Population equilibrium in primitive societies

The Quarterly Review of Economics and Finauce, Vol. 37, No. 4, Fall 1997, pages 747-767 Copyright Q 1997 Tmstees of the University of Illinois All rights of reproduction in any form reserved ISSN 1062.9769 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Focus Population Equilibrium in Primitive Societies zyxwvutsrqponmlkjihg LUIS LOCAY Universityof Miami and DevTech Systems, Inc. zyxwvutsrqponmlkjihgfedcbaZYXWV The a.borigi? zaf d~t~b~Lt~~~of zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA ~a~~~~~a~ irk North Alnerka is found not to be positively related of to the richrkess zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA of then&ml ~~~r~~r~l~, cantmyto thr:~edicti~~ the ~~~u~th~s~ark model, the dominant one irk Anthr~lo~y. Great aln4ndurtce of some reso? &rcescan encourage nomadism or rake thtz productivity of women, two detuminarkts qf the cost qfc/kildr? ? n, which I find are associated with lower abotiginal population density umong a sample of tribes of Norttk American Indians. Economist for the most part have not studied primitive peoples. Some notable exceptions are Eoserup (1965), Grossbard (1974), Posner (1980), and Smit.h (1975). This is unfortunate, for among primitive societies one can often find behavior that is outside the range common in modern societies. In fact, sometimes what we would consider extreme behavior in a modern society is normal behavior in a primitive one. Examples of such behavior that I have come across would be institutionalized cannibalism (Aztecs), common and accepted adultery (Truk), and multiple husbands (Nayar). Applying models of human behavior derived from observation of the modern world to primitive societies can be a real challenge for those models. The extreme behavior pushes models to their limits and is often helpful in choosing between competing model.s, whose implications may be difficult to distinguish within the more restrictive range of modern behavior. There is at least one good reason for not studying primitive peoples-the data problems can be insurmountable. This work, for example, deals with some demographic decisions among a substantial number of tribes and groups of tribes of North American Indians at about the time of contact with Europeans. Ideally, I would have wanted fertility and mortality information on an individual or household level. Unfortunately, no such data exist. Not even aggregate fertility and mortality rates by tribe are available for the early contact period. What is available are rough estimates of population density, and just collecting and con- 747 748 QUARTERLY REVIEW OF ECONOMICS AND FINANCE zyxwvutsrqponmlkjihgfedcbaZYXWVUTSR strutting these has been a major endeavor. As a consequence of data limitations, I have taken a model of household fertility and mortality decisions, and turned it into a model of the distribution of population density. In this study I will argue that the aboriginal distribution of population in North America is not consistent with the Malthusian model, the dominant one in anthropology. I will further argue that the observed relationship between the natural environment and population density can be explained by richer environments sometimes having higher costs of bearing and rearing children. The two mechanisms by which the natural environment can affect the cost of children are (1) the nomadic way of life, and (2) the productivity of women. The first section introduces the basic framework in the form of simple models with Malthusian type implications. I provide evidence that is inconsistent with the implication of those models. The nature of this evidence is that in some dimensions a richer natural environment is associated with lower, not higher, population density. Section II incorporates into the basic model the choice of whether to be sedentary or nomadic. In Section III, I estimate a switching regression model with the sedentary-nomadic choice being endogenous. While the nomadic way of life can explain some of the previous anomalies, there are still some puzzling results. In Section IV, I incorporate the sexual distribution of labor and the productivity of women into the model to help explain the empirical findings of Section III. I. MALTHUSIAN, OF POPULATION MIGRATION AND CARRYING CAPACITY MODELS In a region that experiences no in or out migration the change in population over a period of time is simply the number of births minus deaths occurring in that time period. If the population of such a region tends to a steady state, it is because population change acts upon fertility and mortality so as to reduce population growth when the population is above its steady state level, and to increase population when it is below it. Population systems exhibiting this stable steady state property are said to be homeostatic. An example of a homeostatic model is the simple Malthusian model, where population growth leads to lower wages, delayed marriage and increased mortality. If immigration and emigration are possible, population change in a given region over a period of time also includes net immigration. If population grows, mechanisms to adjust population size to resources, such as the Malthusian one of impoverishment leading to greater mortality, need not come into play, as people migrate to other locations. The first occupants of the Americas probably faced such a situation. They initially had a wide variety of unoccupied environments to choose from. If population in the preferred environments grew, people could migrate to unoccupied territories of similar quality. Eventually, of course, the preferred environments would all be occupied, and population growth would lead to lower standards of POPULATION EQUILIBRIUM IN PRIMITIVE SOCIETIES 749 zyxwvutsrqponm living. At some point the occupied territories would cease to be “ preferred.” Environments that had been previously uninhabited would become relatively attractive, and they in turn would be occupied, starting the cycle again.’ If we take an extreme position and assume that migration was costless, then the concentration of population in any region of the New World before European contact would reflect the relative attractiveness of that region. People would live in regions poor in natural resources, only if congestion had sufficiently lowered productivity in the rich regions. The empirical implication of costless migration is that abundance of natural resources is positively related to population density. This implication holds regardless of what is the effect of population growth on fertility and mortality. Population density would tell us nothing about fertility and mortality. The assumption of costless migration may not be a bad one when explaining the distribution of people in a modern industrialized country. It may even be applicable to a primitive people just entering an unoccupied continent, which will take them several thousand years to occupy. But under primitive conditions an occupied continent is a different matter. Would-be immigrants to an occupied area may well have faced resistance from the current occupants. The opposite assumption to costless migration, is that migration is so costly that it does not take place. Without migration each closed area has its own population history (at least from the time it became closed), and differences in standards of living across areas are sustainable. Neither of the two extreme assumptions is descriptively accurate, and how close each is to reality depends on the size of the area being considered. Within an area of villages belonging to the same tribe migration is probably not very costly. An example would be the agricultural Huron, whose aboriginal population distribution within their settled area seems to have been closely related to soil quality (Heidenreich, 1971). But movement across tribal boundaries, over great distances, over natural obstacles, or into regions requiring very different subsistence pursuits, would be much more costly. Suppose that the decision unit is the household, consisting of adults and children. The household of this analysis is representative of those belonging to a larger group, such as a tribe. The household allocates the labor services of its members across various subsistence activities. The activities considered here are gathering, hunting, fishing, and agriculture.2 Agriculture is further subdivided into irrigation agriculture, which was practiced in some of the drier regions and in parts of Mexico, and agriculture that did not use irrigation, which I refer to as horticulture. From the outputs of these activities the household produces a single good, X, which I will refer to as food or subsistence. A household can produce more food in a rich environment than in a poor one. The productivity of the natural environment of a tribe will be measured by the vector E (abundance of game, of fish, of wild plants, etc.). Land availability is also important, as a household cannot produce much food if its natural environment is very productive, but it has very little land it can exploit. Land availability 750 QUARTERLY REVIEW will be measured OF ECONOMICS by population capita. Food production AND FINANCE zyxwvutsrqponmlkjihgfedcbaZYXWVUTSR density, P, which is just the inverse of land per can be expressed as a function of environmental pro- density, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONM P, as follows: ductivity, E, and of population X = F(E, P) (1) The function F(E, P) is increasing in E and decreasing in P. Suppose that North America is divided into K regions. The utility or value a household places on being in region k is given by: I+ = V(X’“ ), K = l,..., K, where V(X’“ ) is an increasing function. function of Xk. The function It should not be interpreted only about food production. tive people (2) V is an indirect utility to mean that primitive As a number of time allocation devote surprisingly little time to work activities can think of Xk as the food production households care studies show, primi(Gross, 1984). possible in region K. The household We pro- duces Xk and then “ buys” back some of the time of its members for leisure activities. In the absence of any migration costs, households simply move to the location they value most. Since at the time of contact all of North America was occupied, it must have been the case that all locations Let V* be the level of utility corresponding pied, it follows from Equations 1 and 2 that: V(F(Ek, 9) It follows directly from were equally attractive. to any region. If all regions are occu- Equation = V*, k = l,..., K 3 that a region (a high Ek) must have a high population (3) with a rich density (a high 9) call this model the “ Migration Model.” Table 1 presents the results from regressing environment to compensate. the log of population on five indices of environmental productivity of resource abundance North American Indian tribes or groups of tribes. In the construction population estimates, I have taken into account, I will density for 89 of the as well as I have been able to, the devastating impact of European diseases on native sures of resource abundance reflect the productivity of five subsistence activities of hunting, fishing, gathering, tion agriculture. The results are not presented here, populations. The meathe environment in the horticulture and irrigabut the five indices of resource abundance explain well the relative dependence on each of the four subsistence activities across Indian tribes. The data set is described a little more in the Appendix. The results of Table 1 do not support the costless migration hypothesis. Hunting resources has an insignificant effect on population density (and a nega- POPULATION Table I. Regression Density on Indicesof EQUILIBRIUM IN PRIMITIVE SOCIETIES 751 zyxwvutsrqponm of Log of Population Environmental Productivity zyxwvutsrqponmlkjihgfedcbaZYXW (Dependent Variable: Log of Population Density in Persons/ l OOkm*) Coefficient Variable -1.03 Constant zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFED Index for: -0.53 Hunting 0.93a Fishing 4.3ga Gathering -0.80a Horticulture 1.17= IrrigationAgriculture N&s: a. Significantly different Observations-89 R2 = 0.522 See appendix from zero at the 1% level. No. of for data sources. tive sign). More importantly, horticultural productivity is negatively related to population density and is statistically significant at the five percent level. While it is true that the coefficients of three of the five indices are positive and significantly different from zero, this is not good enough. That all productivity indices be positively related to population density is not a very strong test of this model (equality of the @‘s would be). Such a relationship is consistent with many models. It can be concluded, therefore, that migration costs were sufficiently high to keep people from always moving to their preferred regions. We can turn now to models where the population equilibrium is achieved internally. The common opulation models in anthropology seem to be adaptations of biological models. r One model is that populations will tend toward the sustainable limit-the so called carrying capacity-that a given environmenttechnology combination will permit. This is the biological version of the simple Malthusian model mentioned above. One implication of this model is that population density is positively related to the abundance of natural resources, irrespective of whether or not migration is costly. At this level the model is indistinguishable from one that assumes costless migration. Many non-human populations seem to regulate their numbers below the limit of their resources. Primitive human societies seem to do the same (Blanton, 19’75). Keeping the population below carrying capacity has survival value in uncertain environments. For long-term survival, a group must gear its numbers to the carrying capacity of bad years. Still, since more people can normally be supported in bad years in