Among MENA countries, only Morocco is clearly lagging behind others with 3.6 average years of schooling in 2000 instead of 6 on average. This is a consequence of a very low enrolment rate for girls in rural zones before 1980-1990. At last, in Sub-Saharan Africa, we observe some contrast stemming from the two main colonial policies of UK and France, which explain the gap between French-speaking and English-speaking countries. In 1960, average years of schooling were much higher in Ghana and Kenya than in Côte-d'Ivoire and Senegal (1.9 versus 0.4 years) and in 2000 they are twice as large. Among French-speaking countries, Cameroon is the only relatively advanced country (1.3 years in 1960), as it was a German colony before 1918.

Differences in educational policies account for these results: in English or German colonies, primary school was often taken over by Christian missionaries, whereas in French colonies preference was given to state schools which displayed a much higher financial burden for the ruling power.

On Convergence in Education

Let us now focus on countries rather than on geographical areas, and look at particular sub-periods. It makes sense to investigate whether countries have converged or diverged in terms of average education. Indeed, convergence in education might trigger that of income as education enters directly the production function via labor, and possibly indirectly via the growth rate of technological change, the demographic structure of the labor force, the participation rate of females and so on.

Figure 15 depicts the variation in average schooling among the 15-64 population with respect to initial schooling over two periods: 1870-1910 and 1910-1960. One is a period of marked integration of goods, financial and labor markets, while the other has witnessed two world wars and a dramatic "deglobalization" process. The evidence is striking: there is a convergence process at work during the globalization of the late nineteenth century, but only for the most advanced countries; there is no particular trend during the following period.

The convergence in schooling during the globalization period concerns all developed countries with average years of schooling roughly greater than 2 in 187030 , in other words, the group of Western countries. Among those, the less advanced countries in 1870 such as Australia, Ireland or New-Zealand have clearly caught up with others. The average increase in schooling in this convergence club has been of 2.2 years of schooling. This contrasts with countries with initial years of schooling lower than 2, which acknowledged marginal increases in schooling of 0.5 years on average.

On the other hand, the following "deglobalization" period has not witnessed any particular trend. Except maybe for the less advanced countries, the increase in education between 1910 and 1960 was seemingly unrelated to the initial level in 1910.

Indeed, for countries initially between 1 and 3 years (respectively 3 and 6 years and above 6 years), the average increase in schooling was 2.1 years (respectively 2.3 and 1.9 years). Countries below 1 year in 1910 had an average increase of 0.9 years. Hence, education was increasing overall, but without any specific pattern. Table 3 presents simple OLS estimations of absolute convergence: the difference in average schooling is regressed on initial schooling and a constant, and the implied annual convergence rate 31 is calculated. This confirms former graphical evidences: in any period the group of low-education countries follows a divergence process where education grows proportionally to its initial level. On the other hand, middle-education countries -initially more than two years of schooling -have acknowledged a convergence process during the former globalization era with a high annual convergence rate of 3.7%. This process has vanished during the following deglobalization period, and has barely started to regain strength after 1980 as shown by the low 0.7% annual convergence rate over that period.

Certainly, these descriptive evidences have to be refined with the help of an extended database comprising other determinants of educational attainment. Conditional convergence has to be tested. It might well be the case that conditional convergence in education has been intense after 1960 for those countries displaying similar characteristics. Also, panel data should be used rather than cross-section regressions 32 .

What are the historical and current determinants triggering convergence in schooling? Is globalization an important driver of educational investments and a major force acting for the catch-up with more advanced countries? Why are some countries left aside in the process? These issues are complicated as education is the outcome of many forces: economic factors such as the net return to education, institutional factors such as the constraint of attending compulsory years of schooling, the existence of church schools or pro-literacy political ideology. Disentangling these factors is difficult. It is the task of economic history to address the facts and historical motives sustaining the development of education, and in the appendix we review briefly those facts for a handful of countries. In a more quantitative way, Murtin-Viarengo (2008) show that one particular determinant of education -compulsory years of schoolinghas been converging in fifteen Western European countries over the postwar period.

They argue that decreasing returns to education at the aggregate level can explain this convergence process. They also find that openness is a significant determinant of com-32 With panel data the dependent variable should be a flow variable such as average schooling of the 20-30 years old rather than a stock variable as it is here. A stock variable creates mechanical correlation across time that contaminates the estimation of the economic phenomenon at stake. pulsory schooling. Hence, these results are consistent with the view that globalization has fostered investments in education but that decreasing aggregate returns to education have limited its expansion33 .

