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The Mortality Transition, Malthusian Dynamics,
and the Rise of Poor Mega-Cities∗
Remi Jedwab† and Dietrich Vollrath‡
Abstract: The largest cities in the world today lie mainly in poor countries, which
is a departure from historical experience, when they were typically found in the
richest places. We use new demographic data to establish several stylized facts
distinguishing poor mega-cities from historically rich mega-cities. To account for
these facts we develop a model that combines Malthusian models of endogenous
population growth with urban models of agglomeration and congestion, and it
shows that a city’s absolute population growth can determine whether it becomes
a poor or rich mega-city. We posit that poor mega-cities arose because the postwar mortality transition dramatically lowered their mortality rates and raised
their absolute growth above a crucial threshold. They then continued to grow
in size but not in living standards because their poverty kept their fertility rates
high. Poor mega-cities thus grew precisely because they were poor.
Keywords: Unified Growth Theory; Urban Malthusianism; Demographic Regime;
Epidemics; Megacities; Congestion; Long-Run Growth
JEL classification: O11; O14; O18; L16; N10; N90; R10
∗
We would like to thank Quamrul Ashraf, Alain Bertaud, Hoyt Bleakley, Edward Glaeser, Stelios
Michalopoulos, Paul Romer, Nico Voigtlaender, Hans-Joachim Voth, David Weil and seminar audiences
at George Mason-George Washington Economic History Workshop, George Mason (Economics, Public
Policy), George Washington, George Washington Urban Day, HKS (NEUDC), Los Andes, Michigan, New
South Wales, NYU, Oxford, Paris 1, PSE, Rosario, UCLA (PACDEV), U.S. Department of State, Williams,
World Bank Urbanization Conference, and World Bank-UNESCAP for helpful comments. We thank the
Institute for International Economic Policy and the Elliott School of International Affairs (SOAR) at George
Washington University for financial assistance.
†
Remi Jedwab, Department of Economics, George Washington University, 2115 G Street, NW,
Washington, DC 20052, USA (e-mail: jedwab@gwu.edu).
‡
Corresponding Author: Dietrich Vollrath, Department of Economics, University of Houston, 201C
McElhinney Hall, Houston, TX 77204, USA (e-mail: devollrath@uh.edu).
Urbanization has gone hand in hand with economic growth throughout history, and
the majority of world population now lives in cities. However, post-war developing
countries have urbanized in a different manner compared to the historical experience
of currently developed countries. Specifically, the post-war period has seen the rise of
poor mega-cities in developing nations. Delhi, Dhaka, Karachi, Kinshasa, Lagos, and
Manila are some of the largest agglomerations on the planet today, each with over 10
million inhabitants. Only six of the currently largest 30 cities (London, Los Angeles,
New York, Osaka, Paris, and Tokyo) are in high income countries. The prevalence of
poor mega-cities today runs counter to historical experience. In the first half of the 20th
century, the largest cities in the world were all in the most advanced economies.
The mega-cities of today’s developing world are unlike their historical peers in that
their massive size is not indicative of rapid economic growth. This “poor country
urbanization” (Glaeser, 2013) has generated poor mega-cities that do not appear
to be able to take advantage of the agglomeration economies of their rich-country
peers.1
In this paper, we first document how the poor mega-cities of the 20th century differ
from rich mega-cities of the past. In particular, we show that poor mega-cities have
lower crude death rates and higher absolute growth in population compared to historical
mega-cities. Second, to explain the importance of this demographic difference, we build
a model that combines the insights of Malthusian models of endogenous population
growth (Galor & Weil, 1999, 2000; Ashraf & Galor, 2011) with the urban literature
on equilibrium city size (Henderson, 1974; Duranton & Puga, 2004; Duranton, 2014).
The model shows that above a threshold on absolute growth in city size, there is a poor
mega-city equilibrium with persistently high population growth but stagnant wages.
Finally, in light of the model we argue that the onset of the mortality transition after
World War II contributed to the rise of poor mega-cities in the 20th century. We show
in a calibration exercise that the decline in death rates observed in post-war developing
countries was sufficient to push their cities above the threshold and turn them into poor
mega-cities.
To begin, we collect data for mega-cities from antiquity to modern times, and document
the differences in demographics between historical mega-cities and the poor mega-cities
1
While there is some work on urbanization without growth (Fay & Opal, 2000), in general there
has been less attention given to poor mega-cities. See Duranton (2008, 2014), Henderson (2010), and
Desmet & Henderson (2014) for recent surveys of cities in developing countries which reference poor
mega-cities briefly.
1
of the developing world today. Relative to history, the poor mega-cities of the 20th
century experienced extremely large absolute population growth, attributable to the
mortality transition of the 1940’s and 1950’s (what Acemoglu & Johnson (2007) refer
to as the “International Epidemiological Transition”). Their rates of natural increase the birth rate minus the death rate - in the 1960’s were well above levels seen in earlier
mega-cities, and this is exclusively due to the severe drop in urban death rates following
the mortality transition. Poor mega-cities grew in absolute terms both because of inmigration from rural areas and natural increase in the cities themselves, in contrast to
historical “killer” cities that grew only through in-migration.2
Beyond the absolute pace of growth, we further document that poor mega-cities of
today display characteristics that suggest positive agglomeration benefits may not
necessarily outweigh the congestion effects of their size. Poor mega-cities are much
more densely populated than rich mega-cities, with large parts of their residents in
slums, reflecting a lack of city infrastructure. Their human capital level is relatively low,
with high dependent population shares, and low secondary and tertiary completion
rates compared to rich mega-cities.
To explain the emergence of these poor mega-cities, we construct a model of city
production and endogenous demographics. As mentioned, it combines elements of the
Malthusian literature with models of urban agglomeration and congestion. In our model
the growth rate of wages depends on the city productivity growth rate relative to the
absolute change in the city population. A sufficiently large change in city population
will produce so much additional congestion that it offsets productivity growth, leaving
wages stagnant or falling. Wage growth can be sustained in cities only if the absolute
growth in city population remains below a critical threshold, and this leads to two
possible long-run equilibrium outcomes. In the first, the absolute growth of city size
is above this threshold, and the economy ends up with poor mega-cities. They fall into
a bad cycle where low wages keep city fertility rates and thus population growth high,
and this keeps the absolute growth of the city above the threshold so that wages remain
low. In contrast, a second equilibrium occurs when a city has small absolute increases
2
Our paper on city sizes is related to Jedwab, Christiaensen & Gindelsky (2014) who study the effects
of natural increase on urbanization rates for 7 European countries in 1700-1950 and 35 developing
countries from 1960-2010. They focus their analysis on the growth of the urban population as a
whole relative to the total population, hence urbanization rates, while here we look specifically at the
absolute population growth of the largest cities in the world, hence mega-city growth. Their work is also
purely empirical, while we provide a theoretical analysis of the growth of mega-cities. Studying megacity population growth is particularly important in the light of unified growth theory since Malthusian
congestion effects disproportionately affect the largest cities.
2
in population size, leading to a rich mega-city. In these cities, low absolute population
growth each period allows for positive wage growth, and this in turn leads to lower
population growth rates, which further accelerates wage growth. Both poor and rich
mega-cities grow in population size over time, but poor mega-cities grow because they
are poor, while rich mega-cities grow because they are rich.
Given the predictions of the model, we then examine the rise of poor mega-cities
as a consequence of the mortality transition after World War II. Significant health
improvements in poor countries occurred due to the dissemination of penicillin and
streptomycin, the use of DDT to control malaria, and vaccination campaigns by the
World Health Organization (Stolnitz, 1955; Davis, 1956; Preston, 1975; Acemoglu &
Johnson, 2007). While saving significant numbers of lives, the mortality transition led
to unprecedented increases in city population growth in poor countries. For example,
poor mega-cities such as Dhaka, Lagos and Karachi grew by roughly 400,000 persons
per year in the last decade, while historic mega-cities like New York, Paris and London
grew by only 220,000, 110,000 or 90,000 per year, respectively, at the very height of
their growth.
We posit that this shock to city growth may have been sufficient to push developing
country cities above the crucial threshold identified in the model, and put them into
the poor mega-city equilibrium. We evaluate this argument quantitatively, using a
calibrated version of our model. We first show that changes in crude death rates
matching those seen during the mortality transition are sufficient to create large gaps
in wages over fifty or one-hundred years. Second, we use the calibrated model to
predict the long-run outcomes of cities. The calibration successfully classifies 65-80%
of cities as rich or poor mega-cities in 2000-2010 based on their characteristics in 1960.
The mortality transition was a shock to population growth sufficient to push many
developing country cities into the poor mega-city equilibrium.
The poor mega-city equilibrium is one that arises perversely because of the success of
interventions that limited urban mortality rates while urban fertility remained relatively
high. In this, our work is similar to others that emphasize the negative economic effect
of mortality interventions and/or the positive economic impacts of mortality increases
(see Young (2005) and Acemoglu & Johnson (2007) for prime examples).3
3
Our work is also linked to studies that consider the effect of lower mortality on population and
economic growth (Acemoglu & Johnson, 2007; Weil, 2007; Bleakley, 2007, 2010; Bleakley & Lange, 2009;
Cutler et al., 2010; Bloom, Canning & Fink, 2014) as well as those examining the effect of unexpected
decreases in population on development (Davis & Weinstein, 2002; Young, 2005; Voigtländer & Voth,
3
Our paper is close in subject matter to Voigtländer & Voth (2013a), who study the
possibility of multiple equilibria in the development and urbanization processes in
historical Europe and China, but do not consider the modern arrival of poor megacities in the developing world. In terms of mechanisms, they introduce a non-linearity
in mortality rates tied to a threshold urbanization rate, and thus an exogenous shock
like the Black Death allows Europe to move to a better equilibrium. In comparison, our
model introduces a Malthusian force in city size, and the equilibrium that a city ends up
in is not a result of an exogenous shock to city size, but rather to the absolute growth
of city population.
In addition to this, our work adds to the literature on the effects of demography on
economic growth in general. Population growth promotes economic growth if high
population densities encourage human capital accumulation or technological progress
(Glaeser et al., 1992; Becker, Glaeser & Murphy, 1999; Galor & Weil, 2000; Jones, 2001;
Lucas, 2004). On the other hand, rapid population growth dilutes capital stocks and is
associated with lower rates of human capital acquisition, leading to lower economic
growth. In Malthusian and many unified growth models, the presence of a fixed
factor of production (e.g. agricultural land) implies that living standards are inversely
proportional to population size.4
In the urban setting we consider, greater population allows for agglomeration effects,
but only over some range of population size. But population also induces congestion
effects, which negatively affects living standards, similar to models that have a fixed
resource in the production function. Our work shows that Malthusian pressures leading
to stagnant wages arise not only because of limits on natural resources, but also due to
the nature of urbanization itself. Significantly, this implies that Malthusian forces need
not disappear just because economies urbanize.
