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: Matthew.Baker@hutner.cuny.edu

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.

2

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

3

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 hunter-

gatherer 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

4

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.

5

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-food-

producing 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.

6

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.

7

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.

8

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.

9

agriculture) to a maximum of 6 (exclusive agriculture). In labeling societies as agricultural or hunter-

gatherer, 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.

10

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

14

The formula for computing primary production is: 66.1

219.0 EPP = , 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.

11

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.

12

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.”

13

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 nZz /= . The initial endowment of land is the inverse

of population density, which I define as Znp /= . 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:

1=++EFH!!! . (1)

The time costs of enclosing e units of land are ce / , 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 ceE

/=! , the time constraint (1) may be rewritten as:

1/ =++ ceFH

!! , nZe /! . (2)

19

This is similar to the approach employed in Baker (2003) and De Meza and Gould (1992). 20

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.

14

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, HZ , and on total effort devoted to hunting and gathering by

the population, H

n! , according to the production function:

HH

HHHHZnX

!!"#

$=

1)( , (3)

In equation (3), H

! measures total factor productivity in hunting and gathering. Agents

receive a share of H

X 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:

HH

HHH

H

H

HZn

nx

!!"#

"

" $=

1)( . (4)

The aggregate amount of land available for hunting and gathering depends upon how much

land remains unenclosed. Thus,

*enZZ

H!= , nZe /

*! . (5)

In equation (5), *e represents the amount of land enclosed by the average agent in

equilibrium; therefore *en is total enclosed land. If it should happen that nZe /

*= , then all land is

enclosed in equilibrium, which results in 0=HZ , 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:

FF exFFF

!!"#

$=

1. (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

15

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:

HHFF

HHH

H

F

FFZn

n

ceex

!!!!"#

"

""#

$$ $$+=

11)()(

)/1(. (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 andF

! :

HF

H

HHF

FF

n

Z

cee

x!!

"

#"#!

$

%%&

'(()

*$%

&

'()

*$=

+

+1

)1( ,

HF

H

H

H

F

FF

Fn

Zex!!

"#

"#!

"

$$

%%&

'(()

*$%%

&

'(()

*=

+

+11

. (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:

F

F

F

ce

!

!

"

#=1

*

*

. (9)

Substituting the optimal ratio in (9) into either equation in (8) results in the following

equality:

16

H

ecn

neZ

F

HF

!

!"#"

$

$ %%&

'(()

*

$$

$=

1

1 )))1((1(, ( ) FF

FFc

!! !!"#

#=1)1( (10)

The left-hand side of equation (10) is the marginal product of effort devoted to

enclosure/agriculture at the optimal F

e !/ ratio, given that nZe /! . That is, !" FFmp = . 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:

H

ecn

neZeap

F

HH

!

!"

#

# $$%

&''(

)

##

#=

1

1 )))1((1()( . (11)

Both land enclosure and time allocation decisions can be described in terms of Fmp and

)(eapH . 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:

FH mpap <)0( . (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 )(eapH overtakes Fmp at some point

nZe /*< . This can only happen if 0)( >! epa H , so that the average product of effort in hunting and

gathering must increase as enclosures increase. The condition 0)( >! epa H 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 Hap in (11)

17

reveals that 0)( >! epa H if population density Znp /= is less than some critical level of population

density, which I label *

2p :

*

2)1(

1p

cp

F

=!

<"

. (13)

If inequality (13) is satisfied, then !")(eap as nZe /! . Thus, condition (13) is

sufficient to guarantee that 0)( >! epa H and also that FH mpeap =!)( at some nZe /<! . 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:

H

n

Z

HF

!

"#"$

%&

'()

*+

1

. (14)

Solving (14) for population density gives a threshold value of population density necessary

for the emergence of agriculture:

*

1

1

1

ppH

F

H =!!"

#$$%

&'

()

*+

+. (15)

I shall assume throughout that*

2

*

1pp < .

22 Together, the critical population densities

*

1p and

*

2p 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

22

If it were the case that*

1

*

2pp < , the model would generate multiple equilibria for ),(/ *

1

*

2 ppZn ! : 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.

