A Structural Model of the Neolithic Revolution !
By
Matthew J. Baker
Department of Economics
Hunter College – City University of New York
New York, NY 10021
Email: [email protected]
February 19, 2007
Abstract:
I develop a model of mankind’s initial transition to agriculture in which population, technological
sophistication, and the degree of land enclosure are endogenous variables. The theoretical model
describes the conditions under which population density and technological sophistication will
provoke land enclosure and a switch to agriculture. The steady-states of the theoretical model
comprise a simultaneous system of log-linear equations describing equilibrium population density
and technological sophistication, the form of which depends upon whether or not the economy has
switched to agriculture. I estimate the steady-state relationships using information on technological
sophistication, population density, and environment from a cross section of 186 indigenous cultures.
The empirical model allows for estimation of the importance of endogenous growth effects and
technological spillovers in generating a switch to agriculture. Estimation results suggest that
technological progress appears to be exogenous among hunter gatherers. Among agricultural peoples,
however, endogenous growth effects appear to be present and important - a 10% increase in
population density increases technological sophistication by about 5% while a 10% increase in
technological sophistication increases population density by about 7%. Hunter-gatherer population
density is apparently quite elastic with respect to environmental factors such as rainfall and habitat
diversity.
I thank Erwin Bulte, Brendan Cunningham, Partha Deb, and seminar participants at Hunter College, Rutgers
University – Newark, the United States Naval Academy, the University of Ottawa, Tilburg University and the
First Conference on Early Economic Developments at Copenhagen University for helpful comments and
suggestions.
!
The agricultural or “Neolithic” revolution – the process by which the peoples of the earth
switched from hunting and gathering to agriculture beginning some 10000 years ago – is a subject of
growing interest to economists. Much recent research has focused on describing the dynamics of the
transition. A lesser known branch of research, pioneered by Pryor (1986, 2004) develops an empirical
picture of the transition using cross-cultural data on environment and material culture from known
hunter-gatherer and agricultural peoples from around the world. In this paper, I make a first step in
bringing these two branches of literature together. I accomplish this by developing a representative
theoretical model of the transition which can be taken to cross-cultural data. I apply the model to
cross-sectional data describing the incidence of agriculture, population density, and technological
sophistication in a sample of 186 indigenous peoples.
The three critical assumptions driving my theoretical model are 1) that agriculture involves
some degree of land ownership, 2) that agriculture is a more knowledge-intensive activity than
hunting and gathering, and 3) that there exists a symbiotic relationship between technological
progress and population growth. I model the land enclosure process coincident with the transition to
agriculture following De Meza and Gould (1992). Following Kremer (1993) and Galor and Weil
(1999, 2000), I apply the idea that higher population density increases the level of technological
sophistication, which in turn increases total factor productivity, allowing for further increases in
population density through the Malthusian dynamic. The resulting model is similar to Jones (2001).
The theoretical model results in a pair of two-equation systems describing steady-state
population density and technological sophistication – one set of equations applies to hunter-gatherer
societies, and the other set to agricultural societies. I identify the model using environmental
information as instruments in the population density equations, and distance from centers of
civilization as instruments in the technology equations. The empirical results then allow for a
quantitative assessment of the importance of such things as endogenous growth effects, spillovers,
and environment in provoking a switch to agriculture. The results also allow assessment of the
2
relative importance of different types of resources in fueling hunter-gatherer and agricultural
productivity.
My results provide support for one of the fundamental ideas of endogenous growth theory –
the idea that the level of technological sophistication is influenced by the density of population.
Among agricultural peoples, I find that a 10% increase in technological sophistication increases
population density by about 4.8%, while a 10% increase in population increases population density by
about 6.5%. I find evidence in support of Diamond’s (1997) conjecture that technological spillovers
occur more slowly along the North-South axis than along the East-West axis, and that some
environmental factors, such as closeness to an ocean, touch of a dynamic which may approximately
double both the population density and technological sophistication of the typical agricultural society.
I also find that there is no evidence suggesting that endogenous growth is important among huntergatherer peoples, and no evidence that hunter-gatherers benefit from technological spillovers from
other societies. Hunter-gatherer population density, however, appears to be quite elastic with respect
to environmental factors.
The rest of this paper is organized as follows. Section I reviews previous work on the
agricultural revolution and concludes with a discussion as to how this paper builds on this literature.
Section II reviews some stylized facts about the transition to agriculture and introduces the data used
in the empirical analysis. In section III the theoretical model is presented, and in section IV the
estimation procedure is discussed and implemented. Section V concludes.
I.
Literature on the Neolithic revolution
It is generally agreed that the lifting of the last ice age around 10000 BC created conditions
amenable to agriculture in some parts of the world. Archaeological evidence suggests that agriculture
first appeared c. 8500 BC (perhaps earlier) in the Fertile Crescent with wheat and barley cultivation,
in Central Mexico (8000 BC) with maize cultivation and in Southern China (7500 BC) with the
cultivation of rice. Other initial centers where it is possible agriculture developed independently
3
include Northern China (7500 BC – millet) the South Central Andes (5800 BC – potato, manioc), the
Eastern United States (3200 BC- sunflower) and Sub-Saharan Africa (2500 BC - sorghum).1 From
these centers, the practice of agriculture spread rapidly. Cohen (1977) writes that: “Slightly more than
10000 years ago, the overwhelming majority of people lived by hunting and gathering. By 2000 years
ago, the overwhelming majority of people lived by farming…”2
The primary role played by economists in explaining the transition to agriculture has been in
elaborating the precise nature of the causal mechanism provoking and propagating the switch.3 North
and Thomas (1977) present a model in which a switch to agriculture is caused by diminishing returns
due to the common property nature of production in the hunter-gatherer economy, and point to the
property rights necessary for agriculture as a critical factor in mitigating diminishing returns.
Similarly, V. Smith (1975) describes a model in which overexploitation of common resources
generates diminishing returns to hunting and gathering. Locay (1989) presents a well-developed
formal treatment of the transition in which agents simultaneously make fertility decisions, choose
whether or not to engage in agriculture, and choose a degree of sedentism. In his model, population
pressure encourages sedentism, which in turn raises the relative returns to engaging in agriculture and
lowers the costs of child-rearing. Myers and Marceau (2006) view technological progress as the
engine which produces a shift to agriculture though a more nuanced causal mechanism. They show
that technological progress places disproportionate stress on cooperative modes of production like
hunting and gathering; thus, technological progress may eventually result in a collapse of the
cooperative band style of life and a switch to agriculture.4
1
I have relied upon the account in Olsson (2001). His information on crops comes from Diamond (1997), while
the dates of initial cultivation derive from Smith (1998). This list might be expanded to include parts of
Indonesia and sub-Saharan Africa.
2
Cohen (1977, p. 5-6), quoted in Pryor (1983, p. 94).
3
The interested reader should consult Pryor (1983) and Weisdorf (2005) for a detailed discussion of
anthropological and archaeological theories of the transition; see also Dow, Olewiler, and Reed (2005).
4
A related line of research is explored in Bowles and Choi (2003). While they do not provide a theory of the
transition itself, they do discuss a closely related idea: conditions under which maintenance of and respect for
private property is an evolutionarily stable strategy.
4
Other work has focused on the idea that technological progress itself depends on population
and environment, and has sought to more clearly elucidate the relationship between hunting and
gathering, agriculture, technology, and population growth. Wiesdorf (2003a) attributes recent interest
in this approach to the growing popularity of the economics of very-long-run growth, as exemplified
in Kremer (1993) and Galor and Weil (1999, 2000). Olsson and Hibbs (2005) describe a model in
which geography and environmental conditions directly determine the subsequent rate of
technological progress by allowing for expanded opportunities for experimentation. Morand (2002)
focuses on the relationship between human capital accumulation, interfamilial household transfers,
and foraging/hunting and agriculture. Weisdorf (2003) focuses on the emergence of non-foodproducing specialists and the switch to agriculture - agriculture generates more food per unit land, but
also involves more learning time. He shows that as technological progress occurs, more intensive
methods of production are adopted that require non-food specialists.5 Dow, Oleweiler, and Reed
(2005) develop a theory in which sudden climate reversals play the critical role in provoking a switch
to agriculture. Sudden adverse environmental conditions cause a transition to agriculture by causing
population spikes at those sites where resource endowments remain relatively plentiful.6
While the literature on the Neolithic revolution is notable for its methodological diversity,
there appears to be a consensus building that a model of the transition should allow for some degree
of interplay between population pressure, which for fixed technology increases the returns to
engaging in agriculture relative to hunting and gathering, and also allow for the possibility that
5
Issues not pursued in this paper are welfare changes resulting from the shift to agriculture. Olsson and Hibbs
(2005) discuss this issue, and Robson (2003) also discusses this issue in a bioeconomic interpretation of the
Neolithic revolution.
6
It is worth noting that parallel ideas have emerged in other disciplines. For example, Rindos (1984) and
MacNeish (1992) represent two attempts in the anthropological/archaeological literature to characterize the
relationships between population, environment, and technological progress. In their work, population growth
and technological progress are seen as complementary processes that may enhance one another in a variety of
different ways in a variety of different circumstances. Indeed, Diamond (1997), who links differences in initial
conditions to the subsequent development of a wide variety of institutions and technological progress is perhaps
the epitome of this line of research.
