1
NUMERACY IN CENTRAL NEW SPAIN DURING THE
ENLIGHTENMENT
ANDRÉS CALDERÓN-FERNÁNDEZ
UNAM-FE
a
RAFAEL DOBADO-GONZÁLEZ
Universidad Complutense de Madrid
b
ALFREDO GARCÍA-HIERNAUX
DANAE e ICAE (Universidad Complutense de Madrid)
c
Preliminary version
ABSTRACT
This article presents new evidence and analysis on age heaping -a proxy for numeracy
and therefore for human capital- in New Spain during the Enlightenment. Human
capital plays an important role in economic growth and welfare. It is also one of the
dimensions of inequality. Our results are at odds with many of the usual assumptions
on which most Mexicanist historiography is based. Age heaping levels of males and
females and ethnic groups across locations in Central New Spain are estimated and
compared through ad hoc indicators with other countries. We infer that a more
empirical emphasis on the institutional legacy of the viceregal period and more
attention to human capital since pre-Conquest times will benefit the progress of
Hispanic American economic history.
JEL Classification: I00, N00, N16
Keywords: Age Heaping, numeracy, human capital, eighteenth-century Mexico,
international comparisons.
a
Departamento de Historia Económica. andrescalderonfernandez@yahoo.com.mex
b
Departamento de Economía Aplicada, Estructura e Historia. rdobado@ccee.ucm.es
c
Fundamentos del Análisis Económico. agarciah@ucm.es
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1. INTRODUCTION
Institutions have enjoyed an important, if perhaps somewhat undeserved, role in the
explanation of long-term economic growth by economists and economic historians
during the last two decades or so. In spite of this, human capital has remained widely
accepted as one of the main explanatory variables of economic growth (Crayen and
Baten, 2010; Földvári et al., 2012). Thus, Glaeser et al. (2004) offer a convincing answer
to Acemoglu et al. (2001, 2002), which is very relevant to our purposes.
1
In turn,
Engerman and Sokoloff (2005) attribute great importance to the differences in human
capital between Europeans and Aboriginals for explaining inequality in the conquered
teerritories. Additionaly, a new scholarship is investigating the place of women in the
process of human capital formation (De Moor and Van Zanden, 2010; Baten and De
Pleijt, 2018; De Moor, s.d.).
Numeracy may be taken as a reliable proxy for human capital in historical
populations (Crayen and Baten, 2010a; Hippe, 2012). Numeracy is defined as the
“ability to count, keep records of these counts, and make rational calculations” by
Manzel et al. (2012, p. 933). Crayen and Baten (2010a) base their argument on several
convincing key points.
2
Among other advantages, numeracy can be measured. This is
because humans do not always know their exact age when asked about it.
Paradoxically, the absence of precision regarding their age by individuals in past and
present societies makes it possible to estimate numeracy. As explained by A’Hearn et
al. (2009, pp. 785-786):
“Approximation in age awareness manifests itself in the phenomenon of
‘heaping’ in self-reported age data. Individuals lacking certain knowledge of
their age rarely state this openly but choose instead a figure they deem
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“The Europeans who settled in the New World may have brought with them not so much their
institutions, but themselves, that is, their human capital.” Glaeser et al., 2004, p. 274.
2
“Numeracy should be considered as a historical measure of human capital since knowledge
about numbers and numeric discipline are even more crucial for economic growth than the
ability to sign one’s name on a marriage certificate. Numeracy goes hand-in-hand with
technological abilities, and it is a necessity for modern commercial economies. For Weber,
Sombart, and Schumpeter, numeracy was at the very heart of modern rational capitalism. They
traced the latter’s roots back to the invention of double-entry bookkeeping in late-medieval
Italy.” Crayen and Baten, (2010a, p. 83).
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plausible. They do not choose randomly but have a systematic tendency to
prefer ‘attractive’ numbers, such as those ending in 5 or 0, even numbers, or –in
some societies- numbers with other specific terminal digits.”
Age heaping can be estimated using ad hoc techniques –see next section. Thus,
age heaping becomes a convincing indicator of numeracy (Tollnek and Baten, 2017, p.
799). For these, and many other, authors: “The share of persons able to report an exact
age is highly correlated with other indicators of human capital, such as literacy and
schooling, across countries and over time.”
Additionally, as pointed out by A’Hearn et al. (2009), the historical sources
allowing us to estimate age heaping are comparatively abundant (e.g., census returns,
tombstones, necrologies, muster lists, legal records and tax data). This advantage over
alternative proxies for human capital is relevant for economic historians of the Early
Modern Era. All in all, a wide consensus exists regarding the causal relationship
between age heaping, numeracy and human capital formation.
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Although a contemporaneous positive correlation between living standards and
human capital is not always found, it seems reasonable to assume that in the long or
very long run these two dimensions of welfare interact reinforcing each other over
time.
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Despite its interest, literature on numeracy in the Hispanic world during the
Early Modern era is rather scarce. To the best of our knowledge, only Baten and
collaborators have studied the topic for Spanish American countries before
independence (Baten and Mumme, 2010; Manzel et al. (2012); Juif and Baten, 2013).
