A stochastic version of the malthusian trap model: Consequences for the empirical relationship between economic growth and population growth in LDC's

A stochastic version of the Malthusian trap model relating the growth rate of income per capita to the population growth rate of a given country is described. This model is applied to the a priori evaluation of the cross‐sectional correlation between these two growth rates under two additional assumptions: i) the relations in the model at national levels include country‐specific and time‐invariant random components, and ii) these growth rates are measured with a certain degree of temporal aggregation. It is shown that these two assumptions can explain near‐zero correlations between the two growth rates even if there exist a strongly negative effect of population growth on economic growth. However it is not clear whether these assumptions fully explain such insignificant correlations. Indeed, the implementation of the model is complicated by the structural shifts which are likely to occur in the equations over the course of the demographic transition.     

Age structure,growth, attrition and accession: A new synthesis

This paper shows that each equation describing relationships among demographic parameters in a stable population is a special case of a similar and equally simple equation that applies to any closed population and demonstrates some implications of these new equations for demographic theory and practice. Much of formal demography deals with functions that pertain to individuals passing through life, or to a stationary population in which births of individuals are evenly distributed over time. These functions include life expectancy, probabilities of survival, net and gross reproduction rates, expected years spent in various states and the probability that certain events will occur in the course of life. The stable population model permits the translation of population structure or processes in a more general type of population, with constant growth rates, back into equivalent populations for a stationary population. The method for translation developed in this paper, requiring only a set of age-specific growth rates is even more general, applying to any population. Age specific growth rates may also be useful for performing reverse translations, between a population's life table and its birth rate or its age distribution. Tables of numbers of females by single years of age in Sweden are used to illustrate applications. Tables summarize the basic relations among certain functions in a stationary population, a stable population and any population. Applications of new equations, particularly to demographic estimation of mortality, fertility and migration, from incomplete data, are described. Some other applications include; the 2 sex problem, increment decrement tables, convergence of population to its stable form, and cyclical changes in vital rates. Stable population models will continue to demonstrate long term implications of changes in mortality and fertility. However, in demographic estimation and measurement, new procedures will support most of those based on stable assumptions.     

Age-specific growth rates: The legacy of past population dynamics

Recent developments in population mathematics have focused attention on a function that is widely available but rarely examined: the set of age-specific growth rates in a population. In particular, this set of rates is sufficient for translating the current birth rate and age-specific mortality rates into the current age distribution. This growth-rate function contains all of the pertinent features of a population's demographic history that are required to relate major demographic functions for a particular period to one another. This article presents an expression for the age-specific growth rate and uses it to derive an equation for age distribution. We show how the value of the age-specific growth rate is determined by a population's demographic past and present various sets of growth rates corresponding to stylized demographic scenarios. Several noteworthy sets of growth rates observed in human populations are discussed. Finally, we explain why age-specific growth rates make it possible to determine the age distribution solely from information on current demographic conditions.     

A stochastic computer model for simulating population growth

Summary A model is described for investigating the interactions of age-specific birth and death rates, age distribution and density-governing factors determining the growth form of single-species populations. It employs Monte Carlo techniques to simulate the births and deaths of individuals while density-governing factors are represented by simple algebraic equations relating survival and fecundity to population density. In all respects the model’s behavior agrees with the results of more conventional mathematical approaches, including the logistic model andLotka’s Law, which predicts a relationship betwen age-specific rates, rate of increase and age distribution. Situations involving exponential growth, three different age-independent density functions affecting survival, three affecting fecundity and their nine combinations were tested. The one function meeting the assumptions of the logistic model produced a logistic growth curve embodying the correct values orr _m andK. The others generated sigmoid curves to which arbitrary logistic curves could be fitted with varying success. Because of populational time lags, two of the functions affecting fecundity produced overshoots and damped oscillations during the initial approach to the steady state. The general behavior of age-dependent density functions is briefly explored and a complex example is described that produces population fluctuations by an egg cannibalism mechanism similar to that found in the flour beetleTribolium. The model is free of inherent time lags found in other discrete time models yet these may be easily introduced. Because it manipulates separate individuals, the model may be combined readily with the Monte Carlo simulation models of population genetics to study eco-genetic phenomena.     

The present value of population growth in the western world

Abstract In conventional steady-state growth theory with technical progress exogenous, faster population growth causes lower consumption. This conclusion has influenced national policies. With technical progress endogenous, however, higher population growth causes higher consumption. Steady-state equilibrium analysis is not appropriate for policy decisions, though. Rather, appropriate analysis compares two or more growth rates beginning from equal initial positions, with comparison of the present value of consumption streams per person. In the paper the supply of and demand for knowledge is first analysed and the most plausible technical progress functions are derived. Various population growth rates are then simulated with different specifications and parameters. With virtually every variant, faster population growth shows better consumption with discount rates up to between five and ten per cent above the long-run adjusted riskless rate. With pensions included in the analysis, faster population growth would seem even more beneficial. Even at very high discount rates, lower population growth rates imply present values only a little higher than those for higher population growth rates. The advantage is overwhelmingly with higher population growth in this growth-theoretic analysis.     