5
greater population density itself might change relative returns by increasing the rate of technological
progress.
My theoretical model seeks to capture these basic ideas with one straightforward extension. I
expand the model to include decisions over whether or not to enforce property rights following De
Meza and Gould (1992). The inclusion of property rights enforcement decisions may seem to be of
little consequence, but it has important implications. The resulting model allows for mutually
exclusive common property hunter-gatherer and full ownership agricultural steady-states.7 Second,
this approach allows derivation of some features of the economy that are assumed in other papers. For
example, V. Smith (1975), and North and Thomas (1977) all assume that agriculture is a constant
returns to scale activity, while hunting and gathering is subject to diminishing returns. The inclusion
of an enclosure process allows for a range of population density for which agriculture exhibits
constant returns to scale, but when all land is enclosed, diminishing marginal returns to agriculture set
in, and the economy approaches a fully agricultural steady-state.
Theories of the Neolithic revolution generally match the broad anecdotal evidence; however
there has been only limited empirical assessment of theory for the obvious reason: lack of data.8 The
notable exception is Pryor (1986, 2004), who asks: what can the incidence of agriculture across
known indigenous peoples tell us about the likely characteristics of the initial transition to
agriculture? Pryor’s (2004, p.2) principal findings suggest that the evidence does not support
geographic, social/political or demographic theories of the transition. However, Pryor does not
consider a well-described theoretical structure in his modeling, and perhaps crucially, does not
address the impact of technology or endogenous technological progress on the decision to adopt
7
Indeed, Pryor (1983) criticized models of the Neolithic Revolution because they focused only on the transition
to agriculture, while ignoring the question: why did some peoples apparently not switch to agriculture?
8
While Olsson and Hibbs (2005) do not exclusively assess the transition to agriculture; they do discuss the
impact of initial resource endowments on the growth history of regions of the world. Their empirical work relies
upon modern, cross-country data. Fendon (1959) attempted to catalogue the environmental characteristics of 11
initial hearths in which agriculture developed. While detailed, his analysis serves to illustrate the point that one
cannot reach definitive conclusions with so few observations.
6
agriculture. Thus, the blending of theories of the origins of agriculture and a reconsideration of the
data seems to be a timely exercise.
II.
The incidence of agriculture in cross-cultural data
In this section I develop as complete picture as is possible of the environmental, material, and
technological situation of hunter-gatherers and subsistence agricultural societies using a relatively
recent but representative cross-cultural sample of world cultures. While one might think it obvious
that technological progress, population growth, environment, and the transition to agriculture are
related, it is important to develop a factual picture as to how exactly agricultural societies differ from
hunter-gatherer societies in each dimension. This section also serves to introduce the reader to the
data that will be used in the empirical implementation of the theoretical model.
Following Pryor (1986, 2004), I employ the Standard Cross Cultural Sample (henceforth
SCCS), an extensive and well-documented cross cultural data set originating in the work of Murdock
and White (1969).9 The SCCS contains information on the technological sophistication,
environmental conditions, and material and social culture of 186 indigenous cultures situated around
the world. The majority of the cultures in the SCCS was sampled at a time coinciding with or just
after contact with western cultures (the mean date of contact among the cultures is 1850, but some
observations – e.g., the ancient Babylonians – date from considerably earlier), and can be taken to be
reasonably representative of cultural, social, and technological diversity of the recent past.10 In
developing the SCCS, Murdock and White selected societies for inclusion so that the resulting sample
9
While the original work describing the SCCS is Murdock and White (1969), this work was the result of a
process that began with Murdock’s efforts to quantitatively summarize what was known about the world’s
cultures. Murdock’s first effort in the 1930’s and 1940’s resulted in the Human Relations Areas Files. Murdock
(1957) introduced the World Ethnographic Sample, which was subsequently honed into the Ethnographic Atlas
(Murdock, 1967). The Ethnographic Atlas summarized crucial aspects of the technology and cultural life of 862
different cultures. The SCCS resulted from an effort to systematize the evidence in the Ethnographic Atlas and
account for problems such as over-counting of similar cultures and missing data.
10
The mean contact year for societies in the SCCS is 1853. However, it must be said that there is great variance
in the amount of contact the societies in the SCCS have had with the modern western world, and the SCCS does
not include any information about the degree to which societies have had contact with other centers of
development, such as the Far East. In the empirical model, I develop several proxies for the degree of contact
with the west.
7
of world cultures would be representative of known historical and indigenous cultures, while at the
same time allowing for maximal geographic and cultural diversity.
Each observation in the SCCS corresponds to a separate culture. As separate data points, the
SCCS includes sub-Saharan African hunter-gatherers (such as the !Kung bushmen), Native American
hunter-gatherers (such as the Pomo), indigenous European peoples (such as the historical Basque
society and the Lapps), large-scale agricultural nation-state cultures of Meso-America (such as the
Aztecs), and historical nation-state peoples (such as the ancient Hebrews and Egyptians). The
geographical distribution of those societies in the SCCS is displayed on Map 1.11 The position of each
society on the map is labeled according to its numbering in the SCCS. Agricultural societies are
marked with rectangles, while hunter-gatherers are marked with circles. Those societies marked with
hexagons and trapezoids are not quite so easily classified; hexagons denote peoples which practice
some degree of agriculture but are best described as hunter-gatherers, while those marked with
trapezoids are cultures which are societies that practice little agriculture, but are not hunter-gatherers
(typically, pastoral peoples that rely primarily on animal husbandry for subsistence).
The SCCS contains not only information on the incidence of agriculture in different societies,
but also includes information on each society’s technological sophistication, population density, and
environment. Table 1 describes the nature of the variables in the SCCS which I employ in this
analysis and the source of each variable.12 One weakness of the data is that environmental information
derives from present sources, and is predated by the information reported by ethnographers. There is
simply no practical way to collect detailed environmental information from earlier time periods.
The SCCS reports the relative contribution of agriculture to subsistence, as described in the
first column of table 1. The contribution of agriculture scale runs from a minimum of 1 (no
11
Locations are approximate; I constructed this figure freehand using the continental maps in Murdock and
Provost (1973).
12
I reduced the larger set of characteristics in the data set to those here through a process of experimentation,
and also by observing that many different sorts of environmental characteristics are heavily correlated. The
journal World Cultures publishes a continually growing version of the SCCS twice a year. There are now about
2000 variables for each society in the expanded version of the SCCS.
8
agriculture) to a maximum of 6 (exclusive agriculture). In labeling societies as agricultural or huntergatherer, I classified those societies that received a 1, 2, or 3 on the scale as hunter-gatherers, and
those societies that received a 4, 5, or 6 on the scale as agricultural societies. A small group of
societies in the SCCS rely heavily on animal husbandry, and these societies I classified as
agricultural; as Denton (2004) argues, these societies bear closer resemblance to agricultural societies
than hunter-gatherers.13 Table 2 is a histogram of the SCCS’s measure of importance of agriculture in
subsistence, and shows that most of the observations are concentrated at the tails. Thus, the
characterization of societies as either agricultural or hunter-gatherers, while an approximation of
reality, is a fairly accurate working representation. The bulk of the societies in the SCCS tend to
either practice agriculture more or less exclusively, or practice little to no agriculture.
Table 1 also describes information on population density for each culture, rated on a scale of
1 to 7; the density measure in the SCCS is essentially the logarithm of population density. The next
two variables on Table 1 are measures of the level of technological sophistication of the societies in
the SCCS. The first measures the degree to which the society is specialized in the performance of
three tasks: metal working, pottery making, and leather working, while the second measures the
sophistication of the writing and record-keeping system present in each society. I shall rely primarily
on these two measures of technological sophistication to track the overall level of technological
sophistication present in a society.
The list of variables on table 1 concludes with several measures of environmental conditions
present in each society’s location. The first three variables derive from Cashdan’s (2003) data on
rainfall, which she computed using data from the weather station nearest the society’s location (the
SCCS reports a position for each of its societies in longitude and latitude). The first rainfall variable is
13
These are the societies marked with trapezoids on Figure 5. They are best described as pastoral peoples and
include: Kazaks (65), Khalka Mongols (66), Yurak Samoyed (53), Lapps (52), Goajiro (159), Somali (36),
Pastoral Fulani (25), Nama Hottentot (1), Chukchee (121), Teda (40), Masai (34), Rwala Bedouin (46), and
Toda (61). The bulks of these societies received a score of 3 on the agriculture contribution scale, but obtain
about 70% of their livelihood from animal husbandry. Excluding these societies from the empirical work does
not have any substantial impact on the results.
9
simply the mean yearly rainfall measured in centimeters, and the second captures the presence of
exceptionally high rainfall, which I computed using information on the distribution of mean rainfall
across all societies in the SCCS, defining “high rainfall” to be yearly rainfall greater than one
standard deviation over the average SCCS value. The third variable is Cashdan’s (2003) measure of
the year-to-year coefficient of variation in mean rainfall.
Other environmental conditions described in table 1 are from Pryor (1986). Pryor created
these measures by inspecting FAO/UNESCO maps and making an assessment as to how amenable
climatic and soil conditions were to agriculture. His scale variables range from 0 to 4, with 4 denoting
the presence of climatic or soil conditions very favorable to agriculture, and zero denoting that the
climate or soil conditions render agriculture basically impossible. The third variable is a measure of
the degree of land slope in each society’s area; this scale also runs from 0 to 4. A zero indicates the
presence of a nearly flat landscape, while a 4 indicates a mountainous landscape with rapid elevation
changes.