3
Recently, some authors have questioned the validity of age heaping as a proxy for human
capital formation (A’Hearn et al., 2017; Beltrán et al., 2017). On the contrary, an article as
recent as that by Blum and Krauss (2018) still supports the most extended view. Criticism of
the use of age heaping as a proxy for human capital ought to be taken into consideration.
However, even if, as claimed by A’Hearn et al. (2017), age heaping might be interpreted as an
indicator of cultural and institutional modernization rather than as a direct measure of
cognitive skills, the fact still remains that it is unlikely that modernization does not positively
correlate with human capital accumulation.
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Baten et al. (2010) show that the combination of low living standards with high human capital
is present in traditional China –or even today, if compared with the OECD countries-. No
correlation between age heaping and height is found in a sample of more than 20,000
observations from Central New Spain for circa 1790.
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As for Spain, the scarcity of works is even more acute (Álvarez and Ramos 2018 for
Castile; Gómez Aznar 2019 for Catalonia and Juif et. al., forthcoming).
We contribute to the limited existing literature analyzing numeracy in late
eighteenth-century Central New Spain. Our research is relevant because of the sample
size as well as the fact that all ethnic groups and females are included. The comparison
with other societies is another asset of our work. The well-known age heaping
methodology is used in this paper. Our micro approach allows us to explore a rich data
set privileging focus over scope.
Our results partially contradict some of the usual assumptions (be they explicit
or, more commonly, implicit), behind mainstream thinking on socioeconomic
conditions prevailing in pre-independent Mexico. This is especially the case in terms of
what can be described as the “inequality question”. This issue was raised in the late
1990s and early 2000s in a series of widespread papers written by Engerman and
Sokoloff (1994, 2002 and 2005) and Acemoglu et al. (2002). They depict New Spain,
along with most Spanish American countries, as an extreme case of inequality. This
“original sin” would continue to be rooted in the post-independence institutions and
constitute the main cause of the development problems (low growth and high
inequality) experienced by Spanish America. The enormous influence exerted by this
institutionalist approach is somehow surprising since no empirical evidence on
inequality is offered for the pre-independent period.
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On the contrary, Milanovic et al. (2010) deal with inequality in 28 historical
societies (ranging from the first-century Roman Empire to 1947 British-ruled India) in
an empirical, although not unproblematic, way. They do so by using mainly social
tables and tax censuses to estimate Gini coefficients. They found that inequality in
New Spain circa 1790, derived from the Escritos that the bishop Abad y Queipo wrote
between 1799 and 1813, was so high that it lay beyond the theoretical maximum
represented by the inequality possibility frontier. In this respect, some Mexican
historians (e.g., Tanck and Marichal, 2010), based on qualitative evidence, claim that
wealth was concentrated in the hands of the Spaniards born in America.
5
Further argumentation in Dobado (2009).
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Thus, our results contribute to offer a more nuanced picture of Central New
Spain’s society in the late viceregal period. Numeracy, proxied by age heaping, is
comparable to that of peripheral Europe and much lower than in the backward regions
of the world (most of Asia and Africa). Spatial differences within our region are
observed, as occurs across Europe.
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Inequalities based on ethnicity existed. As could be
expected, españoles were at the top of the distribution, indios and mulatos (also
classified as negros) at the bottom, while other castas (castizos and mestizos) generally
fell in between.
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However, these disparities were not significantly larger than those
found between the upper and lower strata of core countries in Early Modern Europe,
not to mention the Cape Colony around the same time. Nevertheless, geographical
heterogeneity is more significant than that caused by ethnicity. A sexual gap is found,
but it is not higher than in the European samples for different periods and sometimes
it even favors females (as in the city of Oaxaca). Finally, we point out that the
comparatively high numeracy levels found in late viceregal times did not lead to a
higher GDP per capita in Mexico by 1870.
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Thus, we consider that the explanation for
the poor results shown by the Mexican economy after independence are to be found
rather after 1810 than before.
The rest of this article is organized as follows. After this introduction, it
comprises four sections: the first one introduces the concepts of numeracy and age
heaping and presents the sources used; the levels of age heaping estimated for three
samples belonging to late eighteenth-century Central New Spain (Oaxaca, Mexico City
and 24 localities in Central Mexico, including Guanajuato, Queretaro and Tlaxcala) are
presented in the following section; the next section focuses on the international
6
See e.g., Hippe and Baten (2011) and Tollnek and Baten (2017).
7
“Racial classifications in New Spain were not strict and totally precise divisions between the
different groups. Before the mid-seventeenth century, official documents made little effort to
distinguish beyond Spaniards, Indians, and Blacks (Hausberger and Mazín, 2010). Our
translation. Any misinterpretation remains our sole responsibility. Nonetheless, by the late
eighteenth century, the enlightened spirits of New Spain tried to order and classify their
environment, including “races”. Thus, at that time, a castizo was someone closer to a Spaniard
in looks but with some degree of racial mixture; mestizos were those of Spanish and Indian
descent, although this group would certainly encompass also those Indians living outside the
Indian town councils; and mulatos were those with Spanish and African ancestors.
Nonetheless, ethnic classification was not independent from the social position of the person
and the context in which he or she would be acting.
8
See both Maddison Historical Statistics and Maddison Project Database 2018.
https://www.rug.nl/ggdc/historicaldevelopment/maddison/. Accessed in February 2018.
