Economic Consequences of Rapid Population Growth Author(s): Stephen Enke Reviewed work(s): Source: The Economic Journal, Vol. 81, No. 324 (Dec., 1971), pp. 800-811 Published by: Wiley on behalf of the Royal Economic Society Stable URL: http://www.jstor.org/stable/2230318 . Accessed: 13/02/2013 15:43
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ECONOMIC CONSEQUENCES OF RAPID POPULATION GROWTH1
I. INTRODUCTION
"POPULATION" was a major concern of the early classical economists. But subsequently it was forgotten by the profession for over half a century. Today, when the consequences of population growth are so especially im- portant for the Less Developed Countries (L.D.C.s), barely a dozen econo- mists are writing articles on population issues.2
Described below are the principal conceptual findings of a small group of economists that has been working together during the past few years on various projects concerning interactions between population growth and economic development.3 None of their conclusions has hitherto appeared in an economic journal.4 The time has come to present to economists the more important conclusions of this team research as described in various TEMPO publications.5
These conclusions for Less Developed Countries (L.D.C.s) relate to (a) distinctions between size, growth and fertility of population; (b) the impact of fertility reduction on income per capita; and (c) the international conse- quences of fertility differentials among countries.6
II. DISTINGUISHING POPULATION SIZE, GROWTH AND FERTILITY
It is necessary for economic analysts to distinguish among the economic incidence of population size, population growth, and population fertility.
Whether a country has a " large " or " small " absolute population usually should refer to the size of its total population (or labour force) relative
1 The author is Manager of Economic Development Programs, TEMPO, General Electric's Centerfor Advanced Studies, located in Santa Barbara, California. He wishes to acknowledge the assistance of Richard A. Brown of the TEMPO staff. He also has an obvious indebtedness to present and former colleagues as listed below, in footnote 3.
2 Including J. J. Spengler, James E. Meade, Goran Ohlin, Colin Clark, Henry Leibenstein, AnsleyJ. Coale and the author.
3Most of the analyses presented here were done under contract to the United States Agency for International Development. Colleagues have included Richard G. Zind, James P. Bennett, William E. McFarland, DonaldJ. O'Hara, Ross D. kckert, Arthur S. DeVany, David N. Holmes and Richard A. Brown. However, the author is alone responsible for the views expressed here.
4 Instead they have appeared in such non-economic journals as Science [3], the Journal of Biosocial Sciences, [6], and Policy Sciences [5].
5 See [1, 2, 4, 12, 13, 14 and 15], all published by TEMPO, Santa Barbara, California, and available through it or U.S.A.I.D., Office of Population, in Washington, D.C.
6 TEMPO studies in population have also concerned the incidence of zero population growth in the United States, hardly attainable before A.D. 2040, upon different industries and factor incomes [10].
800
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DEC. 1971] ECONOMIC CONSEQUENCES OF RAPID POPULATION GROWTH 801
to the availabilities of usable natural resources and/or produced domestic capital. This contrasts with population densities per square kilometer, which by themselves have little economic meaning. An economy with little capital per worker is likely to have a low level of consumption, and this situation will be worsened if " land " (natural resources) is also scarce. A population in this sense may be too large or small regardless of its rate of growth. In terms of available capital, Mauritius has a " large " population compared to that ofJapan, for example.
Where an already " large " population is combined with rapid natural increase and high fertility, as in lands of ancient culture such as China and India, the demographic-economic situation is at its worst.
The economic danger of rapid population growth lies in the consequent inability of a country both to increase its stock of capital and to improve its state of art rapidly enough for its per capita income not to be less than it otherwise would be. If the rate of technological innovation cannot be forced, and is not advanced by faster population growth, a rapid propor- tionate growth in population can cause an actual reduction in income per capita. Rapid population growth inhibits an increase in capital per worker, especially if associated with high crude birth rates that make for a very young age distribution. This is regardless of population densities. Al- though Brazil has a low population density in terms of " land," its population growth rate appears uneconomically high for adequate capital accumulation, and more babies cannot usefully populate its " empty " lands.'