2009, 2013a,b; Acemoglu, Hassan & Robinson, 2011; Ashraf, Weil & Wilde, 2011). Relative to those
works we consider the implications of unexpected mortality changes from the perspective of cities and
highlights that absolute changes in city populations are a crucial component of development. We also
abstract from the more direct welfare-improving consequences of increases in urban life expectancy.
4
The literature on the relationship of population and economic growth is vast. Barro & Becker (1989);
Becker, Murphy & Tamura (1990) and Manuelli & Seshadri (2009) provide models of the negative
relationship of income and fertility. Unified growth models depend on a rise in the demand for human
capital to induce sustained growth, which is driven by acceleration in technological change (Galor &
Weil, 1999, 2000; Lehr, 2009; Ashraf & Galor, 2011). This demand may also be driven by gender-biased
technological change (Galor & Weil, 1996), the decline in benefits of child labor (Doepke, 2004; Doepke
& Zilibotti, 2005), improvements in health (Kalemli-Ozcan, 2002; Lagerlof, 2003; Cervellati & Sunde,
2005; Soares & Falcao, 2008; Cervellati & Sunde, 2011), trade (Galor & Mountford, 2006, 2008), the
evolution of preferences for child quality (Galor & Moav, 2002), culture (Tertilt, 2005), or structural
change (Vollrath, 2011). Galor (2011, 2012) provide more thorough reviews of the literature in this
area.
4
The origin of poor mega-cities is certainly not mono-causal. Our explanation involving
the mortality transition does not rule out slow productivity growth, poor institutions,
or relatively high fertility rates as additional factors. The mortality transition also is
compatible with other urban-specific factors such as changes in urban transportation
and housing technologies, changes in preferences towards large cities, urban-biased
policies, and others, that may increasingly create a disconnect between city sizes and
city living standards (Jedwab & Vollrath, 2015).5 Glaeser (2013) begins with the same
set of motivating facts regarding the rise of poor mega-cities, but looks at them in a
different light. His paper focuses on the internal institutional structure that prevents
mega-cities from reducing the overwhelming congestion effects of their size, examining
the trade-off between disorder and dictatorship.6
In the following section we document more fully the rise of poor mega-cities in the
developing world, and the underlying demographic features of these cities. Then, with
those stylized facts in place, we present our model of urban Malthusian dynamics,
showing how an economy may find itself in an equilibrium with poor mega-cities. We
then compare this equilibrium to historical mega-city development, and discuss the role
of the mortality transition in creating poor mega-cities and show its importance in a
calibrated version of the model. The final section discusses the policy implications of
the findings.
1. RICH AND POOR MEGA-CITIES IN HISTORY
There are not standard definitions for poor mega-cities. By “mega-cities” we mean the
largest cities in the world, typically considering the largest 30 or 100 cities in a given
year. Further, the absolute size of the largest cities grows over time. Table 1 shows the
largest 30 cities in select years from 1700 to 2015 (Chandler, 1987; United Nations,
2014). In 1700, the mega-cities of the time were all under 1 million persons in size,
with Istanbul, Tokyo, and Beijing all at 700,000 inhabitants. By 2015, even the 30th
largest city in the world (Lima) has close to 10 million inhabitants.
5
Notable alternatives include urban bias (Ades & Glaeser, 1995; Davis & Henderson, 2003; Henderson,
2003), natural disasters (Barrios, Bertinelli & Strobl, 2006; Henderson, Storeygard & Deichmann, 2013),
natural resource exports (Jedwab, 2013; Gollin, Jedwab & Vollrath, 2015), and food imports (Glaeser,
2013).
6
A recent literature attempts to measure congestion effects in developing countries. See for example
Desmet & Rossi-Hansberg (2013), Greenstone & Hanna (2014) and Ebenstein et al. (2015). A particular
form of congestion that we document is the fact that poor mega-cities grow without accumulating human
capital. The development of lowly-skilled mega-cities contradicts the literature that shows how cities
help disseminate knowledge, which then further promotes their growth (Glaeser, Scheinkman & Shleifer,
1995; Glaeser & Saiz, 2004; Moretti, 2004; Shapiro, 2006; Gennaioli et al., 2013).
5
Classifying cities as “rich” or “poor” mega-cities is more difficult, as city-level measures
of living standards are harder to come by than population data. Similar to Glaeser
(2013), we distinguish between rich and poor mega-cities based on the overall level of
development (i.e. GDP per capita) in the country they are located in, supplemented
where possible with limited data from a “city product index” from United Nations
Habitat (1998, 2012) for the 2000s.7 For the descriptive purposes of this section, we
believe this is sufficient.
Turning to Table 1, one can see how the size and location of mega-cities has changed
over time. While small in absolute size, the mega-cities of 1700 were located in the most
economically advanced areas of the world in that period. While London and Amsterdam
had wages that were high relative to the rest of the world, cities such as Istanbul, Tokyo,
and Beijing all had wages equivalent to those found in cities such as Paris and Naples
(Özmucur & Pamuk, 2002; Allen et al., 2011).
By 1900, the nature of the list of largest cities changed along several dimensions. First,
the absolute sizes were roughly ten times larger than in 1700. The largest city was
London, with 6.5 million inhabitants, and there were 17 cities with over one million
residents. Second, the cities that dominate this list were the leading cities from the
richest countries. London, New York, Paris, and Tokyo are all found on the list. Further
down, we see Birmingham, Boston, Hamburg, Liverpool, Manchester, Newcastle, and
Philadelphia, all centers of industrialization.
There were several agglomerations of around 1 million in poor countries in 1900:
Beijing, Kolkata, and Rio de Janeiro. But none approached the size of the leaders like
London or New York. Comparing 1900 to 1700, one can also see that their growth in
this period was not on the same scale as the richer cities. Beijing increased only from
700,000 to 1.1 million in the same 200 years that London went from 600,000 to 6.5
million. Istanbul had 900,000 residents in 1900, up from 700,000 in 1700.
In 1950 the top cities remained those in advanced nations, but we see the very
beginnings of mega-city growth in poor countries. Kolkata and Shanghai both had more
than four million inhabitants in 1950, putting them in the top 10 cities in the world in
1950. Beijing, Cairo, Mexico City, Mumbai, and Rio de Janeiro were all over 2 million
7
The city product index is measured using such inputs as capital investment, formal employment,
trade, savings, exports and imports, and household income (full details are available in the UN-Habitat
reports). We use the 1998 product index as the main source of city income information for the 2000s, and
complement our data using the 2012 product index when the information for the year 1998 is missing
(using Stockholm for which we have information in both years to link the two data sets).
6
inhabitants, reflecting rapid growth for most of them from earlier periods.
By 2015, the nature of the largest cities has changed dramatically. First, the absolute
scale of cities is 3-5 times larger than in 1950. Second, the composition of the list is now
dominated by cities in poor countries. Only London, Los Angeles, New York, Osaka,
Paris, and Tokyo are in rich countries. Instead we see cities such as Delhi, Mexico
City, Mumbai, and Sao Paulo. Countries that rank low in GDP per capita levels have
cities present on this list, such as Dhaka (Bangladesh), Manila (Philippines), Karachi
(Pakistan), Lagos (Nigeria), and Kinshasa (DRC). Each of those poor cities have at least
11 million people, making them larger in absolute size than nearly every city in the
world in 1950.
The shift of the world’s largest cities from rich countries to poor countries can be more
easily seen in Figure 1. This plots the number of cities with more than one million
inhabitants for two groups, developed countries (based on their 2013 GDP per capita)
and developing countries. In 1700 there were no such cities in either set of countries.
In 1900 and 1950 nearly all of the million-plus sized cities were in currently developed
nations. This switches between 1950 and 2015, however, and this reversal is projected
to increase well into this century.8
This change in the composition of the largest cities is only going to be exacerbated in the
future. The final column of Table 1 shows the projected growth rate from 2015–2030
for each mega-city (∆% 2015-30). The largest values are all for poor mega-cities such
as Lagos (4.2%), Kinshasa (3.7), Dhaka (3.0), and Karachi (2.7). In comparison, rich
mega-cities have growth rates close to zero (London, New York, Tokyo).9
2. THE CHARACTERISTICS OF POOR MEGA-CITIES
2.1
The Mortality Transition and Mega-city Growth
The rapid growth of poor mega-cities is different from that experienced during earlier
urbanization episodes. The poor mega-cities of today grow in large part through natural
increase, in addition to in-migration. Historically, in-migration was the dominant source
8
The patterns hold if we exclude China and India (see Web Appendix Figure 1) or focus on the
proportion of population living in mega-cities (Web Appx. Fig. 2). Countries are also more and more
urbanized at a constant income level (Web Appx. Fig. 3).
9
Among the 100 largest mega-cities in 2030 according to United Nations (2014), the fastest projected
growth rates over 2015-2030 are in Ouagadougou (5.2), Dar es Salaam (5.1), Bamako (5.0), Luanda
(4.4) and Lagos (4.1) (Web Appendix Table 2 Column (2)).
7
of new city dwellers as the rates of natural increase were low in urban areas, typically
because of high mortality rates (Jedwab, Christiaensen & Gindelsky, 2014).
This can be seen in Figure 2, where we compare the crude birth rate (CBR) and crude
death rate (CDR) of cities across different historical eras. We used various sources
described in the Web Appendix to reconstruct historical demographic data for the 100
largest cities in 2030 according to the United Nations (2014). In addition, we collected
demographic data for cities that were among the mega-cities of their time.
Panel A plots these rates for a collection of 20 pre-Industrial Revolution cities, such as
ancient Rome, Renaissance Florence, and London in the 17th century. As can be seen,
the cities all lie near or below the 45-degree line, indicating that the cities experienced
negative rates of natural increase. Their growth could occur only through in-migration.
Those that do lie above the line (Beijing and Moscow in the 19th century) are barely
above the line, and the crude rate of natural increase is low.
These data do not give a full account of the effects of major disease outbreaks. During
the Black Death, crude death rates of 250-750 (i.e., 25-75%) were seen across European
cities (Christakos et al., 2005). All the points in Panel A thus represent “normal” periods,
but each city was at times afflicted by very severe shocks to mortality.
Panel B of Figure 2 shows similar data for 66 cities during the Industrial Revolution.
Here we can see that while crude birth rates are roughly on the same level with the
pre-industrial era, the crude death rate has declined slightly. There remain several cities
below the 45-degree line but most cities experienced some small positive rate of natural
increase. These cities grew not only through in-migration, but in part through a modest
increase in their own population. Note, though, that crude death rates remain high, in
the range of roughly 15-40 for these cities.