rich environments than in bad years in poor environments, once again the empirical implication is that population density is positively related to the abundance of natural resources. We can easily give a formal presentation, like that of the migration model presented above, to the carrying capacity model. Suppose that the tribal area is 752 QUARTERLY REVIEW OF ECONOMICS fixed, and that no migration AND FINANCE zyxwvutsrqponmlkjihgfedcbaZYXWVUTSR in or out takes place. Define the amount of food consumed by adults as Z. What is not consumed by adults goes to the children of the household. Since I cannot separate births from deaths, in referring to children I will always mean children constraint surviving to adulthood, S. The household food is as follows: x=z+rs (4) where r is the food requirement per child (the location subscripts are no longer needed and have been dropped). Suppose the household behaves so as to maximize the number of children, S, subject to satisfying the food needs, Z,, of the adults. In this case the indirect utility function follows easily from Equation 4. It is simply: V(X) = (X-Z,) s= ~ 7” (5) A certain number of surviving children is necessary to maintain the size of the population. Suppose that there are two adults in each household (any number will do), and each child that survives to adulthood goes on to be an adult in a two adult household. If S exceeds two, the population will grow. As the population grows, food production per household declines according to Equation 1, and S falls according to Equation 5. The reverse happens if S is less than two. A steady state equilibrium exists when S equals two. Let fl be the steady state population density of a given environment. The formal definition of the steady state is obtained by setting S = 2 and substituting Equation 1 into Equation 5. The result is 2= (R-K PE) - Zo) 7” (6) As can be seen from Equation 6, any increase in zyxwvutsrqponmlkjihgfedcbaZYXWVU E will be compensated by an increase in P. Once again population density is positively related to environmental productivity. The results already presented argue, therefore, as much against the Carrying Capacity Model as the Migration Model. The human carrying capacity is actually equal to PE in this case. 4 If one could measure carrying capacity one could test these models directly. The attempts I know of reject the Carrying Capacity Model completely, but I do not believe it is really possible to estimate carrying capacity with existing data (Baumhoff, 1963; Casteel, 1972; Locay, 1992). The carrying capacity model imposes (implicitly) some very restrictive assumptions on tastes. Suppose the representative household’s tastes are repre- POPULATION EQUILIBRIUM IN PRIMITIVE SOCIETIES 753 zyxwvutsrqponm sented by a standard utility function, lJ(Z, S), where both 2 and S are normal goods. The household optimization problem is to maximize U(Z, S) subject to the food constraint, given in Equation 4. The optimal number of surviving children, S*, will be an increasing function of food production, X, and a decreasing function of r, the cost of children, S(X, r). If we assume once again that a steady state equilibrium exists when S = 2, the steady state population density is implicitly defined by: S(F(E,PE, Y) = 2 (7) It follows directly from the properties of S(X, r) that PE is an increasing function of E. I will refer to this model as the Malthusian Model. The Carrying Capacity Model is just a special case. The Malthusian, Carrying Capacity and Migration models all share the implication that all the environmental productivity indices should be positively related to steady state population density. Consequently the results of Table 1 also provide evidence against this Malthusian Model. II. THE NOMADIC WAY OF LIFE The results of Table 1 suggest that the cost of children, r, may vary systematically with the natural environment. Suppose that hunting, for example, somehow raised the cost of children. Societies where the natural environment was very productive in hunting, and consequently depended considerably on that subsistence pursuit, would face a higher cost of children. This could account for the insignificant negative effect on population density of the hunting index. I believe one important way the natural environment affects the cost of children is through the nomadic way of life. Every Indian community had to decide on how frequently to move its village or camp site. Frequent movement-being very nomadic-would keep people close to the resources they harvested. If the tribe is sedentary, by which I mean that the village or camp is not moved during the year, the length of trips to the area to be harvested can become substantial, as villagers harvested their way out from camp. Nomadism is complementary with subsistence pursuits, like hunting, which are intensive in land. Because hunting requires so much land relative to labor, one will soon harvest the area close to a camp. If camp is not moved, one ends up using more and more time just travelling to the hunting area, and less in actual hunting. By the same reasoning, labor intensive activities, such as agriculture, would not benefit from nomadism, and in fact may be discouraged, since moving camp itself takes time.5 Agriculture is not complementary with nomadism for a reason other than its labor intensity. The other subsistence pursuits are like the harvesting stage of agriculture. The stages corresponding to clearing land, planting seeds, and tending crops, are either done by nature or they are not done at all. That is 754 QUARTERLY precisely REVIEW OF ECONOMICS what distinguishes AND FINANCE zyxwvutsrqponmlkjihgfedcbaZYXWVUTSR agriculture from point is that all the stages must be performed ment of the tribe away from the agricultural plant gathering. The obvious on the same piece of land. Movelands during the growing season would mean either increased travel time to work the fields, or their neglect. The costs of nomadism will be lower for those who travel light, not only in material goods, but also in the type of persons who impose burdens on others (Sahlins, 1972; Sussman, 1972). As Marshall Sahlins describes it: ... minimum necessary equipment, elimination of duplicates, and so forththat is to say, infanticide, senilicide, sexual continence for the duration of the nursing period, etc., practices for which many food collecting peoples are well known ... the people eliminated, as hunters sometimes sadly tell, are precisely those who cannot effectively transport themselves, who hinder the movement of family and camp. Children increase the difficulty of moving, or alternatively, nomadism increases the cost of children. Continuing with the formal model, let the subscript j take on the value S if the household is sedentary, and the value N if the household is nomadic. The above discussion implies that the food requirements of children are higher in a nomadic than in a sedentary household.6 That is, rN > rs. The household food constraint, Equation 