The Micro-Evidence for Malthus. Testing the Positive and
Preventative Check, and the Iron Law, in France 1650-1820
Neil Cummins
∗
April 20, 2019
Abstract
I test the assumptions of the Malthusian model of population and stagnation at the indi-
vidual level for France, 1650-1820. Using husband’s occupation from the parish records of 41
French rural villages, I assign three different measures of status. There is no evidence for the
existence of the positive check; infant deaths are unrelated to status. However, the preventative
check operates strongly, acting through female age at first marriage. The wives of rich men
are younger brides than those of poorer men. This drives a positive net-fertility gradient in
living standards. By comparing estimates of village wealth and population I also find support
for Malthus’s Iron law. Villages follow a Malthusian frontier over the period 1670-1820.
1 The Legacy of Mathus
The shadow of Thomas Robert Malthus (1766-1834) looms large.
Malthus’s ideas inspired Charles Darwin’s theory of Natural Selection for the origin of species
and of mankind itself. Today, his model (from On the Principle of Population (1798)) is commonly
used by economists to explain both living standards and demographics before 1800 (Becker et al.
(1990); Galor and Weil (2000); Hansen and Prescott (2002); Galor (2004)). Greg Clark argues that
natural selection within the Malthusian world is itself responsible for the origin of economic growth
in Industrial Revolution England (2007).
No other social scientist appears to solicit the emotion and energy that arises with Malthus.
220 Years after his essay, fresh news articles fizzle with disdain and venom. Table 1.1 reports a
selection of news articles from major international outlets, 2008-16. Taken together the titles are
wildly contradictory.
Disagreement about the future is one matter. Disagreement about the past is a failure for
historical demography and economic history. The unsettled empirical picture is mainly drawn from
aggregate correlations. Our micro evidence base is vanishingly thin. This paper attempts to correct
that.
∗
Version 0.2. Thanks to Jane Humphries for excellent and useful commentary, Greg Clark and participants at
the New Malthusian Symposium in Jesus College, Cambridge on the 13 December 2019 (in particular Massimo
Livi-Bacci) and to Wesley Jessie for research assitance.
1
Title Date Source
Malthus was right! 25 March 2008 The New York Times
1
Malthus, the False Prophet 15 May 2008 The Economist
Are Malthus’s Predicted 1798 Food Shortages
Coming True?
1 Sep 2008 The Scientific American
2
Was Malthus right? 15 July 2011 Time
A World of Woe: Why Malthus was Right 7 July 2014 PBS News Hour
3
.
Why Malthus Is Still Wrong 1 May 2016 Scientific American
Africa’s high birth rate is keeping the
continent poor
22 Sep 2018 The Economist
Table 1.1: Recent News Articles on Malthusian Thinking from Major International Outlets
1.1 Testing Malthus’s Assumptions
To summarise Malthus (1798): Food is essential, fertility is constant within marriage [quote M1
in table 1.2], deaths are negative in living standards [M2 and M3], the probability of marriage is
positive in living standards, age at first marriage is negative in living standards [both M5]. These
observations lead to the first two assumptions of the Malthusian model used by contemporary
economists:
1. Births respond positively to living standards.
2. Deaths respond negatively to living standards.
Clark (2007) details how these 2 assumptions lead to the Iron Law of Malthus:
• There is an inverse relationship between population and living standards.
Demography determines living standards in an endogenous system. All population growth will lead
to reductions in living standards inducing deaths to rise and births to fall until a no-population
growth equilibrium is reached. The model is illustrated in figure 1.1.
The model explains income per capita and population for a given level of technology, all macro
level concepts, via assumption 3 but rests on micro level assumptions (1 and 2 above).
4
This paper
tests the Malthusian assumptions at the individual and village level for France, 1650-1820.
In general, empirical tests of the Malthusian model rely on the correlations of aggregate time
series of the real wage and vital rates (Lee and Anderson (2002); Crafts and Mills (2009) are a
selection for England, Fernihough (2013) for Italy). Weir (1984) compares the elasticities of births,
marriages and deaths to grain price shocks in England and France, 1670-1870. France exhibits much
1
In this article, Paul Krugman states “The fact is that Malthus was right about the whole of human history up
until his own era.”
2
In this article Jeffrey Sachs states “Have we beaten Malthus? After two centuries, we still do not really know.”
3
This is an interview with Greg Clark on Clark (2007)
4
In other words, “The Malthusian model of population and economic growth has two key components. First,
there is a positive effect of the standard of living on the growth rate of population, resulting either from a purely
biological effect of consumption on birth and death rates, or a behavioral response on the part of potential parents
to their economic circumstances” (Weil and Wilde (2009), my italics).
2
I think I may fairly make two postulata. First, That food is necessary to the existence
of man. Secondly, That the passion between the sexes is necessary and will remain
nearly in its present state. These two laws, ever since we have had any knowledge of
mankind, appear to have been fixed laws of our nature...Assuming then my postulata
as granted, I say, that the power of population is indefinitely greater than the power
in the earth to produce subsistence for man. [M1]
...the actual distresses of some of the lower classes, by which they are disabled from giving
the proper food and attention to their children, act as a positive check to the natural
increase of population. [M2]
The positive check to population, by which I mean the check that represses an increase
which is already begun, is confined chiefly, though not perhaps solely, to the lowest
orders of society. [M3]
This check is not so obvious to common view as the other I have mentioned, and, to prove
distinctly the force and extent of its operation would require, perhaps, more data than
we are in possession of. But I believe it has been very generally remarked by those who
have attended to bills of mortality that of the number of children who die annually,
much too great a proportion belongs to those who may be supposed unable to give their
offspring proper food and attention, exposed as they are occasionally to severe distress
and confined, perhaps, to unwholesome habitations and hard labour. This mortality
among the children of the poor has been constantly taken notice of in all towns. [M4]
a foresight of the difficulties attending the rearing of a family acts as a preventive check
[M5]
Malthus, 1798
Table 1.2: Malthus Original Words
Notes: M1 indicates the assumption that within marriage fertility is uncontrolled. M2 is the famous positive check,
M3 and M4 both indicate that the positive check should be detectable by cross-sectional status differences in mortality
as does M5 for the preventative check.
