NYU Dynamics and Stagnation in the Malthusian Epoch Discussion

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American Economic Association
Dynamics and Stagnation in the Malthusian Epoch
Author(s): Quamrul Ashraf and Oded Galor
Source: The American Economic Review, Vol. 101, No. 5 (AUGUST 2011), pp. 2003-2041
Published by: American Economic Association
Stable URL: https://www.jstor.org/stable/23045629
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American Economic Review 101 (August 2011): 2003-2041
http://www.aeaweb.org/articles.php?doi=10.1257/aer. 101.5.2003
Dynamics and Stagnation in the Malthusian Epocht
By Quamrul Ashraf and Oded Galor*
This paper examines the central hypothesis of the influential
Malthusian theory, according to which improvements in the tech
nological environment during the preindustrial era had generated
only temporary gains in income per capita, eventually leading to a
larger, but not significantly richer, population. Exploiting exogenous
sources of cross-country variations in land productivity and the level
of technological advancement, the analysis demonstrates that, in
accordance with the theory, technological superiority and higher
land productivity had significant positive effects on population den
sity but insignificant effects on the standard of living, during the time
period 1-1500 CE. (JEL N10, N30, N50, OlO, 040, 050)
The transition from an epoch of stagnation to an era of sustained economic growth
has marked the onset of one of the most remarkable transformations in the course
of human history. While living standards in the world economy stagnated during the
millennia preceding the Industrial Revolution, income per capita has encountered
an unprecedented tenfold increase in the past two centuries, profoundly altering the
level and the distribution of education, health, and wealth across the globe.1
The Malthusian theory has been a central pillar in the interpretation of the process
of development during the preindustrial era and in the exploration of the forces that
brought about the transition from stagnation to growth. Nevertheless, the underlying
premise of the theory, that technological progress and resource expansion during
this epoch had contributed primarily to the size of the population leaving income per
capita relatively unaffected in the long run, has not been tested.2
*Ashraf: Department of Economics, Williams College, Schapiro Hall, 24 Hopkins Hall Dr., Williamstown, MA
01267 (e-mail: [email protected]); Galor: Department of Economics, Brown University, Robinson
Hall, 64 Waterman St., Providence, RI 02912 (e-mail: [email protected]). The authors are grateful to four
anonymous referees and Yona Rubinstein for detailed and insightful comments, and to David de la Croix, Peter
Howitt, Oksana Leukhina, Ross Levine, Joachim Voth, and David Weil for helpful suggestions. Nathan Greenberg
provided able research assistance. Financial support from the Watson Institute at Brown University is gratefully
acknowledged. Galor’s research is supported by NSF grant SES-0921573.
* To view additional materials, visit the article page at
http://www.aeaweb.org/articles.php ?doi= 10.1257/aer. 101.5.2003.
‘The transition from stagnation to growth has been examined by Galor and David N. Weil (1999, 2000), Galor
and Omer Moav (2002), Gary D. Hansen and Edward C. Prescott (2002), Robert E. Lucas, Jr. (2002), Nils-Petter
Lagerlof (2003, 2006), Matthias Doepke (2004), Galor (2005), Kevin H. O’Rourke, Ahmed S. Rahman, and Alan M.
Taylor (2008), Holger Strulik and Jacob Weisdorf (2008), and others, while the associated phenomenon of the Great
Divergence in income per capita has been analyzed by Galor and Andrew Mountford (2006, 2008), Nico Voigtlander
and Hans-Joachim Voth (2006,2009), Ashraf and Galor (2007), and Galor (2010), among others.
2 Recent country-specific studies provide evidence in support of one of the elements of the Malthusian hypoth
esis—the positive effect of income on fertility and its negative effect on mortality. See Nicholas Crafts and Terence
C. Mills (2009) for England in the sixteenth to eighteenth centuries, Morgan Kelly and Cormac 6 Grada (2010) in
the context of medieval and early modern England, and Lagerlof (2009) for Sweden in the eighteenth to nineteenth
centuries.