Additional environmental characteristics include Cashdan’s (2003) count of the number of
habitats occurring within 200 miles of the society’s SCCS location – a rough measure of habitat
diversity in each society’s location. The final environmental variable, primary production, measures
the capacity of the environment for production of plant life. I computed this number through a
transformation of mean solar radiation/evapotranspiration data derived from UNESCO/FAO maps.14
The last set of variables described in table 1 pertains to location and distance from known
ancient centers of civilization. The first is simple great-circle distance from the Fertile Crescent in
miles.15 The logic behind including measures of distance from the Fertile Crescent is that there have
undoubtedly throughout history been technological spillovers between societies. The inclusion of
1.66
The formula for computing primary production is: PP = 0.219 E
, where E is the measure of
evapotranspiration. See Kelly (1995, p. 69) for a discussion. The FAO/UNESCO maps only report gradations of
100 cm/year (for example, clines within which evapotranspiration is between 50 and 150 cm/year), and the
maps disallow the possibility of being completely accurate in assessing this number. I used the midpoint of the
clines reported on the maps.
15
The exact coordinates I use for the Fertile Crescent are 45E 35N.
14
10
distance data is a crude way of measuring the likelihood that such spillovers have occurred. However,
some have argued (notably Diamond 1997) that “vertical” distance is more inhibitory than
“horizontal” distance, in the sense that innovation and technological improvements have a more
difficult time traveling along the North-South axis than they do along the East-West axis. For this
reason, I also include a North-South distance measure. There have, of course, been other initial
hearths of agriculture and civilization. Accordingly, I also developed distance measures from other
possible initial hearths of agriculture. The four hearths I rely on are those known to be places in which
agriculture originated independently: Southeastern Asia, Mesoamerica, the Northeastern United
States, and the Fertile Crescent.16 The last variable records the time at which the ethnographer’s
report was developed; I treat this variable as another measure of the likelihood that a society has
experienced contact with other, more developed societies, reasoning that relative isolation from
modern society should increase with the date of contact.
Table 2 presents basic summary statistics for all the variables described in table 1, and
compares mean values for those societies that can be said to practice agriculture (agriculture in
use=1) with those that do not (agriculture in use=0). On table 3, I have also computed a rough index
of the technological sophistication of each society (called simply “technology” on the table) by
simply summing up the two scale variables measuring technological sophistication.17 The result is a
measure of technological sophistication which runs from 0 (no specialization, only spoken language)
to 8 (complete specialization in leather-working, metal-working, and pottery-making, and a fully
16
It should be noted that there is some disagreement as to how many initial hearths there really were; estimates
typically range from as few as 4 or as many as 9 (see Weisdorf 2005). The coordinates I used for China, the
Eastern United States, and Meso America are, respectively, 115E 30N, 82.5W 40N, and 100W 20N.
17
One might use a more scientific approach in building this index, such as principal components. Principal
components analysis reveals that the two measures share a strong positive component. I opted to not use the
index based on principal components because it changed nothing about the analysis and introduced an
additional degree of complexity.
11
developed system of writing and record-keeping). I shall treat this measure as a proxy for the
sophistication of the general purpose technology present in a society.18
The data on table 2 indicate that those societies that practice agriculture tend to have both
higher population densities and larger degrees of technological sophistication. Agricultural societies
also operate in environments that seem to be richer and more suitable to agriculture in several
dimensions. Among agricultural societies in the sample, climate suitability, soil suitability, yearly
rainfall, and primary production are all significantly higher than in hunter-gatherer societies.
The data on table 3 also reveal that agricultural societies are typically closer on average to the
Fertile Crescent than hunter-gatherers, while the latter are disproportionately closer to another initial
hearth of agriculture – this is also reflected by the geographical distribution of hunter-gatherers on
Map 1. Table 3 also indicates that agricultural societies are on average more technologically
sophisticated than hunter-gatherers. The mean value of my technological sophistication scale for
hunter-gatherers is 1.52, while the mean value for agricultural societies is 4.00. The final row of table
3 computes the mean of the contribution of agriculture variable, which emphasizes the point
underlying table 2, that those societies in the hunter-gatherer group tend to engage in almost no
agriculture (mean of 1.52 on the scale), while those that are in the agricultural group tend to engage in
agriculture almost exclusively (5.19).
Not surprisingly, this evidence suggests that those societies that practice agriculture are more
technologically sophisticated, have greater population densities, and operate in environments which
appear to be richer and more amenable to agriculture. Agricultural societies in the sample tend to be
closer to the Fertile Crescent as well. In the next section, I describe a simple theoretical model which
may be estimated using this data.
III.
Theory
18
Galor and Weil (1999, 2000) describe how increasing population density generates incentives for further
specialization and human capital investment. From this sort of argument, one might reason that an index of task
specialization would function as a good measure of overall “knowledge” or “technological sophistication.”
12
1. Hunting and gathering, agriculture, and the enclosure decision
The essential features of the model can be laid out in a static framework. The model can then
rendered dynamic through inclusion of fertility decisions and describing a process by which
technological progress occurs. The static formulation of the model is a simplified version of De Meza
and Gould’s (1992) model of the enclosure process, but also resembles Locay (1989) in that agents
make output-maximizing decisions as to whether to engage in agriculture or hunting and gathering,
and utility-maximizing fertility decisions. The full dynamic model is similar to Jones (2001).
Otherwise, the model is a standard model of the transition in that the basic engines for the transition
to agriculture are improvements in technology and population pressure.
There is a population of n agents, and a fixed amount of land, Z . Initially each agent is
allocated an equal share of the available land z = Z / n . The initial endowment of land is the inverse
of population density, which I define as p = n / Z . The initial endowment of land given to an agent
does not convey property rights in the land, but merely affords the agent the opportunity to enclose
some portion of the endowment.19 Agents are endowed with one unit of time, which may be allocated
to three different activities: hunting and gathering, agriculture, and enclosure of land.20 The time
constraint each agent faces is:
! H + ! F + ! E = 1.
(1)
The time costs of enclosing e units of land are e / c , where c is a parameter capturing (the
inverse of) enclosure costs. Enclosure generates exclusive property rights over land.21 Taking into
account that each agent may not enclose more land than they are originally allocated, and
that ! E = e / c , the time constraint (1) may be rewritten as:
! H + ! F + e / c = 1,
e ! Z /n.
(2)
19
This is similar to the approach employed in Baker (2003) and De Meza and Gould (1992).
There are other interpretations of this setup. For example, one might think of enclosure effort as representing
all effort that must be exerted prior to engaging in farming.
21
Thus, I do not consider the possibility that land rights may be contested through conflict. Baker (2003),
Grossman and Kim (1995), and Skaperdas (1992) model interactions of this sort.
20
13
All agents may engage in hunting and gathering in common on unenclosed land, and earn
returns equal to the average product of labor on this land. Let ! H represent time devoted to hunting
and gathering by the average agent. Aggregate output in hunting and gathering depends on the total
land available for hunting and gathering, Z H , and on total effort devoted to hunting and gathering by
the population, n! H , according to the production function:
X H = # H (n" H )! H Z H1$! H ,
(3)
In equation (3), ! H measures total factor productivity in hunting and gathering. Agents
receive a share of X H proportional to their own efforts. Thus, if an agent devotes ! H units of time to
hunting and gathering, and the population average time allocated to hunting and gathering time is
! H , the agent receives output:
xH =
"H
# H (n" H )! H Z H1$! H .
n" H
(4)
The aggregate amount of land available for hunting and gathering depends upon how much
land remains unenclosed. Thus,
Z H = Z ! ne * ,
e* ! Z / n.
(5)
In equation (5), e * represents the amount of land enclosed by the average agent in
equilibrium; therefore ne * is total enclosed land. If it should happen that e * = Z / n , then all land is
enclosed in equilibrium, which results in Z H = 0 , rendering hunting and gathering infeasible.
Agricultural production requires two inputs: enclosed land e and labor time ! F . The
production function for agriculture is given by:
x F = # F " !F F e1$! F .
(6)
The parameter ! F in equation (6) measures total factor productivity in agriculture. Equations
(1-6) allow description of agents’ equilibrium output-maximizing time allocation decisions, and may
14
be solved for a symmetric equilibrium in which agents maximize total food production subject to the
time constraint and initial allocation of land, given the decisions of other agents (i.e., taking as given
population averages). Using the time constraint (2), the hunting and gathering production function
(4), and the agricultural production function (5), any agent’s total output of food may be written as:
x = # F " !F F e1$! F +
(1 $ " F $ e / c)
# H (n" H )! H ( Z H )1$! H .
n" H
(7)
Equation (7) describes agents’ output as a function of ! F and e only. Equilibrium output
maximizing decisions may result in three different kinds of equilibria: one in which agents hunt
exclusively; one in which agents allocate time to enclosure, agriculture, and hunting; and one in
which all time is allocated to enclosure and agriculture. To understand the conditions under which of
these alternatives occur, differentiate (7) with respect to e and ! F :
+x
*" '
= (1 $ ! F )# F ( F %
+e
) e &
* e
+x
= ! F # F ((
+" F
)" F
'
%%
&
1$! F
!F
#
$ H
c
* ZH
((
) n" H
* Z
$ # H (( H
) n" H
'
%%
&
'
%%
&
1$! H
,
1$! H
.