4, must be modified as follows: xj = z + q&j = N, S (8) The household must now choose 2, S, and the level of nomadism that maximize utility, U(Z, S), subject to the food constraints given in Equation 8. Food production, X, is now also subscripted zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPON by j. Equation 1 has to be modified to: Xj = 3j(E, P), j = zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQ N, S (9) where each zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Fj has the same properties as function F(E, P) did before. The solution is shown graphically in Figure 1. The household is faced with the two constraints labelled Sedentary Constraint and Initial Nomadic Constraint. Since the highest indifference curve attainable by being sedentary, the one labelled Initial Indifference Curve, corresponds to a higher level of utility than any indifference curve attainable by being nomadic, the household chooses to be sedentary. As depicted, the household chooses two children (steady state population), and adult consumption of Z*. Suppose now that there is an environmental improvement, which shifts the nomadic constraint but leaves the sedentary constraint to Improved Nomadic Constraint, unchanged. The household now prefers to be nomadic, attaining the indifference curve labelled Preferred Indifference Curve. What is of interest is that POPULATION EQUILIBRIUM IN PRIMITIVE SOCIETIES 755 surviving Children sI Z* zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Adult Initial Consumption Nomadic Z zyxwvutsrqponmlkjih constraint Choice zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA of Sedentary vs Nomadic Way of Life and Its Impact on Population Growth Figure 1. the number of children declines from two to S,,,. Population will therefore fall. The hypothetical environmental improvement made the household better off, meaning that the income effect would lead to more children and more adult 756 QUARTERLY REVIEW OF ECONOMICS AND FINANCE zyxwvutsrqponmlkjihgfedcbaZYXWVUTSR consumption. The change to nomadism, however, increased the relative price of children, making them relatively less attractive. As depicted in Figure 1, the substitution effect dominated the income effect, though of course, this need not have been the case. In general, high environmental productivity in activities that are complementary with nomadism may lead to lower population density. This is a promising explanation for the results of the index of productivity reported in Table 1. It is an unlikely explanation for the effect of the horticultural index, which had the strongest negative effect on population density, as that activity is not one I believe is complementary with nomadism. In fact it is possible that the positive effects of the productivity of some of the activities, especially irrigation agriculture and fishing, were due in part to their complementarity with sedentism, and not any income effect. In any case, it will be valuable to estimate the income and substitution effects. For that one must estimate population equations conditional on being sedentary or nomadic. If it then turns out that some activities have negative effects, one can search for what distinguishes them from those activities that have positive effects. The population equations estimated previously are not conditioned on whether or not a tribe was nomadic. The positive sign of a given variable may be due to that activity being complementary with sedentism, or it may be due to a positive income effect. There is no way to tell. In the next section I derive consistent estimates of the conditional population equations. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONM III. ESTIMATION OF CONDITIONAL POPULATION EQUATIONS For the empirical work I will assume that the utility function and the food production functions are both Cobb-Douglas.7 In logarithmic form the utility function is the following: U(Z,S) = In(S) + pin(Z) The food production Equations (10) 8, will be given the following form: (11) where P = In(P), &j is a normally distributed random variable, and PjE, & > 0 for both values ofj. The E.‘S represent unobserved variables that affect food production. They are the only source of error assumed in the model. The elasticity of food production with respect to population density is pj$. As argued before, the activities complementary with nomadism will be those that are land intensive. We would expect, therefore, that food production is more sensitive to population density changes (changes in land availability) when a household is nomadic, than when it is sedentary. In other words, a one percent increase in population should reduce food production by a larger percent under POPULATION the nomadic alternative. EQUILIBRIUM Algebraically in Equation Z, and the number of children, given in Equation SOCIETIES 757 zyxwvutsrqponm this means that l3+ > psfi. This assump- tion will be maintained throughout. Maximization of the utility function consumption, IN PRIMITIVE 10 with respect to adult S, subject to the food constraints 11, gives the following indirect utility functions: t$ = Ot + (1 + P)ln(Xj) - ln(rj), j = N, S (12) where a = Pin(P) - (1 + P)ln(l + p). A household will choose to be sedentary (nomadic) if V, > V,, (V, < V,). The steady state population density can then be obtained by setting S(Xj, rj) = 2. Given the sedentary-nomadism given by: choice, the steady state population Pj = bjo - kj + bjE E + density, in logs, is (13) Uj where k. = ln(2(1 + p)~j)/Bjp, Bj, = bjdBi*, bjE = BjEJBjp, and ~j = EjlBjF. De Ime p* as the population density at which a household is indifferent between being nomadic and substituting and being sedentary. Equation 11 into Equation tion densities above p* households p* households It is obtained prefer to be sedentary, prefer to be nomadic. by setting V, = VN, 12. It can be shown that at populaand at densities below Suppose that at low, initial population lev- els, the households of a tribe are nomadic. If they remain so, they will eventually reach steady state population density PN, given by Equation 13. If@, is below p*, the tribe will be observed to be nomadic. If p, is above p*, it will reach popula- tion density p* before it reached the steady state. At p* the tribe’s households will be sedentary. Their population will continue to grow until they reach steady state density ps, given by Equation 13. Figure 2 shows the path of children and population entary For low population labelled and the path if it is nomadic. Nomadic lies above the one labelled Sedentary. density if a tribe is seddensities the path At low population den- sities households have more children if they are nomadic. Since the cost of children is higher with nomadism, they must also have higher adult consumption. The nomadic way of life is preferred, and that is why it is drawn as a solid line, while the Sedentary path is a broken line. At population density corresponding to the point labelled Equality in Number of Children the same number