Ethnic population projections for the UK, 2001–2051

This paper reports on projections of the United Kingdom’s ethnic group populations for 2001–2051. For the years 2001–2007 we estimate fertility rates, survival probabilities, internal migration probabilities and international migration flows for 16 ethnic groups and 355 UK areas. We make assumptions about future component rates, probabilities and flows and feed these into our projection model. This model is a cohort-component model specified for single years of age to 100+. To handle this large state space, we employed a bi-regional model. We implement four projections: (1) a benchmark projection that uses the component inputs for 2001; (2) a trend projection where assumptions beyond 2007 are adjusted to those in the UK 2008-based National Population Projections (NPP); (3) a projection that modifies the NPP assumptions and (4) a projection that uses a different emigration assumption. The projected UK population ranges between a low of 63 millions in 2051 under the first projection to a high of 79 million in the third projection. Under all projections ethnic composition continues to change: the White British, White Irish and Black Caribbean groups experience the slowest growth and lose population share; the Other White and Mixed groups to experience relative increases in share; South Asian groups grow strongly as do the Chinese and Other Ethnic groups. The ethnic minority share of the population increases from 13% (2001) to 25% in the trend projection but to only 20% under our modified emigration projection. However, what is certain is that the UK can look forward to be becoming a more diverse nation by mid-century.     

Aids and population growth in sub-Saharan Africa: Assessing the sensitivity of projections

Despite different models to project the course of the AIDS pandemic and a scarcity of data to provide standard input parameters for those models, a limited consensus emerges from distinct sets of population projections. In sub-Saharan Africa, population growth rates are projected to remain positive in spite of the pandemic over the next few decades. To investigate this conclusion, alternative projections of an HIV/AIDS epidemic and its related mortality are first produced from different sets of input parameters and assumptions. Their incorporation into the population projections of a fast-growing country illustrates the robustness of projected population growth rates under very different scenarios of the future epidemic but with the common assumption that it will not affect the mortality of the uninfected population, fertility nor migration. This paper then shows that the projected growth rates are much less robust when interactions between the epidemic and the demographic regime are allowed and identifies several potential mechanisms for such interactions. In particular, it suggests that improving our confidence in the medium-term projections of the demographic impact of AIDS in the region requires less a refinement of the projections of the epidemic than a better understanding of its impact on the timing of the postulated fertility decline.     

A population dynamic model of Batesian mimicry

Summary A population dynamic model of Batesian mimicry, in which populations of both model and mimetic species were considered, was analyzed. The probability of a predator catching prey on each encouter was assumed to depend on the frequency of the mimic. The change in population size of each species was considered to have two components, growth at the intrinsic growth rate and carrying capacity, and reduction by predation. For simplicity in the analyses, three assumptions were made concerning the carrying capacities of each population: (1) with no density effects on the mimic population growth rate; (2) with no density effects on the model species; and (3) with density effects on both species. The first and second cases were solved analytically, whereas the last was, for the most part, investigated numerically. Under assumption (1), two stable equilibria are possible, in which both species either coexist or go to extinction. Under assumption (2), there are also two stable equilibria possible, in which either only the mimic persists or both go to extinction. These results explain the field records of butterflies (Pachliopta aristolochiae and its mimicPapilio polytes) in the Ryukyu Islands, Japan.     

The optimum growth rate for population reconsidered

This article gives exact general conditions for the existence of an interior optimum growth rate for population in the neoclassical two-generations-overlapping model. In an economy where high (low) growth rates of population lead to a growth path that is efficient (inefficient), there always exists an interior optimum growth rate for population. In all other cases, there exists no interior optimum. The Serendipity Theorem, however, does, in general, not hold in an economy with government debt. Moreover, the growth rate for population that leads an economy with debt to a golden rule allocation can never be optimal.      

Age structure and capital dilution effects in neo-classical growth models

Economists often over estimate capital dilution effects when applying neoclassical growth models which use age structured population and depreciation of capital stock. This occurs because capital stock is improperly characterized. A standard model which assumes a constant depreciation of capital intimates that a population growth rate equal to a negative constant savings ratio is preferable to any higher growth rate. Growth rates which are lower than a negative constant savings ratio suggest an ever growing capital/labor ratio and an ever growing standard of living, even if people do not save. This is suggested because the natural reduction of the capital stock through depreciation is slower than the population decrease which is simply unrealistic. This model overlooks the fact that low or negative growth rates result in an ageing of the capital stock, and this ageing subsequently results in an increase of the overall rate of capital depreciation. In that overly simplistic model, depreciation was assumed independent of the age of the captial stock. Incorporating depreciation as a variable into a model allows a more symmetric treatment of capital. Using models with heterogenous capital, this article explores what occurs when more than 1 kind of capital good is involved in production and when these various captial goods have different lengths of life. Applying economic models, it also examines what occurs when the length of life of capital may vary. These variations correct the negative impact that population growth can have on per capital production and consumption.     