High fertility rates have the demographic effect of increasing the propor- tionate number of children.2 A country with a crude birth rate of over 40/1000 a year is likely to have over 40 % of its population under 15 years of age. Youngsters under 15 years of age are significant consumers but in- significant producers. Large families including many children, with conse- quently low incomes per family member, are comparatively poor contribu- tors to domestic saving. Low savings per capita are associated with " young" populations and high fertility.3
1 Many less developed countries (L.D.C.s) include large areas of unpeopled " empty " land that superficially seem to invite extra population for their development-as for instance the Amazon Basin of Brazil. Unfortunately for this easy analysis, high fertility means more babies born, not in the Amazon Basin but where their mothers are in Sao Paulo, Rio, Recife, etc. Even assuming that high fertility eventually causes a migration of adult workers into the Amazon Basin, they would have very low productivity without accompanying capital. And it is no accident that capital does not flow into this area, bringing people with it as during the rubber boom days, but instead is profitably invested elsewhere. The " empty " land argument for high fertility proves invalid on analysis for most L.D.C.s.
2 Age distribution is far more sensitive to age-specific fertility rates than to age-specific mortality rates.
3A very young age distribution, resulting from high fertility rates, ordinarily reduces the absolute value of domestic savings and investment. This is because there are disproportionately few adults of working age, so that G.N.P. is less than otherwise. This lower output effect is not fully offset by the fact that a population with disproportionately many children usually consumes less from a given G.N.P., even allowing in less developed countries for increasing expenditures on schooling.
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802 THE ECONOMIC JOURNAL [DEC.
Public health measures have led to rather dramatic reductions in age specific death rates, especially during the past 25 to 35 years, in poor and backward countries. The " killing" epidemics such as cholera have been far more successfully controlled than "crippling " diseases such as bilharzia. Continued high fertility rates have meanwhile led to natural population increases of 2-3 % a year that double population every 35 to 23 years respec- tively. Indeed, although often ignored, one of the characteristics most distinguishing backward from advanced countries is a high birth rate of over 35 per 1,000 a year (e.g., Indonesia as contrasted withJapan). Among countries as within countries, high fertility seems to cause relative poverty, besides often being a consequence of it.
If a nation's population is to increase naturally at X% a year, it is better that this result from low rather than high crude birth and crude death rates. A 1 % annual increase for example, resulting from birth and death rates of 45 and 35 per 1,000, will be associated with more brutish living than if it were the outcome respectively of rates of 25 and 15 per 1,000 a year. In the latter case the ratio of children to work age adults will be lower, investment from domestic savings should be absolutely greater, and the income per equivalent consumer will be greater.'
In human terms, and perhaps far more important, low birth and death rates mean that there are fewer unwanted infants born too soon and fewer premature deaths. "Balanced " public health programmes that include birth as well as death" control " could give each family a little more security. Perhaps the true essence of economic development is that it gives families and individuals more command over their lives.2
III. ECONOMIc DEVELOPMENT THROUGH REDUCING FERTILITY
The economic development of L.D.C.s has many facets, but most of these, such as levels of education and health, availability of capital per worker and adequacy of infrastructure, tend to be associated with output and hence also income per capita. Thus higher ratios of G.N.P. to population can usually serve as a surrogate for economic improvement. Moreover, although
1 The " equivalent consumer " concept accounts for the fact that relative consumption varies with age and sex. Thus children typically consume less private and public sector goods and services than do adult males of working age. Hence, the increase in output (or income) per head that ordinarily follows in an L.D.C. from a reduction in fertility somewhat overstates the improvement in individual welfare, simply because there are now relatively fewer children and more adults. One solution is over time to divide G.N.P. not by absolute population but by the estimated number of equivalent consumers. (See [6], pp. 48, 49.)
2 It is sometimes erroneously supposed that, because income per capita can arithmetically be increased by having a smaller population, public health programmes should concentrate more on preventing births and less on postponing deaths. However, families are more likely to save, invest and innovate, making and following plans for their own financial advancement, if uncertainties regarding deaths can be reduced. In circumstances of frequent, unpredictable and premature deaths in a family, planning and executing courses of action are inhibited, except that of having more births to replace deaths.
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1971] ECONOMIC CONSEQUENCES OF RAPID POPULATION GROWTH 803
governments have customarily concentrated on accelerating the G.N.P. growth numerator, an increasing number of L.D.C.s are now also concerned with slowing the population growth denominator.
Rationally, if a government intends to spend $X over, say, 10 years to increase output per head, it should estimate whether it could achieve a greater increase in this ratio through expenditures on birth control than on invest- ments in physical capital. Certainly, where the marginal product of labour approaches zero, a reduction in births for, say, a decade must raise per capita income later. In this case, expenditures for contraception must be many times more effective per dollar in raising per capita income than expenditures for plant and equipment.'