18

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 2/12/1

2 ncu = ,

and assume that the resource costs of having a child are given by 2/b . Given lifetime food

production of tx , a particular agent i at time t chooses the number of children to have to maximize

utility:

2/1

1

2/1

12)(

1

++!+

itit

b

tn

nnxMaxiit

. (16)

Solving the problem in (16) yields the following optimal number of children:

bxntit/

*

1=+ . (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 relationship1

1

!

+ = bxnnttt

, or:

!"

#$%

&'=

(1

b

x

n

nt

t

t . (18)

Dividing equation (18) through by Z (the aggregate land endowment) gives equation (18) in

terms of population density:

!"

#$%

&'=

(1

b

x

p

p t

t

t . (19)

Equation (19) is a Malthusian population dynamic describing the evolution of population

density. When the ratio bxt/ is greater than unity, population density increases. In this way,

population growth depends upon the underlying mode of production of the economy, as summarized

19

in table 4. Substituting in the exact form for agents’ output from table 4 gives the following

description of population dynamics:

t

t

p

p! = 1

11

!""#

$%%&

'! H

t

H

pb

()

, ],0[*

1ppt! ;

= 1!"#

b

F , ),( *

2

*

1 pppt! ;

= 111

1

1

!""#

$%%&

'""#

$%%&

'!

! FF

tt

F

pcpb

(()

. ),[ *

2 !" ppt

. (20)

Equation (20) shows how the organization of production influences population growth. When

],0[*

1ppt! agents are engaged exclusively in hunting and gathering, and when ),[ *

2 !" ppt

,

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 ),( *

2

*

1 pppt! , 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 *

1pp ! 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 hunter-

gatherer population density, which I refer to as Hp , is compatible with the no-agriculture condition

*

1pp < . The steady-state hunter gatherer population is obtained by solving 0/ =!

ttpp for

],0[*

1ppt! in (20). This gives:

H

bp HH

!" #

$%

&'(

)=

1

1

.

Thus, Hp is less than *

1p so long as:

20

bF!"# . (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

! FHi ,= , depend upon the resource

base available for each production technology, which I refer to as FHiri

,, = , and the amount of

technology available, A , according to the functions:

HH ArHH

!µ" = ;, FF Ar

FF

!µ" = , (22)

I assume that HF

!! > . The functions in (22) posit a relationship between environment,

technology, and total factor productivity, while the assumption that HF

!! > 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.

21

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:

),,( Ettt ApAA !=" . (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:

tHttHt AApkA HH !"# $=% , 0=

E! ,

tFttFt AApkA FF !"# $=% 0>

E! . (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 parameteri

! . As a working hypothesis, it seems reasonable to suppose that:

HF!! > ,

HF!! > ,

HFkk > . (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).

22

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 *

1p .

Substituting the productivity parameters in (22) into equation (15) gives a new necessary condition

for a switch to agriculture:

)(1 *

1

1

1

t

tF

H

t ApAr

rp

H

HFF

H

=!!

"

#

$$

%

&>

'

'

(

))µ

µ

*. (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:

t

t

p

p! = 1

11

!""#

$%%&

'! H

HH

t

H

pb

Ar()µ

, )](,0[ *

1 Appt ! ;

= ( ) 1)1(1

!!! FF

FF

cb

Ar

FF

tF ""

#µ

"" )),(( *

2

*

1 pAppt ! ,

= 111

1

1

!""#

$%%&

'""#

$%%&

'!

! FFFF

tt

tF

pcpb

Ar(()µ

. ),( *

2 !" ppt

(27.a)

t

t

A

A! = HttH

HH Apk !"#

$$1

.24

)](,0[ *

1 Appt ! ,

= FttFFF Apk !"#

$$1

]),([ *

1 !" Appt (27.b)

Assumptions sufficient to generate an interior, stable steady state are:

1<+ii!" ; 1<+

ii!" . (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 21 )( !! <A ; I shall discuss this case in a moment.

23

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 )(*1 Ap 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:

H

HHH

HH

H Ab

rp

!

"!µ

##

$$%

&''(

)=

11

1

, HH

H

HHH

pkA

!"

#

$

%%&

'(()

*=

1

1

, )(*1 HH App < . (29)

If, however, the inequality in (29) does not hold the following equations describe the ultimate

steady-state values of population density and technology:

111

1

1

=!!"

#$$%

&!!"

#$$%

&'

' FFFF

FF

FF

ppcb

Ar(()µ

, FF

F

FFF

pkA

!"