In the post-war period, and the 1960s in particular, there is a distinct change in city
demographics. In Panel C, focus first on the collection of relatively rich cities in the
lower left, such as London, New York, and Paris. These cities were already large. But
their crude birth rates have fallen along with their crude death rates, and so their rate
of natural increase (CBR minus CDR) remains relatively muted, similar in size to that
seen during the Industrial Revolution. Overall, it is apparent from Panels A to C that
historically cities were “sliding down” the 45 degree line as they grew. Natural increase
in these cities was never large. As these places developed, the CDR and CBR drop in
tandem.
8
In comparison are the nascent poor mega-cities in the upper left of Panel C, well above
the 45 degree line. In the immediate post-war era these cities differed from earlier eras
in one distinct way: their crude death rates are very low. Lagos, Karachi, and Jakarta,
despite being in countries with much lower levels of income per capita, all have death
rates in the 1960s that are roughly similar to those seen in London, New York, or Paris
in the same year. The birth rates in these cities are large, but not larger than those seen
in pre-industrial or industrial revolution era cities. Developing cities in the 1960s were
“shifted left” compared to their historical peers. This led to very large rates of natural
increase for emerging mega-cities. For example, in the African mega-cities in the figure,
crude rates of natural increase are roughly 30, or 3% per year. Absent migration, this
implies that these cities double in size roughly every 20 years.
This difference continues in the 2000s, as shown in Panel D. Rich mega-cities (London,
New York, Paris) remain in roughly the same position as in the 1960s. The developing
mega-cities have shifted down to lower birth rates. However, the death rates in these
poor mega-cities are lower than the historical comparisons, for the most part falling
below 10 per thousand. Thus in the 2000s poor mega-cities continued to have rapid
rates of natural increase. A notable exception are Chinese cities, which in the 1960s
(Panel C) looked similar to other developing cities, but after the introduction of the onechild policy moved in the 2000s (Panel D) to a pattern of death and birth rates similar
to rich mega-cities. Johannesburg is also an outlier with a high death rate due to HIV.
This gives Johannesburg demographics similar to Paris when it was industrializing in
1900 (panel B).
The deviation of the developing countries in Panels C and D from the historical norms
appears due, in large part, to the mortality transition. Following World War II, there was
a rapid improvement in health, particularly in infant mortality, in many poor countries.
Perhaps the most notable example is the eradication of smallpox, which was achieved
through the development of a freeze-dried vaccine that could be stored safely in tropical
environments. A global effort to eradicate the disease was launched, and by 1980
smallpox had been eliminated. Beyond that success, a variety of other public health
interventions were rolled out in the same period. Vaccines for yellow fever and measles
were developed. Discovery of effective techniques for mass production of antibiotics
such as penicillin and streptomycin allowed them to disseminate to the developing
world, where they were able to treat diseases such as cholera and dysentery. DDT
provided an inexpensive way of dealing with malaria, leading to eradication of that
disease in many countries. The establishment of the World Health Organization was
9
itself a major step towards lowering death rates, as it actively disseminated knowledge
of the new technologies to poor countries (Stolnitz, 1955; Davis, 1956; Preston, 1975).
From the perspective of the developing countries of that period, these new technologies
represented an exogenous shock to mortality rates (Acemoglu & Johnson, 2007).10
A consequence of the decline in mortality was that the absolute growth of cities
expanded to previously unseen levels. Returning to Table 1, the final column contains
the largest decadal change in population experienced by a city, as well as the decade
this occurred (see [max∆# pre-2015]). Poor mega-cities such as Delhi (620,000 per
year), Sao Paulo (450,000), and Dhaka (440,000) added population at rates well above
those seen in historical mega-cities. New York (220,000; 1920s) and London (90,000;
1890s) never received inflows of people at rates like those seen in the poor mega-cities of
today, even during their most rapid growth. For poor countries in the 20th century, the
mortality transition created a positive shock to the absolute growth of cities, and given
congestion effects, this created the potential for poor mega-cities to emerge.
2.2
Congestion in Poor Mega-cities
The rapid growth in size of poor mega-cities generates congestion along a number of
dimensions. There is no definitive way of measuring congestion, so in this section
we document several characteristics that proxy for congestion and how they relate to
growth in the 100 largest cities of the world today. In the empirics, we examine city-level
correlations with respect to the crude rate of natural increase, to show that mega-cities
growing more quickly tend to be both more congested and less productive than slowergrowing peers.
Population growth in poor mega-cities is driven in large part by natural increase, and
not simply in-migration. Figure 3.A plots the projected growth rate from 2015-2030
of the 100 projected largest cities in 2030 against their rates of natural increase in the
2000s. The projected growth rates are based on non-linear extrapolation given the
rates of growth pre-2015, estimated independently of the rates of natural increase. The
relationship is clearly positive, which indicates that natural increase will be a meaningful
10
Another consequence of the mortality transition was to raise crude rates of natural increase in cities
up to the rates typically seen in rural areas, another anomaly compared to historical experience (see Web
Appendix Figure 4). During the Industrial Revolution the CRNI was only 5 per thousand (see Panel B
of Figure 2), while the rural CRNI averaged 17. By the 1960’s the CRNI in the largest cities was 23, on
average, while in rural areas of the same countries the CRNI was 23 as well. Poor mega-cities tend to
have urban rates of natural increase similar to rural areas, while historically mega-cities had much lower
rates of natural increase than their associated rural areas.
10
driver of overall city population growth (R-squared of 0.50). The Chinese cities (e.g.
Beijing) are the main outliers to this relationship, with relatively low rates of natural
increase, but relatively high expected growth rates due to in-migration (excluding the
Chinese cities raises the R-squared to 0.70). Cities that are expected to stagnate in size
(Tokyo) all have crude rates of natural increase of roughly zero.
In Panel 3.B we find a similar correlation between past city natural increase (1960s)
and past city growth (1960-2010) (R-squared of 0.52), but for 55 mega-cities only. The
effect of city natural increase (per 1,000 people) on city growth (%) is similar, at 0.110.13, in both panels A and B. This suggests that each newborn in a city increases the
city population by about one in the long run. As explained in Jedwab, Christiaensen &
Gindelsky (2014), the long-run effect of urban natural increase could be lower than one
if, for example, rural potential migrants endogenously adjust their migration decision
as a result of urban congestion due to urban natural increase. However, they show that
the long-term effect is not significantly different from one, which implies that natural
increase simply compounds the effect of migration. They discuss various reasons why
this adjustment does not take place, in particular the fact that the countryside is also
becoming congested due to rural natural increase, which, in the aggregate, preserves
the incentives of potential migrants to migrate to (congested) cities. We come back to
this issue when explaining the model. In the rest of the descriptive analysis, we use the
rate of natural increase in the 2000s as we have then data for the 100 top cities.
Poor mega-cities that grow through high rates of natural increase are different from
historical cities that grew mainly through in-migration. Panels C through L of Figure
3 plot several characteristics of cities against their rate of natural increase. The Web
Appendix contains full information on sources for this data. Please note that the
correlations seen in the figures do not show causal relationships. Our goal is simply
to characterize the empirical conditions for a self-reinforcing equilibrium in poor megacities.
First, in panel C is log density (persons per square kilometer), which shows a positive
relationship. Perhaps surprisingly, rich mega-cities such as New York (2,000 people per
sq km) or Paris (4,000) are less densely populated than poor mega-cities such as Dhaka
(44,000), Karachi (23,000) or Kinshasa (17,000). Poor mega-cities have both high rates
of natural increase and are already highly dense, meaning they are likely to become even
more dense in the future.11
11
Densities are defined using both the population and the area of the whole urban agglomeration,
11
This density is potentially indicative of congestion rather than positive agglomeration
effects. Panel D shows that slum shares (measured at the national level) are much
higher in countries with poor mega-cities. Roughly two-thirds of the urban residents
live in slums in countries containing Dhaka, Kinshasa, or Lagos. In Panel D, we also
show the strong negative correlation between our main measure of city infrastructure,
the “city infrastructure index” designed by United Nations Habitat (1998, 2012), and
the city crude rate of natural increase in the 2000s (R-squared of 0.66). This is not
surprising considering that poor mega-cities had growth rates of 3-6% in 1960-2010
(see Panel B). They thus doubled in population size every 12-24 years. If infrastructure
could not be built as fast, fast mega-city growth necessarily produced congestion.12
The high density of poor mega-cities does not necessarily indicate a large supply of
skilled workers. Panel F shows that these mega-cities are more informal (we only have
data for 20 cities). Panel G then shows the dependency ratio (the share of those under
14 and 65-plus to population aged 15-64) across our sample of cities. In poor megacities with high crude rates of natural increase, this dependency ratio reaches more
than 50 percent. While there are several richer cities with relatively high values due to
large elderly populations (e.g., Tokyo), in general the dependency ratio is lower the
smaller the rate of natural increase (R-squared of 0.44). However, when the child
dependency ratio (the share of those under 14 to population aged 15-64) is the lefthand side variable, the relationship is even stronger as the R-squared increases to 0.72
(see Panel H).
Further, the labor force that does exist in poor mega-cities tends to be low skilled. Panel
I and J plots the secondary and tertiary school completion rates (for adults aged 25 or
over) against the crude rate of natural increase, respectively. In the poorest mega-cities,
not just the central place. Focusing on the central place or slums only should not affect the results.
Manhattan’s density is about 28,000 people per sq km today. This is higher than many cities in developing
countries on average, but such cities also contain many areas with even higher densities. For example, the
main slums of Mumbai, Nairobi, Dhaka, Cairo, and Karachi have densities of 350,000, 300,000, 200,000,
110,000 and 100,000 respectively. The Lower East Side in New York City was historically the densest
slum of the developed world, and even reached 145,000 in 1910 (Angel & Lamson-Hall, 2014). Other
slums in currently developed cities were relatively less dense: Les Halles in Paris (100,000) and the East
End in London (90,000).
12
The city infrastructure index combines information on access to water, sanitation, electricity, roads,
and housing (full details are available in the UN-Habitat reports). We use the 1998 index as the main
source of city infrastructure information for the 2000s, and complement our data using the 2012 index
when the information for the year 1998 is missing (using Stockholm for which we have information in
both years to link the two data sets). The results are then similar if we use data on the slum share at the
city level for fewer observations (Web Appendix Figure 5), the housing price-to-income ratio (Web Appx.
Fig. 6), access to water (Web Appx. Fig. 7), waste management (Web Appx. Fig. 8-9), or measures of
commuting, pollution and quality of life (Web Appx. Fig. 10-13).