Where labour has a very low marginal product relative to that of capital, which is reputedly the case in most backward as compared with most ad- vanced countries, practically all economic-demographic models indicate that a gradual halving of fertility over several decades raises income per head substantially. The loss of labour force after 15 years is more than offset by the more immediate increase in per capita income and in aggregate saving. After 15 years there is less labour but more investment than otherwise, with more capital and output per worker, a lower underemployment rate, and fewer consumers to share in a G.N.P. that has grown about as rapidly as it would have done with unchanged fertility.
This has been shown in several analyses, both for an abstract country called Developa, and for Guatemala, Turkey and most recently Chile.2
The main elements of the dynamic model used are:
V/P, Gross domestic product per head, which by wiser public and/or private actions one hopes to see rising faster than it would otherwise;
B, births, which depend on initial and changing age distributions and on projected age-specific fertility rates;
D, deaths, which depend on projected age-specific mortalities, age dis- tributions, etc.;
P, population, which is arithmetically last year's population plus B minus D; 3
1 Where the marginal product of labour is zero, or when the analysis is for a 10-year period during which prevented babies do not reach 15 years to become lost workers, a reduction in births cannot reduce G.N.P. and must raise income per head above what it otherwise would be. This is also because the cost of the contraceptives needed to prevent a birth is so much less than the discounted cost of the investment otherwise needed to provide a typical annual flow of goods and services to an extra person. Such a benefit/cost comparison is repugnant to some, but no less valid on that account. See also [9].
2 See [1 1, 14 and 15]. 3 International migration is here ignored. For countries with the worst population densities
and growths, there is almost no in-migration and net out-migration is trivial in percentage terms. Emigration can seldom provide relief for population pressure either. A 1% emigration from India would mean 5 million people (net) moving permanently abroad each year. In itself this would constitute a major transportation job, greater than current air travel across the North Atlantic. More seriously perhaps, there are not enough countries willing and able to receive such a flow of
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804 THE ECONOMIC JOURNAL [DEC.
V, gross domestic product, which is a function of employed labour force, domestic capital stock and state of technology;
K, stock of capital, which increases according to aggregate domestic saving plus capital borrowings from abroad; 1
S, aggregate domestic saving, which is positively related to V and nega- tively to P;
E, employed labour force, positively related to L and K, with E/L being monotonically related to K/E;
L, available labour force, a function of population size and age distri- bution;
T, technology, with improvements in the state of art resulting in more V from a given E and K.
In the models usually employed to date, V has been determined by a modified Cobb-Douglas function, in which the output elasticities of E and K have sometimes summed to less than unity to reflect scarcity of natural resources. The influence of technology has been compounded at a fixed annual rate and is incorporated in the aggregate production function as a shift factor.2 Births and deaths have influenced V indirectly through L, K and hence E, while affecting P directly.3
The models have been used to examine contrasting fertility projections upon projected V and P, and hence V/P, over the next 35 years or so. Calcula- tions are year by year. Results are usually tabulated at 5-year intervals.
In Table I, for an abstract country named Developa, a constant G.R.R. (gross reproduction rate) of 3-025 is contrasted with the case of a G.R.R. that falls by arithmetic retrogression from 3.025 to 1-479 over 25 years.4 Subsequent V is hardly affected, the decline in fertility raising K enough to compensate for the fall in L. This increase in K results from a " release " of consumption, part of which is additional saving, because the number of
people. The few small countries that do receive a considerable population growth from im- migration-over 5% in Kuwait's case-are atypical. The migration that does affect economic development is the internal flow to city from countryside. These effects are now being incorporated into a two sector economic-demographic model being developed at TEMPO.
1 The basic model assumes no net international transfers of capital. It is programmed however to allow for any year to year exogenous capital movements that the analyst cares to assume. A modified programme also provides for enough inflow of capital in each year to maintain a stipulated constant annual improvement in V/P.
2 This reflects an agnostic uncertainty as to whether technology is especially associated with, say, increased capital stock, improved worker education, or general level of welfare. In effect *' technology " here is the residual source of all increased output that cannot be attributed to capital or labour increments. The main impact of a high rate of " technology " improvement in this model is to reduce the comparative importance of reducing fertility in raising projected V/P.