(8)
The two partial derivatives in (8) indicate that, in an equilibrium in which agents engage in all
three tasks (hunting and gathering, enclosure, and agriculture), 1) the marginal product of agricultural
effort must equal the average product of hunting and gathering effort, and 2) the marginal product of
enclosure effort must equal the average product of effort in hunting and gathering. If the equilibrium
is interior, the two first-order conditions in (8) may be set equal to zero and solved directly for the
optimal ratio of agricultural effort to enclosure effort:
1#!F
e*
.
=c
*
!F
"F
(9)
Substituting the optimal ratio in (9) into either equation in (8) results in the following
equality:
15
*
'
Z $ ne
%%
" F# = " H ((
$1
n
(
1
$
(
c
(
1
$
!
))
e
)
F
)
&
1$! H
1#! F
" = ! F! F (c(1 # ! F ) )
,
(10)
The left-hand side of equation (10) is the marginal product of effort devoted to
enclosure/agriculture at the optimal e / ! F ratio, given that e ! Z / n . That is, mp F = " F! . The
right-hand side of equation (10) is the average product of effort in hunting and gathering, described as
a function of equilibrium enclosure decisions:
)
&
Z # ne
$$
ap H (e) = " H ''
#1
( n(1 # (c(1 # ! F )) e) %
1#! H
.
(11)
Both land enclosure and time allocation decisions can be described in terms of mp F and
ap H (e) . Through comparison of these two functions, it is also easy to assess when corner solutions
occur, i. e., when agents engage in only hunting and gathering or only in enclosure and agriculture. If
agents devote time to all three tasks, it must be the case that agents have an incentive to engage in
agriculture, but not so much an incentive that they decide to completely enclose all available land.
Formally, agents will enclose some land and engage in agriculture so long as:
ap H (0) < mp F .
(12)
Inequality (12) means that the value of a unit of effort in hunting and gathering is lower than
a unit of effort devoted to enclosure and agriculture when agents are devoting no time to enclosure
and agriculture. If agents are to engage in some hunting and gathering while simultaneously engaging
in agriculture and enclosure, it must be the case that ap H (e) overtakes mp F at some point
e * < Z / n . This can only happen if ap !H (e) > 0 , so that the average product of effort in hunting and
gathering must increase as enclosures increase. The condition ap !H (e) > 0 means that the removal of
labor from the commons due to enclosure must exert a larger impact on commons returns than the
removal of land from the commons due to enclosure. Using the functional form for ap H in (11)
16
reveals that ap !H (e) > 0 if population density p = n / Z is less than some critical level of population
density, which I label p 2* :
p<
1
= p 2* .
c(1 ! " F )
(13)
If inequality (13) is satisfied, then ap (e) " ! as e ! Z / n . Thus, condition (13) is
sufficient to guarantee that ap !H (e) > 0 and also that ap H (e!) = mp F at some e! < Z / n . Given
(13) is satisfied, condition (12) can be viewed as both a necessary and sufficient condition for the
emergence of agriculture. That is, from (12) the emergence of agriculture requires that:
*Z'
" F# + " H ( %
)n&
1$! H
.
(14)
Solving (14) for population density gives a threshold value of population density necessary
for the emergence of agriculture:
&+
p ' $$ H
% + F*
#
!!
"
1
1() H
= p1* .
(15)
I shall assume throughout that p1* < p 2* .22 Together, the critical population densities p1* and
p 2* admit a complete description of the effort allocation decisions across the population, and table 4
summarizes results that are essential for what follows: 1) the effort allocation decisions of agents
given different population densities and parameter values, and 2) the total amount of food agents
produce in each type of equilibrium.
If this model is to describe how a transition to agriculture occurs, population density must
somehow reach the critical values, or something must change the relative magnitudes of total factor
productivities in hunting and gathering and agriculture. In the next subsection I address population
*
*
*
*
If it were the case that p 2 < p1 , the model would generate multiple equilibria for n / Z ! ( p 2 , p1 ) : an
equilibrium with no agriculture, and an equilibrium with no hunting. De Meza and Gould (1992) discuss results
of this sort. I rule out this case strictly for convenience, and the decision to do so is supported by the results of
the calibration and estimation exercises in the empirical section of the paper.
22
17
dynamics, and follow the discussion with a specification describing how technological sophistication
influences total factor productivity.
2. Population Dynamics
The static equilibrium can be rendered dynamic by adding in fertility decisions. Suppose that
agents have utility over consumption and children described by the utility function u = 2c 1 / 2 n1 / 2 ,
and assume that the resource costs of having a child are given by b / 2 . Given lifetime food
production of xt , a particular agent i at time t chooses the number of children to have to maximize
utility:
1/ 2
Max( xt ! b2 nit +1 )1 / 2 nit +1
niit +1
.
(16)
Solving the problem in (16) yields the following optimal number of children:
nit* +1 = xt / b .
(17)
In equilibrium all agents make the same effort allocation decisions, earn the same payoffs,
and have the same number of children, so (17) implies that aggregate population grows according to
the relationship nt +1 = nt xt b !1 , or:
(nt & xt
#
= $ ' 1! .
nt
%b
"
(18)
Dividing equation (18) through by Z (the aggregate land endowment) gives equation (18) in
terms of population density:
(pt & xt
#
= $ ' 1! .
pt
%b
"
(19)
Equation (19) is a Malthusian population dynamic describing the evolution of population
density. When the ratio xt / b is greater than unity, population density increases. In this way,
population growth depends upon the underlying mode of production of the economy, as summarized
18
in table 4. Substituting in the exact form for agents’ output from table 4 gives the following
description of population dynamics:
!pt
pt
)H
b
=
' 1 $
%% ""
& pt #
1!( H
#F
" !1,
b
)F '
1
%%1 !
b & cpt
=
=
pt ! [0, p1* ] ;
!1,
pt ! ( p1* , p 2* ) ;
$
""
#
(F
' 1 $
%% ""
& pt #
1!( F
! 1 . pt " [ p 2* , !) .
(20)
Equation (20) shows how the organization of production influences population growth. When
pt ! [0, p1* ] agents are engaged exclusively in hunting and gathering, and when pt " [ p 2* , !) ,
agents are engaged exclusively in agriculture. In these two cases, one can see from (20) that
population density increases at a decreasing rate towards a steady state level. However,
when pt ! ( p1* , p 2* ) , so that agents engage in both hunting and gathering and agriculture, density
grows at a constant rate. Thus, the model produces a population “explosion,” during which population
growth occurs at a steady pace and the economy progresses towards the point at which full enclosure
of land occurs. Population growth slows once the full enclosure point is reached.
If a population density p ! p1* is not achieved, the economy will never progress past the
hunter-gatherer stage. One way of making this assessment is to see whether or not steady state huntergatherer population density, which I refer to as p H , is compatible with the no-agriculture condition
p < p1* . The steady-state hunter gatherer population is obtained by solving !pt / pt = 0 for
pt ! [0, p1* ] in (20). This gives:
1
) " & 1#! H
.
pH = ' H $
( b %
Thus, p H is less than p1* so long as:
19
"# F ! b .
(21)
Inequality (21) describes a threshold value for total factor productivity in agriculture. If (21)
does not hold, the hunter gatherer society will eventually reach a point at which agents begin to
enclose land and engage in agriculture, and steady population eventually leading to a fully
agricultural economy will begin.
3. Technological Progress
Here I describe a process by which what can be thought of as a general purpose technology
develops, and I shall then describe the relationship between the overall level of technological
sophistication and the total factor productivity parameters ! H and ! F . The productivity of
agriculture and of hunting and gathering are influenced by things other than just technological
capability; indeed, for both types of production, environmental conditions also matter. There is,
however, no reason to believe that technological capability and environment influence hunting and
gathering and agriculture in the same way, and a useful model should be flexible enough to reflect
these concerns. Accordingly, I assume that the parameters ! i i = H , F , depend upon the resource
base available for each production technology, which I refer to as ri , i = H , F , and the amount of
technology available, A , according to the functions:
" H = rHµ H A! H ;,
" F = rFµ F A! F ,
(22)
I assume that ! F > ! H . The functions in (22) posit a relationship between environment,
technology, and total factor productivity, while the assumption that ! F > ! H means that agricultural
TFP is relatively more responsive to improvements in technology than hunting and gathering TFP.
This implies that any improvement in technology disproportionately increases the relative returns to
engaging in agriculture given environmental conditions.
20
I suppose that the state of technology depends upon the existing knowledge base and the
current population density as in Kremer (1993) and Galor and Weil (1999, 2000). However, I allow
the process describing technological progress to depend upon ! E , the fraction of time spent enclosing
land, as well:
"At = A( pt , At ,! E ) .
(23)
I include ! E in (23) as a proxy for changes in lifestyle that follow from land enclosure.
Enclosure of land implies some degree of sedentism, and this lifestyle change should alter the way in
which new technology is generated, processed, and disseminated, in addition to influencing the
applicability of the existing stock of knowledge in new situations.23 Individuals who stay in one place
may have more occasions to learn from past experience in this location, and also have better
incentives to engage in innovative activity if working parcels that they own.