Education, Inequality, Demography and Democracy Across the XXth Century

Beyond the issue of explaining the dynamics of education, we believe that this database will make many empirical investigations possible. One is the relation between income and education. Cohen-Soto (2007), among others, provide a very clear proof of the relevance of data quality for growth regressions. Cohen-Soto show that significant results for education are obtained with their data, whereas regressions using other data sets provide non-significant results. However their regressions start only in 1960. With our data set, growth regressions could be estimated for the first time over the whole twentieth century, provided that data on physical capital become available.

Second, economic historians have analyzed in detail how education has allowed technological accumulation in a few countries. This process is critical for growth as it has a positive impact on total factor productivity and on exports of manufactured goods. With a large education database, scholars can now compare and explain successes and failures of many countries in such a process. The relative advance in years of education of some Asian countries in 1870 and the lag of Sub-Saharan Africa at the same date is interesting from that perspective. This database will certainly allow a revised and enlarged analysis of the relationships between education, technological diffusion/innovation and growth.

A third issue would be the link between education and the demographic transition.

At first glance, one observes that fertility started decreasing a century ago only in some Western European countries where illiteracy had nearly disappeared. Today, we observe high fertility rates in Sub-Saharan Africa and Southern Asia, the only regions in the world where the number of years of education is still low, and where strong discrimination prevails against women who often have no access to primary school (Morrisson and Jutting, 2005). Over the long run, a rich literature has sought to explain the global observed decrease in fertility in the course of economic development, and competing theories have emphasized for instance the role of the demand for human capital, the effects of child and adult mortality, or the impact of income standards. In practice, this education database, which starts in 1870 and pertains to a large sample of countries, allows for an empirical test of the latter theories. In that respect, Murtin (2009) reveals that the most robust explanation for the global decline in fertility is the rise in education 34 . Other potential determinants, such as income, infant mortality or total mortality, lack of statistical robustness across the various econometric procedures (pooled OLS regressions, panel fixed-effects, SYS-GMM.). In contrast, even after controling for persistence in fertility across time and including lagged fertility in the right-hand side of the regression, average schooling appears to be highly significant and its coefficient unchanged.

Fourth, this database can shed light on the interactions between education and inequality. Education certainly plays a direct role in the variations in income inequality, which is partially determined by inequality in human capital (as defined by the Mincerian approach). Futhermore, education entails externalities which could reduce income inequality. Indeed, Bourguignon-Verdier (2001) suggests that political participation of poor people increases with their educational level and that consequently redistributive policies arise with educational development. In practice, Morrisson-Murtin (2008) use Bourguignon-Morrisson (2002) global data on income distributions and find that mass education has indeed triggered a dramatic decline in income inequality from 1870, aside from any variations linked to GDP per capita or human capital inequality.

Fifth, education is likely to interact with institutions, which are a key factor of longterm growth. For instance, there is an abundant literature on the interaction between economic development and the extent of democracy. This literature is dominated by the "modernization hypothesis", which has been originally developed by Lipset (1960) and has attracted some attention in the recent literature. Examining the empirical evidence over the XXth century, Murtin-Wacziarg (2009) reveal that schooling, and more precisely primary education, has been a significant and robust determinant of democracy over the long run. Again, this finding is robust to econometric methods, as well as to the inclusion of lagged GDP per capita in the set of explanatory variables. It holds for any time period starting from 1870, even if the evidence is more fragile over the contemporary period as many countries have already achieved high standards of democracy in 1960, and therefore make less progress relatively to former periods.

To sum up, recent evidence tend to show that education is key to economic development, as it has triggered a decline in fertility, a rise in democracy, and most likely an associated decline in income inequality. There are several other economic relationships that this database could enlight. We truly hope it will help building original answers to pervasive and crucial issues of social sciences.