3
Y pc
B/D
Births
Deaths
P op
Y pc
Y
∗
p
c
P op
∗
Figure 1.1: The Modern Malthusian Model
Notes: The top axes illustrate the birth and death schedules as implied by the positive and preventative check (see
table 1.2 and text). Where Births > Deaths, population grows. But due to the Malthusian Iron Law, there is a
negative relationship between the level of population and living standards per capita. So population growth leads
to declining income per capita and subsequently to higher mortality and lower fertility. This results in the long run
equilibrium of a Malthusian society being one where Births = Deaths and population growth is zero. (The same
logic works in reverse where Deaths > Births.)
4
stronger positive and preventative checks than England throughout this period (table 6, p.42).
5
However this is a short run analysis based on annual elasticities. The Macro-level correlations
can mask micro-level variation, especially in a country as vast and heterogeneous as pre-Industrial
France.
Studies explicitly testing the Malthusian assumptions at the individual level are rare. For
England, Clark and Hamilton (2006); Clark and Cummins (2015) report a strong correlation of
wealth and fertility in cross-section for English men, 1500-1879. This conclusion has been supported
by recent work by de la Croix et al. (2019) who similarly find a strong effect of status on net fertility
but also point out that the ‘upper class’ elites married less and were more often childless.
6
For
France, Weir (1995) linked tax data to one village near Paris, Rosny-Sous-Bois, and documents a
clear reproductive advantage for the rich, driven by earlier marriage and lower infant mortality.
This finding is also supported by those of Hadeishi (2003) for another village, Nuits in Burgundy.
7
This paper uses the Henry family reconstitution database to test Malthus’s assumptions at the
individual and village level. Firstly, by measuring the effect of a twin birth on terminal family size,
I test whether Malthus was right about the passion between the sexes. Before the Revolution, he is
spot on. Twins add exactly one to final family size. There is no adjustment of parents to a random
twin birth. After, 1789 parents adjust. This finding has implications for economic models that have
endogenous fertility where parents choose family size (Becker et al. (1990); Galor and Weil (2000);
Hansen and Prescott (2002); Galor (2004)). For pre-Revolutionary France, this is not a realistic
assumption.
8
Using the occupational listings of husbands in the marriage registers, I assign three different
measures of status to test the power of the positive and preventative check in cross-section, before
and after the Revolution. I find strong evidence for the primacy of the preventative check - acting
through female age at first marriage - over the positive check. In fact, I find no evidence for any
status-mortality gradient. The micro-level operation of the preventative check in France is consistent
with Malthus’s reasoning. For those that trace Europe’s rise to the operation of its marriage markets
(as described by Hajnal (1965)) this is a crucial finding (see for example Voigtländer and Voth
(2013)).
The Malthusian status-marriage relationship drives a strong and positive fertility-status gradi-
ent. Survival of the richest operated in pre-Revolutionary France, just as in pre Industrial England
(Clark and Cummins (2015)). However, the top elite group, the Gentry/Independent group, do
not display higher fertility. I suspect this is due to the early fertility decline of French elites (see
Livi-Bacci (1986)).
Finally, by estimating village level population and living standards, I test the Malthusian Iron
law. From 1760 to 1820, increases in estimated village population led to decreases in living stan-
dards, as measured by average village occupational wealth, and vice versa. This effect is dependent
however on the size of a village. Only more populated villages, I speculate as being closer to the
Malthusian frontier, have a statistically significant negative correlation between population and
living standards. For these large villages, the Malthusian Iron law is evident, 1650-1820.
Section 2 describes the data for analysis, section 3 the methodology. The individual results for
5
Perhaps due to the absence of a Poor Law system in France (See Kelly et al. (2014)).
6
Due to the earlier decline of elite fertility in England (about 1800 Clark and Cummins (2015)), they are unable
to generalize this pattern to their entire sample period.
7
Cummins (2013) was focused on estimating marital fertility controlling for age at marriage and child mortality,
did not explicitly test the Malthusian assumption of a positive wealth-fertility gradient.
8
This result is also discussed and reported, along with similar results for pre-Industrial England and Quebec in a
related paper, solely devoted to estimating the response of pre-transition fertility to twins, in Clark et al. (2019)
5
the presence of random fertility, and the positive and preventative check are presented in section 4.
Section 5 tests Malthus Iron law at the village level and section 6 concludes.
2 Data
The data for analysis are the Family Reconstitution data of Louis Henry. This was a detailed
demographic reconstruction of 41 randomly selected French villages, 1650-1829, mapped in figure
2.1a.
9
The 41 villages represent a random sample of one-tenth of one-percent of the 40,000 odd
villages in France at this time.