To keep things as simple as possible, I assume that (23) has the following form:
%At = k H pt# H At
%At = k F pt# F At
"H
"F
$ ! H At ,
!E = 0,
$ ! F At
!E > 0.
(24)
In addition to allowing for lifestyle changes to impact the nature of knowledge accumulation,
(24) allows for vintage effects, captured by the depreciation of knowledge at a rate captured by the
depreciation parameter ! i . As a working hypothesis, it seems reasonable to suppose that:
!F > !H ,
!F > !H ,
kF > kH .
(25)
The collective assumptions in (25) capture the idea that the agricultural environment is more
amenable to the accumulation of knowledge. Ultimately, whether or not the assumptions in (25) are
warranted is ultimately an empirical matter, and I shall offer support for these assumptions in the
empirical section of the paper. The first two assumptions in (25), respectively, mean that that the
23
I refer here to the tendency for agricultural societies to be less nomadic than hunter gatherers, though, there
are examples of hunter-gatherers that are relatively sedentary, and examples of agricultural societies which are
relatively nomadic. Pryor (2004) discusses some of the nuances of the relationship between nomadism,
foraging, and agriculture. See also Locay (1989).
21
marginal impact of population density on knowledge and the marginal impact of knowledge on the
change in knowledge is larger for an agricultural society than for a hunter-gatherer society.
The immediate consequence of this specification for the beginnings of agriculture are made
clear by reinterpreting the analog condition used to derive the critical population density p1* .
Substituting the productivity parameters in (22) into equation (15) gives a new necessary condition
for a switch to agriculture:
1
& r µH
1
pt > $$ Hµ F
) F ') H
% rF *At
# 1'( H
!
= p1* ( At ) .
!
"
(26)
Condition (26) shows how higher population density, higher levels of technological
sophistication, the hunting and gathering resource base, and the agricultural resource base influence
the likelihood that agriculture will begin to be practiced, given a level of population density. The
model may now be summarized by the following two-equation system of difference equations:
!pt
pt
!At
At
1!( H
=
rHµ H A) H
b
=
rFµ F At# F " F
" F ((1 ! " F )c)1!" F ! 1
b
=
rFµ F At) F
b
=
k H pt
#H
' 1 $
%% ""
& pt #
'
1
%%1 !
& cpt
At
" H $1
pt ! [0, p1* ( A)] ;
!1,
$
""
#
(F
' 1 $
%% ""
& pt #
pt ! ( p1* ( A), p 2* ) ,
1!( F
!1 .
pt " ( p 2* , !) (27.a)
pt ! [0, p1* ( A)] ,
$ ! H .24
pt " [ p1* ( A), !] (27.b)
=
k F pt F At F $ ! F
Assumptions sufficient to generate an interior, stable steady state are:
#
" i + !i < 1 ;
" $1
" i + !i < 1.
(28)
The inequalities in equation (28) mean, respectively, that the production function exhibits
diminishing returns to scale in its two arguments, population density and knowledge, and that
24
Note that for high values of
A , it may be the case that ! 1 ( A) < ! 2 ; I shall discuss this case in a moment.
22
production is not overly technology-dependent or labor intensive.25 Given these assumptions, there
are two possible outcomes of the system dynamics described by equations (27a-b), displayed as phase
diagrams in figures 1 and 2. Consider first figure 1, which describes how a simple-hunter-gatherer
economy might progress into a fully-agricultural economy. The initial state of this economy might be
represented by a point in the phase space very close to the origin, between the null-clines, where
population density and technological sophistication are very low. At this point, the system dynamics
call for increasing technology and increasing population density until the line p1* ( A) is encountered.
At this point, land enclosure and the practice of agriculture begin and population growth occurs at a
steady rate. Coincident with this sustained population growth are increasing levels of knowledge and
increasing levels of land enclosure. Eventually, all land is enclosed, and population growth and
technology approach agricultural steady states. The end result of this process is a steady state in
which all land is enclosed, technological progress ceases, and population levels off. Figure 2,
alternatively, shows the case in which density and sophistication level off at a point where no switch
occurs and the economy remains in a hunter-gatherer steady state.
In the hunter-gatherer steady-state described on figure 4, the following two equations
describe equilibrium population density and technological sophistication:
1
) r µH
p H = '' H
( b
1
"
* k p"H
AH = (( H H
) #H
& 1#! H 1#!HH
$
AH ,
$
%
' 1$!H
%
,
%
&
p H < p1* ( AH ) .
(29)
If, however, the inequality in (29) does not hold the following equations describe the ultimate
steady-state values of population density and technology:
rFµ F AF) F
b
&
1
$$1 '
% cp F
#
!!
"
(F
& 1 #
$$
!!
% pF "
1
1'( F
= 1,
* k p"F
AF = (( F F
) #F
25
' 1$!F
%
.
%
&
p H ! p1* ( A)
(30)
These conditions are in fact more restrictive than they have to be to guarantee stable steady-states for the
model. I shall also present evidence in a subsequent section of the paper that these restrictions in fact hold.
23
The equations in (30) have no closed-form solution, but can be written in the same form as
those in (29) using the approximation:
cp F " 1
! 1.
cp F
(31)
Then, the following two equations describe equilibrium technology and population density at
the agricultural steady state:
1
) r µF
p F = '' F
( b
"
& 1#! F 1#!FF
$
AF ,
$
%
1
* k p"F
AF = (( F F
) #F
' 1$!F
%
.
%
&
p H ! p1* ( A)
(32)
The steady-state values in (29) and (32), and the switching inequality (26) are the basic
building blocks for the empirical implementation of the model.
IV.
Estimation of the Model
Taking logs of the equations in (32) gives the following econometric model:
µH
"H
1
ln b +
ln rH +
ln AH
1#!H
1#!H
1#!H
"
1
1
1
ln AH =
ln k H +
ln
+ H ln p H , p H < p1* ( AH ) ;
1 $ !H
1 $ !H # H 1 $ !H
µF
"F
1
ln p F = #
ln b +
ln rF +
ln AF
1#!F
1#!F
1#!F
"
1
1
1
p H ! p1* ( AH )
ln AF =
ln k F +
ln
+ F ln p F .
1 $ !F
1 $ !F # F 1 $ !F
ln p H = #
(33)
The model in (33) is a two-equation system with endogenous regime switching, meaning that
the relevant steady-state regime (hunting-gathering or agriculture) depends on both endogenous and
exogenous variables. As such, the model can be estimated using the two-step procedure developed by
Maddala (1983). The procedure involve first fitting a probit model with the prevailing regime
(hunting and gathering or agriculture) as the dependent variable with all exogenous variables as
explanatory variables, and then estimating each of the two steady-state systems separately, but
including a selection term derived from the predictions of the probit model.
24
Since each of the two possible regimes in (34) consists of a two-equation simultaneous
system, if one is to recover model parameters, each system must be exactly identified. The population
density equations have been endowed through the theoretical model with a natural set of instruments:
the resource base. To round out the empirical model, an instrument for the technology equations is
required.
Virtually every society in the data set has had some contact with the western world or some
other advanced culture at the time at which the data for the SCCS was assembled.26 Therefore, natural
instruments for use in the technological sophistication equations are measures of distance from a
center of civilization. As an exogenous instrument for the technology equation, I employ great-circle
distance measures from the Fertile Crescent, and, in the event that the society in question is closer to
some other initial center of civilization and agriculture, I also include great circle distances from the
other initial hearth.27 Diamond (1997) numbers among those who believe that distance is not
homogenous, and that diffusion occurs more slowly along a north-south axis than along the east west
axis. For this reason, I also include in the empirical analysis measures of north-south distance.
To implement the distance measures, let d ( vd for “vertical distance”) denote distance from
the Fertile Crescent, let d ! ( vd ! ) denote distance to an alternative closest point of agricultural origins,
and let ! be an indicator variable which equals one if the society is situated closer to an initial hearth
of agricultural besides the Fertile Crescent. Then, the constant term in each of the technology
equations in (33) can be written as:
ki = kiA d " i d $#" i$ (vd )" vi (vd $)#" vi$ y!i .
i = H,F .
(34)
The specification in equation (34) allows for the possibility that knowledge spillovers affect
hunter-gatherers and agricultural societies differently; ! H measures the elasticity of technological
26
The fact that an anthropologist collected the data signifies some contact, and the data described in table 3
indicate that there is a systematic difference relationship between distance and model variables.
27
Recall that these other initial hearths are the Eastern United States, Southeastern China, and Mesoamerica. I
experimented with a wide variety of additional instruments to capture spillovers: for example, the technological
sophistication of the nearest society with no success.
25
progress with respect to distance from the Fertile Crescent for a hunter-gatherer society, while ! F
measures the Fertile Crescent distance elasticity for an agricultural society, and ! vF denotes the
elasticity of spillovers with respect to north-south distance. The ! i" and ! vi" terms have an analogous
interpretation with respect to distance from another initial hearth, and also allow for the fact that
societies positioned closer to another initial hearth may enjoy spillovers from both that hearth and
from the Fertile Crescent. It seems reasonable to suppose that a society that had been contacted later
by ethnographers is also in some sense more isolated; therefore, I also include also the date of contact
as an additional instrument for technological spillovers. The corresponding parameter is ! i .