#

$

%%&

'(()

*=

1

1

. )(*1 AppH ! (30)

25

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.

24

The equations in (30) have no closed-form solution, but can be written in the same form as

those in (29) using the approximation:

11!

"

F

F

pc

pc. (31)

Then, the following two equations describe equilibrium technology and population density at

the agricultural steady state:

F

FFF

FF

F Ab

rp

!

"!µ

##

$$%

&''(

)=

11

1

, FF

F

FFF

pkA

!"

#

$

%%&

'(()

*=

1

1

. )(*1 AppH ! (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:

H

H

HH

H

H

H

H Arbp ln1

ln1

ln1

1ln

!

"

!

µ

! #+

#+

##=

H

H

H

HH

H

H

H pkA ln1

1ln

1

1ln

1

1ln

!

"

#!! $+

$+

$= , )(*1 HH App < ;

F

F

FF

F

F

F

F Arbp ln1

ln1

ln1

1ln

!

"

!

µ

! #+

#+

##=

F

F

F

FF

F

F

F pkA ln1

1ln

1

1ln

1

1ln

!

"

#!! $+

$+

$= . )(*1 HH App ! (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.

25

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 ! ( dv ! ) 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:

iviviii ydvvdddkk iAi

!"#""#" $$ $$= )()( . FHi ,= . (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.

26

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:

!=

=i

ik

M

i

ikriirkr

1

", FHi ,= . (35)

In equation (35) i

M 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 , FHi ,= . Substituting (34) and (35) into (33) gives:

!="

+"

+"

=HH M

k

HkHk

H

HH

H

HHr

H

H rAb

kp

1

ln1

ln1

ln1

1ln #

$

µ

$

%

$

µ

. (36a)

ypk

AH

HH

H

H

H

HA

H

H ln1

ln1

ln1

1ln

!

"

!

#

$! %+

%+

%= ;

dvvddd

H

vH

H

vH

H

H

H

H !"

!+

"+!

"

!+

"+ ln

1ln

1ln

1ln

1 #

$%

#

$

#

$%

#

$; )(*1 HH App <

!="

+"

+"

=FF M

k

FkFk

F

FH

F

FFr

F

F rAb

kp

1

ln1

ln1

ln1

1ln #

$

µ

$

%

$

µ

. (36b)

ypk

AF

FF

F

F

F

FA

F

F ln1

ln1

ln1

1ln

!

"

!

#

$! %+

%+

%= ;

dvvddd

F

vF

F

vF

F

F

F

F !"

!+

"+!

"

!+

"+ ln

1ln

1ln

1ln

1 #

$%

#

$

#

$%

#

$; )(*1 HH App !

27

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 two-

step 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 hunter-

gatherers (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 1))(1)(( !"! ZZ# as an additional instrument in the hunter-gatherer system of equations and 1)()( !" ZZ# as an additional instrument in the agricultural system. Each system may then be estimated

separately using standard methods.

28

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 hunter-

gatherer 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.

29

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 hunter-

gatherers. 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 two-

equation system gives:

31

See Baker and Swope (2004) for background discussion on labor supply in hunter-gatherer economies.

30

)ln(p )200ln(82.1)ln(53.0)ln(70.079.5 oceanvdistfcdistfc +!!=

)ln(83.0)ln(29.1 primprodsoilsuit ++

)ln(A )200ln(87.0)ln(82.0)ln(08.115.15 oceanvdistfcdistfc +!!=

)ln(40.0)ln(62.0 primprodsoilsuit ++ (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 kA

eA+

=!~

. 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).

31

record keeping (w ) and the degree of technological sophistication ( t ) according to kwt

eA++

=)(~ !

.

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 1~=A , 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 52.1

for my technological sophistication variable (see table 3), is approximately =52.1

e 4.57 times as

sophisticated as the typical Paleolithic society. The implication is then that the average agricultural

society in the sample is about 6.544=e 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 ii Arii

!µ" = , so a natural, albeit ad hoc, assumption is that:

FHiii

,,1 ==+!µ . (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:

FHi

iM

i

ik,,1

1

==!=

" , (39)

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.

32

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 FrHrkk , ). I choose to set 1=b . 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 iAk ), or a smaller vintage effect (as captured by a

i! ), the

choice is arbitrary, so I choose to set 1=iA! . 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

1=++FvFF

!"" . (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 1, =b! 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.