10
Figure 2.1b reports the fertility patterns before and after the
French Revolution and table 2.1 reports the village level summary statistics. These are small rural
villages, illustrated from the 18th century Carte Cassini in figure 2.2.
11
The occupational listings of fathers in the sample were coded to the equivalent HISCO code (a
standardized occupational classification scheme) and HISCAM occupational score and additionally
a 7 level scale as described in Clark and Cummins (2015). HISCAM scores are a stratification scale
based on social interactions.
12
Table 2.2 reports the occupational characteristics of the Henry data.
Only 18.7% of husbands have a marital occupation recorded that we have been able to code.
This is a small proportion but it compares favorably to other data. For example, only 10.3% of
husbands in the CAMPOP English parish reconstitution have an occupation recorded at marriage
(own calculations based on the underlying data from Wrigley et al. (1997)).
I link each occupation to its observed median wealth. The source for this wealth data are
the Tables des Successions et Absences. The TSAs were an innovation of the Napoleonic era and
recorded all deaths in a locality, along with detailed information on the date of death, residence,
profession, age at death and marital status. Every death was recorded, even those with no taxable
assets at death, typically recorded as “rien” (25%, see Cummins (2013) for more detail).
Table 2.2 also reports the average real wealth of men who died under various occupations from
4 sample villages observed in the Napoleonic-era wealth taxation books. I apply the observed
medians, of the sum of both cash and property wealth„ by individual occupation, to the sample.
Figure 2.3 reports the average occupational wealth level for the 41 Henry villages, 1650-1820. The
richest village by this measure is Saint-Chely-D’Apcher. Inspecting the occupational distribution
by eye, it displays unusual prestige: 35 Lords (each assigned a wealth of 85,834 Francs in 1850
prices, 2 Notaries to the King (39,596), and 7 doctors (14,666). In contrast, the poorest village,
Belloy-Saint-Leonard, is domainted by labourers.
9
The summary papers of the Enquête Henry are: Henry (1972); Henry and Houdaille (1973); Houdaille (1976) and
Henry (1978). A summary of all studies using the Henry data (before 1997) is listed in Renard (1997), and detailed
discussion of the database can be found in Séguy and Méric (1997); Séguy (1999); Séguy and Colençon (1999); Séguy
and la Sager (1999); Séguy et al. (2001).
10
I use 40 villages only as the sample size for Suze-Sur-Sarthe is insufficient for any statitcial inference.
11
It is worth noting that the sample period reflects a country whose urbanization rate is declining during the
sample period (De Vries (2013)).
12
See http://www.camsis.stir.ac.uk/hiscam/ for more detail.
6
(a) The 41 Reconstitution Villages
0.0
0.1
0.2
0.3
0.4
0.5
15-9 20-4 25-9 30-4 35-9 40-4 45-9
Age Group
Births per Year
Revolution
Before
1789
P
ost 1789
(b) French Marital Fertility, Before and After 1789
Figure 2.1: Aspects of the Henry Data
Notes: The 41 communes are generally small, rural villages. The data capture the fertility decline that was underway
in some villages before the French Revolution (Cummins (2013)).
7
BELLO
Y-SAINT-LEONARD
QUIERS-SUR-BEZONDE
CUISE-LA-MOTTE
NESLE-NORMANDEUSE
VOIVRES-LES-LE-MANS
ESBAREICH
GUIMAEC
CHAMPETIERES
BERMONT
GOULAFRIERE
SAMOUILLAN
IPPECOUR
T
MAIZIERES
TR
OUILLAS
ORMANCEY
ECHEVR
ONNE
CHAMPIGNY
CONNIGIS
SAINT-AIGNAN-GRANDLIEU
GR
OZON
R
OSNY-SOUS-BOIS
CHILL
Y
SAINT-ANDRE-EN-BRESSE
D
AMPIERRE-SOUS-BOUHY
VERD
ALLE
VIDEIX
GERMOND-R
OUVRE
CABRIS
HALLINES
MASSONGY
CHENICOUR
T
BA
GNEUX-LA-FOSSE
TR
ONCHE
SAINT-LEGER
BELLEGARDE
VIC-SUR-SEILLE
SAINT-P
AUL-LA-ROCHE
ANNEVILLE-EN-SAIRE
MAX
OU
SAINT-CHEL
Y-D’APCHER
0 2000 4000 6000
Mean Occupational Wealth
Figure 2.3: Mean Occupational Wealth, by Village
Notes: For every individual occupation listed in the marriage registers I assign the median value for that occupation
observed in the Napoleonic-era tax books. The figure then plots the median for this measure, by village.
9
Table 2.1: Summary Statistics, Villages
Village Dept. Pop.
1821
Year
Min.
Year
Max.
N
Par-
ents
N
Chil-
dren
Avg.
Births
pre
1789
Avg.