Conclusion

This paper has presented a new database on average years of schooling in 74 countries over the period 1870-2010. We have assessed measurement errors potentially due to missing data on total enrolment, age pyramids, dropout rates or duration of primary schooling. Simulations indicate that the quality of estimates reaches a satisfactory level for all countries around 1900. Besides, a comparison with Cohen-Soto database in 1960 enabled us to infer those measurement errors explicitely, and to correct simultaneously Cohen-Soto data from a bias linked to differential mortality across educational groups. We have derived a core group of 54 countries for which the standard error of measurement errors equals 0.32, or 5 percentage points of enrolment in primary. Basic descriptive results suggest that global achievements in education have accelerated in the 1960s, but that our global distribution of schooling has widened since 1870. For a sub-sample of countries, we find evidence of fast absolute convergence in years of schooling during the former globalization period and of modest convergence during the current one. In each case less advanced countries have been excluded from the convergence club. [START_REF] Bourguignon | Inequality among world citizens: 1820-1992[END_REF] 0.21 [START_REF] Bourguignon | Inequality among world citizens: 1820-1992[END_REF] 0.97 0.97 0.13 [START_REF] Bourguignon | Inequality among world citizens: 1820-1992[END_REF] 0.15 (3) (1) Average years of schooling taken from historical data for corresponding populations. [START_REF] Barro | International Comparisons of Educational Attainment: Updates and Implications[END_REF] Constrained. [START_REF] Bourguignon | Inequality among world citizens: 1820-1992[END_REF] Adjusted R 2 of the difference between dependant variable and h mm . 1 [START_REF] Barro | International Comparisons of Educational Attainment: Updates and Implications[END_REF] 1.00 -0.01 [START_REF] Bourguignon | Inequality among world citizens: 1820-1992[END_REF] 0.66 0.74 0.15 (3) 0.16 [START_REF] Bourguignon | Inequality among world citizens: 1820-1992[END_REF] (1)

Average years of schooling taken from historical data for corresponding populations.

(2)

Constrained.

(3) Adjusted R 2 of the difference between dependant variable and h mm .

Figure 3 reports the distribution of these shares by continent 8 .

 8 It is striking to see that except for Europe, all median shares of young people are close to 0.35 at any date in any continent. Europe is an exception but age pyramids are available very early for all European countries. Some historical facts on the world demographic transition are summarized in the companion appendix. They shed light upon the variations of the latter distributions. Shares of 6-20 years-old remain approximatively constant until 1870 in Europe, increase until 1900 due to a generalized fall in infant mortality, then experience a dramatic decrease with fertility reduction. The group "Americas and Oceania" gathers quite heterogeneous countries. The fall in the median shares between 1810 and 1870 mainly picks up the US fertility decrease. The decrease in the lower quartile from 1890 still corresponds to the fall in fertility in the US, Canada, Australia and New-Zealand. The median shares stay quite constant, then increase around 1920-1960. This reflects partly compositional effects as statistics become available for Latin and South-ern America, but also the same phenomenom taking place in Europe 50 years before:

  ondary schooling and at university to a lesser extent. In 2000, Western countries remained on top of the world education distribution. But the situation of other countries has changed dramatically: Japan has caught up with Western countries with average schooling exceeding 12 years; in many Southern European countries as well as in Russia, schooling has reached 10 years; in all other regions, average education exceeds 6 years, except in India and in Sub-Saharan Africa, which are characterized by an important gap with the rest of the world as schooling is around 4 years on average. The performances of Russia -Eastern Europe in general -are partially linked to the progress of education during the communist era. Until 1920, education has increased slowly in Russia and was equal to 2 years, whereas it was about 3 or 4 years in Italy and Spain. But thanks to a steady growth after 1920, Russia is slightly ahead of Southern Europe (comprising Chile and Argentina) in 2000.

Figure 16

 16 Figure 16 focuses on the contemporary period 1960-2000 and the recent period of intense globalization (1980-2010). At first sight, it is not clear whether an absolute convergence process holds for countries with initial schooling above 2 years in 1960 or in 1980. If it does, it is certainly moderate. Indeed, countries initially comprised between 2 and 6 years of schooling in 1960 reduced the gap with countries initially above 6 years by a modest 0.5 years; over the period 1980-2010, the reduction of the latter gap is equal to one year.

Table 2 -

 2 Average Years of Primary, Secondary and Tertiary Schooling inCohen-

Figure 1 :Figure 2 :

 12 Figure 1: Sensibility Analysis -Adjustment Factor of Average Years of Schooling

Figure 5 :Figure 6 :Figure 9 :

 569 Figure 5: Pseudo-Coefficient of Variation of Average Schooling Generated by Missing Data

Figure 10 :Figure 11 :Figure 12 :-

 101112 Figure 10: Comparison of Average Years of Primary Schooling in 1960

Figure 13 :

 13 Figure 13: Quantiles of Measurement Error versus Quantiles of a Standard Normal Distribution

  scatter each set of data for those 82 countries versus the corre-As a sum, our final sample has 82-7-1=74 countries; among those, we have a sample of 74 -5 -1 = 68 countries for which inventory methods ran throughout the XXth century and surveys have lead to close results in 1960. However, canonical correlations can sometimes hide important structural differences in the data. For instance,Cohen- Soto (2007) data are highly correlated with those of De la Fuente-Domenech(2001)

sponding one in Cohen-Soto. It turns out that total stock of average years of schooling are remarkably well correlated. For instance, including (resp. excluding) countries built with inventory methods in Cohen-Soto, the correlation amounts to 0.961 (resp. 0.956) for the 15-64 population. Stocks of schooling by grades in the population aged over 15 turn out to be somewhat noisier: for primary schooling, the correlation equals to 0.954 (resp. 0.945) when the 20 non-surveyed countries are included (resp. excluded); for secondary, to 0.838 (resp. 0.827); for higher education, to 0.853 (resp.