33

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

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37

p

A

Hunter Gatherer

Incipient Agriculture

Agriculture

)(*1 Ap

*

2p

Fp

FA

Figure 3: Population growth and technological progress with a Neolithic revolution.

38

p

A

)(*1 Ap

*

2p

Hp

HA

Figure 4: The stable hunter-gatherer economy.

39

Table 1: Description of Variables and Sources used in the analysis

Description Source

Technology and

population

Contribution of

Agriculture to food

supply

=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.

SCCS

Agriculture in use? =1 if Contribution of Agriculture to food supply >3

=0 otherwise

SCCS

Population Density =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

SCCS

Technological

specialization

=0 if no specialization present, =1 if pottery only,

=2 if loom weaving only, =3 if metalwork only,

=4 if smiths, weavers, and potters

SCCS

Writing and

Record-Keeping

=0 none, =1 Mnemonic devices, =2 Non-written records, =3

True writing, no records, =4 True writing, records

SCCS

Environmental

Characteristics

Mean Rainfall Mean yearly rainfall (cm) Cashdan (2003)

High Rainfall? =1 if mean yearly rainfall is more than 1 standard deviation

above SCCS mean yearly rainfall

CV Rainfall Coefficient of variation in mean yearly rainfall Cashdan (2003)

Climate suitability

for agriculture

Scale ranging from 0 (impossible) to 4 (very good)

developed by Pryor using FAO/UNESCO reports

Pryor (1986)

Soil suitability for

agriculture

Scale ranging from 0 (impossible) to 4 (very good)

developed by Pryor using FAO/UNESCO

Pryor (1986)

Land slope Scale ranging from 2 to 4, 2=steep, 4=relatively flat Pryor (1986)

No. habitats w/in

200 miles

Based on counting the number of vegetation types, ocean

and lake presence within 200 mile diameter

Cashdan (2003)

Ocean w/in 200 mi? =1 if the society is within 200 miles of an ocean Cashdan (2003)

Number of frost

months per year

Number of frost months per year SCCS

Primary Production Cubic meters of plant production per year, calculated using

Kelly (1995) and UNESCO data (1976).

Geography/Time

Distance from fertile

crescent

Calculated using society coordinates in SCCS, with the

fertile crescent at 45E, 35N (.786, .611 in radians)

“Vertical” distance

from fertile crescent

Calculated as the previous entry, using only mile differences

in latitude

Closer to another

hearth?

=1 if closest to another original hearth of agriculture

(Northeastern U. S., Central America, South China)

Distance from

closest hearth

Calculated using society coordinates in SCCS, with the NE

U. S., Central America, and South China as other hearths.

“Vertical” distance

from closest hearth

Calculated as the previous entry, using only mile differences

in latitude.

Date of Contact Date for which the reported information pertains SCCS

40

Table 2: Frequencies of values of reliance on agriculture scale

Contribution of

Agriculture to

Food Supply

Frequency Percent

1

2

3

4

5

6

35

3

17

12

42

77

18.82

1.61

9.14

6.45

22.58

41.40

186 100.00

41

Table 3: means of selected variables compiled from the standard cross cultural sample (Murdock and

White, 1969), Cashdan (2003), and Pryor (1984).

Variable Complete sample

N=186

Hunter-gatherers

N=42

Agricultural

societies

N=144

Population Density

(Log scale) (N=184)

3.76

(1.98)

1.78***

(1.12)

4.35***

(1.79)

Technology Index

(Log scale)

3.44

(2.49)

1.52***

(1.23)

4.00***

(2.48)

Mean rainfall (cm/year) 140.74

(106.00)

110.55***

(86.55)

149.54***

(109.76)

High Rainfall? 0.17

(0.37)

0.12

(0.33)

0.18

(0.39)

100*(Rainfall CV)

23.53

(17.88)

22.15

(8.44)

23.93

(19.81)

Climate suitability for

agriculture

3.13

(1.16)

2.58***

(1.62)

3.29***

(0.94)

Soil suitability for

agriculture

2.07

(0.77)

1.81**

(0.86)

2.14**

(0.74)

Land slope 3.29

(0.74)

3.23

(0.81)

3.31

(0.71)

Number habitats w/in

200 miles (N=172)

3.93

(1.35)

3.95

(1.43)

3.92

(1.33)

Ocean w/in 200 miles?