2003
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2004
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AUGUST20I1
The Malthusian theory, inspired by Thomas R. Malthus (1798), suggests that
worldwide stagnation in income per capita during the preindustrial epoch refle
the counterbalancing effect of population growth on the expansion of resour
in an environment characterized by the positive effect of the standard of livin
population growth along with diminishing labor productivity. Periods marked
the absence of changes in the level of technology or in the availability of land
characterized by a stable population size as well as a constant income per capit
whereas periods characterized by improvements in the technological environm
or in the availability of land generated only temporary gains in income per cap
eventually leading to a larger but not richer population. Technologically super
economies ultimately had denser populations but their standard of living did
reflect their technological advancement.
This research conducts a cross-country empirical analysis of the predictions of
influential Malthusian theory.3 It exploits exogenous sources of cross-country
tion in land productivity and technological levels to examine their hypothesiz
differential effects on population density versus income per capita during the
period 1-1500 CE.
In light of the potential endogeneity of population and technological progre
(Boserup 1965), this research develops a novel identification strategy to exam
the hypothesized effects of technological advancement on population density
income per capita. It establishes that the onset of the Neolithic Revolution th
marked the transition of societies from hunting and gathering to agriculture, as ear
as 10,000 years ago, triggered a sequence of technological advancements that
significant effect on the level of technology in the Middle Ages. As argued by
Diamond (1997), an earlier onset of the Neolithic Revolution has been assoc
with a developmental head start that enabled the rise of a non-food-producing
whose members were essential for the advancement of written language, scie
and technology, and for the formation of cities, technology-based military po
and nation states. Thus, variations in favorable biogeographical factors (i.e., p
toric domesticable species of wild plants and animals) that led to an earlier on
of the Neolithic Revolution across the globe are exploited as exogenous source
variation in the onset of the Neolithic Revolution and, consequently, in the lev
technological advancement during the time period 1-1500 CE.
Consistent with Malthusian predictions, the analysis uncovers statistically sig
cant positive effects of land productivity and the technological level on popula
density in the years 1 CE, 1000 CE, and 1500 CE. In contrast, the effects of l
productivity and technology on income per capita in these periods are not sig
cantly different from zero. Moreover, the estimated elasticities of income per
3 In contrast to the current study, which tests the Malthusian prediction regarding the positive effect o
technological environment on population density but its neutrality for income per capita, Michael Kremer (
examines the prediction of a Malthusian-Boserupian interaction. Accordingly, if population size has a p
effect on the rate of technological progress, as argued by Ester Boserup (1965), this effect should manifest
as a proportional effect on the rate of population growth, taking as given the positive Malthusian feedback
technology to population size. Based on this premise, Kremer’s study defends the role of scale effects in
enous growth models by empirically demonstrating that the rate of population growth in the world has inde
proportional to the level of world population throughout human history. Thus, Kremer does not test the abs
a long-run effect of the technological environment on income per capita, nor does he examine the positive ef
technology on population size.
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VOL. 101 NO. 5 ASHRAF AND GALOR: DYNAMICS AND STAGNATION IN THE MALTHUSIAN EPOCH 2005
with respect to these two channels are about an order of magnitude smaller than the
corresponding elasticities of population density.
Importantly, the qualitative results remain robust to controls for the confounding
effects of a large number of geographical factors, including absolute latitude, access
to waterways, distance to the technological frontier, and the share of land in tropi
cal versus temperate climatic zones, which may have had an impact on aggregate
productivity either directly, by affecting the productivity of land, or indirectly via
the prevalence of trade and the diffusion of technologies. Furthermore, the results
are qualitatively unaffected when a direct measure of technological sophistication,
rather than the timing of the Neolithic Revolution, is employed as an indicator of
the level of aggregate productivity. Finally, the study establishes that the results are
not driven by unobserved time-invariant country fixed effects. In particular, it dem
onstrates that, while the change in the level of technology between 1000 BCE and 1
CE was indeed associated with a significant change in population density over the
1-1000 CE time horizon, the level of income per capita during this time period was
relatively unaffected, as suggested by the Malthusian theory.
I. The Malthusian Model
A. The Basic Structure of the Model
Consider an overlapping-generations economy in which activity extends over infi
nite discrete time. In every period, the economy produces a single homogeneous
good using land and labor as inputs. The supply of land is exogenous and fixed over
time, whereas the evolution of labor supply is governed by households’ decisions in
the preceding period regarding the number of their children.