Population aging, health care, and growth: a comment on the effects of capital accumulation

In a recent paper, Hashimoto and Tabata (J Popul Econ 23:571–593, 2010) present a theoretical model in which the increase in the rate of dependence due to aging of the population leads to a reallocation of labor from non-health to health production and, as a consequence, to a decline in economic growth. We argue that these results rely heavily on assumptions of a “small economy” and perfect capital mobility, which tie down the amount of capital. In this paper, we proceed by analyzing the case of an economy in which the availability of capital is endogenously determined by domestic savings. We find that the new “capital accumulation effect” is opposite to the previous “dependency rate effect,” leaving the effect on economic growth ambiguous. In particular, if the former prevailed, population aging would foster economic growth, a result that finds support in recent empirical work.     

The effects of economic and population growth on national saving and inequality

This is a progress report on ongoing research into the effects of economic and population growth on national saving rates and inequality. The theoretical basis for the investigation is the life cycle model of saving and inequality. We report evidence that is conditional on the validity of the model, as well as evidence that casts doubt on it. Using time series of cross-sectional household surveys from Taiwan, Thailand, Britain, and the United States, we show that it is possible to force a life cycle interpretation on the data on consumption, income, and saving, but that the evidence is not consistent with large rate-of-growth effects, whereby economic and population growth enhances rates of national saving. The well-established cross-country link between economic growth and saving cannot be attributed to life cycle saving, nor will changes in economic or population growth exert large effects on saving within individual countries. There is evidence in favor of the life cycle model’s prediction that within-cohort inequality of consumption and of total income—though not necessarily inequality of earnings-—should increase with the age of the cohort. Decreases in the population growth rate redistribute population toward older, more unequal, cohorts, and can increase national inequality. We provide calculations on the magnitude of these effects.     

An interest-group theory of population growth

This paper applies the interest-group theory of government to explain population growth. The main argument is that countries whose populations are more ethnically heterogeneous will tend to have higher fertility rates because there are more interest groups which compete for control of the political process of wealth redistribution. The theoretical model is supported by empirical evidence using data on 130 countries for 1980.Wangui Kimenyi helped code the data set. Remaining errors are our responsibility.     

Population growth,economic development and family planning

This report discusses research conducted to determine whether reduction in population growth rates contributed to the rapid economic growth of Indonesia, South Korea, Japan and Thailand. The 5-year research projects, jointly sponsored by the UN Fund for Population Activities, the Nihon University Population Research Institute, and the East-West Population Institute, concluded that development and family planning programs contributed substantially to fertility decline in these countries. The project examined 3 factors that influence the long-term productive capacity and growth of the 4 Asian economies: savings, the size of the labor force, and the quality of labor (measured by educational attainment). Available evidence indicates a strong positive contribution of population decline toward growth of savings, a growth in labor force concurrent with a decline in fertility rates which enables per capita income to rise, and an increase in 2ndary education enrollment ratios as fertility is lowered. Development factors by themselves explain no more than 1/2 of the decline in fertility observed, suggesting that family planning programs particularly in Thailand, South Korea and Indonesia since 1976 have had an important impact on fertility and economic development.     

World population growth and the food supply]

The general trend in the last several hundred years has been that the speed of growth in the food supply exceeds the speed of the population growth. For the time being, 2 major problems still exist. The 1st problem is that food production is still influenced by natural conditions. For example, abnormal weather conditions may cause regional food shortages. The 2nd problem is the imbalance of food consumption by the world population. This phenomenon exists between different social classes as well as between developed and developing countries. According to statistics released by the World Bank, 1 billion suffer from malnutrition today and most of them are in developing countries. In developed countries, about half of their increase in the food supply is for feed grains, and those countries follow the policy of reducing farm land for the purpose of maintaing stabl e grain prices. Up to the present time, grain prices have been unstable, and this has become a rather heavy economic burden for numerous developing countries. Many developing countries are trying to increase grain production by increasing their arable land and promoting their cultivating techniques. However, these countries are facing the problems of finding and adequate water supply, fertilizer, and pesticides. In addition, a rapid population growth in these countries has offset their endeavors in agriculture. In recent years, these counties have realized the necessity of birth control. The world population growth rate has decreased from 2% to about 1.7% in 1981. Birth control and an increase in the food supply will bring new hope to the world's problems of overpopulation and food supply.     