Births
post
1789
Anneville-En-Saire Manche 807 1666 1819 1,303 3,148 5.3 5.3
Bagneux-La-Fosse Aube 798 1670 1819 1,097 3,533 7.3 7.3
Bellegarde Loiret 1,295 1675 1819 2,659 7,104 6.6 6.6
Belloy-Saint-Leonard Somme 284 1684 1819 501 1,326 3.9 3.9
Bermont Territoire de Belfort 88 1670 1819 1,321 4,026 6.1 6.1
Cabris Alpes-Maritimes 1,879 1688 1819 2,500 7,741 5.8 5.8
Champetieres Puy-de-Dome 1,457 1673 1819 2,068 7,327 5.5 5.5
Champigny Yonne 1,473 1670 1819 2,131 7,494 6.7 6.7
Chenicourt Meurthe-et-Moselle 279 1676 1819 473 1,186 7.8 7.8
Chilly Ardennes 328 1670 1819 510 1,384 4.7 4.7
Connigis Aisne 271 1675 1819 760 1,850 6.3 6.3
Cuise-La-Motte Oise 959 1672 1819 1,615 5,260 6.8 6.8
Dampierre-Sous-Bouhy Nievre 1,226 1670 1819 2,019 6,461 6.2 6.2
Echevronne Cote-d’Or 415 1664 1819 558 1,672 5.4 5.4
Esbareich Hautes-Pyrenees 894 1673 1819 867 2,597 6.1 6.1
Germond-Rouvre Deux-Sevres 673 1670 1819 1,482 3,215 4.9 4.9
Goulafriere Eure 444 1670 1819 1,046 2,346 4.5 4.5
Grozon Jura 781 1671 1819 1,516 4,684 6.2 6.2
Guimaec Finistere 1,789 1670 1819 3,173 9,704 5.1 5.1
Hallines Pas-de-Calais 501 1678 1819 693 1,958 6.3 6.3
Ippecourt Meuse 400 1674 1819 726 2,456 5.9 5.9
Maizieres Calvados 652 1671 1819 931 2,298 5.4 5.4
Massongy Haute-Savoie 705 1671 1819 934 2,487 6.3 6.3
Maxou Lot 953 1674 1819 1,397 3,484 4.0 4.0
Nesle-Normandeuse Seine-Maritime 315 1671 1819 619 1,462 4.7 4.7
Ormancey Haute-Marne 295 1670 1819 558 1,738 6.5 6.5
Quiers-Sur-Bezonde Loiret 465 1670 1819 745 2,143 6.9 6.9
Rosny-Sous-Bois Seine-Saint-Denis 822 1632 1819 1,448 4,833 6.5 6.5
Saint-Aignan-Grandlieu Loire-Atlantique 1,172 1670 1819 2,557 7,568 5.9 5.9
Saint-Andre-En-Bresse Saone-et-Loire 188 1671 1819 728 1,554 7.2 7.2
Saint-Chely-D’Apcher Lozere 1,366 1690 1847 3,908 12,433 6.5 6.5
Saint-Leger Charente-Maritime 656 1686 1819 1,407 3,547 5.0 5.0
Saint-Paul-La-Roche Dordogne 1,692 1670 1819 4,891 11,225 6.4 6.4
Samouillan Haute-Garonne 389 1680 1819 325 1,085 6.6 6.6
Tronche Isere 1,109 1670 1819 3,025 7,059 5.7 5.7
Trouillas Pyrenees-Orientales 622 1737 1818 748 2,101 6.8 6.8
Verdalle Tarn 1,137 1670 1819 1,855 4,826 5.0 5.0
Vic-Sur-Seille Moselle 3,196 1670 1819 7,028 19,240 6.8 6.8
Videix Haute-Vienne 781 1685 1819 2,278 4,720 6.2 6.2
Voivres-Les-Le-Mans Sarthe 448 1670 1818 1,261 2,727 4.0 4.0
Notes: Year is year of marriage. Village Suze-Sur-Sarthe is dropped due to small numbers.
10
Table 2.2: Summary Statistics, Occupations
Rank Examples N HISCAM
/100
TSA
Wealth
7 Gentry/Independent 744 63.9 18,280.7
6 Merchants/Professionals 568 77.0 17,984.7
5 Farmers 4,070 47.1 2,780.9
4 Traders 2,136 51.5 1,734.6
3 Craftsmen 1,652 50.2 1,271.0
2 Weavers/Shoemakers 1,355 48.9 886.7
1 Laborers/Servants 1,817 45.5 237.5
53,321
Notes: The source for the wealth data are the Tables des Suc-
cessions et Absences, Cummins (2013).
11
3 Methodology
This paper tests the Malthusian assumptions at the individual level, in cross section, for a sample
of French rural villages 1650-1820.
First I test the assumption of Malthusian constant marital fertility. As quote [M1] indicates,
Malthus did not conceive of any fertility control within marriage. The ‘constant passion between
the sexes’ drives the birth schedule in figure 1.1. I use the random occurrence of a twin birth to test
whether twin-parents adjust their terminal family size to this ‘shock’. The Henry sample contains
180,000 children, 4,000 of whom are twins. Conditional on a woman’s age and parity, twins are
essentially a random occurrence. If Malthus is right about constant marital fertility - then the
expected effect of a twin on terminal family size should equal 1. If we regress
B
i
= c + β
1
D
j
T win
+
X
Age
J
i
+
X
P arity
j
i
(1)
with B the number of births to a mother i, D
T win)
and indicator variable for child j being a twin,
Age a set of mother’s age at child j birth dummies and P arity being the number of children born
at said birth. If there is no adjustment of mother’s to the random shock of a twin, we would expect
β = 1. This would consistent with ‘natural fertility’ (Henry (1961)) and Malthus’s assumptions
about sex.
Next I test the Henry data for the status gradient in Mortality and fertility (the top schedule
of figure 1.1). The empirical strategy is simple. I test for the presence of cross-sectional differences
by 3 different measure of status, through the main empirical estimation formula;
Y
i
= c +
X
βS
Occ
i
+ D
V illage
+ Y ear (2)
where S
Occ
i
is a measure of occupational status for couple i - either occupational wealth, HISCAM
score or a set of 7 dummies for the occupational categories in table 2.2. Y
i
is an outcome; child
mortality, proportion of children marrying, age at first marriage of wives, and both total births and
surviving family size.