I also construct a flexible multivariate measure of environmental quality. Consider the
following indices of the resource base in a given area:
Mi
ri = k ri ! rik" ik ,
i = H,F .
(35)
i =1
In equation (35) M i is the number of environmental factors important to each respective
mode of production, and ! ik is the elasticity of overall environmental quality with respect to the k th
environmental factor for regime i , i = H , F . Substituting (34) and (35) into (33) gives:
1
k µH
%H
µH MH
(36a)
ln Hr +
ln AH +
! # Hk ln rHk .
1"$H
b
1"$H
1 " $ H k =1
1
k
#
"
ln AH =
ln HA + H ln p H + H ln y ;
1 % !H $ H 1 % !H
1 % !H
!
$
%$ vH
$
%$ H!
+ H ln d +
ln d ! + vH ln vd +
ln vd ! ; p H < p1* ( AH )
1 " #H
1 " #H
1 " #H
1 " #H
ln p H =
µF
1
k Fr
%F
µF MF
(36b)
ln pF =
ln
+
ln AH +
! # Fk ln rFk .
1"$F
b 1"$F
1 " $ F k =1
1
k
#
"
ln AF =
ln FA + F ln p F + F ln y ;
1 % !F $ F 1 % !F
1 % !F
!
$
%$ vF
$
%$ F!
+ F ln d +
ln d ! + vF ln vd +
ln vd ! ; p H ! p1* ( AH )
1 " #F
1 " #F
1 " #F
1 " #F
26
Model (36) constitutes an exactly identified system of simultaneous equations with
endogenous switching – the population equations are identified by environmental information, while
the technology equations are identified by the various measures of distance.
Table 5 presents the estimates of this first-stage probit model, where the dependent variable is
reliance on agriculture, as described in table 1. A brief discussion of these results is warranted, since
the probit model can be interpreted as a predictive model of the incidence of agriculture. The critical
point to note is that, in addition to environmental characteristics, the distance proxies for
technological spillovers are important in controlling for the incidence of agriculture. In terms of the
theoretical model, this is because the greater technological spillovers occurring at closer distances
increase total factor productivity in agriculture disproportionately. It is interesting to contrast these
results with those of Pryor (1986, p. 883), who finds that “…agricultural potential variable[s] only
explain about one-sixth (R2=0.16) of the variation in the importance of agriculture.”28 While the
pseudo-R2 from a probit is not directly comparable to Pryor’s results, the model does show that the
predictive power of the model is in fact considerably enhanced by inclusion of distance measures.
Table 6, columns II-V shows the full set of estimation results obtained using Maddala’s twostep procedure, while column I presents pooled results.29 The second and third columns present
estimates for agricultural societies and the fourth and fifth columns present estimates for huntergatherers (note that, due to missing data, 17 observations of the 186 in the SCCS have been lost). The
third and fifth columns drop insignificant variables to rid the model of some of the multicollinearity
present between exogenous variables and sharpen parameter estimates.
28
Pryor’s dependent variable was the reliance on agriculture scale variable described by table 1. As an aside,
Pryor also explores the implications of including population density in his analysis (my modeling approach
implies including population density in this fashion is a specification error, as it is endogenous), and does not
mention technological sophistication. I obtain an R2 of 0.30 if I use the agricultural contribution scale as a
dependent variable in a linear regression including distance measures.
29
Maddala’s (1982) two-step procedure calls for obtaining the Z-scores associated with the probit regression,
and using # ( Z )(1 ! " ( Z )) !1 as an additional instrument in the hunter-gatherer system of equations and
# ( Z )" ( Z ) !1 as an additional instrument in the agricultural system. Each system may then be estimated
separately using standard methods.
27
What do the estimation results imply about the importance of endogenous growth effects
(feedback effects between population growth and technology) in generating a switch to agriculture?
The pooled results (column I), and both sets of results pertaining to agricultural societies (columns II
and III) indicate that higher levels of population density result in higher levels of technological
sophistication and vice versa. The coefficient estimates for agricultural societies (column III) suggest
that a 10% increase in population density increases the level of technological sophistication by about
4.8%, while a 10% increase in technological sophistication increases population density by about
6.5%. Closeness to an ocean has a powerful impact on population density – if a society could be
moved within 200 miles of an ocean, the population would increase by about 124%. In terms of the
technology equation, a 10% reduction in horizontal distance from the Fertile Crescent would increase
the level of technological sophistication by approximately 7.4%, while a 10% reduction in vertical
distance from the Fertile Crescent would increase technological sophistication by 7.4%+5.7%=13.1%.
Thus, one might conclude from this that vertical spillovers in technology travel with about twice the
difficulty of horizontal technological spillovers.
The results from the hunter-gatherer sample imply similar effects do not materialize among
hunter-gatherers (columns IV and V). Among hunter-gatherers, the technology coefficient in the
population equation and the population coefficient in the technology equation are small, of the wrong
sign, and insignificant. It also appears that hunter-gatherers in the sample have not benefited from
technological spillovers.30 The results presented in table 6 suggest that the best way of modeling
hunter-gatherer technological sophistication is to assume that it is exogenous. This evidence might be
interpreted to mean that the switch to agriculture was instrumental in beginning the endogenous
growth process. It is interesting to observe that some of the estimated population elasticities with
respect to environmental factors are quite large; from column V, it appears that population density is
30
Indeed, I employed a variety of specifications to try to develop some sort of predictive model of huntergatherer technology, and the relationship proved quite elusive. One of the more interesting hypotheses I
experimented with was the idea that habitat diversity might influence the rate of accumulation, an idea
described by Olsson and Hibbs (2005). I could not find any evidence for this hypothesis either.
28
quite elastic with respect to land slope, habitat diversity, and the presence of abnormally high rainfall.
Living in an exceptionally rainy environment appears to more than double population density among
hunter-gatherers. These results contrast sharply with Locay (1997), who finds little evidence of a
systematic relationship between population and environmental characteristics among a sample of
North American hunter-gatherers.
One can think of a variety of reasons why technology appears to be unimportant for huntergatherers. It might be the case that better technology in the hunting and gathering economy does not
result in increased output and population density, because the binding constraint for hunter-gatherers
is the level of the natural resource. Better technology and consequent improvements in total factor
productivity might simply encourage hunter-gatherers to enjoy more leisure rather than increasing
output; in support of this hypothesis, some evidence suggests that labor supply in hunter-gatherer
economies is quite elastic.31 This would interfere with the direct link between technology, production,
and population growth posited by the model. Finally, it is possible that endogenous growth effects
among hunter-gatherers, when present, are simply too subtle to be detected in the data used to
estimate the model.
The estimated equations imply that the environmental features related to each mode of
production are different, implying that a good hunting and gathering environment may not be a good
agricultural environment. Those factors which intuition suggests should be more important for
successful hunting and gathering (such as habitat diversity and land slope) do not appear in the
agricultural population density equation, while those that intuition suggests should be most important
to agriculture (climate and soil suitability for agriculture) do not appear to influence hunter-gatherer
population density.
Given the estimates in column III, for agricultural societies it is possible to solve for long-run
elasticities which consider both population and technology to be endogenous. Solving the twoequation system gives:
31
See Baker and Swope (2004) for background discussion on labor supply in hunter-gatherer economies.
29
ln( p ) = 5.79 ! 0.70 ln(distfc ) ! 0.53 ln(vdistfc) + 1.82 ln(ocean200)
+ 1.29 ln(soilsuit ) + 0.83 ln( primprod )
ln(A) = 15.15 ! 1.08 ln(distfc ) ! 0.82 ln(vdistfc) + 0.87 ln(ocean200)
+ 0.62 ln(soilsuit ) + 0.40 ln( primprod )
(37)
The equations in (37) suggest that when one considers technology and population to be fully
endogenous, the elasticity estimates are magnified considerably. A 10% reduction in vertical distance
from the Fertile Crescent increase technological sophistication by approximately 19%. Being close to
an ocean sets in motion a dynamic that virtually triples the population and doubles technological
sophistication.
Researchers might find exact values for model parameters of some interest, and given the
presence of exclusive instruments in each of the two equations in (37), it is possible to solve for the
underlying parameters of the model through additional parameter restrictions, as a concluding
exercise I now propose one means of doing so. As in any situation where one solves for underlying
model parameters, decisions on how to restrict coefficients and how to normalize equations must be
made. It must also be decided how to literally interpret the scale variable used to measure
technological sophistication. This task is somewhat delicate, so I discuss interpretation of the
technological scale variable first.
Denton (2004) argues that the technological scale variable should be interpreted as
representing the log of the true level of technological sophistication, and this is how I interpret the
~
technological scale variable.32 Thus, Denton’s claim is that if A is the actual level of technological
sophistication of the society, and A is the value of the index, the relationship between the value of
~
the index and underlying technological sophistication should be A = e A! + k . This implies that the
~
actual technological sophistication of a society A should be related to the scale measuring writing and
32
There are a variety of complexity indices in Murdock and Provost (1973) covering things such as hierarchy,
political integration, etc., and Denton (2004) argues that they are effectively measuring the logarithm of the
underlying actual variable of interest. For an application of these measures and further discussion, see Baker
and Miceli (2005).
30
~
record keeping ( w ) and the degree of technological sophistication ( t ) according to A = e ! ( t + w) + k .