Production.—Production occurs according to a constant-returns-to-scale technol
ogy. The output produced at time t, Yt, is
(1)
Y, = 0AX)aL-a; a € (0,1),
where L, and X are, respectively, labor and land employed in production in period
t, and A measures the technological level.4 The technological level may capture the
percentage of arable land, soil quality, climate, cultivation and irrigation methods,
as well as the knowledge required for engagement in agriculture (i.e., domestication
of plants and animals). Thus, AX captures the effective resources used in production.
Output per worker produced at time t, y, = Yt/L„ is therefore
(2)
= (AX/Lt)a.
Preferences and Budget Constraints.—In each period t, a generation consisting
of Lt identical individuals joins the workforce. Each individual has a single parent.
4The pace of technological progress, and thus the level of technology, may be determined by the size of the
population (e.g., Kremer 1993; Galor and Weil 2000; Shekhar Aiyar, Carl-Johan Dalgaard, and Moav 2008) without
disrupting the long-run Malthusian equilibrium.
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Members of generation t live for two periods. In the first period of life (childhood),
t — 1, they are supported by their parents. In the second period of life (parenthood),
t, they inelastically supply their labor, generating an income that is equal to the out
put per worker, yt, which they allocate between their own consumption and that of
their children.
Individuals generate utility from consumption and the number of their (surviving)
children:5
(3) u’ = (cty~W, 7 6(0,1),
where ct is consumption and n, is the number of children
tion t.
Members of generation t allocate their income between their consumption, c„ and
expenditure on children, pn,, where p is the cost of raising a child.6 Hence, the bud
get constraint for a member of generation t (in the second period of life) is
(4) pn, + c, < yt. Optimization.—Members of generation t a consumption and child rearing, so as to m tion (3) subject to the budget constraint ( (1 — 7) to consumption and a fraction 7 of (5) ct = (1 - 7)yt n, = If y tip Thus, in accordance with the Malthusian para the number of surviving children. B. The Evolution of the Economy Population Dynamics.—The evolution of the by the initial size of the working population ing) children per adult, nt. Specifically, the s t + 1, Lt+1, is (6) A+i — ntLf, 5 For simplicity, parents derive utility from the expected number of surviving offspring and the parental cost of child rearing is associated only with surviving children. The incorporation of parental cost for nonsurviving children would not affect the qualitative predictions of the model. 6If the cost of children is a time cost, then the qualitative results will be maintained as long as individuals are subjected to a subsistence consumption constraint (Galor and Weil 2000), possibly reflecting the Malthusian effects on body size (Dalgaard and Strulik 2010). If both time and goods are required to produce children, the results of the model will not be affected qualitatively. As the economy develops and wages increase, the time cost will rise proportionately with the increase in income, but the cost in terms of goods will decline. Hence, individuals will be able to afford more children. This content downloaded from 128.122.149.92 on Mon, 27 Jan 2020 14:03:06 UTC All use subject to https://about.jstor.org/terms VOL. 101 NO. 5 ASHRAF AND GALOR: DYNAMICS AND STAGNATION IN THE MALTHUSIAN EPOCH 2007 Figure 1. The Evolution of Population Size where L, is the size of the working population in period t, and L0 > 0 is given.
Substituting (2) and (5) into (6), the time path of the working population is gov
erned by the first-order difference equation
Lt+l = (i/p)(AX)aL)-a = 4>{L,-A),
(?)
where, as depicted in Figure 1, 4>l{L,-,A) > 0 and 4>ll(L,-,A) < 0, so l(L,A) = oo, and = 0. Hence, for a given level of technology, A, noting that L0 > 0, there exists a unique,
stable steady-state level of the adult population, L :7
L = (7 /p)l/°(AX) = L(A),
(8)
and population density, Pd:
(9)
Pd = L/X = (7/p)1/QA = Pd(A).
7 The trivial steady state, L = 0, is unstable. Thus, given that L0 > 0, this equilibrium will not be an absorbing
state for the population dynamics.
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THE AMERICAN ECONOMIC REVIEW AUGUST 2011
Figure 2. The Evolution of Income per Worker
Importantly, as is evident from (8) and (9), an improvement in the technological
environment, A, increases the steady-state levels of the adult population, L, and
population density, Pd:
(10)
As depicted in Figure 1, if the economy is in a steady-state equilibrium, an increase
in the technological level from A to Ah generates a transition process in which popu
lation gradually increases from its initial steady-state level, L, to a higher one, Lh.