3 In this formulation the demographic " side " of the model affects the economic side, but not conversely. Conceptually it could be supposed for instance that a rising V/P after some lag would reduce age specific fertilities. However, while this relation is often asserted, it has still to be demonstrated.
4 The gross reproduction rate is the number of live female births a typical woman will have during her child-bearing years.
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1971] ECONOMIC CONSEQUENCES OF RAPID POPULATION GROWTH 805
children declines relatively. There is less unemployment, and more output per worker, because the K/E ratio is higher. With similar V, but a smaller- than-otherwise P, V/P is higher.'
Specifically, taking the case summarised in Table I, V/P rises from $200 a year in 1970 to $419 with low fertility as against $293 with high fertility by A.D. 2000. After thirty years, with low fertility the capital stock is larger
TABLE I
Effects of Declining Fertility on Output and Per Capita Income in " Developa"
Item. 1970 1985 2000 High Low High Low
fertility. fertility. fertility. fertility.
P, Population (106) 10-0 15.9 14-4 25-7 18-8 V, Output ($109) 2-00 3.54 3-63 7.53 7-87 VIP, Income per head ($) 200 223 251 293 419 L, Available labour (106) 3-61 5-69 5-69 9l10 8.32 Unemployment rate (%) 15 18 16 10 6 K, Capital stock ($109) 5 00 7-06 7-28 13-20 15-57 K/E, Capital per worker ($) 1,626 1,509 1,521 1,637 1,984 SIV, Savings from income (%) 4.7 6-4 79 9-6 12-5 Earnings per worker ($) 325 378 378 459 501 Return on capital (%) 16 20 20 23 20 Children/Population (%) 44 44 39 45 32 G.R.R., gross reproduction rate 3-025 3-025 2-092 3-025 1479 Female life expectancy (years) 55 0 58-0 58-0 610 61-0
N.B. These numerical results, employing the initial conditions of 1970 and the economic para- meters listed in the text, were developed from the TEMPO demographic-economic model, described in detail in Reference [1, 12].
($15.57 billion as against $13-20 billion), capital per worker is higher($1,984 as against $1,637), and the unemployment rate is lower (6% as against 10%). The relative scarcity of labour has increased after 30 years, with annual earnings per full-time equivalent worker of $501 as against $459, while the return on capital is 3 percentile points lower than with high fertility. One basic reason for better economic performance is that by A.D. 2000 children are 32% of the population with low fertility as compared with 45 % with unchanged high fertility.
The outcome of a higher-than-otherwise V/P with declining fertility has been shown to be most insensitive to labour and capital output elasticities, technology improvement rates, the savings equation, the employment of labour function, or the projected exogenous decline in mortality rates. For each single comparison of projected fertility differences, these assumptions, and of course the initial conditions of population size, age distribution and
1 The tables are for a case where technology improves 0-015 a year compounded, the output elasticities of employment and capital are 0 5 and 0-4 respectively, and aggregate domestic savings are 0-8V-$35P.
No. 324.-VOL. LXXXI. 3H
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806 THE ECONOMIC JOURNAL [DEC.
capital stock, are always similar. In every case, if fertility is declining faster, V/P is nevertheless rising faster.'
A related point is that a lower fertility means slower population growth and hence more time for domestic capital to accumulate and the state of art to improve. This is shown in Table II, based on the same case as Table I,
TABLE II
Contrasting Attainment of Same Population in Different Years: Unfavourable Economic Consequences of Fast Population Growth in " Developa"
Item. 1985 1990 (High fertility). (Low fertility).
P, Population (106) 15-9 15-9 V, Output ($109) 3-54 4-68 V/P, Income per head ($) 223 295 L, Available labour (106) 5-69 6-57 Unemployment rate (%) 18 18 K, Capital stock ($109) 7 06 8-98 K/E, Capital per worker ($) 1,509 1,543 S/V, Savings from income (%) 6-4 9.4 Earnings per worker ($) 378 402 Return on capital (%) 20 21 Gross reproduction rate 3-025 1 817 Female life expectancy (years) 58-0 59.0
Source: Same as Table I.
the difference being that Developa attains a population of 15-9 million in A.D. 1985 with unchanged fertility but only in A.D. 1990 with declining fertility. By waiting 5 more years for its population of 15-9 million, De- velopa can provide this size of population with a yearly V/P of $295 instead of $223, having a larger labour force (6.57 million as against 5-69 million) and a larger capital stock ($8.98 billion as against $7-06 billion). The argu- ment is not that Developa should never have a much larger population. It is rather that population growth must be slow, regardless of" empty " lands waiting to be populated.