of children would be chosen regardless of whether households are sedentary or nomadic. The nomadic option is still preferred, since it corresponds to higher adult consumption. This continues to be the case until population density p*, at which point the tribe becomes sedentary. If So is equal to two, the steady state population densities will be p,u and phi@ As shown in Figure 2, at p,u households prefer to be nomadic, so that L’s c V,, where the I$‘s are evaluated at p,,. It can be shown that this occurs when 758 QUARTERLY REVIEW OF ECONOMICS AND FINANCE Slllviving Children zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA S PN” P* PN1 PS’ Log of Population Density, p zyxwvutsrqponm F@re 2. Population Density and the Transition from Nomadic to Sedentary Way of Life zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA u = UN - us > b,, where A = pln(rs/rN)/((l - bNo + k, - KS + (bSE - bNE)E + zyxwvutsrqponmlkjihgfedcbaZ A (14) + P)Bs$. The right hand side of Equation 14 is just the difference between fi, and PN (see Equation 13), except for the term A. If p = 0, i.e., households care only about children after satisfying adult food needs, it is POPULATION EQUILIBRIUM IN PRIMITIVE SQCIETIES 759 zyxwvutsrqponm easy to see that A = 0. The tribe would be nomadic only if it could achieve a higher population by being so. This is exactly the carrying capacity model modified to allow for endogenous determination of whether to be sedentary or nomadic. The point of transition from nomadic to sedentary would be the one labelled Equal Number of Children in Figure 2. If p > 0, then A < 0, since rs < rN The nomadic way of life need not be as productive as in the case where l3 = 0 to be preferred, and the transition to the sedentary state will take place at a population density to the right of the one corresponding to the point Equal Number of Children. If S1 is equal to two, the steady state population densities would be p,l and ~~1. At $, households would prefer to be sedentary, and this occurs when the inequality in Equation 14 is reversed. From Maddala (I 983, p. 227) the expectation of Equation 13 can be written as follows: zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA &$I$ = b,, - k, + bs,E + (b,, -b,, + k, - k,)Q + (b,, - b,,)Ea, + (~su - ~Nu)Q, where @ and Cpare the standard normal distribution and density evaluated at {(&vo - hsoi + CbNE - bsEjE - (kh~ - ksj I- A>,%,, osTJand o,, are the covariances of US and u.,+iwith 16, and o, is the standard deviation of u. @ is the probability of being nomadic. A two step procedure described in Maddala (1983, pp. 227-228) involves using Equation 14 to estimate @ and 9. The estimated Q, and Cp are then substituted into Equation 15, and that equation is estimated by ordinary least squares. Since the error term u in Equation 14 is normally distributed, the probability that a tribe is nomadic is a probit. The data on nomadism is available in five categories; more sedentary, less sedentary, intermediate, less nomadic, more nomadic (Driver and Massey, 1957). The two sedentary categories were combined into one, as were the two nomadic categories. The intermediate category is small and was excluded from the analysis. The probit was estimated by maximum likelihood. The results are not reported here, but they are available from the autbor upon request. The results of the second stage are shown in Table 2. The environmental indices are the same, except that the index for hunting was divided into two indices, one if game animals in a tribe’s territory were primarily sedentary, and one if game animals were primarily nomadic. An interesting comparison is that of Table 1, which shows the parameter estimates of the unconditional popuhtion equation, and column one of Table 2, which shows the parameter estimates of the sedentary population equation. The most dramatically different results have to do with hunting and gathering productivity. Conditional on being sedentary, hunting productivity has a large positive effect on population density, which is s&-nificant, for both sedentary and nomadic game, at the one percent confidence level. One reason for the negative 760 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA QUARTERLY REVIEW OF ECONOMICS AND FINANCE zyxwvutsrqponmlkjihgfedcbaZYXWVU TabZe2. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Regression of Log of Population Density on Indices of Environmental Productivity Conditional on Sedentary-Nomadic Choice zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHG (Dependent Variable: Log of Population Density in Persons/ l00 km*) Variable Sedentary Constant Index for: Hunting (Sedentary Hunting (Nomadic Fishing Gathering Horticulture Irrigation Notes: Game) Game) Agriculture Nomadic -0.134 -2.235 2.130a 3.335a 1.997a -0.134 -l.lloa 3.676 1.764 -1.996 4.254 - 0.804b a. Significantly different from zero at the 1% level. b. Significantly different from zero at the 5% level. No. of Observations - 80 See Appendix for data sources. effect of hunting high hunting productivity productivity, the tribe being nomadic. in the unconditional especially The population change sedentary. high population Tribes with high gathering productivity productivity, density because they are sedentary, not because 2 than in Table complementary 1. This is as expected, with being sedentary. is due to being sedentary and not directly to the productivity productivity 1. This is surprising, with being sedentary. have gathering pro- are smaller in Part of their effect on population has an even larger, negative effect on population than in Table is associated since both of those activities This means that when you adjust for being sedentary, ture a smaller positive effect. The coefficient of fishing with coefficient therefore, ductivity has a direct positive effect on population density. The coefficients of both horticulture and irrigation agriculture Table is that is associated in the sign of the gathering seems to be due to the opposite effect. High gathering with being equation when game is nomadic, of those activities. horticultural productivity density, and irrigation is larger in column since high fishing Also of interest is the difference are density agricul- one of Table productivity 2 is associated in sign in the coefficient on fishing between the sedentary and the nomadic population equation (column two of Table 2). A possible explanation for this result will be considered in the next section. The nomadic population equation sedentary population ent from zero at the ten percent equation. with less precision None of the coefficients come closest to being significant reason is estimated for the lack of precision level. The at conventional hunting than the are significantly productivity differ- coefficients levels. I suspect that part of the in the nomadic population equation is the POPULATION EQUILIBRIUM IN PRIMITIVE SOCIETIES 761 zyxwvutsrqponm smaller number of nomadic tribes with population data, and the fact that many of them were located