Empirical analysis of the contribution of age composition to population growth

The method of decomposition is applied to rates of natural increase in order to elucidate the role played by age composition in the growth of populations. A population’s age distribution and fertility schedule are contrasted to those in a "stationary" population having the same mortality rates and having a fertility schedule equal to that of the observed population divided by its net reproduction rate. In this manner it is shown that about one-quarter to one-third of the growth of most current high-growth populations can be attributed to non-stationarity of their age distributions. This fraction will rise, as it has in most industrialized countries, if fertility is reduced and age distributions become middle-heavy. In projections of the 1963 Venezuelan female population with fertility rates declining by 20/0 and 1% annually, more than half of the growth (in numbers) that occurs prior to zero-growth attainment is contributed by non-stationarity of its intervening age distributions.

     

A preliminary analysis of negative population growth in Taicang County]

This report attempts to analyze the negative population growth and its significance in Tai-Cang County, China. Based on population data provided by local Tai-Cang authorities, family planning effectively lowered the birth rate from 11.9% between 1960-1969 to 3.0% between 1979-1983. The rate of single-child families grew enormously while the number of 2-child families reached a record low. Families with more than 2 children virtually vanished by 1983. Moreover, while a younger marriage age in 1981 and 1982 contributed to a slight increase in the birth rate, new marriage laws in 1983 caused an older marriage age and acted to lower the birth rate due to the fact that mothers were bearing children at an older age. A change in population components also influenced this low birth rate: the county population below the age of 14 is 21.2% compared with 33.6% nationally; however, the percentage of the population in this county over the age of 65 is 8.5% while the national figure is 4.9%. Finally, the marriagable population of females (i.e., 23 years old) was slightly lower between 1982-1984 due to the low birth rate seen from 1959-1961. The findings indicate that family planning is effective in lowering birth rates along with late marriages and older childbearing ages. The negative population growth in Tai-Cang County, however, is a temporary phenomenon. The indications are that the problems and shortcomings of family planning must be overcome, regional population planning must be improved, and the study of eugenics and optimum population reinforced. The report also notes that the population trend is toward aging.     

Land tenure, population, and long-run growth

This paper brings together the development literature on land tenure with current research on population and long-run growth. Landowners make a decision between fixed rent, fixed wage, and sharecropping contracts to hire tenants to operate their land. The choice of tenure contract affects the share of output going to tenants, and within a simple unified growth model, this affects the relative price of food and therefore fertility. Fixed wage contracts elicit the lowest fertility rate and fixed rent contracts the highest, with sharecropping as an intermediate case. The implications of this for long-run growth depend on the assumptions one makes about scale effects in the aggregate economy. With increasing returns to scale, as in several models of innovation, fixed rent contracts imply higher growth through a market size effect. Without such increasing returns, though, fixed rent contracts reduce output per capita through a depressing effect on accumulation.     

Polygyny and the rate of population growth

Summary The roots, motives and feasibility of practising polygyny in societies with a balanced sex structure and the effect of polygyny on the rate of population growth are considered. High demand for labour combined with limited supply over the last several centuries, had been conducive to the evolution of a polygynous nuptiality pattern. The unprecedentedly high rates of population growth during the last several decades combined with progressive economic development have led to a change in the role of the labour factor and consequently diminished its impact upon polygyny. Polygyny is feasible because of a sex-age differential at first marriage, which enables younger cohorts of women to enter the marriage market, and thus results in a very early age at first marriage and universal incidence of marriage among women. A very young pattern of nuptiality inevitably evolves under polygyny, which tends to raise the rate of population growth. No significant variation in fertility between polygynous and monogamous women was found but substantial gaps in standards of living, child mortality, and educational attainment were noted for polygynous households. The findings imply that during the transition from polygyny to monogamy family size will tend to diminish, although initially fertility may not decline concurrently with changing socio-economic status. The most important effects on the rate of population growth thus result from the increase in age at first marriage and declining proportions of ever married women.     

Major studies on population authorized by United States Congress

The Office of Technology Assessment, acting on a request from the U.S. Congress, will undertake 2 major population studies in the near future. The goal of the studies will be to facilitate U.S. policy formulation over the next couple of decades. The 1st study will attempt 1) to assess the impact of efforts make by national government to alter birth rates between 1960-1980; 2) to predict the effects of population growth utilizing different assumptions concerning family planning; 3) to identify the types of population issues which will emerge in the period 1980-2000; and 4) identify research priorities aimed at clarifying these issues. The 2nd study will 1) investigate current contraceptive technology; 2) attempt to define a perfect contraceptive; and 3) examine the prospects of contraceptive technology between 1980-2000.