Dynamic models of this kind can also be used to sense the " return "
1 See [13] for a detailed account of the sensitivity analysis. However, some feeling for the insensitivity of the main conclusion of the analysis, namely that a more rapid decline in fertility hardly affects V while significantly lowering P below what it would otherwise be, can be gained from the following ratios given in the cited document (which used slightly different parameters for its production function.) In that case, by A.D. 2000, the " low fertility P " was 27% below the " high fertility P " in all the calculations, and for the standard set of parameters, the ratio of " high fertility V " to " low fertility V " was 1 005. If the rate of annual technological improve- ment was 2.5% instead of 1-5%, this ratio was 1-022. If the savings function were not 0*2V-$30P but rather 0 07V, this ratio was 1 036. If the respective output elasticities of capital and labour were not 0 4 and 0-6 but rather 0 5 and 0 5, this ratio was not 1-005 but 0-988. The results are also very insensitive to economies or diseconomies of scale: thus, if the output elasticities sum not to unity but to 0 7 and 1-25 respectively, the A.D. 2000 ratios of V were not 1-005 but respectively 0-987 and 1-016. Altogether, the interactions of the model seem to dampen the effect of altering assumed parameters and initial conditions, a state of affairs that strengthens the credibility of the conclusions.
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1971] ECONOMIC CONSEQUENCES OF RAPID POPULATION GROWTH 807
from " investments " in contraception. This of course requires an assump- tion as to the annual cost per effective contraceptive user and the age distri- bution of these voluntary " acceptors." The " return " or gain can reasonably be defined as the gain in income per head times the population enjoying it. Over a period of 35 years this benefit-to-cost ratio ranges between 50 and 150 to 1.1 But for any historic period this arithmetic ratio must understate the return, especially for shorter periods, for even with no future costs there will always be future and generally increasing gains from past contraceptive expenditures.2
In these cases initial " size " of population is of minor importance. If natural resources are very scarce, so that there are markedly diminishing returns to labour and capital taken together, it is true that reduced labour employment because of reduced fertility occasions a smaller loss in V attri- butable to E. But by the same token the increase in V attributable to more K with fewer births is also smaller.
More important than size of population is the changing rate of its growth. An increasing growth rate, especially when due to a declining death rate, is economically disastrous. A decreasing population growth rate, because of declining fertility rates, is a major source of economic development.3
IV. INTERNATIONAL CONSEQUENCES OF FERTILITY DIFFERENCES
High fertility rates tend to limit what L.D.C.s can export and in addition make them less creditworthy as international borrowers.
International trade theory has always emphasised that what countries export and import depends largely on relative factor prices. Countries with high fertility rates have a comparative advantage in labour intensive products, because comparatively their labour's marginal productivity is low and their capital's marginal productivity is high. However, because high fertility countries have low per capita incomes, there are additional trade consequences.
High-fertility, low-income countries generally export primary agricul- tural commodities, except for those few and fortunate nations possessed of
1 In the Table I case this benefit/cost ratio is 116 to 1 by A.D. 2000. The annual cost of prac- ticing contraception is assumed to be $5 a year per user and effectiveness is supposed to be 0-8. The distribution of users by age is proportionate to the reduction in age specific fertilities assumed for the lower fertility case in the comparison. Thus the benefit/cost ratios obtained from these dynamic economic-demographic models are very similar in magnitude to the benefit/cost ratios estimated in 1966 by far simpler and static means and published in thisJouRNAL. [9]
2 See References [6] and [8]. 3 Of course an L.D.C. can instead raise its annual rate ofper capita income improvement by faster
innovating or saving. It is simple to calculate for any given case what these " trade-offs " are among fertility, savings, and innovating rate changes. (See Reference [6].) But calculating arithmetical equivalences in terms of VIP improvement does not create operational alternatives. Families do not save or innovate more because they increase their fertility. In fact a more plausible argument might be that the sort of families which practice birth control effectively are likely to be exceptional savers and innovators.