0.837).

Although most countries have comparable stocks of schooling, some of them are outliers. We temporarily exclude 5 countries that are clear outliers in Figures

(9)

to

(12)

: France, Switzerland, Australia, Canada, New-Zealand. As mentioned before, the United States is a particular case treated in detail in

Murtin-Viarengo (2009)

. Also, we excluded definitively Singapore and the following 7 less advanced countries for which the gap was much too high: Bolivia, Colombia, Ecuador, Korea, Romania, Tanzania and Zambia.

  one has

	Ill cs = 0.07 (0.04)	+ 0.89 (0.05)	* * Ill 0 -0.11 (0.04)	* * α i(1990) -0.09 (0.04)	* * α i(1980) -0.05 (0.03)

Table 1 -

 1 Average Years of Schooling Among 15-64 and 15+ from Cohen-Soto

		Population Aged Between 15 and 64	Population Aged 15 and Over
		(I)		(II)		(III)		(IV)		(I)		(II)		(III)		(IV)
	h mm,(1)	1.08	* *	1.03	* *	1 (2)		1 (2)		1.06	* *	1.01	* *	1 (2)		1 (2)
		(0.03)		(0.03)						(0.02)		(0.03)
	Survey in 1970-1979	-		0.08 (0.20)		0.09 (0.20)		-		-		0.10 (0.18)		0.11 (0.18)		-
	Survey in 1980-1989	-		-0.11 (0.23)	-0.07 (0.22)	-		-		-0.01 (0.21)	0.01 (0.21)		-
	Survey post-1990	-		0.49 (0.20)	* *	0.59 (0.15)	* *	0.59 (0.14)	* *	-		(0.18) 0.42	* *	(0.14) 0.48	* *	(0.13) 0.45	* *
	Constant	(0.11) 0.08		(0.12) 0.10		(0.10) 0.15		(0.08) 0.16	* *	(0.10) 0.17	*	(0.11) 0.17		(0.09) 0.19	* *	(0.07) 0.22	* *
	Adj. R 2	0.96		0.97		0.19

Table 3 -

 3 OLS Estimation of Absolute Convergence in Average Schooling For Low-Education and Middle-Education Countries L stands for countries with initial average schooling lower than 2 years, M for other countries. * * * (respectively * * and * ) means significant at 1% (resp. 5% and 10%)

	Dependent Variable: Difference in Average Schooling
		1870-1910	1910-1960	1960-2000	1980-2010
		L	M	L	M	L	M	L	M
	Initial Schooling	0.96 * * * (0.13)	-0.77 * * * (0.17)	0.89 * * * (0.30)	-0.16 (0.10)	0.97 * * (0.40)	-0.09 * (0.40)	0.91 * * (0.38)	-0.19 * * * (0.03)
	Convergence rate	-1.7	3.7	-1.3	0.3	-1.7	0.2	-2.2	0.7
	in percents
	N	58	16	46	28	28	46	11	63
	R 2	0.48	0.56	0.15	0.05	0.15	0.05	0.32	0.33
	notes:

According to Unesco (2007), the minimal world survival rate in primary has been around 60% in 2000.

Detailed assumptions for each country are available in a separate appendix.

Most of the time those reports have been corrected in our final sample in order to preserve homogeneity of data -see Annex on enrolment series.

More precisely, notice E P t total enrolment in primary, P its unknown duration that has to be guessed, and P[6,6+P ] the size of the cohort aged between 6 and 6 + P . Then we make P vary and select the value for which the ratio E P t /P [6,6+P ] will flatten around 1 at some point.

It is also important to stress that enrolment rates can differ from those depicted in the literature because of a comparability issue: the literature has usually reported enrolment rates relative to cohorts of pupils aged between 5 and 14 (see[START_REF] Lindert | Growing Public[END_REF]), which is a larger reference population than ours.

Boxes have lines at the lower quartile, median, and upper quartile values. The whiskers are lines extending from each end of the boxes to show the extent of the rest of the data.

In order to give an approximate perspective, this peak has been observed in Europe between 1870 and 1920 -excluding the Baby-Boom variations -, and in Latin and South America between 1940 and 1970. The same phenomenom was at stake in Asia, and had barely started in Africa at that time. The fall in median shares in the early twentieth century corresponds to that happening in Algeria and Egypt.