in the fairly homogeneous area of Baja California. One counter intuitive result is the relative magnitudes of the sedentary and nomadic game productivity indices in the sedentary and nomadic population equations. One would expect that relative to sedentary game, nomadic game would have a more important effect on population in the nomadic population equation than in the sedentary population equation. The reverse is the case. I believe this is also due to the small size of the sample. Only a few tribes with population data were in environments with nomadic game. Among sedentary tribes, only two, the Arikara and the Mandan, had nomadic game. These two horticultural tribes of the Northern Plains had population densities that were higher than expected. The nomadic game variable “ accounts” for those two unusually high population densities. Among the nomadic tribes, the most important nomadic game areas are those of three Plains tribes that were classified as “ more nomadic.” The “ more nomadic” category was combined with the “ less nomadic” because of the smallness of the sample, though the two groups may differ in terms of costs of children. If being “ more nomadic” implied higher costs of children, and therefore lower population density, then the nomadic game variable could well pick up this effect. I suspect, therefore, that the coefftcient on nomadic game is an overestimate in the sedentary population equation and an underestimate in the nomadic population equation. A similar argument about bias is applicable to the irrigation agriculture coefficient. All but one of the irrigation agriculture tribes with population data were in the “ more sedentary” category, which was combined with “ less sedentary.” If being “ more sedentary” had some cost advantage over “ less sedentary” in the production of children, then the coefficient of the irrigation agriculture productivity index will be biased upward. It will combine the direct effects of irrigation agriculture on population density, as well as some indirect effect through lower nomadism. The model of this chapter predicts that all the coefficients reported in Table 2 should be positive. They clearly are not. I have nevertheless taken the estimated coefficients in Table 2 and the probit results to estimate the term A in Equation 14. It was expected that A would be positive. It is indeed positive and statistically significant at the one percent level. This rejects the utility function that gave rise to the carrying capacity model, and also supports the assumption that the costs of children are higher if the household is nomadic. zyxwvutsrqponmlkjihgfedcbaZYX IV. THE SEXUAL DIVISION OF LABOR The results of this study reported in the previous section are consistent with the idea that population density is lower among nomadic peoples not because they are poorer (the model implies they are better off), but because the nomadic way of life encourages adult consumption and discourages children. Even after 162 QUARTERLY REVIEW OF ECONOMICS AND FINANCE zyxwvutsrqponmlkjihgfedcbaZYXWVUTSR accounting for the price effect of nomadism, however, environmental productivity often has no effect or a negative one on population density. This implies that there are overlooked price effects, and the pattern of coefficients in Table 2 suggests that I look for an explanation in the sexual division of labor. Among the Indians of North America big game hunting was an activity performed by men (Murdoc 1967). Hunting involved travelling further from camp than any other subsistence pursuit. It involved alternating periods of intensive physical effort and idleness. It is the one activity where the practitioner would have been most hampered by being pregnant or having to care for a small child. Women did most of the child rearing, and would therefore have had a comparative advantage in tasks that kept them close to camp, and which involved less fluctuation in the level of work effort. Following this line of reasoning, one would expect that women would have done most of the household chores, the plant gathering, and the agriculture. That was indeed the case. Fishing was somewhere in between gathering and hunting. Besides regular fishing, it involved shellfish gathering, which seems to be similar to plant gathering, and sea mammal hunting, which was like hunting of land animals. Women contributed to fishing, but it was predominantly a male activity. This explanation of the sexual division of labor can be restated in a more useful way. In any subsistence activity women engage in, they will be hampered to some extent by children. The cost that children will impose is the difference in the output attainable by women with and without having to care for children. This cost is so large for some activities, such as hunting, that women do not engage in them. For activities that women do perform, the output foregone because of children will be larger the more productive is the environment. Where women are productive, therefore, children are expensive. Any environmental improvement has the previously mentioned income effects, and a new price effect (the other price effect was through nomadism). Because there is always some substitutability directly between male and female labor, or indirectly between the products of their work, any increase in productivity, even in hunting, will have both income and price effects (Locay, 1992). It is reasonable to assume, however, that price effects will be larger relative to income effects, when the improvement occurs in an activity performed by women. Because hunting was practiced only by men, it would be the one activity whose productivity would most likely be positively related to population density. That has been a consistent result. At the other extreme is non-irrigation agriculture, whose productivity has been negatively related to population density. AS can be seen in Table 3, wherever that activity was practiced, women were engaged in it. Furthermore, women did nearly 90% of the work. In terms of female participation, gathering was just like non-irrigation agriculture. This is consistent with the previous finding of an insignificant or negative effect of gathering productivity on population density after accounting for the effects of nomadism. POPULATION EQUILIBRIUM IN PRIMITIVE SOCIETIES 763 zyxwvutsrqpon Table 3. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA The Sexual Division of Labor zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONM Activity Percent of Societies Whose Women Participate in this Activity Percent of Output Accounted for by Women Percent of Societies with no Overlap Between Men and Women Horticulture Gathering Irrigation Agriculture Fishing: Sedentary Nomadic 100 100 80 49 40 60 88 89 23 14 10 17 44 35 10 30 42 25 Nok: zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA See appendix for data sources. The productivity effect on population of irrigation agriculture was found to have a very different density than the productivity of horticulture. It was puz- zling because superficially they appear to be very similar activities. The big difference between these two forms of agriculture is that while participation of women in irrigation agriculture was high, they performed less than a quarter of the work. Irrigation agriculture was carried out primarily by men. Fishing was another activity which had an effect on population mediate between Conditional that of hunting on being sedentary, and that of fishing productivity non-irrigation density interagriculture. had a positive effect, while conditional on being nomadic its effect was negative. It can be seen in Table 3 that female participation in fishing was higher among nomadic societies (60%), than among sedentary ones (40%). Women in nomadic societies also performed nearly twice as much of the work in fishing as women in sedentary societies. While fishing was never a female people. In column three of Table given subsistence activity, it was even less so among 3 are given the percent of societies sedentary practicing pursuit in which men and women were not both engaged some activity. This is potentially important, for if men and women a in perform totally different activities, they will be less substitutable. The degree of substitutability between men and women will affect the relative size of price and income effects resulting from any environmental improvement. If there is no overlap between men and women, an environmental improvement in an activity performed by men will have a smaller price relative to income effect, while an improvement in an activity performed by women will have a larger price relative to income effect. The figures in column three of Table 3 support the earlier empirical findings. A higher percent of societies engaged in horticulture had no overlap between men and women, than for those societies engaged in gathering. Since these are primarily female activities, it is consistent with the stronger negative effect on population density found for the productivity of horticulture than for 764 QUARTERLY REVIEW OF ECONOMICS AND FINANCE zyxwvutsrqponmlkjihgfedcbaZYXWVUTSR that of gathering. Among sedentary fisherman there was less overlap between men and women, than among nomadic fisherman. Since fishing was primarily a male activity, this is consistent with the finding of a positive effect for fishing productivity on population density for sedentary peoples, but the opposite for nomads. V. CONCLUSION We are accustomed to thinking of primitive peoples as being like today’s subsistence farmers. The present day’s subsistence farmers, of course, tend to have among the highest fertility rates. But primitive peoples, at least those in aboriginal North America, were in a very different situation from today’s subsistence farmers. For the Indians of North America agriculture was the least land intensive of all major work activities, while today it is among the most land intensive activities. Today’s subsistence farmer is probably not much more sedentary than the town or city dweller. In aboriginal North America only some tribes in acornsalmon-game rich California and in the salmon rich Pacific Northwest were as sedentary as horticulturalists. None were as sedentary as the farmers of the Pueblos. Much of the positive effect on population attributed to agriculture is really due to sedentism. Furthermore, with the exception of the Pueblos and portions of Mexico, which were most like today’s subsistence farmers (and had the highest population densities), agriculture was carried out by women. There are reasons to believe why such women may have been quite productive. First of all they had a large amount of land available per worker, even when one takes into account that much land was not arable by the Indians because of the technology they had available. Secondly, since the men were hunters and fishermen, households had significant supplies of meat that would increase the value of the complementary vegetable foods from agriculture and gathering, and thus increase the productivity of women (the value of their product). It is widely known that nomadic peoples engage in a variety of practices that reduce fertility and increase infant mortality.8 I, too, have found that among the tribes in my data set the period of post partum sexual abstinence is longer for nomadic than for sedentary tribes (Locay, 1992). More surprisingly is my finding that horticultural and gathering productivity is also associated with a substantial lengthening of the period of abstinence. The data used here are hardly of ideal quality, and the sample size is fairly small. When one tries to incorporate information on the sexual division of labor, the size of the sample of societies with all the necessary information becomes too small to do much more than present some simple tables. But the consistency of the results argues strongly that we should reconsider our view of how primitive peoples make their demographic decisions, as we have been forced to rethink our views of so much of their other behavior. POPULATION ~ ~ owl~ grnen~ EQUILIBRIUM IN PRIMITIVE SOCIETIES 765 zyxwvutsrqponm I wish to thank David Weir for his zyxwvutsrqponmlkjihgfedcbaZYXWVUTSR useful comments on an earlier draft. APPENDIX zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQ Sources of zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Data By far the most time consuming part of this work has been putting together the basic data set. I can only give the reader a glimpse of how it was done. The most important variable was population density. The most common sources for population data are the estimates provided by early European explorers. These are most commonly reported in terns of warriors. Sometimes numbers of houses or villages are available, and occasionally a census or archeological information. Conversion to population was made using the best conversion ratios that could be estimated. Some population estimates are from after the first or second epidemic resulting from the introduced European diseases. Such population estimates were adjusted by assuming a 57% mortality rate.9 With a few exceptions, sizes of tribal areas were taken from Kroeber (1939). A tribe by tribe account of how aboriginal population estimates were derived is available from the author. The environmental productivity measures are indices of environmental variables. Hunting productivity is simply the logarithm of large herbivore biomass (number of animals times average weight), which itself was estimated by a laborious process. Fishing productivity is a linear function of the logarithm of the sustainable yield of fresh water fish (from Baumhoff,1963), the fraction of that yield that is accounted for anadromous fish (those that spend part of their lives in salt water and return to freshwater in runs), and the logarithm of one plus shoreline per unit of tribal area. Gathering and agricultural indices were even more complicated. Each tribe’s territory was separated into