12
the share of college-educated workers is close to zero, as compared to rich mega-cities
where it is one-third or more (Panel J). Poor mega-cities have large populations, but
due to age structure and lack of education, this does not translate to a large effective
and potentially productive workforce.13
This is consistent with the final Panels K and L of figure 3, where we show that city
crude rates of natural increase correlate negatively with our measure of city income,
the “city product index” of United Nations Habitat (1998, 2012), for the 2000s (Rsquared of 0.51). Natural increase is extremely high in the African and Asian mega-cities
located in the poorest countries (e.g. Dhaka, Lagos, Karachi, Kinshasa, and others).
Natural increase falls regularly as cities get richer, consistent with their rising education
levels seen in panels I and J.14 The correlations shown in Panels C-L thus suggest
that these mega-cities are developing as giant villages rather than as high-productivity
agglomerations.15
Overall, it is the distinct characteristics of developing countries seen in both figures 2
and 3 that were the source of their move into a poor mega-city equilibrium. The rapid
rate of natural increase in these cities has two effects. First, it implies that they quickly
hit the Malthusian congestion effects in urban areas: high density, a large prevalence
of slums, high dependency ratios, and low education. Second, the high rate of natural
increase is associated with lower living standards due to that congestion. Rapid natural
increase keeps wages low, which given the typical association of low wages with high
fertility keeps natural increase high. Thus the poor mega-cities remain stuck in a lowwage equilibrium. The demographic shock of low mortality rates in the post-war era
seen in figure 2, by increasing the rate of natural increase, contributed to the arrival
13
These results hold if we alternatively look at city unemployment (Web Appendix Figure 14), tertiary
completion rates accounting for country-specific education quality (Web Appx. Fig. 15), and the “city
education index” of United Nations Habitat (1998) that combines information on past and current
enrollments (Web Appx. Fig. 16). The “city health index” of UN-Habitat, however, does not show any
correlation with the rate of natural increase (Web Appx. Fig. 17), consistent with the lack of variation in
death rates across cities. These cities also have lower levels of social capital, as national homicide rates
are positively associated with city natural increase (Web Appx. Fig. 18).
14
These results hold if we alternatively look at national income (Web Appendix Figure 19), city poverty
rates (Web. Appx. Fig. 20), the “city development index” (CDI) of United Nations Habitat (1998) (Web.
Appx. Fig. 21), and the “city prosperity index” (CPI) of United Nations Habitat (2012) (Web. Appx. Fig.
22). The CDI combines information on city infrastructure, waste, education, health and income. The CPI
uses information on city infrastructure, environmental quality, quality of life and income.
15
All the results hold if, instead of using the city crude rate of natural increase in the 2000s on the
right-hand side, we use the same rate in the 1960s for 55 cities only (Web Appendix Figure 23), or the
annual growth rate of the city in 1960-2010 (Web App. Fig. 24). We also find similar results if we split
the sample into countries with an urban primacy rate below the median and countries with a rate above
the median (Web App. Fig. 25 and 26), to show that our theory is complementary to the urban bias
theory.
13
and persistence of the poor mega-city equilibrium.16
3. A MODEL OF RICH AND POOR MEGA-CITIES
The facts presented above established that poor mega-cities have distinctly different
demographic patterns than mega-cities of the past.
One reaction is that these
demographic patterns, while deviating from past experience, are just part of a transitory
phase of growth, and that these cities will become rich mega-cities given sufficient time.
What we will show in the model that follows is that this is likely too optimistic an
outlook. Under reasonable assumptions that match the facts we outlined in the prior
sections, we show that a poor mega-city equilibrium exists. In particular, cities that
experience extremely rapid absolute gains in population can find themselves stuck in
an equilibrium with low wages and high population growth.
Our model is based on two strands of literature.
First, we adopt explicit micro-
foundations for city production that display both agglomeration and congestion,
as emphasized in the urban economics literature. Second, we combine that with
endogenous population growth as in a typical quantity/quality trade-off model. The
combination shows that it is the absolute growth in city population, not the growth rate,
that is crucial in determining whether a city ends up a poor or a rich mega-city.
The baseline model is of a single city, and takes in-migration to that city as exogenous.
While internal population growth is endogenous, we do not explicitly allow for
endogenous human capital accumulation. After presenting the model, we discuss
extensions to the model that allow for a system of cities, endogenous rural-urban
migration, endogenous human capital, and endogenous congestion costs. In short,
while these extensions have quantitative impacts on the model, they do not alter the
qualitative results.
3.1
The City Sector
The city in our model will benefit from agglomeration effects in the sense that output
has increasing returns to scale with respect to city population. This arises in a model
16
It is interesting to note the absence of Malthusian “positive checks” in poor mega-cities. First, these
cities are congested and polluted, but their death rates do not necessarily increase as a result (they are
still as low as in rich mega-cities today). Second, even if these mega-cities are poor and poverty has
been shown to cause both crime and conflict, crude death rates are not necessarily higher in the most
crime-ridden and conflict-ridden cities in our sample (e.g., Abidjan, Nairobi, Rio and Sao Paulo).
14
of differentiated inputs to city production combined with firm fixed costs. As the scale
of the city increases, more firms find they can make enough profits to offset the fixed
cost, the number of intermediate goods in production rises, and this increases output.
The structure for production and agglomeration effects is similar to that in Duranton &
Puga (2004).
3.1.1
City Production and Agglomeration Effects
Urban final goods are produced using a series of intermediate inputs,
‚
Yu =
M
X
1
1+σ
Œ1+σ
(1)
xi
i=0
where x i is the amount of intermediate good i used and M is the number of intermediate
goods used in equilibrium. The elasticity of substitution between intermediate goods is
(1+σ)/σ, with σ > 0. Letting pi represent the price of intermediate good i, the inverse
demand function for good i is
σ
− 1+σ
pi = x i
Yr .
(2)
Each intermediate good is produced by a monopolistically competitive firm using the
production function
x i = B Li − F
(3)
where B is the productivity of the firm (assumed to be identical across all firms), L i is
the labor used by firm i, and F is a fixed cost for a firm to operate. The fixed costs imply
that there are increasing returns to scale in the production of each intermediate good.
These increasing returns will ultimately capture the agglomeration effects at work in
urban areas.
The intermediate good firms maximize their profits,
πi = pi x i − w u L i ,
(4)
taking the wage wu as given, and knowing the inverse demand curve for their good
given in (2). This leads to the typical markup over marginal cost, with
pi = (1 + σ)
15
wu
B
.
(5)
We further assume that intermediate goods firms can enter and exit freely in the urban
area, so that profits for any individual intermediate goods firm are driven to zero. Using
the production function for firms in (3) and the price given in (5) the only possible level
of output consistent with zero profits is
xi =
F
σ
.
(6)
Given this level of output, each firm hires
Li =
1+σ F
σ
B
.
(7)
As each intermediate good provider is identical, their total demand for labor must equal
the total supply of labor in the urban area, Lu
M
X
L i = Lu ,
(8)
i=0
which can be solved for the equilibrium number of firms,
M=
Lu
Li
=
σ
B
1+σ F
Lu .
(9)
Finally, using (6) and (9) in the production function (1) yields
Yu = Au Lu1+σ
where
Au =
σσ
B 1+σ
(1 + σ)1+σ F σ
(10)
.
(11)
Au is the aggregate productivity term for the urban sector. Note that output in the city
sector has increasing returns to scale with respect to labor, as σ > 0. Each intermediate
good firm operates with a number of workers proportional to the fixed cost. If there
are more workers in the city, then this allows more firms to operate. More intermediate
goods firms increases productivity in the final goods sector by allowing them to access
a wider variety of inputs.
A last assumption is that Au grows at some exogenous rate, g. We do not attempt to
explicitly model this process.
16
3.1.2
City Congestion Effects
All production takes place at a central point in the city, a central business district (CBD).
Residents of the city live along a line extending both directions from the CBD. There is
a time cost to commuting to the CBD, equal to 2τ times the distance from the CBD. As
each worker needs to go back and forth each day, the total time cost for a worker at
distance j from the city center is 4τ j, leaving them with only 1 − 4τ j units of time left
to provide to the labor market.
The distance that each worker has to travel is a function of the number of workers in
the city, Nu . Each worker uses up one unit along the line, so that the maximum distance
a worker is from the center is Nu /2, as workers can live in either direction. Integrating
over all the workers we can find the total labor supply
Lu = 2
Z
Nu /2
1 − 4τ j d j = Nu 1 − τNu .
(12)
0
Here we can see the impact of congestion. Effective labor supply, Lu is increasing in the
population of the city, Nu , but only up to a point. Eventually increased city population
becomes so burdensome that the actual labor effort of workers falls.17
To this point our formulation of congestion is entirely standard with the urban literature
(Duranton & Puga, 2004). However, the effective labor force in (12) has a strict upper
limit of Nu = 1/τ. Above that limit the labor effort provided is zero, and this puts a
hard cap on city size.
We are interested in investigating the growth of mega-cities, and as such we do not
want to put an artificial limit on how large cities can grow in our model. To avoid this
we make a functional modification of this standard model of city congestion. We let τ
be a function of city size itself, specifically setting τ = (1 − ex p(−λNu ))/Nu . λ captures
the speed at which congestion costs adjust to population size. Using this expression for
τ in (12) yields the following expression for effective labor
Lu = Nu e−λNu .
17
(13)
In the standard urban model, congestion dis-amenities are compensated by relatively higher wages
to ensure that utilities are equalized across space. We abstract from the negative effect of congestion
on utility, and only considers the negative effect of congestion on effective labor supply. Congestion thus
enters as a production dis-amenity in our model. Taking into account utility dis-amenities would not alter
the qualitative results.
17
As can be seen, this formulation of congestion preserves the idea that Nu has conflicting
effects on effective labor. More workers increases the available labor, but also creates
congestion which lowers each worker’s effective time. As with standard congestion
costs, there is an inverse U-shaped relationship between population and labor effort.
However, our particular form of the congestion function allows us to work with
unbounded city sizes while preserving the notion of congestion effects. Our specification
makes the subsequent analysis tractable, but it does not sacrifice any of the implications
of typical models of congestion.18
3.1.3
City Wage Determination and Growth
To see the city wage at any given moment in time, combine the expression for output
from (10) with the labor supply equation from (13) to find
Yu = Au Nu1+σ e−λ(1+σ)Nu
(14)
wu = Au Nuσ e−λ(1+σ)Nu .