Choosing k equal to zero is a normalization which determines the units of the underlying
technological sophistication; in this case, when the sum w + t =0, the underlying technological
~
sophistication of the society is given by A = 1 , this can be interpreted to mean that the resulting scale
describes things in terms of a society which has neither writing nor record-keeping, nor any task
specialization – perhaps a prototypical Paleolithic hunter gatherer. If ! =1, then the technological
scale variable means that the typical hunter-gatherer in the sample, which has a mean value of 1.52
for my technological sophistication variable (see table 3), is approximately e1.52 = 4.57 times as
sophisticated as the typical Paleolithic society. The implication is then that the average agricultural
society in the sample is about e 4 = 54.6 times as technologically sophisticated as the typical
Paleolithic society, or 11 times as technologically sophisticated as the typical hunter-gatherer in the
sample. Of course, the choice ! =1 is arbitrary.
In equation (21), the relationship between total factor productivity, resources, and technology
was assumed to be described by " i = ri i A i , so a natural, albeit ad hoc, assumption is that:
µ
!
µ i + ! i = 1, i = H , F .
(38)
The restriction that the coefficients in the expression for TFP add up to one allows one to
interpret the values of µ and ! as the shares of the resource base and technology, respectively, in
total factor productivity for each mode of production. 33 I also assume that:
Mi
!"
ik
= 1, i = H , F ,
(39)
i =1
Equation (39) means that the sum of all exponents in the resource index is equal to one.34 In
addition to restrictions on the relationship between parameters, normalization decisions must be
33
Note that while these sorts of share restrictions are common in growth models, in this context the assumption
is not as natural as it is in the typical growth model, where the sum of coefficients assumption follows directly
from the application of national income data and constant returns to scale production.
31
made. For the population density equations in (36) – see also (30) - a decision must be made about
whether to attribute the constant term to smaller costs of having children (as measured by b ), or
exogenous features of the environment (as measured by k Hr , k Fr ). I choose to set b = 1 . This
normalization effectively pins down the units in the production function as the output necessary to
support the growth of one individual to adulthood. This normalization decision, coupled with the
restrictions (38) and (39), allow solution of population density equations for model parameters.
For the technology equations in (36), a choice must be made as to whether to attribute the
constant term in the technology equation to a larger exogenous capacity to produce technological
developments (as measured by a larger k iA ), or a smaller vintage effect (as captured by a ! i ), the
choice is arbitrary, so I choose to set ! iA = 1 . There remains the issue as to a suitable restriction on the
remaining coefficients ! F , ! F , and ! F in the technological progress equation (27.b). I postulate that
" F + " vF + ! F = 1 .
(41)
With the parameter restrictions (38), (39) and (41); the estimates in column III of table 6, the
expressions for the estimated coefficients in (37); and the normalization decisions that ! , b = 1 one
can solve for the underlying parameters of the model. These reduced-form estimates of the
parameters are presented in table 7. It is hoped that these estimates may be of interest for researchers
interested in simulating economic models in the very long run.
V.
Conclusions
The purpose of this paper has been to design and estimate a representative model of the
origins of agriculture, and explore the quantitative implications of the switch to agriculture using data
on the incidence of agriculture among a sample of indigenous cultures from recent history.
34
I opt to use absolute values in (39), which is the same as redefining the variables with negative coefficients
(such as land slope in the hunter-gatherer equation) in terms of their inverses.
32
In addition to generating some interesting predictive results about the incidence of agriculture
around the pre-modern world, the empirical model performs reasonably well and generates a
quantitative picture as to how technological progress and population growth were impacted by the
switch to agriculture. One interesting finding – well in accord with intuition - is that the
environmental factors explaining population density among hunter-gatherers (for example, greater
habitat diversity, relatively high rainfall, and a flatter landscape) are different than those that predict
population density among agricultural society (primary production, nearness to an ocean). The model
also yields estimates of the degree to which spillovers and endogenous growth effects are important in
understanding the technological sophistication of agricultural societies. Estimation of the model also
allows for solution of the base parameters of the model.
While this paper has presented estimates for some of the base parameters of a growth model
with a transition to agriculture, because of the focus on steady-state relationships, it has avoided not
incorporating explicit information on dynamics, and the time frame within which a switch to
agriculture might occur. It is hoped, however, that the information provided in this paper will aid in
constructing a more exact picture of the nature of these dynamics, perhaps like the experiments
conducted in Jones (2001). A further point of interest would be to explore the connection with other
models of long-run demographic and technological change, such as those that postulate growth from a
Malthusian-type growth regime towards more modern growth regimes, as discussed in Galor and
Weil (1999, 2000), and Galor (2005).
It is perhaps reasonable to say that most of the basic theoretical reasons underlying the
transition to agriculture are by this point fairly well-developed. It is hoped that the research in this
paper will help in propelling this literature towards a debate about how to better estimate and calibrate
models of the transition to agriculture, and other models of growth in the very-long run.
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36
A
p 2*
AF
Agriculture
Incipient Agriculture
Hunter Gatherer
p1* ( A)
pF
p
Figure 3: Population growth and technological progress with a Neolithic revolution.
37
A
p 2*
AH
p1* ( A)
p
pH
Figure 4: The stable hunter-gatherer economy.
38
Table 1: Description of Variables and Sources used in the analysis
Technology and
population
Contribution of
Agriculture to food
supply
Agriculture in use?
Population Density
Technological
specialization
Writing and
Record-Keeping
Environmental
Characteristics
Mean Rainfall
High Rainfall?
CV Rainfall
Climate suitability
for agriculture
Soil suitability for
agriculture
Land slope
No. habitats w/in
200 miles
Ocean w/in 200 mi?
Number of frost
months per year
Primary Production
Geography/Time
Distance from fertile
crescent
“Vertical” distance
from fertile crescent
Closer to another
hearth?
Distance from
closest hearth
“Vertical” distance
from closest hearth
Date of Contact
Description
Source
=1 if none, =2 if only non-food crops, =3 if <10%,
=4 if <50% single source, =5 if > 50% single source,
=6 if primarily agricultural.
=1 if Contribution of Agriculture to food supply >3
=0 otherwise
=1 if < 1 persons per square mile, =2 if 1 persons per 1-5
square miles, =2 if 5.1-25, =3 if 1-5 persons per square mile,
=4 if 1-25, =5 if 26-100, =6 if 101-500, =7 >500
=0 if no specialization present, =1 if pottery only,
=2 if loom weaving only, =3 if metalwork only,
=4 if smiths, weavers, and potters
=0 none, =1 Mnemonic devices, =2 Non-written records, =3
True writing, no records, =4 True writing, records
SCCS
Mean yearly rainfall (cm)
=1 if mean yearly rainfall is more than 1 standard deviation
above SCCS mean yearly rainfall
Coefficient of variation in mean yearly rainfall
Scale ranging from 0 (impossible) to 4 (very good)
developed by Pryor using FAO/UNESCO reports
Scale ranging from 0 (impossible) to 4 (very good)
developed by Pryor using FAO/UNESCO
Scale ranging from 2 to 4, 2=steep, 4=relatively flat
Based on counting the number of vegetation types, ocean
and lake presence within 200 mile diameter
=1 if the society is within 200 miles of an ocean
Number of frost months per year
Cashdan (2003)
SCCS
SCCS
SCCS
SCCS
Cashdan (2003)
Pryor (1986)
Pryor (1986)
Pryor (1986)
Cashdan (2003)
Cashdan (2003)
SCCS
Cubic meters of plant production per year, calculated using
Kelly (1995) and UNESCO data (1976).
Calculated using society coordinates in SCCS, with the
fertile crescent at 45E, 35N (.786, .611 in radians)
Calculated as the previous entry, using only mile differences
in latitude
=1 if closest to another original hearth of agriculture
(Northeastern U. S., Central America, South China)
Calculated using society coordinates in SCCS, with the NE
U. S., Central America, and South China as other hearths.
Calculated as the previous entry, using only mile differences
in latitude.
Date for which the reported information pertains
39
SCCS
Table 2: Frequencies of values of reliance on agriculture scale
Contribution of
Agriculture to
Food Supply
1
2
3
4
5
6
Frequency
Percent
35
3
17
12
42
77
186
18.82
1.61
9.14
6.45
22.58
41.40
100.00
40
Table 3: means of selected variables compiled from the standard cross cultural sample (Murdock and
White, 1969), Cashdan (2003), and Pryor (1984).
Variable
Population Density
(Log scale) (N=184)
Technology Index
(Log scale)
Mean rainfall (cm/year)
High Rainfall?
100*(Rainfall CV)
Climate suitability for
agriculture
Soil suitability for
agriculture
Land slope
Number habitats w/in
200 miles (N=172)
Ocean w/in 200 miles?
(N=172)
Frost months per year
(N=169)
Primary production
(g/m2/year)
Distance from Fertile
Crescent (miles)
Vertical Distance form
Fertile Crescent
Closer to another
hearth?