Similarly, a decline in the population due to an epidemic such as the Black Death
(1348-1350 CE) would temporarily reduce population, while temporarily increas
ing income per capita. The rise in income per capita, however, will generate a grad
ual increase in population back to the initial steady-state level, L.
The Time Path of Income per Worker.—The evolution of income per worker is
determined by the initial level of income per worker and the number of (surviving)
children per adult. Specifically, income per worker in period t + 1, yt+noting (2)
and (6), is
(11)
yt+1 = {AX)/Lt+x}a = [{AX)/n,L,]a = yt/n?.
Substituting (5) into (11), the time path of income per worker is governed by the
first-order difference equation
(12)
ym = (p/i)ay) a =
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VOL. 101 NO. 5 ASHRAF AND GALOR: DYNAMICS AND STAGNATION IN THE MALTHUSIAN EPOCH 2009
where, as depicted in Figure 2, t/j'(yt) > 0 and ?/;”(>’,) < 0, so ip(yt) is strictly con cave, and -0(0) = 0, lim^o ip (yt) - oo and lim^^ tp (yt) = 0. Hence, given y0 > 0, there exists a unique, stable steady-state level of income per
worker, y:8
(13)
y
=
(p/i).
Importantly, as is evident from (2)
A, increases the level of
technology,
not
affect
the
steady-state
level
of
(14) to > 0 and § = 0.
As depicted in Figures 1 and 2, if the economy is in a steady-state equilibrium,
an increase in the technological level from A1 to Ah generates a transition process
in which income per worker initially increases to a higher level, y, reflecting higher
labor productivity in the absence of population adjustment. However, as popula
tion increases, income per worker gradually declines to the initial steady-state equi
librium, y. Similarly, a decline in the population due to an epidemic such as the
Black Death would temporarily reduce population to L, while temporarily increas
ing income per capita to y. The rise in income per worker will generate a gradual
increase in population back to the steady-state level, L, and thus a gradual decline
in income per worker back to y.
C. Testable Predictions
The Malthusian theory generates the following testable predictions:
(i) Within a country, an increase in productivity would lead in the long run to a
larger population, without altering the long-run level of income per capita.
(ii) Across countries, those characterized by superior land productivity or a supe
rior level of technology would have, all else equal, higher population densi
ties in the long run, but their standards of living would not reflect the degree
of their technological advancement.
These predictions emerge from a Malthusian model as long as the model is based
upon two fundamental features: (i) a positive effect of the standard of living on
population growth, and (ii) decreasing returns to labor due to the presence of a fixed
factor of production—land.9
8The trivial steady state, y = 0, is unstable. Thus, given that y0 > 0, this equilibrium will not be an absorbing
state for the income dynamics.
9 Specifically, these predictions would arise in the presence of a dynastic representative agent Malthusian frame
work (Lucas 2002), a reduced-form Malthusian-Boserupian interaction between population size and productivity
growth (Kremer 1993), exogenous technological progress (Hansen and Prescott 2002), and endogenous technologi
cal progress that reflects the positive impact of population size on aggregate productivity (Galor and Weil 2000).
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AUGUST 2011
II. Empirical Framework
A. Empirical Strategy
The empirical examination of the central hypothesis of the Malthusian theory
exploits exogenous sources of cross-country variation in land productivity and tech
nological levels to examine their hypothesized differential effects on population
density and income per capita during the time period 1-1500 CE.
In light of the potential endogeneity of population and technological progress, this
research develops a novel identification strategy to examine the hypothesized effects
of technological advancement on population density and income per capita. First, it
establishes that the onset of the Neolithic Revolution, which marked the transition
of societies from hunting and gathering to agriculture as early as 10,000 years ago,
triggered a sequence of technological advancements that had a significant effect
on the level of technology in the Middle Ages. As argued by Diamond (1997), an
earlier onset of the Neolithic Revolution has been associated with a developmental
head start that enabled the rise of a non-food-producing class whose members were
essential for the advancement of written language, science, and technology, and for
the formation of cities, technology-based military powers, and nation states.10 Thus,
variation in the onset of the Neolithic Revolution across the globe is exploited as a
proxy for variation in the level of technological advancement during the time period
1-1500 CE.