The Malthusian system is an endogenous system of equations with multiple feedback loops. Do
the correlations generated by equation 2 have a causal interpretation? The identification could
be confounded by a causal channel from the outcome variables (Y
i
) to the occupational status of
parents.
As status is measured at marriage this is unlikely. More likely however, is that both husband
occupational status and the outcome variables are jointly determined by the unobserved underlying
characteristics of both parents, X
i
(resilience, family cultures, genetics), as described in equations
3 and 4 below.
Y
i
f(X
i
) (3)
S
Occ
i
f(X
i
) (4)
This identification problem does not confound the empirical exercise. Principally, the determi-
nation of both endogenous variables by a latent factor, X
i
, will not necessarily bias the empirical
corrections. The outcomes of high and low status parents, even if they are determined by a under-
lying process that also determines status, will still reveal the Malthusian forces, if they are present.
In fact this notion is central to Darwin’s use of the Malthusian model to explain the origin of species
12
through natural selection. The observed correlations matter even if they don’t have a causal in-
terpretation. Malthus himself used cross-sectional observations to justify his assumptions (quotes
M2-5).
However, the observation of Malthusian forces in cross section does not mean that we can
conclude that changes in living standards will necessarily invoke changes in the outcome variables
measured by Y
i
. To detect this effect the time-series analysis of Weir (1984) is more appropriate.
The French Revolution of 1789 serves as a natural break point to split the sample for equation
2. Malthus would approve:
the French Revolution ... like a blazing comet, seems destined either to inspire with
fresh life and vigor, or to scorch up and destroy the shrinking inhabitants of the
earth [M6]
Child mortality is calculated as the proportion of children surviving to age 14. By summing up
repeated names within a family’s birth history an adjusted child mortality is calculated for the
analysis (See Houdaille (1984) for a deeper analysis of this important issue).
All estimations are executed as Ordinary Least Squares. This is to ease interpretation of the
marginal effects and their standard errors; the results are not sensitive to estimation method (both
Poisson and Negative Binomial estimates were calculated but are not reported).
4 Results
4.1 Malthus and Natural Fertility
Was Malthus correct about what determined fertility before 1789 in France? Was the passion
between the sexes a God-given constant? Louis Henry himself strongly believed that pre-industrial
populations practiced ‘natural fertility’ just as Malthus would have believed (Henry (1961)).
13
Table 4.1 reports the twin effect, as detailed in equation 1, before 1789 and after 1810, for the
Henry sample. Before 1789, the data is consistent with Henry and Malthus. The twin coefficient is
1.023. Although the 95% confidence interval cannot rule out a small proportion of controllers, the
coefficient is statically indistinguishable from 1.
After 1789, the coefficient estimate is substantially smaller than 1, although the confidence
interval still overlaps 1. Due to the heterogeneous nature of the French fertility decline, this is
suggestive that there is now a significant proportion of controllers, as revealed by this twin test.
At least before 1789, we can conclude that the essential Malthusian assumption, that marital
fertility is controlled (M1) is supported by the French micro data collected by Henry.
4.2 Testing the Checks at the Individual Level
Next I apply estimation equation 2 to child mortality, the proportion of children marrying and finally
gross and net fertility. If Malthus is right we should see a strong positive gradient of occuaptional
status on these outcomes.
13
Some recent papers have claimed to have found empirical evidence of fertility control in a variety of pre-industrial
European populations: England, France, Germany, Sweden (Cinnirella et al. (2017), Amialchuk and Dimitrova (2012),
Anderton and Bean (1985), Bengtsson and Dribe (2006), David and Mroz (1989),Dribe and Scalone (2010), Kolk
(2011), Van Bavel (2004)).
13
Table 4.1: The Effect of a Twin on Final Family Size, France, Before and After the French Revolution
Dependent variable:
Twin Effect on Final Family Size
Before 1789 After 1810
(1) (2)
Twin Birth 1.023 .735
(.877, 1.168) (.466, 1.004)
Parity Dummies? Yes Yes
Mother Age Dummies? Yes Yes
Observations 65,722 11,650
R
2
.467 .608
Note: OLS, (95 percent Confidence Interval)
Table 4.2 reports the results for child mortality. This is our primary measure of the Malthusian
positive check (M2) for this dataset. Surprisingly there is little consistent support for the existence
of the positive check amongst French villagers. Adjusted child mortality does not display cross-
sectional trends with respect to living standards.
After 1789 however, there is evidence that the Merchant/Professional class have substantially
lower child mortality than the omitted category (Labourers/Servants). The proportion of children
dying for this class is about half that of the rest of the sample and the effect is statistically significant
at the 1% level. (As will become evident from table 4.7 this group have substantially lower fertility
post 1789 too.)
Table 4.3 reports the results for the proportion of children known to have married. This measure
is likely to be biased against more mobile classes as children who migrate from the parish will of
course not be observed. So I interpret this set of correlations with caution; Pre 1789, perhaps
unsurprisingly, the children of farmers and local traders are more likely to be observed marrying.
Both period suggest an ‘inverted U’ relationship between marriage probability and occupational
status (using the evidence from column 3 and 6). However, this could purely be the result of the
weakness of the family reconstitution data. Parish records will only observe ‘stayers’ - the more
mobile poorer and elite classes will simply not be observed.