Distance to closest
hearth (miles)
Vertical Distance from
Closest Hearth
Date of contact
Contribution of
agriculture scale
Complete sample
N=186
Hunter-gatherers
N=42
3.76
(1.98)
3.44
(2.49)
140.74
(106.00)
0.17
(0.37)
23.53
(17.88)
3.13
(1.16)
2.07
(0.77)
3.29
(0.74)
3.93
(1.35)
0.59
(0.49)
1.31
(3.21)
1369.80
(939.97)
4996.70
(2456.02)
1859.50
(1248.37)
0.66
(0.47)
2395.27
(1256.75)
1647.46
(1077.28)
1853.38
(358.39)
4.37
(1.90)
1.78***
(1.12)
1.52***
(1.23)
110.55***
(86.55)
0.12
(0.33)
22.15
(8.44)
2.58***
(1.62)
1.81**
(0.86)
3.23
(0.81)
3.95
(1.43)
0.63
(0.49)
4.10***
(4.91)
958.27***
(884.88)
6100.86***
(1545.66)
1999.04
(1484.55)
0.93***
(0.26)
2620.56
(1172.36)
1850.16
(1107.22)
1885.26
(56.88)
1.52***
(1.23)
Agricultural
societies
N=144
4.35***
(1.79)
4.00***
(2.48)
149.54***
(109.76)
0.18
(0.39)
23.93
(19.81)
3.29***
(0.94)
2.14**
(0.74)
3.31
(0.71)
3.92
(1.33)
0.58
(0.50)
0.47***
(1.81)
1489.824***
(924.29)
4674.66***
(2579.96)
1818.81
(1173.40)
0.58***
(0.49)
2329.56
(1276.70)
1588.33
(1065.04)
1844.08
(406.02)
5.19***
(1.18)
** Difference in means significant at 5%
*** Difference in means significant at 1% (assuming unequal variances)
41
Table 4: Equilibrium effort levels and payoffs in the static model
Population density range
!H
!F
!E
Food production per capita
p! p
1
0
0
p1* < p < p2*
>0
>0
>0
)1&
" H '' $$
( p%
" A! ! ((1 # ! )c)1#!
p2* ! p
0
>0
>0
*
1
42
xH + xF
1# !
)
1 &
" A ''1 # $$
( cp %
!
)1&
'' $$
( p%
1#!
Table 5: Probit Model of incidence of agricultural use among SCCS societies.
Dependent variable = Agriculture in use?
Independent variable
Ln(1+Ocean within 200 miles)
Ln(Number of habitats w/in 200 mi.)
Ln(1+Climate suitability for ag.)
Ln(1+Soil suitability for ag.)
Ln(Mean yearly rainfall)
Ln (1+ High rainfall dummy)
Ln(100*Rainfall CV)
Ln(Primary Production)
Ln(Land Slope)
Ln(1+Number of Frost Months)
Ln(Distance from Fertile Crescent)
Ln(V. Distance from Fertile Crescent)
Closest to another hearth *
Ln(Distance from Closest hearth)
Closest to another hearth *
Ln (V. Distance from Closest hearth)
Ln(contact year+5000)
Estimated
coefficient
(Std. Err.)
0.09
(0.43)
-0.26
(0.39)
0.25
(0.40)
0.01
(0.53)
-0.24
(0.36)
0.24
(0.67)
0.34
(0.55)
0.52*
(.28)
-0.42
(0.71)
-.71***
(0.21)
-0.34
(0.47)
-0.23*
(0.13)
0.68*
(0.39)
-0.85**
(0.40)
-5.86
(11.31)
55.04
(100.12)
Constant
Psuedo-R2
* significant at 10%
** significant at 5%
*** significant at 1%
0.35
43
Table 6: Estimated Coefficients of two-stage least squares switching model
I
II
III
Full
Agricultural
Agricultural
Sample
Societies
Societies
Sample Size
N=169
N=128
N=128
Estimate
Estimate
Estimate
(Std. Err.)
(Std. Err.)
(Std. Err.)
Pop. Density equation
Technological Sophication (Log scale)
0.64***
0.45***
0.65***
(0.11)
(0.16)
(0.14)
Ln(1+Ocean w/in 200 miles)
1.03***
1.53***
1.24***
(0.38)
(0.45)
(0.42)
Ln(No. of habitats w/in 200 miles)
0.06
0.04
(0.35)
(0.42)
Ln(1+Climate suitability for ag. scale)
-0.03
0.39
(0.37)
(0.66)
Ln(1+Soil suitability for ag. Scale)
1.13**
1.13**
0.89
(0.46)
(0.57)
(0.57)
Ln(Mean yearly rainfall)
0.12
0.06
(0.27)
(0.30)
Ln(1+High yearly rainfall)
0.06
-0.72
(0.63)
(0.72)
Ln(100*Rainfall CV)
0.11
-0.28
(0.44)
(0.48)
Ln(Primary Production)
0.48*
0.24
0.57***
(0.25)
(0.31)
(0.18)
Ln(Land Slope)
-0.63
-0.20
(0.63)
(0.73)
Ln(1+Number of Frost Months)
-0.00
0.03
(0.17)
(0.28)
Selection term
-0.12
0.42
(0.67)
(0.60)
Constant
-3.56
-1.06
-4.06**
(2.63)
(1.82)
(1.57)
R2
0.47
0.42
0.32
Technology equation
Ln(Pop. Density)
0.38**
0.45***
.48***
(0.15)
(0.18)
(0.16)
Ln(Distance from Fertile Crescent)
-.1.03***
-0.66*
-.74***
(0.31)
(0.34)
(0.27)
Ln(Vertical Distance from Fertile Crescent)
-0.36***
-0.60***
-0.57***
(0.13)
(0.17)
(0.16)
Another hearth * Ln(Dist. From hearth)
-0.10
-0.32
(0.34)
(0.41)
Another hearth * Ln(V. Dist. From hearth)
0.08
0.33
(0.36)
(0.45)
Ln(Year of Contact)
-0.76
-0.44
(2.21)
(2.26)
Selection term
-0.50
-0.34
(0.86)
(0.71)
Constant
20.14
16.12
12.37***
(19.17)
(19.67)
(2.28)
R2
0.45
0.43
0.43
* significant at 10%
** significant at 5%
*** significant at 1%
44
IV
HunterGatherers
N=41
Estimate
(Std. Err.)
V
HunterGatherers
N=41
Estimate
(Std. Err.)
-0.14
(0.36)
0.23
(0.53)
1.24**
(0.51)
-0.05
(0.32)
-0.70
(0.88)
0.17
(0.47)
2.15**
(0.93)
1.60
(0.73)
0.32
(0.41)
-1.95**
(0.77)
0.58**
(0.23)
0.81
(0.52)
-5.33
(3.68)
0.50
-
-0.13
(0.35)
-0.53
(1.13)
-0.02
(0.17)
0.12
(0.81)
-0.02
(0.83)
-24.62
(22.86)
-0.42
(0.55)
232.15
(242.15)
0.12
1.06***
(0.37)
2.30***
(0.71)
1.29**
(0.56)
0.35
(0.26)
-1.98***
(0.67)
0.46***
(0.19)
-0.50
(0.41)
-3.11
(3.26)
0.51
-
Table 7: Model Parameter Estimates deriving from Table 6
Parameter
Technology –
Agriculture
Description
k FA
!F
! vF
Constant term in technology accumulation equation
!F
!F
Estimate
1002.86
Elast. of technology w. r. t. to dist. from Fertile Crescent
0.41
Elast. of technology w. r. t. N-S dist. from Fertile Crescent
0.32
Elast. of technology with respect to population density
0.27
Elast. of technology with respect to past technology
0.44
Population –
Agriculture
Constant term in production function
0.22
Labor share in production function
0.69
Resource share in total factor productivity
0.85
Technology share in total factor productivity
0.15
Elasticity of resource base w. r. t. Soil Suitability
0.33
! F ,Ocean 200
Elasticity of resource base w. r. t. Ocean w/in 200 miles
0.46
! F ,Pr im Pr od
Elasticity of resource base w. r. t. Primary Production
0.21
Constant term in production function
1.00
Labor share in production function
0.87
Elasticity of resource base w. r. t. number of habitats
0.14
Elasticity of resource base w. r. t. frost months
0.06
! H ,Pr im Pr od
Elasticity of resource base w. r. t. Primary Production
0.07
! H ,landslope
Elasticity of resource base w. r. t. Land Slope
0.26
! H ,rainCV
Elasticity of resource base w. r. t. rainfall CV
0.17
! H ,highrain
Elasticity of resource base w. r. t. high rainfall
0.30
k FR
!F
µF
!F
! F ,Soilsuit
Population –
Hunter gatherers
k HR
!H
! H ,nhabs
! H , frost
45
122
123
130
105
129
131
128
132
137
142
143
127
139 140
141
124
133
134 138
135
144
136 150 149 147
145
146
151 148
152
3
125
126
161
162
164
165
168 167 163
153 154
160
155 156
159
158
157
183 180
182181
178
177
169
166 176
170
174 175
171
179
172 173
185
184
186
51
50
42
52
49 48
2
4
47
54
55
56
46 57
78
3
53
81
44 45
58
43
41
39
40
24 25
38
21 22
37
26
27 29
23
30
16
31 32
20
36
19
18 17 15
33
28
35
13 12 11
14
6
9 34
10
5
1
65
64
59
66
115
116
117
90
119
118
109
120
94 95 96 97
93 92 98 99
114
68
67
63
69
113
71
60 62
70 72 73
112
76 7574
61
79
110
78
77
86
111
82
88
85
80
87
83 84
89
91
Map 1: The geographic distribution of hunter-gatherer and agricultural societies in the SCCS.
46
108
100
101
103
102
121
107
104
106