In addition, to address the possibility that the relationship between the timing of
the Neolithic transition and population density in the Common Era may itself be
spurious, being perhaps codetermined by an unobserved channel such as human
capital, the analysis appeals to the role of prehistoric biogeographical endowments
in determining the timing of the Neolithic Revolution. Importantly, the productivity
of land for agriculture in the Common Era is largely independent of the initial geo
graphical and biogeographical endowments that were conducive for the onset of the
Neolithic Revolution. While agriculture originated in regions of the world to which
the most valuable domesticable wild plant and animal species were native, other
regions proved more fertile and climatically favorable once the diffusion of agricul
tural practices brought the domesticated varieties to them (Diamond 1997). Thus,
the analysis adopts an instrumental variables (IV) strategy, exploiting variation in
the numbers of prehistoric domesticable species of plants and animals that were
native to a region prior to the onset of sedentary agricultural practices as exogenous
sources of variation for the number of years elapsed since the Neolithic Revolution
to demonstrate its causal effect on population density in the Common Era.”
10See also Weisdorf (2005, 2009). In the context of the Malthusian model presented earlier, the Neolithic
Revolution should be viewed as a large positive shock to the level of technology, A, followed by a long series of
incremental aftershocks. Thus, at any given point in time, a society that experienced the Neolithic Revolution earlier
would have a longer history of these aftershocks and would therefore reflect a larger steady-state population size (or,
equivalently, a higher steady-state population density).
‘1 The insufficient number of observations arising from the greater paucity of historical income data, as com
pared to data on population density, does not permit a similar instrumental variables strategy to be pursued when
examining the impact of the timing of the Neolithic Revolution on income per capita. In particular, since most
of the cross-sectional variation in the numbers of prehistoric domesticable species of wild plants and animals, as
reported by Ola Olsson and Douglas A. Hibbs, Jr. (2005), occurs between regions rather than within regions, the
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VOL 101 NO. 5 ASHRAF AND GALOR: DYNAMICS AND STAGNATION IN THE MALTHUSIAN EPOCH 2011
Moreover, a direct, period-specific measure of technological sophistication is also
employed as an alternative metric of the level of aggregate productivity to demon
strate the qualitative robustness of the baseline results for the years 1000 CE and 1
CE.12 Once again, the link running from the exogenous prehistoric biogeographical
endowments to the level of technological advancement in the Common Era, via the
timing of the Neolithic transition, enables the analysis to exploit the aforementioned
biogeographical variables as instruments for the indices of technological sophistica
tion in the years 1000 CE and 1 CE to establish their causal effects on population
density in these periods.
Finally, in order to ensure that the results from the level regressions are not driven
by unobserved time-invariant country fixed effects, this research also employs a
first-difference estimation strategy with a lagged explanatory variable. In particular,
the robustness analysis exploits cross-country variation in the change in the level
of technological sophistication between the years 1000 BCE and 1 CE to explain
the cross-country variations in the change in population density and the change in
income per capita over the 1-1000 CE time horizon.
B. The Data
The most comprehensive worldwide cross-country historical estimates of popu
lation and income per capita since the year 1 CE have been assembled by Colin
McEvedy and Richard Jones (1978) and Angus Maddison (2003), respectively.13
Indeed, despite inherent problems of measurement associated with historical data,
these sources remain unparalleled in providing comparable estimates across coun
tries in the last 2,000 years and have, therefore, widely been regarded as standard
sources for such data in the long-run growth literature.14 For the purposes of the
current analysis, the population density of a country for a given year is computed as
population in that year, as reported by McEvedy and Jones (1978), divided by total
land area.
The measure of land productivity employed is the first principal component of
the percentage of arable land and an index reflecting the overall suitability of land
small sample size imposed by the availability of historical income data results in an insufficient amount of variation
in explanatory variables for the first-stage regressions.
12The absence of sufficient variation in the underlying data obtained from Peter N. Peregrine (2003) prevents the
construction of a corresponding technology measure for the year 1500 CE.
13It is important to note that, while the urbanization rate in 1500 CE has sometimes been used as an indicator
of preindustrial economic development, it is not an alternative measure for income per capita. As suggested by the
Malthusian hypothesis, technologically advanced economies have higher population densities and may thus be
more urbanized, but the extent of urbanization has little or no bearing on the standard of living in the long run—it
is largely a reflection of the level of technological sophistication. Indeed, the results in this study are qualitatively
unaffected, particularly with respect to the impact of technological levels (as proxied by the timing of the Neolithic
Revolution), when the urbanization rate in 1500 CE is used in lieu of population density as the outcome variable.