Supporting this are the results of the child marriage probability test, using a smaller sample
consisting of only children observed dying or marrying. Here, there are no status correlations
(reported in table A.1 in the appendix).
Table 4.4 reports the results for female age at marriage. Here we find strong and consistent
correlations with all measures of occupational status before 1789. The wives of higher status men are
constantly younger at marriage than those of lower status men. The wives of the gentry/independent
class marry over 2 years younger than those of laborers and servants. For farmers and merchants,
it is about 1-1.5years. Even craftsmen marry women who are about 9 months younger. The
standardized correlations are powerful too, for both occupational wealth and Hiscam.
After 1789, this Malthusian preventative check in cross section largely disappears. However
craftsmen and the gentry class still marry younger women (of about 1 year). The standardized
14
Table 4.2: Adjusted Child Mortality Rate and Occupational Status
Proportion of Children Dead
Pre 1789 Post 1789
(1) (2) (3) (4) (5) (6)
Occupational Wealth, Z .004 −.013
(.011) (.017)
Hiscam, Z −.011
∗∗∗
−.019
∗∗∗
(.003) (.007)
No Occupation −.056
∗∗∗
−.027
∗
(.009) (.016)
Weavers/Shoemakers .008 −.0003
(.013) (.021)
Craftsmen .003 .014
(.012) (.020)
Traders .028
∗∗
.018
(.012) (.021)
Farmers .006 −.001
(.010) (.017)
Merchants/Professionals −.014 −.091
∗∗∗
(.017) (.032)
Gentry/Independent .024 .023
(.020) (.022)
Constant −1.398
∗∗∗
.327
∗∗∗
.314
∗∗∗
.185
∗∗∗
.180
∗∗∗
.178
∗∗∗
(.190) (.024) (.017) (.027) (.027) (.029)
Village Fixed effects? Yes Yes Yes Yes Yes Yes
Observations 5,308 5,180 17,171 2,453 2,216 5,142
R
2
.142 .136 .132 .083 .084 .071
Note:
∗
p<0.1;
∗∗
p<0.05;
∗∗∗
p<0.01
OLS, Laborers/Servants are the omitted category
15
Table 4.3: Proportion of Children Observed Marrying and Occupational Status
Proportion of Children Known to be Married
Pre 1789 Post 1789
(1) (2) (3) (4) (5) (6)
Occupational Wealth, Z −.043 .014
(.030) (.030)
Hiscam, Z −.011 −.006
(.010) (.014)
No Occupation .007 .028
(.019) (.032)
Weavers/Shoemakers −.035 .054
(.027) (.041)
Craftsmen −.022 .041
(.027) (.042)
Traders −.006 .043
(.024) (.042)
Farmers −.016 .030
(.022) (.034)
Merchants/Professionals −.053 −.066
(.046) (.061)
Gentry/Independent −.022 .065
(.049) (.041)
Constant .100 .921
∗∗∗
.932
∗∗∗
.952
∗∗∗
.946
∗∗∗
.933
∗∗∗
(.456) (.071) (.049) (.054) (.055) (.058)
Village Fixed effects? Yes Yes Yes Yes Yes Yes
Observations 1,556 1,519 4,006 787 697 1,394
R
2
.049 .047 .030 .083 .089 .054
Note:
∗
p<0.1;
∗∗
p<0.05;
∗∗∗
p<0.01
OLS, Laborers/Servants are the omitted category.
Excluding unknowns
16
Table 4.4: Female Age at Marriage and Occupational Status
Female Age at Marriage
Pre 1789 Post 1789
(1) (2) (3) (4) (5) (6)
Occupational Wealth, Z −.993
∗∗∗
−.367
(.292) (.387)
Hiscam, Z −.307
∗∗∗
.154
(.095) (.155)
No Occupation −.402
∗
−.298
(.242) (.365)
Weavers/Shoemakers −.207 .503
(.373) (.494)
Craftsmen −.832
∗∗
−1.012
∗∗
(.344) (.485)
Traders −.177 .120
(.324) (.484)
Farmers −1.275
∗∗∗
−.493
(.290) (.403)
Merchants/Professionals −1.367
∗∗∗
.679
(.489) (.766)
Gentry/Independent −2.108
∗∗∗
−.941
∗
(.499) (.521)
Constant 11.966
∗∗
28.430
∗∗∗
27.915
∗∗∗
27.137
∗∗∗
27.247
∗∗∗
27.639
∗∗∗
(5.659) (.721) (.479) (.544) (.536) (.559)
Village Fixed effects? Yes Yes Yes Yes Yes Yes
Observations 3,769 3,658 12,061 2,616 2,362 6,705
R
2
.076 .074 .070 .090 .089 .063
Note:
∗
p<0.1;
∗∗
p<0.05;
∗∗∗
p<0.01
OLS, Laborers/Servants are the omitted category. First Marriages only
17
correlations are indsitiuqushable from zero.
Before 1789, this set of micro cross-sectional tests of the Malthusian Model suggest that it is
the preventative check, acting through female age at first marriage, that dominates in French rural
villages. The positive check is not evident from the cross sectional differentials in French rural
villages.
Malthus proposed that constant fertility and the preventative check should lead to a positive
fertility gradient (M1 and M5). Was this the case in Ancien Régime France?