(N=172)

0.59

(0.49)

0.63

(0.49)

0.58

(0.50)

Frost months per year

(N=169)

1.31

(3.21)

4.10***

(4.91)

0.47***

(1.81)

Primary production

(g/m2/year)

1369.80

(939.97)

958.27***

(884.88)

1489.824***

(924.29)

Distance from Fertile

Crescent (miles)

4996.70

(2456.02)

6100.86***

(1545.66)

4674.66***

(2579.96)

Vertical Distance form

Fertile Crescent

1859.50

(1248.37)

1999.04

(1484.55)

1818.81

(1173.40)

Closer to another

hearth?

0.66

(0.47)

0.93***

(0.26)

0.58***

(0.49)

Distance to closest

hearth (miles)

2395.27

(1256.75)

2620.56

(1172.36)

2329.56

(1276.70)

Vertical Distance from

Closest Hearth

1647.46

(1077.28)

1850.16

(1107.22)

1588.33

(1065.04)

Date of contact

1853.38

(358.39)

1885.26

(56.88)

1844.08

(406.02)

Contribution of

agriculture scale

4.37

(1.90)

1.52***

(1.23)

5.19***

(1.18)

** Difference in means significant at 5%

*** Difference in means significant at 1% (assuming unequal variances)

42

Table 4: Equilibrium effort levels and payoffs in the static model

Population density range H!

F!

E! Food production per capita

FHxx +

*

1pp !

1 0 0 !

"

#

$$%

&''(

)1

1

pH

*

2

*

1ppp <<

>0 >0 >0 ( ) !! !!" ## 1)1( cA

pp !*

2

0 >0 >0 !!

"

#

$$%

&''(

)$$%

&''(

)#

1

111

pcpA

43

Table 5: Probit Model of incidence of agricultural use among SCCS societies.

Dependent variable = Agriculture in use?

Independent variable Estimated

coefficient

(Std. Err.)

Ln(1+Ocean within 200 miles) 0.09

(0.43)

Ln(Number of habitats w/in 200 mi.)

-0.26

(0.39)

Ln(1+Climate suitability for ag.)

0.25

(0.40)

Ln(1+Soil suitability for ag.)

0.01

(0.53)

Ln(Mean yearly rainfall)

-0.24

(0.36)

Ln (1+ High rainfall dummy)

0.24

(0.67)

Ln(100*Rainfall CV)

0.34

(0.55)

Ln(Primary Production) 0.52*

(.28)

Ln(Land Slope) -0.42

(0.71)

Ln(1+Number of Frost Months) -.71***

(0.21)

Ln(Distance from Fertile Crescent)

-0.34

(0.47)

Ln(V. Distance from Fertile Crescent)

-0.23*

(0.13)

Closest to another hearth *

Ln(Distance from Closest hearth)

0.68*

(0.39)

Closest to another hearth *

Ln (V. Distance from Closest hearth)

-0.85**

(0.40)

Ln(contact year+5000)

-5.86

(11.31)

Constant

55.04

(100.12)

Psuedo-R2

0.35

* significant at 10%

** significant at 5%

*** significant at 1%

44

Table 6: Estimated Coefficients of two-stage least squares switching model

I II III IV V

Full

Sample

Agricultural

Societies

Agricultural

Societies

Hunter-

Gatherers

Hunter-

Gatherers

Sample Size N=169 N=128 N=128 N=41 N=41

Estimate

(Std. Err.)

Estimate

(Std. Err.)

Estimate

(Std. Err.)

Estimate

(Std. Err.)

Estimate

(Std. Err.)

Pop. Density equation

Technological Sophication (Log scale) 0.64***

(0.11)

0.45***

(0.16)

0.65***

(0.14)

-0.14

(0.36)

-

Ln(1+Ocean w/in 200 miles) 1.03***

(0.38)

1.53***

(0.45)

1.24***

(0.42)

0.23

(0.53)

-

Ln(No. of habitats w/in 200 miles) 0.06

(0.35)

0.04

(0.42)

- 1.24**

(0.51)

1.06***

(0.37)

Ln(1+Climate suitability for ag. scale) -0.03

(0.37)

0.39

(0.66)

-

-0.05

(0.32)

-

Ln(1+Soil suitability for ag. Scale) 1.13**

(0.46)

1.13**

(0.57)

0.89

(0.57)