‘”•Nevertheless, in the context of the current study, the use of Maddison’s (2003) income per capita data could
have posed a significant hurdle if the data had in part been imputed with a Malthusian viewpoint of the preindus
trial world in mind. While Maddison (2008) suggests that this is not the case, the empirical investigation to follow
performs a rigorous analysis to demonstrate that the baseline results remain robust under alternative specifications
designed to address this particular concern surrounding Maddison’s income per capita estimates. Regarding the
historical population data from McEvedy and Jones (1978), while some of their estimates remain controversial,
particularly those for sub-Saharan Africa and pre-Columbian Mesoamerica, a recent assessment (see, e.g., www.
census.gov/ipc/www/worldhis.html) conducted by the US Census Bureau finds that their aggregate estimates indeed
compare favorably with those obtained from other studies. Moreover, the regional estimates of McEvedy and Jones
are also very similar to those presented in the more recent study by Massimo Livi-Bacci (2001).
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for agriculture, based on geospatial soil quality and temperature data, as reported
by Navin Ramankutty et al. (2002) and aggregated to the country level by Stelios
Michalopoulos (2008).15 The variable for the timing of the Neolithic Revolution,
constructed by Louis Putterman (2008), measures the number of thousand years
elapsed, relative to the year 2000 CE, since the majority of the population residing
within a country’s modern national borders began practicing sedentary agriculture
as the primary mode of subsistence.
The index of technological sophistication is constructed based on historical cross
cultural technology data, reported with global coverage in Peregrine’s (2003) Atlas
of Cultural Evolution. In particular, for a given time period and for a given culture in
the archaeological record, the Atlas of Cultural Evolution draws on various anthro
pological and historical sources to report the level of technological advancement,
on a three-point scale, in each of four sectors of the economy, including commu
nications, industry (i.e., ceramics and metallurgy), transportation, and agriculture.
The index of technological sophistication is constructed following the aggregation
methodology of Diego A. Comin, William Easterly, and Erick Gong (2008).16
C. The Neolithic Revolution and Technological Advancement
This section establishes that the Neolithic Revolution triggered a cumulative pro
cess of economic development, conferring a developmental head start to societ
ies that experienced the agricultural transition earlier. In line with this assertion,
Table 1 reveals preliminary results indicating that an earlier onset of the Neolithic
Revolution is indeed positively and significantly correlated with the level of techno
logical sophistication in nonagricultural sectors of the economy in the years 1000
CE and 1 CE. For instance, the coefficient estimates for the year 1000 CE, all of
which are statistically significant at the 1 percent level, indicate that a 1 percent
increase in the number of years elapsed since the onset of the Neolithic Revolution
is associated with an increase in the level of technological advancement in the com
munications, industrial, and transportation sectors by 0.37, 0.07, and 0.38 percent,
respectively.
These findings lend credence to the empirical strategy employed by this research
to test the Malthusian theory. Specifically, they provide evidence justifying the use
of the exogenous source of cross-country variation in the timing of the Neolithic
Revolution as a proxy for the variation in the level of technological advancement
across countries during the agricultural stage of development. Moreover, they serve
as an internal consistency check between the cross-country Neolithic transition
timing variable and those on historical levels of technological sophistication, all of
15 The use of contemporary measures of land productivity necessitates an identifying assumption that the spatial
distribution of factors governing the productivity of land for agriculture has not changed significantly in the past
2,000 years. In this regard, it is important to note that the analysis at hand exploits worldwide variation in such
factors, which changes dramatically only in geological time. Hence, while the assumption may not necessarily hold
at a subregional level in some cases (e.g., in regions south of the Sahara where the desert has been known to be
expanding gradually in the past few centuries), it is unlikely that the moments of the global spatial distribution of
land productivity are significantly different today than they were two millennia ago. Moreover, the stability of the
results over the 1-1500 CE time horizon further alleviates this potential concern.
16 For descriptive statistics, as well as the definitions and sources of all the primary and control variables
employed by the analysis, see the online Appendix.
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VOL. 101 NO. 5 ASHRAF AND GALOR: DYNAMICS AND STAGNATI