These countries and the corresponding standard error into parenthesis are respectively: Honduras (0.50), Costa-Rica (0.56), Panama (0.62), Lebanon (0.70), Canada (0.72), Sweden (0.72), Greece (0.78), Bulgaria (0.79), New-Zeland (0.82), Poland (1.09), Czechoslovaquia (1.44), Denmark(1.46). Not surprisingly, these countries constitute the "external envelop" of countries scattered by average schooling and by year of first observation on Figure2.

Lebanon (0.69), Bulgaria (0.54), Denmark (0.66), Greece (0.64), Czechoslovaquia (1.30), Poland (1.17), Panama (0.60).

Another issue related to duration is the possible extension of the schooling term of an academic year. No data is available on this issue except for a few countries.

European countries plus Argentina, Australia, Canada, Japan, New-Zeland, the United States and Uruguay which were mainly populated by Europeans.

This is still reasonnable, even if we have to bear in mind that a handful of countries can be significatively affected in 1960: these are Costa-Rica, Cuba, Guyana, Jamaica, Lebanon, Paraguay, for which the pseudostandard error exceeds 0.5.

In order to maintain comparability with our data set, we had to redefine "primary" and "secondary" schooling in Cohen-Soto accordingly to our own definition, which is the first six years of schooling for the former and the following years for the latter. In practice, some years of primary schooling were attributed to secondary when primary duration exceeded 6 years, and vice-versa when primary duration was strictly smaller than 6 years. For instance, Germany has only 4 years of primary schooling. Then 6-4=2 years of schooling must be counted as primary schooling and not as secondary schooling for individuals with incomplete or completed secondary or tertiary education.

For a use of a comparable measurement-error framework that corrects educational statistics, see[START_REF] Portela | Measurement Error in Education and Growth Regressions[END_REF].

Distortions due to migrations are likely to affect high-immigration OECD countries; in fact, it turns out that OECD countries that have a foreign-born population exceeding 15% of the total population are Australia, Canada, New-Zealand and Switzerland, which have been excluded from the sample and will be examined individually in a subsequent subsection.

i.e. -S h (t) S h (t) < -S 0 (t) S 0 (t)

Empirically, other models have been tested. We have tested models with multiplicative measurement errors, which did not provide any robust finding and had a smaller explanatory power. We also introduced some interactions between survey dummies and h mm , and found them to be not significant.

until 1910 for Canada, as the end of the first globalization period marks the end of fast educational expansion in this country.

The interpolation started from 1920 in Canada and New-Zealand. Interpolation was not assumed to be linear as postwar growth has been more intense -see appendix.

Until 1930 for Egypt.

Western countries (Western Europe, Australia, Canada, New-Zealand and US), Southern-Europe (Italy, Portugal, Spain plus Chile and Argentina of which population had Spanish and Italian origins and similar educational attainments as in these countries), Latin America, Russia, India, Japan, Eastern Asia (China, Indonesia, Malaysia, Myanmar, Philippines, Thailand), MENA (Algeria, Egypt, Iran, Iraq, Morocco, Syria, Tunisia, Turkey) and Sub-Saharan Africa.

In 1870 China had an edge over South-East Asia. The educational gap between the two areas closed around 1950 and remained close to 0 afterwards. This is why we have gathered them in the group of Eastern Asia.

Australia, Belgium, Canada, Denmark, France, Germany, Ireland, Netherlands, New-Zealand, Norway, Spain, Sweden, Switzerland, United Kingdom and the United States.

equal to -1 T log(1 + ρ) where ρ is the estimated coefficient.

However, more research is certainly needed, as the latter authors consider a limited sample and subperiod. Other determinants such as the political regime, the demographic structure, ethnic fractionalization or religion may interfere. Besides, the relationships between actual and compulsory schooling has to be investigated, as the direction of the causality between them is not necessarily identical across countries.

Similarly,[START_REF] Ehrlich | The Evolution of Income and Fertility Inequalities over the Course of Economic Development: A Human Capital Perspective[END_REF] and[START_REF] Murtin | Assessing the Demographic Transition[END_REF] suggest that inequality in fertility within countries is directly linked to the distribution of human capital.

Murtin acknowledges financial support from the Mellon Foundation when he was hosted at the Stanford Centre for the Study of Poverty and Inequality, as well as the EU Marie Curie RTN when he was hosted by the Centre for the Economics of Education (CEE), London School of Economics. The data described in this paper is downloadable from the following address: http://www.pse.ens.fr/