-0.70

(0.88)

-

Ln(Mean yearly rainfall) 0.12

(0.27)

0.06

(0.30)

- 0.17

(0.47)

-

Ln(1+High yearly rainfall) 0.06

(0.63)

-0.72

(0.72)

- 2.15**

(0.93)

2.30***

(0.71)

Ln(100*Rainfall CV)

0.11

(0.44)

-0.28

(0.48)

- 1.60

(0.73)

1.29**

(0.56)

Ln(Primary Production) 0.48*

(0.25)

0.24

(0.31)

0.57***

(0.18)

0.32

(0.41)

0.35

(0.26)

Ln(Land Slope)

-0.63

(0.63)

-0.20

(0.73)

- -1.95**

(0.77)

-1.98***

(0.67)

Ln(1+Number of Frost Months)

-0.00

(0.17)

0.03

(0.28)

- 0.58**

(0.23)

0.46***

(0.19)

Selection term

- -0.12

(0.67)

0.42

(0.60)

0.81

(0.52)

-0.50

(0.41)

Constant -3.56

(2.63)

-1.06

(1.82)

-4.06**

(1.57)

-5.33

(3.68)

-3.11

(3.26)

R2 0.47 0.42 0.32 0.50 0.51

Technology equation

Ln(Pop. Density) 0.38**

(0.15)

0.45***

(0.18)

.48***

(0.16)

-0.13

(0.35)

-

Ln(Distance from Fertile Crescent) -.1.03***

(0.31)

-0.66*

(0.34)

-.74***

(0.27)

-0.53

(1.13)

-

Ln(Vertical Distance from Fertile Crescent)

-0.36***

(0.13)

-0.60***

(0.17)

-0.57***

(0.16)

-0.02

(0.17)

-

Another hearth * Ln(Dist. From hearth)

-0.10

(0.34)

-0.32

(0.41)

- 0.12

(0.81)

-

Another hearth * Ln(V. Dist. From hearth)

0.08

(0.36)

0.33

(0.45)

- -0.02

(0.83)

-

Ln(Year of Contact) -0.76

(2.21)

-0.44

(2.26)

-24.62

(22.86)

-

Selection term

- -0.50

(0.86)

-0.34

(0.71)

-0.42

(0.55)

-

Constant

20.14

(19.17)

16.12

(19.67)

12.37***

(2.28)

232.15

(242.15)

-

R2 0.45 0.43 0.43 0.12 -

* significant at 10%

** significant at 5%

*** significant at 1%

45

Table 7: Model Parameter Estimates deriving from Table 6

Parameter Description Estimate

Technology –

Agriculture

FAk Constant term in technology accumulation equation 1002.86

F! Elast. of technology w. r. t. to dist. from Fertile Crescent 0.41

vF! Elast. of technology w. r. t. N-S dist. from Fertile Crescent 0.32

F! Elast. of technology with respect to population density 0.27

F! Elast. of technology with respect to past technology 0.44

Population –

Agriculture

FRk Constant term in production function 0.22

F! Labor share in production function 0.69

Fµ Resource share in total factor productivity 0.85

F! Technology share in total factor productivity 0.15

SoilsuitF ,! Elasticity of resource base w. r. t. Soil Suitability 0.33

200,OceanF! Elasticity of resource base w. r. t. Ocean w/in 200 miles 0.46

odimF PrPr,! Elasticity of resource base w. r. t. Primary Production 0.21

Population –

Hunter gatherers

HRk Constant term in production function 1.00

H! Labor share in production function 0.87

nhabsH ,! Elasticity of resource base w. r. t. number of habitats 0.14

frostH ,! Elasticity of resource base w. r. t. frost months 0.06

odimH PrPr,! Elasticity of resource base w. r. t. Primary Production 0.07

landslopeH ,! Elasticity of resource base w. r. t. Land Slope 0.26

rainCVH ,! Elasticity of resource base w. r. t. rainfall CV 0.17

highrainH ,! Elasticity of resource base w. r. t. high rainfall 0.30

46

M

ap 1

: Th

e geo

grap

hic d

istribu

tion

of h

un

ter-gath

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d ag

ricultu

ral societies in

the S

CC

S.

42

21

20

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23

19

18

1

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15

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10

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31

32

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35

43

39

38

37

24

41

26

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44

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48

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57

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46