(15)
and income per worker is
What can be seen here is that the number of city workers, Nu , influences earnings in
the city, and that these earnings form an inverted U-shape. That is, levels of Nu near
zero earnings are increasing in city workers as the agglomeration effects outweigh the
congestion effect. Eventually, though, when Nu is large enough the congestion effects
dominate and having more city workers will reduce earnings. Differentiating (15) with
respect to Nu shows the wage-maximizing number of residents is
N∗ =
σ
(16)
(1 + σ)λ
Above N ∗ , wages fall as more residents arrive, or are born, in the city.
Given the wage in (15), take logs and time derivatives to yield
˙u
w
wu
˙u
= g+N
σ
Nu
18
− λ(1 + σ) ,
(17)
As in typical urban models we presume that there is a competitive rental market that ensures each
worker in the city earns, on net, an identical amount. Those workers living closer to the CBD will
supply more labor and have higher gross earnings, but this will be offset by higher rents. Total rents
are distributed equally across workers. Similarly, we abstract from the question of competition for land
between rural and city sectors, assuming that city area can expand costlessly.
18
where recall that g is the exogenous growth rate of Au . City wage growth depends
directly on productivity growth, but this is potentially offset or enhanced by the absolute
˙u . The term in parentheses determines the sign of this effect.
city population growth, N
If Nu < N ∗ , the city is small enough that agglomeration effects outweigh congestion, the
˙u , has a positive effect on wage growth.
term in parentheses is positive, and city growth, N
But if Nu > N ∗ , then congestion effects outweigh agglomeration, and city growth has a
negative effect on wages.
From equation (17) we can already develop the basic intuition behind poor mega-cities,
and the relevance of the mortality transition. In poor countries, the mortality transition
raised the rate of urban natural increase, so that even without any in-migration from
˙u . Even if the
rural areas, cities experienced very large absolute gains in population, N
city began with Nu < N ∗ and the additional population initially raised wage levels, the
rapid growth in city population quickly pushed city size over N ∗ . Further growth in
population then lowers wage growth.
Urbanizing before the mortality transition, as in historically rich mega-cities, avoided
this problem. With high mortality, and particularly with high mortality in urban areas,
the absolute increase in city population was very small over time. Even with in˙u was small, and this ensured that wage growth could
migration from rural areas, N
remain positive.
3.2
City Population Growth
Wage growth in the city sector depends on the absolute change in city population. This
absolute growth will occur through both natural increase (births and deaths) as well as
in-migration. We model overall city growth as
˙u = φ(w, mu )
N
where we have dropped explicit time notation for clarity.
(18)
The φ(w, mu ) function
describes the relationship of city growth to wages and a mortality shifter, mu . The
function φ() is intended to capture demographic behavior related to wages, including
fertility, mortality, and in-migration.
We do not specify precise micro-foundations for the φ() function, as those are
readily available from the literature.19 The specific properties that we assume are as
19
Jones, Schoonbroodt & Tertilt (2010) and Galor (2011) provide reviews of common explanations for
19
follows,
φw (w, mu ) < 0
(19)
φm (w, mu ) < 0
(20)
lim φ(w, mu ) = 0.
(21)
w→∞
The first property simply states that natural increase is decreasing with income. This
is consistent with empirical evidence regarding fertility rates both within and across
countries.20 While in-migration may be positively related to city income, on net we
assume that the fertility response is more powerful, so that the population growth
rate is declining with wages. Note that this does not preclude the absolute number
of immigrants from rising with the wage in the city.21
The second property states that population growth is negatively related to exogenous
mortality, mu . We think of mu as representing level effects on population growth.
In particular, the mortality transition will be captured by a decrease in mu .
The
final property says that regardless of sector, as wages get arbitrarily high, the rate of
population growth reaches a minimum.
Last, for future use define the following term
η(w, mu ) = −
φw (w, mu )w
φ(w, mu )
> 0.
(22)
This term captures the absolute size of the elasticity of population growth with respect
to the wage. Given the assumption regarding φw (w, mu ) < 0 from above, it follows that
η(w, mu ) > 0.
3.3
City Equilibrium Outcomes
We can now characterize the dynamics of wages with respect to city population size.
From equation (17) we know that growth in wages is positive if the congestion costs
the relationship between wages, fertility, and mortality.
20
Becker (1960) observed the negative relationship of incomes and fertility, and see Jones,
Schoonbroodt & Tertilt (2010) for a more recent summary of the available evidence. Allowing for a
positive effect of income on population growth at very low income levels, as in unified growth models
(Galor, 2011), complicates the analysis but does not change the ultimate implications of the model.
21
This assumption that the city population growth rate is declining with wages is in line with the fact
established in Section 2 that rich mega-cities now have growth rates close to zero, whereas poor megacities still have very high growth rates.
20
˙u , are relatively small. We just established, however, that this
of population growth, N
population growth depends negatively on the wage rate itself. So the outcome for a city
will depend on the interaction of population growth and wage growth.
In order to proceed, consider cities that have sufficiently large initial populations such
that σ/Nu (0) is arbitrarily small. In that case, we know from equation (17) that the
sign of wage growth is determined by
˙
w
w
Ò0
if
˙u Ñ
N
g
λ(1 + σ)
.
(23)
If population growth is too large, wages will shrink due to the congestion effects of the
additional population outweighing the positive effects of productivity growth.
Equation (23) simply establishes under what conditions wage growth will be positive
at a point in time. Whether cities can maintain positive wage growth is the subject of
the following proposition. It establishes a more restrictive condition under which a city
will be able to sustain wage growth and become a rich mega-city. If a city fails to meet
this condition, wages will fall and the city will become a poor mega-city.
Proposition 1. Given initial conditions w(0) and Nu (0), there is a threshold
N (w(0), mu ) ≡
g
λ(1 + σ)
−
φ(w(0), mu )
η(w(0), mu )λ(1 + σ)
(24)
such that there are two possible equilibrium outcomes:
(a) Poor Mega-City: If
˙u (0) ≥ N (w(0), mu )
N
(25)
then wages will approach zero, lim t→∞ w = 0, and population growth will remain
strictly above zero.
(b) Rich Mega-City: If
˙u (0) < N (w(0), mu )
N
(26)
˙
then wage growth is always positive, w/w
> 0∀t, and the population growth
approaches zero.
Proof. Please see Web Theory Appendix 1.
The intuition for poor mega-cities is easiest to see if one thinks of a city that has negative
wage growth to begin with because of high population growth. As wages fall this
raises the rate of natural increase, φ(w, mu ), which implies that absolute city growth
21
˙u rises as well. The city will thus continue to grow too rapidly to generate positive
N
wage growth.
The threshold for a poor mega-city in Proposition 1 is below the cutoff for positive wage
growth from equation (23). That is, a city can initially have positive wage growth but
still end up a poor mega-city. The reasoning is that even though wage growth is positive
initially, the rate of natural increase φ(w, mu ) may not be falling quickly enough to
˙u is still rising over time. Eventually it
offset the increased population size, and so N
will rise higher than the threshold in equation (23), and wage growth will become
negative.
The term involving the ratio φ(w, mu )/η(w, mu ) in N (w(0), mu ) reflects this. Recall that
η(w, mu ) is the size of the elasticity of natural increase with respect to the wage. If this
elasticity is small, then wage growth does not lower natural increase much, and so the
absolute growth of city population will continue to go up even as wages rise. This makes
˙u to achieve rich megaN (w(0), mu ) lower, meaning that a city must have very small N
city status. On the other hand, if the elasticity is large, then positive wage growth will
lower natural increase by a large amount, which makes N (w(0), mu ) large, making it
easier for a city to achieve rich mega-city status.
The role of initial demographic conditions becomes clear from Proposition 1. Anything
˙u that is above N (w(0), mu ) will create a poor mega-city, ceteris
that generates a value of N
paribus. What we will establish below is that the mortality transition was a shock to
˙u above N (w(0), mu ) for many developing country
city population growth that pushed N
cities, and put them on the path to becoming poor mega-cities.
3.4
Extensions of the Model
We have made several simplifying assumptions to make clear the role of initial
demographics for long-run city outcomes. We can show that relaxing those assumptions
generates a more realistic model without overturning the qualitative predictions.
Urban Informal Sector (Web Appendix Theory 2). The first extension concerns the
lower limit to wages. In the model, wages in poor mega-cities go towards zero over
time as the population increases so fast that congestion effects dominate. We can adapt
the model to allow for an informal city sector that enjoys no agglomeration economies
but also does not suffer from congestion costs. One can imagine small-scale, informal
stalls and shops. This informal sector pays a minimum wage of w in f . We establish in
the appendix that if this sector exists, then in poor mega-cities the formal sector will
22
become stagnant in size, and the city will be dominated by a population of informal
workers.
Endogenous Human Capital (Web Appendix Theory 3). While human capital is
obviously important in the context of economic growth, we ignored it in the baseline
model to focus on the pure effect of demographic changes. If we allow human capital
to be an input to production, and let the level of human capital be positively related to
the wage, then this will exaggerate the difference between poor and rich mega-cities.
Rich mega-cities will have even more rapid wage growth because as they get richer, they
acquire more human capital. Allowing for this changes the exact value of N (w(0), mu )
that separates poor and rich mega-cities, but does not change the qualitative prediction
of Proposition 1 that such a threshold exists.
Dependency Ratios (Web Appendix Theory 4). Likewise, including city dependency
ratios would only accentuate, and not minimize, our prediction that fast city growth
leads to poor mega-cities. If natural increase skews the age composition of the
city towards children, and these children increase congestion but do not add to
the workforce, then rapid population growth has an additional negative effect on
wages.22
Endogenous Congestion Costs (Web Appendix Theory 5). Allowing for congestion
costs, λ, to decline with wages w would also accentuate, and not minimize, our
prediction that fast city growth leads to poor mega-cities. Poor mega-cities, with low
wages, will not invest in congestion-alleviating technologies, and this will ensure that
wages stay low. Rich mega-cities will invest in lowering congestion costs (i.e. mass
transit systems) and this will accelerate wage growth even further.
Multiple Cities (Web Appendix Theory 6). Perhaps the biggest question regarding the
baseline model is why people do not leave the poor mega-city for other cities if the wage
continues to fall? What if migration (in or out) was endogenous to the city wage? We
can allow for a system of cities inside an economy, and free migration between these
cities. As shown in the appendix, this mitigates congestion costs by allowing additional
population to be spread around, but it does not eliminate the costs. What we have
with multiple cities is a threshold for total urban population growth. If aggregate urban
population growth is too big, then all cities in the economy will find themselves in the
poor mega-city equilibrium, and vice versa. Having more cities is like lowering λ, so the
22
Obviously, it could be that the congestion costs per capita are relatively lower for children than for
adults. Children could also work if there is no child labor ban. As long as having an age composition
skewed towards children is costly on net for a city, an increase in the number of children will reduce total
earnings per capita.