4.3 Malthus and the Fertility Gradient
Building on Malthus and Darwin, Clark (2007) claims that the positive wealth-fertility gradient in
English history was responsible for a ’survival of the Richest’ and, perhaps, through selection, also
responsible for the origin of modern economic behavior and growth. For France, Cummins (2013)
failed to find any positive effect of wealth on family size during the fertility transition. However, that
study confined itself to wealth measured during the Napoleonic era. What was the status-fertility
gradient in France before the secular decline, roughly coincident with 1789?
First I look at the village level. Before 1789, the mean wealth of a village is highly correlated
with surviving children (but not births), as reported in table 4.5. After 1789, this correlation
reverses. ’Survival of the richest’ operated at the village level in France. The economic size of this
effect is large. Evaluated at the mean, the elasticities in table 4.5 reveal that a village twice as rich
as it’s neighbor would have an extra 1.8 children on average. After 1789, the richer village has 1.3
kids less than it’s poorer neighbor. (See figure 2.3 reports the spread of wealth across the randomly
sampled values in the Henry data. Prerevolutionary France is very unequal.)
Table 4.5: Village Level Correlations of Wealth and Individual Surviving Children
ln(Fertility)
Gross Net Gross Net
pre 1789 post 1789
(1) (2) (3) (4)
ln(Mean Village Wealth) −.041 .056
∗∗∗
.020 −.045
∗∗
(.040) (.010) (.069) (.020)
Observations 26,678 17,171 8,127 5,141
Adjusted R
2
.002 .002 .001 .004
Note:
∗
p<0.1;
∗∗
p<0.05;
∗∗∗
p<0.01
OLS
Decadal time trend included.
Is this village-level pattern reflected at the individual level? Tables 4.6 and 4.7 report the
individual correlations of occupational wealth, Hiscam score (both standardized) and the 7 point
occupational division, before and after 1789. Before 1789, fertility is positive in status. This effect
disappears after the revolution.
In general, at the micro-level, the richer occupational groups outbred the poor; the correlations
for occupational wealth and Hiscam are sizable and statistically significant across the specifications.
18
Table 4.6: Individual Level Correlations of Occupational Status and Fertility, pre 1789
Fertility
Gross Fertility Net Fertility
(1) (2) (3) (4) (5) (6)
Occupational Wealth, Z .652
∗∗∗
.468
∗∗∗
(.144) (.103)
Hiscam, Z .081
∗
.128
∗∗∗
(.043) (.030)
No Occupation −1.411
∗∗∗
−.867
∗∗∗
(.096) (.072)
Weavers/Shoemakers .269
∗
.141
(.146) (.111)
Craftsmen .495
∗∗∗
.384
∗∗∗
(.137) (.104)
Traders .563
∗∗∗
.236
∗∗
(.130) (.099)
Farmers .610
∗∗∗
.474
∗∗∗
(.118) (.089)
Merchants/Professionals .734
∗∗∗
.657
∗∗∗
(.194) (.147)
Gentry/Independent .051 .105
(.216) (.163)
Village Fixed effects? Yes Yes Yes Yes Yes Yes
Observations 6,665 6,491 26,678 6,281 6,117 25,238
Adjusted R
2
.036 .033 .088 .076 .076 .088
Note:
∗
p<0.1;
∗∗
p<0.05;
∗∗∗
p<0.01
OLS, Laborers/Servants are the omitted category
19
Table 4.7: Individual Level Correlations of Occupational Status and Fertility, post 1789
Fertility
Gross Fertility Net Fertility
(1) (2) (3) (4) (5) (6)
Occupational Wealth, Z −.240 −.131
(.173) (.129)
Hiscam, Z −.174
∗∗
−.071
(.069) (.050)
No Occupation −1.442
∗∗∗
−1.062
∗∗∗
(.147) (.108)
Weavers/Shoemakers .230 .071
(.200) (.148)
Craftsmen .402
∗∗
.314
∗∗
(.196) (.145)
Traders .350
∗
.250
∗
(.195) (.145)
Farmers .264 .210
∗
(.163) (.120)
Merchants/Professionals −.577
∗
−.211
(.296) (.217)
Gentry/Independent .327 .050
(.214) (.158)
Village Fixed effects? Yes Yes Yes Yes Yes Yes
Observations 3,121 2,826 8,129 2,979 2,694 7,738
Adjusted R
2
.063 .069 .104 .075 .083 .105
Note:
∗
p<0.1;
∗∗
p<0.05;
∗∗∗
p<0.01
OLS, Laborers/Servants are the omitted category
20
The surprising finding from table 4.6 is the low gross and net fertility of the most elite occupational
group; the Gentry and Independent class. They have a fertility statistically indistinguishable from
that of Laborers and Servants. This non-Malthusian finding could reflect an earlier fertility decline
of these elites as reported by Livi-Bacci (1986) (p.185). This result is also worth comparing to the
recent finding of surprising low fertility by the same socioeconomic class in England, using similair
data de la Croix et al. (2019).
The tables conclusively show that the early French fertility decline was not a neo-Malthusian
response supporting earlier analyses of a smaller sample of villages (Weir (1994); Cummins (2013)).
If marital fertility limitation replaced marriage as the lever of individual’s control over family size
we would expect the Malthusian gradient in fertility to persist after 1789 just as it dominated
before. What we in fact observe is the disappearance of the Malthusian fertility gradient entirely.
In several villages, it actually become sharply negative (see Cummins (2013)).