grassland, shrubland or scrubland, woodland, needle leaf forest, broad leaf forest, and tundra. Estimates of seed production for each vegetation type (by location) were made, along with estimates of canopy height for forest environments. The gathering index is a linear combination of seed production by vegetation type times the share of the total territory covered by that vegetation type, and the product of canopy height, seed production, and share of territory, for each forest environment. Separate indices were constructed for horticulture and irrigation agriculture. The non-irrigation index takes on the value zero if the territory was unsuitable for agriculture, or if irrigation was used. An environment was classified as being unsuitable, if the average growing season was less than 100 days, if the probability of drought in July was very high, and if solar efftciency was below 50%. For suitable environments the horticulture index is a linear combination of the length of the growing season above 100 days and below 130, the length of the growing season above 130 days and below 160, growing season rainfall, the frac- 766 QUARTERLY REVIEW OF ECONOMICS AND FINANCE zyxwvutsrqponmlkjihgfedcbaZYXWVUTSR tion of the territory in forest, the fraction in broad leaf forest, and a dummy for whether or not there was any territory covered by broad leaf forest.” The irrigation agriculture index consists of a dummy variable for the presence of irrigation, and the product of that dummy variable and growing season rainfall. With the exception of the hunting index, all indices are linear functions of several variables. The weights were computed by fitting a transformation of the share of subsistence accounted for by each of the four subsistence pursuits to the environmental variables just described. The fit was good, and the signs of the coefficients were reasonable. A more detailed explanation is available from the author. Shares of subsistence accounted for by the various pursuits were taken from Murdoc (1967), as was information on the sexual division of labor. Murdoc (1967) classifies the participation of women in the various subsistence activities as follows: 1. 2. 3. 4. 5. Females alone perform the activity, male participation being negligible. Both sexes participate, but females do appreciably more. Equal participation by both sexes. Both sexes participate, but males do appreciably more. Males alone perform the activity, female participation being negligible. I have assigned the values of 1, 0.75, 0.5, 0.25 and 0 to the above categories for the computations in Table 3 of the share of work performed by women. Finally, data on the degree of nomadism were taken from Driver and Massey (1957). NOTES *Direct all correspondence to: Luis Locay, University of Miami, Department of Economics, P.O. Box 248126, Coral Gables, FL 33124-6550. 1. For an account of the occupation of the Old and the New World and its relationship to population growth, see Cohen (1977). A model of the effects of such population growth on the transition to agriculture is given in Locay (1988). 2. This is the form in which the data are available. Animal husbandry was not practiced in North America. The data come from Murdoc (1967). 3. There is also the view that population growth is itself a major cause of change in technology and in the organization of production. See Boserup (1965) and Cohen (1977). This is considered below, but the main concern here is with the determinants of population density. 4. I am assuming that carrying capacity is appropriately defined. As mentioned previously, it may have to defined as the carrying capacity of the worse year. 5. It may seem strange to the reader to think of agriculture as labor intensive and not land intensive, but remember that the comparison is with activities such as hunting, gathering and fishing. 6. Again recall that food is the only resource here. In reality nomadic children may not require more food to survive, but more of other resources, such as their parents’ time and care (e.q., by being carried). 7. Cobb-Douglas is easy to work with and sufficiently general for my purposes here. POPUIATION EQUILIBRIUM IN PRIMITIVE SOCIETIES 767 zyxwvutsrqponm 8. See the earlier quotation from Marshall Sahlins. 9. This rate was computed from those societies with both pre and post-epidemic estimates. 10. The important role of forest is because the implements of the Indians were not suitable for breaking up the tough grasses of open land (Driver and Massey, 1957, p. 225). REFERENCES Branhoff, M. H. 1963. “ Ecological Determinants of Aboroginal California Populations,” University of California Publications in zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONML Avnerican Archeology and Ethnology, 49(2). Berkeley: University of California Press. Blanton, R.E. 1975. “ The Cybernetic Analysis of Human Population Growth,” The Memoirs of the Society for American Archeology, 30: 116-125. ‘Boserup, E. 1981. Population and Technological Change: A Study of Long-Term Trends. Chicago: University of Chicago Press. Casteel, R.W. 1972. “ Two Static Maximum Population-Density Models for HunterGatherers: A First Approximation,” W orld Archeology, 4: 19-39. Cohen, M. 1977. The Food Crisis in Prehistovy: Overpopulation avnd the Origins ofAgriculture. New Haven: Yale University Press. Driver, H.E. and W.C. Massey. 1957. “ Comparative Studies of North American Indians,” Transactions of the Avnerican Philosophical Society, 4 7: 165-456. Gross, D. 1984. “ Time Allocation: A Tool for the Study of Cultural Behavior,” Annual Review of Anthropology, 13: 5 19-558. Grossbard, A. 1974. “ An Economic Analysis of Polygyny: The Case of the Maiduguri,” Current Anthropology, 17: 701-707. Heindenreich, C. 197 1. Huronia: A History and Geography of the Huron Indians 1600-l 650. Ontario: McClelland and Stewart. Kroeber, A.L. 1953. Cultural and Natural Areas of North America. Berkeley: University of California Press. Locay, L. 1989. “ From Hunting and Gathering to Agriculture,” Econovnic Development and Cultural Change, 37: 737-756. 1992. Population Equilibriuvn in Privnitiue Societies. Unpublished manuscript. -. Maddala, G.S. 1983. Livnited-Dependent and Other Qualitative Variables in Econometrics. Cambridge: Cambridge University Press. Murdoc, G.P. 1967. Ethnographic Atlas. Pittsburgh: University of Pittsburgh Press. Posner, R.A. 1980. “ A Theory of Primitive Society, with Special Reference to Law,” Journal Rostlund, of Law and Economics, 23: 1-53. E. 1952. “ Freshwater Fish and Fishing in Native North America,” University of California Publications in Geography, 9. Berkeley: University of California Press. Sahlins, M. 1972. Stone Age Economics. Chicago: Aldine Press. Smith, V. 1975. “ The Primitive Hunter Culture, Pleistocene Extinction, and the Rise of Agriculture,” Journal of Political Economy, 83: 165- 174. Sussman, R.W. 1972. “ Addendum: Child Transport, Family Size and Increase in Human Population During the Neolithic,” Current Anthropology, 13: 258-259.