23
more cities that exist the more likely it will be that they become rich mega-cities.23
Changes in Urbanization Rate (Web Appendix Theory 7). Likewise, why do people
not leave the poor mega-city for the countryside if the wage continues to fall? We could
allow for endogenous movement between a city (or system of cities) and rural areas.
Rural areas, though, have their own congestion costs in the form of limited resources
(land), as in a classic Malthusian model. So outflows of urban residents to rural areas
would ultimately result in lower wages in those rural areas as well. Eventually the
economy would hit some equilibrium distribution of population across the two regions.
In a system that is at this equilibrium, some portion of any aggregate population growth
will end up in cities. If the absolute growth in total population is sufficiently large,
then city wages will fall. Factors such as preferences for city living, or preferences for
remaining in the region of birth, would change the equilibrium distribution of people
across regions, but not change the fact that population growth would result in higher
populations in both regions.24
4. MORTALITY TRANSITION AND POOR MEGA-CITIES
Given our model, how do we explain the divergence of poor mega-cities from the
historical norms? We focus on the distinct change in demographics following the
mortality transition that occurred after World War II. Recall from Figure 2 that crude
death rates in developing cities fell dramatically relative to their crude birth rates, and
23
This suggests that one possible way of alleviating conditions in poor mega-cities is to create a new
large city. But a new large city would not endogenously arise through individual action, as no single
individual has any incentive to start their own city, because they would enjoy no agglomeration benefits
and their own wage would be lower than in the poor mega-city. A new large city would require a
successful, centralized, coordinated effort. Additionally, mega-city-born residents may develop, from
birth, a strong preference for living in the largest city. In that case, they may not out-migrate although
wages relatively decrease. Among our sample of developing country cities, 10 of them are in countries
that have massively invested in the creation of a new capital city: Karachi and Lahore in Pakistan
(Islamabad became the capital city in 1958), Belo Horizonte, Rio and Sao Paulo in Brazil (Brasilia, in
1960), Dar es Salaam in Tanzania (Dodoma, in 1974), Abidjan in Ivory Coast (Yamoussoukro, in 1983),
and Ibadan, Kano and Lagos in Nigeria (Abuja, in 1991). Web Appendix Figures 27 (for slums) and 28 (for
infrastructure) show, however, that these cities are not relatively less congested than other mega-cities,
which highlights the role of coordination failures and preferences.
24
If the absolute change in rural population is also high due to rural natural increase, which is clearly
the case in developing countries, rural wages may decrease as much as or even more than urban wages.
This will of course depend on how rural congestion effects compare with urban congestion effects. We
may be in a situation where a mega-city can become highly congested and see its wage fall, but still
attract migrants. Additionally, mega-city-born residents may develop, since birth, a strong preference for
urban living. In that case, they may not out-migrate in the face of falling wages. In Subfigure 3A and 3B,
we find that city natural increase (per 1,000 people) has an effect of about 0.11 (0.13) on city growth
(%) in 2015-2030 (1960-2010). This suggests that each city newborn increases the city’s population by
about at least 1 in the longer run. In other words, city natural increase simply compounds the effect of
migration (Jedwab, Christiaensen & Gindelsky, 2014).
24
thus the crude rate of natural increase in developing cities became very large. We
propose that in developing countries after the mortality transition, mu fell below a
critical threshold that pushed these cities into the poor mega-city equilibrium by raising
their absolute growth. We first establish this threshold formally in the model, and then
calibrate the model to show that the observed changes in mortality after World War II
were sufficient to create poor mega-cities.
4.1
The Mortality Threshold
Given the model described above, the following proposition holds
Proposition 2. For any given initial conditions w(0) and Nu (0) there is a threshold level
mu such that
• if mu ≤ mu the city becomes a Poor Mega-City
• if mu > mu the city becomes a Rich Mega-City
Proof. Please see Web Theory Appendix 1.
˙u , is
Low mortality cities become poor mega-cities because their population growth, N
too large, and thus lies above N (w(0), mu ) from Proposition 1. But note that there is
a non-linear effect of mu on city development. Cities with mortality rates just above
and just below the threshold mu will look very similar at first, but the slightly faster
population growth in a city with a low mortality rate will eventually create congestion
effects that cannot be overcome. The implication is that cities in developing countries
in the post-war era need not have been very poor or very large compared with their
historical peers to end up as poor mega-cities. The demographic shock of the mortality
transition, by pushing mu below mu , would have been sufficient to send them into the
poor mega-city equilibrium.
Proposition 2 does not imply that mu is the only parameter that could have created
poor mega-cites. Shocks to fertility behavior, productivity growth, or congestion costs
could equally move cities from one equilibrium to the other. We focus on the mortality
transition because it was so significant a shock to the existing demographic patterns, and
as will be seen this captures the behavior of cities in the post-war era quite well.
4.2
Calibration
Theoretically, a sufficiently low level of mu will cause a city to become a poor megacity. But quantitatively, was the shock to crude death rates from the mortality transition
25
actually capable of pushing cities into that equilibrium?
We calibrate our model to try and answer this question. We first use the calibrated model
to simulate population and wages for hypothetical cities to establish that the decline in
CDR from roughly 35 to 10, consistent with what was seen in Figure 2, is sufficient to
change the long-run outcome for a city.
Timing and Initial Conditions: We use a discrete time version of the model to allow
us to match observed data and simulate the model over 50, 100, and 150 periods. In
each simulation, we normalize the initial population to be Nu0 = 1 and the initial wage
to wu0 = 1.
Demographic Structure and Parameters: We assume that the rate of natural increase
in cities is given by
I
ε
ε
φ(w t , mu ) = τ b w t b − mu w t m + .
(27)
Nt
The first term captures birth rates, the second death rates, and the third immigration
flows relative to existing population. ε b and εm are the elasticities of births and deaths,
respectively, with respect to wages. τ b is a scaling parameter for births, and mu is the
mortality shifter. The flow of immigrants into the city, I, is held constant over time.
For the fertility parameters, Jones, Schoonbroodt & Tertilt (2010) provide elasticities of
fertility with respect to income for the U.S. from 1826-1960, and find that they generally
decline from between -0.30 and -0.40 in the 1800’s to about -0.20 in the 1950’s. Young
(2005) estimates an elasticity of fertility with respect to wages of -0.35 using household
survey data from South Africa. These estimates refer to total fertility rates or individual
fertility, respectively, and not to crude birth rates, which depend on the age structure.
Using data from the United Nations (2012), we have also run our own regressions of
the log crude birth rate on log GDP per capita using a panel of developing countries
between 1950-2010, and these yields estimates of -0.20. Based on this, we adopt a
value of ε b = −0.30, which is consistent with both the elasticities for both total fertility
rates and crude birth rates. The value of τ b is equal to the CBR when wages are equal
to one. As we normalize the initial wage to be equal to one in the calibration, the value
of τ b is set to match the initial value of the CBR. We set τ b = 35, which is roughly the
value in either pre-industrial cities in Europe or the pre-industrial cities of the developing
world in 1960, as seen in Figure 2.
With respect to the mortality parameters, using the same panel of country-level data,
we find a value of -0.10 for the elasticity of the crude death rate with respect to GDP per
capita, and a value of zero if we use only developing countries. Pritchett & Summers
26
(1996) estimate that the elasticity of infant and child mortality with respect to income
is between -0.2 and -0.4 for developing countries. The elasticity for the crude death
rate would be smaller, depending on the exact population age structure. In the end, we
use a value of εm = −0.10, consistent with a small relationship in the post-war period.
We have experimented with several different values for this elasticity, and it does not
materially impact our simulations.25 The value of mu is the CDR when wages are equal
to one. We simulate cities that vary in their mu value, using values of 10, 20, 30, and
40. A CDR of 10-20 is equivalent to the post-mortality transition levels seen in 1960,
while a CDR in the range 30-40 was typical for pre-industrial cities (see Figure 2).
The last demographic item to calibrate is the flow of in-migration, I. The amount of inmigration varies widely over time for individual cities, and widely across cities as well.
Hence there is no single value that will make sense in all cases. We set I = 0.05, which
given our normalization of initial city size to one, implies that the constant absolute
flow of migrants into the city in each period is equal to 5% of the initial city size. Thus
the rate of immigration falls as cities grow larger, but a constant absolute number of
people continue to arrive each period.
City Productivity Parameters: For city production, three parameters must be set.
First, we have the agglomeration parameter σ. Recall that (1 + σ)/σ is the elasticity
of substitution between intermediate goods produced in the urban sector by separate
firms. Recent research has used an elasticity of 3 (Broda & Weinstein, 2006; Hsieh &
Klenow, 2009), implying a value of σ = 0.5. Second, the congestion term, λ, has no
obvious empirical analogue. However, in our model the wage-maximizing size of a city
is N ∗ = σ/[(1 + σ)λ]. Given the value of σ, if we set a value for N ∗ , then this will allow
us to back out the appropriate value for λ. There is no obvious answer, though, for the
size of N ∗ , either. What we do is normalize N ∗ = 1. We are thus assuming each city
begins the simulation at the wage-maximizing population size. Recall from the model
that this implies that any additional population will have a negative impact on wages.
Changing the value of N ∗ to be larger, implying that cities can still experience some
agglomeration benefits from larger populations, does not change the long-run outcomes
for the cities we simulate. Setting N ∗ = 1 and σ = 0.5 implies that λ = 0.33. The final
parameter to set is the growth rate of productivity, g. To set this we note that for a rich
mega-city, in the long-run the rate of natural increase will go to zero, and in-migration
Voigtländer & Voth (2013a) use elasticities of ε b = 1.41 and εm = −0.55 for their calibration. The
positive elasticity on birth rates is consistent with their focus on Malthusian-era outcomes, but is not
necessarily appropriate for examining modern developing cities. The large elasticity of death rates with
respect to income is also consistent with Malthusian-era outcomes, but is less relevant to the cities we
consider.
25
27
will be the only source of population growth. This implies that in the long-run wage
˙
growth is w/w
= g − Iλ(1 + σ). We target long-run wage growth of 1.5% per year in
rich mega-cities, which given the other parameters implies that g = 0.04.
A last point is that for the simulation we include a city informal sector (see Web Theory
Appendix 2 for details) that provides a minimum wage of w in f = 0.8, and is available
to all city residents. This is done so that wages do not asymptote to zero for poor megacities.
Results: Table 2 summarizes all of the parameter values used in the initial simulations.
Table 3 presents the results of the simulations for four cities, varying only in their initial
crude death rate, but sharing an identical initial crude birth rate of 35. The CDR of 10
is observed in 1960 after the mortality transition. And the predicted 7.3-fold increase
in population from the simulation is in line with the increases in population seen in the
50 years from 1960 to 2010 in cities like Delhi, Karachi, and Manila. The wages in our
simulated low-mortality city fall to the informal minimum. It is a poor mega-city.