5 Malthus Iron Law: Population and Living Standards at the
Village Level
In this final section I calculate the revealed Malthusian ‘Iron Law’ schedule, as sketched theoretically
in figure 1.1 b) for French rural villages over the sample period. The idea is simple; do the 41
randomly selected villages display a Malthusian constraint? This is a period in which urbanization
rates are not dramatically increasing De Vries (2013) and most of the French population live in
small villages like the ones used here. By triangulating population and village wealth from the
census, the birth records and the occupational classifications of marriage I can report the observed
relationship between population and living standards.
Figure 5.1 reports the naive relationship between village population and village mean occupa-
tional wealth for 1821. There is a positive relationship. Does thus nullify Malthus ‘Iron law’ of
population? As these villages will potential have different levels of technology (different resources,
land quality etc. as suggests by figure 2.2), the Malthusian frontier for each of them is unidentified
and this observed correlation is no evidence that Malthusian forces are absent.
To identify the Malthusian frontier I use village-level movements in population and living stan-
dards. Figure 5.2 maps out conceptual Malthusian Iron law technology frontiers (red lines) and
alternatively Boserupian paths (where population has a positive effect on living standards). Start-
ing from the mid-point of a graph, if a village is ruled by Malthusian forces it is forced to move along
the red line. (Of course it could obey neither Malthus nor Boserup and move in any conceivable
direction, or back and forth.)
I use the relationship between actual population in 1821 and 1793, and observed village births
in the 20 year period around both those years to estimate population from births in 1760, 1720 and
1670
14
.
Figure 5.3 and table 5.1 report the results. The sample villages split evenly into Malthusian and
Boserupian paths, approximately speaking. However, small villages could be well inside the frontier
and their movements could not reflect a binding Malthusian constrain. Table 5.1 reports fixed-effect
estimates for the ‘within-village’ slope of population and living standards. Over a population of
750, the effect is strongly Malthusian.
14
Population is taken from http://cassini.ehess.fr/cassini/fr/html/6_index.htm. The estimated β in P op
i
= βN B
i
where i is village and P op is population in either 1793 or 1821 and N B is number of births in the 20 year period
surrounding 1793 or 1821 is .67 with an r
2
of .95.
21
0
1,000
2,000
3,000
0 1,000 2,000 3,000 4,000
Village Avg.
Occupational Wealth
Population, 1821
Figure 5.1: Village Population and Average Occupational Wealth in 1821
0
1
2
3
4
5
0 1 2 3 4 5
Living Standards
Population
World
Bosrupian
Malth
usian
Figure 5.2: Identifying Malthusian and Boserupian Frontiers
22
4
5
6
7
8
6.4 6.8 7.2 7.6
Village Avg.
Occupational Wealth
Population, 1821
Period
1600-1700
1700-1740
1740-1780
1780-1820
1800-40
Slope
-
+
Figure 5.3: Population and Living Standards, French Villages, 1650-1840
23
Table 5.1: Village-Period Correlations of Population and Village Mean Occupational Wealth
ln(Wealth)
All All <500 >500 >750 1,000
(1) (2) (3) (4) (5) (6)
ln(Population) .066
∗
−.042 −.135 −.099 −.667
∗∗∗
−.614
∗
(.039) (.071) (.110) (.176) (.234) (.328)
Village Fixed effects? No Yes Yes Yes Yes Yes
Observations 95 95 34 60 42 28
Adjusted R
2
.019 .441 .300 .502 .617 .706
Note:
∗
p<0.1;
∗∗
p<0.05;
∗∗∗
p<0.01
OLS
6 Conclusion
In sum, Malthusian forces existed in pre-Revolutionary France. However a close analysis of the
Henry micro-data, reveal that the preventative check, acting through female age at first marriage,
dominated the positive check of child mortality. Pre 1789, Survival of the richest was a French
reality just as it was in England. However, the elites of the small French villages display surprisingly
low fertility. All Malthusian characteristics more or less disappeared after the Revolution. However
throughout the entire sample period, 1650-1870, these small rural villages moved along a Malthusian
frontier. Increases in population meant decreases in living standards.
The emergence of modern economic growth during the Industrial Revolution was followed by a
fertility transition in England. In France the fertility transition preceded modern growth by over a
century. The role of elites and their non-Malthusian fertility choices is a potential fruitful avenue
for future research which seeks to understand these two events, whether the are connected a child
quality-quanittiy trade-off or some other as yet unspecified mechanism.
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A Extra Results
27
Table A.1: Proportion of Children Observed Marrying and Occupational Status
Proportion of Children Known to be Married
Pre 1789 Post 1789
(1) (2) (3) (4) (5) (6)
Occupational Wealth, Z −.043 .014
(.030) (.030)
Hiscam, Z −.011 −.006
(.010) (.014)
No Occupation .007 .028
(.019) (.032)
Weavers/Shoemakers −.035 .054
(.027) (.041)
Craftsmen −.022 .041
(.027) (.042)
Traders −.006 .043
(.024) (.042)
Farmers −.016 .030
(.022) (.034)
Merchants/Professionals −.053 −.066
(.046) (.061)
Gentry/Independent −.022 .065
(.049) (.041)
Constant .100 .921
∗∗∗
.932
∗∗∗
.952
∗∗∗
.946
∗∗∗
.933
∗∗∗
(.456) (.071) (.049) (.054) (.055) (.058)
Village Fixed effects? Yes Yes Yes Yes Yes Yes
Observations 1,556 1,519 4,006 787 697 1,394
R
2
.049 .047 .030 .083 .089 .054
Note:
∗
p<0.1;
∗∗
p<0.05;
∗∗∗
p<0.01
OLS, Laborers/Servants are the omitted category.
Excluding unknowns
28