A city with initial CDR of 20 fares better after 50 years, with wages 2.5 times higher and
a population size of only 4.6 times the original. Even after 100 years, the wage is still 3
times the initial value, but eventually population growth is too large and wage growth
becomes negative. By 150 years out, this city is 17 times its original size, but has a wage
that has fallen to the informal minimum. It too has become a poor mega-city.
In contrast, pre-mortality transition cities with initial CDR of 30 or 40 end up rich megacities. Their population growth is slow enough that wages grow appreciably after 50
years, to roughly 3.8 times the initial value. Their populations do grow, but only 3.5
times the initial value. They continue to grow slowly in size, but rapidly in wages, for
150 periods. By then, they are both roughly 8.5 times larger in size. Note that this is
comparable to the size gain seen by the poorest mega-city after only 50 years. Their
increase in size over 150 years is similar to that of Paris between 1850 and 2000.
The model can thus generate large quantitative differences in living standards and size
based solely on differences in mortality rates that match those seen after the mortality
transition. The mortality transition was capable of shifting these cities into the poor
mega-city equilibrium. Comparable historical cities with CDR’s of 30-40 were able to
develop into rich mega-cities because their absolute growth of population was small
enough to allow wage growth.
28
4.3
Predictions of Poor Mega-city Status
As a second experiment, we use our data on mega-cities, and examine the predictions
of the calibrated model for each of them individually. For each city-year observation,
we will use our calibrated model to calculate mu , the threshold death rate dividing the
rich and poor mega-city equilibria. This exercise will show that cities in developing
countries affected by the mortality transition after World War II were almost unique in
our dataset in having mu < mu , putting them on track to become poor mega-cities.
Most of the parameters are held identical across all cities. The demographic parameters
ε b , εm , I, and the productivity parameters g, σ, and λ, are all set to the values in Table
2. For each city, we normalize its size when observed to Nu0 = 1, and initial wage
to wu0 = 1. The value of τ b for each given city-year is set equal to the observed size
of the crude birth rate. Our parameters and initial conditions imply that each city is
presumed to begin at exactly N ∗ in population. This does not imply that each city has
a high absolute level for wages, it simply implies that each city is at the point where
additional population will, ceteris paribus, lower wages. It also does not imply that they
are all the same size, just that their observed size is equivalent to N ∗ . This puts every
city we work with on an even footing. Developing country cities in 1960, for example,
are not presumed to have any worse congestion than Industrial Revolution era cities,
even though they might have been larger in absolute size. For each city, we then solve
for the unique mu .
Figure 6 shows the results of the calibration using all cities in our dataset. It plots the
actual crude death rate in each city, mu , on the y-axis against the value of mu on the xaxis. Panel A shows the pre-Industrial cities. They all have observed mu well above their
threshold values of mu , indicating that the model expects these cities to have become
rich mega-cities. Places such as London and New York obviously did. Cities such as
Cairo or Delhi did not, but if the growth rate of productivity was much lower in these
cities than we assumed, they would not have necessarily been rich mega-cities. The
interpretation of panel A is simply that there is nothing about the demographics of Cairo,
Delhi, or any other city in the panel that would have led them to become poor.
Panel B shows cities from countries that had all entered the Industrial Revolution. Here,
note that again all cities lie well above their threshold values of mu . Some, such as
London in the 1750’s, are well above the line due to very high mortality. Thus its growth
would have been very slow and wage growth was predicted to occur. One can trace the
evolutions of London, New York and Paris through the panel, seeing that as the 1800’s
progressed the decline in mortality rates pushed these cities closer to the threshold, but
29
they never quite crossed. These cities almost became poor mega-cities, but the changes
in their demographics were never dramatic enough to cause this.26
The cities in Panel C are all from 1960. Note that all cities have actual crude death rates
that are very low by historical standards, averaging only about 11. But to the right of
the 45 degree line are a host of developing country cities such as Karachi, Kinshasa, and
Lagos, whose crude death rates were pushed to mu < mu by the mortality transition.
These cities had high crude birth rates at the time, as seen in Figure 2, and the drop in
mortality rates meant that the absolute growth in city size was too large to support wage
growth. They thus became stuck in the poor mega-city equilibrium. If these cities had
retained death rates above 20 or 30, as in historical cities, they would have grown slow
enough for wages to increase and been on the path to becoming rich mega-cities.27
For comparison, note the group of relatively rich cities in Panel C such as London, New
York, and Tokyo, whose development level was such that the low mortality rate did not
cause them to develop into poor mega-cities. These cities already had low enough birth
rates that death rates of around 11 were not sufficient to push their absolute city growth
above the critical threshold. The mortality transition was uniquely bad for developing
country cities in 1960 because they were still at such high birth rates.
We can provide some rough evidence of the model’s predictive ability by asking whether
cities in 1960 that had mu < mu did in fact become poor mega-cities (and vice versa) by
2000-2010. We count a "success" if a city with mu < mu in 1960 was in a country with
an average GDP per capita in 2000-2010 of less than $4,036, meaning it was in the low
income or lower middle income categories of the World Bank. An example is Lagos.
Similarly, we count a "success" if a city with mu > mu in 1960 was in a country with an
average GDP per capita in 2000-2010 of more than $4,036 (e.g. New York). We count a
"failure" if a city predicted to be a poor mega-city in 1960 is located in a country above
the GDP per capita threshold in 2000-2010 (e.g. Seoul), or if a city predicted to be a
rich mega-city in 1960 is below the GDP per capita threshold in 2000-2010 (e.g. Addis
Ababa). Given this classification, the model is successful for 65% of the cities in Panel
C.28
26
Note that over this period these cities did become quite congested. Slums expanded rapidly in LateVictorian London. Likewise, slum density peaked around 1900 in New York (Angel & Lamson-Hall, 2014).
Officials and popular figures were then rather pessimistic about the future economic development of their
city.
27
Developing country cities have similar crude death rates as for developed country cities, around 020. But they significantly differ in their threshold crude death rate because their crude birth rates were
initially higher when the mortality transition hit.
28
We obtain similar prediction results by alternatively defining as poor any city with a city product
index below the index value for Mumbai (incl., see figure 2.K).
30
Our failures are actually quite instructive. The model incorrectly predicts that
Hong Kong, Seoul, Singapore, four Chinese cities (e.g., Beijing and Shanghai) and
Johannesburg will be poor mega-cities based on their 1960 data. What all those cities
have in common is a distinct demographic shock after 1960. China and Singapore both
pursued coercive fertility-control policies to limit population growth around 1970. Hong
Kong and South Korea pursued non-coercive, but nonetheless effective, campaigns to
educate families about having fewer children. China, Singapore, South Korea, and Hong
Kong are all ranked as having the strongest family planning programs in developing
countries from 1972-1994 (Ross & Mauldin, 1996). Johannesburg did not actively limit
fertility, but the HIV crisis raised the mortality rate so much that its rate of natural
increase fell dramatically in the last two decades. These cities were all predicted to
have become poor mega-cities based on their 1960 characteristics, but distinct changes
to demographic behavior after 1960 allowed them to escape that trap. Had these cities
not had such significant shocks to their demographic regimes, the predictive power of
model would have increased to 80%.29
Finally, Panel D of Figure 6 plots cities using data from 2000, and so the location of
cities is the model’s prediction of their future status as rich or poor. Note that there is a
noticeable collection of cities to the left of the line, with mu > mu , indicating that they
are predicted to become rich mega-cities eventually. This includes most cities in China
and India. Note that the model is not saying that these cities are currently rich, only
that they are on the right demographic path towards becoming rich (this may still take
100 years). Panel D shows that level shifts in demographic behavior, such as the fertility
control campaigns mentioned above, can alter the equilibrium outcome for cities.
Finally, using the calibrated model, we can give some idea of the size of demographic or
productivity shocks necessary to move any of the cities currently predicted to stay poor
mega-cities into the rich mega-city equilibrium. For the cities in Panel D with mu < mu ,
we compute the average increase in the crude death rate that would shift them into
the rich mega-city equilibrium. The result is an increase of 4 per 1,000 people. This is
about half of the increase in the crude death rate due to HIV in Johannesburg (+10).
Similarly, we find the average drop in the crude birth rate that would push these cities
above the rich mega-city threshold is 6 per 1,000. This is about one-half to one-third
of the changes in birth rates in Hong Kong, Singapore, and urban China and South
Korea between 1960 and 1990.30 Lastly, the average increase in productivity growth,
29
The cities that remain misclassified are very close to the 45-degree line, showing that the model was
not far off even if ultimately incorrect. These include Bogota (poor according to our simulation, rich in
reality), Lima (poor; rich), Mexico (poor; rich), Rio (poor; rich), and Sao Paulo (rich; poor).
30
Note that the reduction is fertility needed to escape the poor mega-city equilibrium (-6) is higher in
31
g, that would push these cities to become rich mega-cities is 0.7 percentage points.
This increase is roughly one-third of the increase in productivity growth experienced
by England during the Industrial Revolution (Crafts & Harley, 1992). While we have
focused on the mortality transition as a shock that pushed many of these cities into the
poor mega-city equilibrium, there are numerous routes out of that condition.
5. CONCLUSION
We set out to explain the rise of poor mega-cities after World War II, attributing it in part
to the severe decline in death rates that occurred due to the mortality transition. These
lower death rates led these large absolute gains in city size in many developing cities.
The model of urban production and endogenous fertility that we constructed shows that
absolute growth above a certain threshold allows congestion effects to lead to negative
wage growth, which in turn perpetuates high population growth rates. In this analysis,
poor mega-cities arose after World War II because of the mortality transition, and they
continued to grow due to their poverty.
A critical implication of our model is that the poor mega-city equilibrium is stable. Once
upon that path a city will remain a poor mega-city indefinitely, even if it shares the same
underlying rate of productivity growth as rich mega-cities. The poor mega-cities of today
are not simply in a transitional state towards becoming the next New York or Tokyo,
but rather have grown so fast they are actively working against their own prosperity.
However, our calibrations have shown that the same poor mega-cities can potentially
escape their poverty trap, depending on how mortality, fertility and productivity growth
evolve in the future.
Other explanations for the rise of poor mega-cities certainly exist. Urban bias, changing
urban preferences and technologies, and rural poverty are some of the possibilities.
While we focused on mortality changes, our model is flexible enough to incorporate
those alternatives easily.
The rise of poor mega-cities is a distinct change from the historical experience. Given
that nearly 2 billion people in developing countries live in cities of greater than 1
million residents, understanding these mega-cities is an important part of understanding
growth and development in general. Urbanization is often presumed to be synonymous
with economic growth, but the evidence on these poor mega-cities and the implications
of our model suggest that this is too broad a generalization.
absolute value than the mortality increase that would produce the same transition (+4), due to the fact
that we use a higher elasticity of the birth rate with regard to the wage than for the death rate.
32
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TABLE 1: WORLD’S LARGEST MEGACITIES (MILLIONS), 1700-2015
1700
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Istanbul
Tokyo
Beijing
London
Paris
Ahmedabad
Osaka
Isfahan
Kyoto
Hangzhou
Amsterdam
Naples
Guangzhou
Aurangabad
Lisbon
Cairo
Xian
Seoul
Dacca
Ayutthaya
Venice
Suzhou
Nanking
Rome
Smyrna
Srinagar
Palermo
Moscow
Milan
Madrid
1900
0.7
0.7
0.7
0.6
0.5
0.4
0.4
0.4
0.4
0.3
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
London
New York
Paris
Berlin
Chicago
Vienna
Tokyo
St.Petersburg
Manchester
Philadelphia
Birmingham
Moscow
Beijing
Kolkata
Boston
Glasgow
Osaka
Liverpool
Istanbul
Hamburg
Buenos Aires
Budapest
Mumbai
Ruhr
Rio
Warsaw
Tientsin
Shanghai
Newcastle
St.Louis
2015 (4%2015-30) [max4# pre-2015]
1950
6.5
4.2
3.3
2.7
1.7
1.7
1.5
1.4
1.4
1.4
1.2
1.1
1.1
1.1
1.1
1.0
1.0
0.9
0.9
0.9
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.6
0.6
0.6
New York
Tokyo
London
Paris
Moscow
Buenos Aires
Chicago
Kolkata
Shanghai
Osaka
Los Angeles
Berlin
Philadelphia
Rio
St.Petersburg
Mexico
Mumbai
Detroit
Boston
Cairo
Tianjin
Manchester
Sao Paulo
Birmingham
Shenyang
Roma
Milano
SanFrancisco
Barcelona
Glasgow
12.3
11.3
8.4
6.3
5.4
5.1
5.0
4.5
4.3
4.1
4.0
3.3
3.1
3.0
2.9
2.9
2.9
2.8
2.6
2.5
2.5
2.4
2.3
2.2
2.1
1.9
1.9
1.9
1.8
1.8
Tokyo
Delhi
Shanghai
Sao Paulo
Mumbai
Mexico
Beijing
Osaka
Cairo
New York
Dhaka
Karachi
Buenos Aires
Kolkata
Istanbul
Chongqing
Lagos
Manila
Rio
Guangzhou
Los Angeles
Moscow
Kinshasa
Tianjin
Paris
Shenzhen
Jakarta
London
Bangalore
Lima
38.0 (-0.1) [6.6; 2000s]
25.7 (2.3) [6.2; 2000s]
23.7 (1.8) [6.1; 1990s]
21.1 (0.7) [4.5; 1970s]
21.0 (1.9) [3.9; 1990s]
21.0 (0.9) [4.2; 1970s]
20.4 (2.1) [6.0; 2000s]
20.2 (-0.1) [4.7; 1960s]
18.8 (1.8) [3.7; 1990s]
18.6 (0.5) [2.2; 1920s]
17.6 (3.0) [4.4; 2000s]
16.6 (2.7) [4.1; 2000s]
15.2 (0.7) [1.9; 1990s]
14.9 (1.7) [2.2; 1990s]
14.2 (1.1) [4.0; 2000s]
13.3 (1.8) [3.9; 1990s]
13.1 (4.2) [3.5; 2000s]
12.9 (1.8) [2.4; 1970s]
12.9 (0.6) [2.3; 1960s]
12.5 (2.3) [4.3; 1990s]
12.3 (0.5) [2.5; 1950s]
12.2 (0.0) [1.8; 1920s]
11.6 (3.7) [3.2; 2000s]
11.2 (1.8) [2.8; 2000s]
10.8 (0.6) [1.1; 1950s]
10.7 (1.1) [5.7; 1990s]
10.3 (2.0) [2.2; 1980s]
10.3 (0.7) [0.9; 1890s]
10.1 (2.6) [2.7; 2000s]
9.9 (1.4) [1.7; 2000s]
Notes: The main sources of the data are Chandler (1987) and United Nations (2014). (4% 2015-30) is
the projected annual growth rate (%) of the city between 2015 and 2030 according to United Nations
(2014). These growth rates are based on non-linear extrapolation given the rates of growth pre-2015.
[max4# pre-2015] is the maximal decadal change in absolute terms (millions) ever registered for
each city (the decade is also indicated). See Web Appendix for more details on data sources.
TABLE 2: PARAMETER VALUES FOR SIMULATION
Parameter
Value
Description
g
σ
λ
εb
εm
τb
I
w in f
Nu (0)
wu (0)
0.04
0.50
0.33
-0.30
0.00
35.0
0.05
0.80
1.00
1.00
Growth rate of city productivity
Agglomeration effect of city population
Congestion effect of city population
Elasticity of CBR w.r.t wage
Elasticity of CDR w.r.t. wage
Initial level of CBR
Fixed in-migration as fraction of initial city size
Informal wage floor
Initial city population size
Initial city wage
Notes: The table shows the parameter values used in the baseline calibration of the model.
Parameters are generally set using outside sources, see text for details. Two exceptions are the
value of g, which is found by targeting a long run growth rate for wages of 1.5% per year in rich
mega-cities, and the value of λ, which is found by targeting a wage-maximizing city size of N ∗ = 1.
36
TABLE 3: CITY WAGE AND POPULATION, BY INITIAL DEATH RATE
Results after:
Initial CDR
(mu )
10
20
30
40
50 Years
100 Years
Population Wage
Population Wage
7.3
4.6
3.5
3.5
0.8
2.5
3.8
3.8
33.5
8.9
6.0
5.9
0.8
3.0
10.4
10.6
150 Years
Population Wage
134.7
17.1
8.5
8.5
0.8
0.8
25.9
26.4
Notes: The table shows the population and wage after each number of periods in cities that
have identical initial crude birth rates of 35, and differ only by their initial crude death rate
(CDR). All cities are simulated using the calibrated model with parameters given in Table 2.
Note that both initial population, Nu (0), and initial wage, wu (0), are normalized to one, so
that entries in the table can be read as ratios relative to initial values.
FIGURE 1: NUMBER OF MILLION-PLUS MEGACITIES, 1700-2030
Notes: This figure shows the number of urban agglomerations of at least 1 million inhabitants in developed
countries and developing countries in 1700, 1900, 1950, 2015 and 2030. Developed (developing)
countries are countries whose GDP per capita (PPP, constant 2011 international $) is above (below)
$12,476 in 2013. Sources: Maddison (2008), World Bank (2013) and United Nations (2014). See Web
Appendix for more details on data sources.
37
38
Notes: This figure shows the crude birth and death rates for 20 pre-Industrial Revolution cities, 66 Industrial Revolution observations, 55 cities in the 1960s,
and 100 cities in the 2000s (the cities in the 1960s-2000s were selected because they will be among the 100 top cities in 2030 according to United Nations
(2014)). The mean crude birth rates (CBR), death rates (CDR) and rates of natural increase (CRNI) are shown. See Web Appendix for data sources.
FIGURE 2: CITY CRUDE BIRTH AND DEATH RATES, FROM ANTIQUITY TO DATE
FIGURE 3: CITY NATURAL INCREASE AND CITY CHARACTERISTICS
a) Future City Growth
b) Past City Growth
Y = 0.11***X + 0.71***; R2 = 0.50; Obs. = 100
Y = 0.13***X + 0.24; R2 = 0.52; Obs. = 55
c) City Population Density
d) National Slum Share
Y = 0.04***X +8.35***; R2 = 0.18; Obs. = 100
Y = 1.76***X + 13.47***; R2 = 0.36; Obs. = 100
e) City Infrastructure Index
f) City Informal Employment
Y = -2.39***X + 106.21***; R2 = 0.66; Obs. = 47
Y = 1.32***X + 14.671***; R2 = 0.31; Obs. = 20
Notes: This figure shows various characteristics of the 100 largest cities in 2030 according to United Nations (2014). Subfigure
(a) shows the relationship between the city projected annual growth rate in 2015-2030 and the city rate of natural increase in
the 2000s. Subfigure (b) shows the relationship between the city projected annual growth rate in 1960-2015 and the city rate of
natural increase in the 1960s. Subfigures (b), (c), (d) and (e) show the relationships between four measures of city congestion and
the city rate of natural increase in the 2000s: the city density (b), the national slum share (c), the city infrastructure index (d) and
the city informal employment rate (e). See Web Appendix for data sources. ... CONTINUED ON NEXT PAGE.
39
g) City Total Dependency Ratio
h) City Child Dependency Ratio
Y = 1.19***X + 33.72***; R2 = 0.44; Obs. = 84
Y = 1.85***X + 15.58***; R2 = 0.72; Obs. = 84
i) City Secondary Education
j) City Tertiary Education
Y = -2.07***X + 76.58***; R2 = 0.37; Obs. = 66
Y = -1.00***X + 31.67***; R2 = 0.43; Obs. = 66
k) City Product Index
l) City Development-Size Gap
Y = -0.36***X + 37.22***; R2 = 0.51; Obs. = 47
Y = -0.13***X + 9.35***; R2 = 0.42; Obs. = 47
Notes: This figure shows various characteristics of the 100 largest cities in 2030 according to United Nations (2014). Subfigures
(g), (h), (i) and (j) show the relationships between four measures of city congestion and the city rate of natural increase in the
2000s: the city total dependency ratio (g), the city child dependency ratio (h), the city secondary education completion rate (i)
and the city tertiary education completion rate. Subfigure (k) shows the relationship between the city rate of natural increase and
the city product index in the 2000s. Subfigure (l) shows the relationship between the city rate of natural increase and the ratio of
the city product index to the log of the city size in the 2000s. See Web Appendix for data sources.
40
41
Notes: The panels show the actual crude death rate (CDR) versus the threshold crude death rate (m) calculated for each city using the calibrated model.
Parameters for this calibration are as in Table 2, with the exception of τ b (initial crude birth rate), which is set to observed value for each city. Cities
with actual CDR above the threshold are in the “rich mega-city” equilibrium of the model, and cities with actual CDR below the threshold are in the “poor
mega-city” equilibrium. Note that in panel (d) the scale of both axes differs from the prior panels in order to make the data points clearer.
FIGURE 4: ACTUAL CRUDE DEATH RATES AND CALIBRATED mu VALUES, FROM ANTIQUITY TO DATE