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808 THE ECONOMIC JOURNAL [DEC.
valuable mineral assets such as petroleum. Poverty makes for a consumption pattern of basic " necessaries," and hence a domestic production pattern of limited variety. Poor countries cannot afford the technological education and do not have the high-income market needed for products that are tech- nically advanced, superior in performance or which incorporate high styling. With less capital, the workers of these countries must compete for foreign exchange largely through muscle power, usually applied to exporting sugar, coffee and other products of tropical agriculture. Such a worsening of the terms of trade between backward and advanced countries as may in fact have occurred 1 is probably as much due to continued fertility differentials among nations as to any other single cause. Those L.D.C.s that are too much dependent on agricultural exports to finance adequate industrial product imports should usually blame their own excessive fertility.
The same high fertility rates that increase the " need " for assistance of L.D.C.s also make them less creditworthy as borrowers and hence more dependent on grants. Aspirations for G.N.P. increase are often several per- centile points higher than is realistic because of the typically expected 3% annual growth in population. This in turn " requires " a larger yearly increment in capital stock. But the low ratio of work age population to children caused by high fertility reduces output and aggregate savings for investment. Unfortunately, the very inability to save that "requires" external borrowing also makes subsequent repayment difficult or impossible. Savings are after all the ultimate source of repayment.
These interactions can also be explored by the TEMPO economic- demographic model. A " required " annual improvement in per capita income can be stipulated. The computer can be programmed to assume an inflow or outflow of capital in each year depending on whether domestic savings are respectively insufficient or excessive to occasion precisely the stipulated improvement in per capita income. Ordinarily, if an L.D.C. stipulates an unrealistic annual improvement, it will never be able to repay its borrowings with interest. Alternatively, an L.D.C. with a lower fertility may be able to realise a higher annual improvement in per capita income, and eventually service all borrowings from abroad, than can an L.D.C. with higher fertility.
Considering Developa again, Table III indicates some borrowing and repayment consequences of aspiring to alternative constant improvements in per capita income, contrasting again the two economic projections based on the same high and low fertility projections. Thus the highest sustainable annual improvement in per capita income is under 2 0% (actually 1.8%) with high (unchanged) fertility and over 2-5% (actually 2-9%) with low fertility if external borrowings are ever to be repaid (including a 5 % annual
1 It is by no means clear that the barter terms of trade have generally worsened for backward countries when unquantified improvements in industrial products exported from advanced coun- tries are taken into account.
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1971] ECONOMIC CONSEQUENCES OF RAPID POPULATION GROWTH 809
interest rate on the outstanding balance). Even at 1.5% yearly improve- ment, high-fertility Developa does not commence repayment before 30 years, but a low-fertility Developa can aspire to a 2-5 % annual improvement and start repayment after 21 years. Alternatively, for a 1.5% sustained annual improvement in VIP, completed debt service takes 42 and 16 years
TABLE III
Effects of Fertility on Developa's Ability to Service Debts while realising a Stipulated Annual Improvement in Income Per Capita.
Future year Future year Debt outstanding Stipulated when repayment when loans are when repayment
annual of principal completely begins (a) improvement begins. (b) repaid. (millions of
in G.N.P. _ _ _ _ _ _ __ _ _ _ __ dollars). per capita. Fertility Fertility Fertility
High Low High Low High Low
10 14 5 23 10 482 130 15 30 1 1 42 16 2643 415 2.0 (a) 14 (a) 23 (a) 1066 2.5 (a) 21 (a) 33 (a) 2743
(aj Debt never repaid. (b) Repayment begins in the year that domestic saving first becomes greater than is required to realise the stipulated annual improvement in per capita income. (c) To be compared with initial year G.N.P. of $2,000 million. Source: Same as Table I, plus Reference [7].
respectively with high and low fertility, with a respective maximum out- standing debt of $2,643 and $415 million.1
The credit unworthiness associated with high fertility may give inter- national lending agencies a powerful and more acceptable means of in- ducing certain L.D.C.s to undertake vigorous birth control programmes. It may be politically impossible for, say, the World Bank Group to make a loan for infrastructure conditional upon the borrowing government's pro- moting contraception. But development assistance agencies when making loans are certainly entitled to consider all factors influencing a borrowing L.D.C.'s ability or inability to repay. It is, after all, a normal practice of borrowers to accept loan conditions. One problem throughout the 'Fifties and early 'Sixties was that international lending agencies were not prepared to do anything about perhaps the most important single cause of poverty in L.D.C.s-excessive population growth.
1 Table III is based on the assumption that each year Developa borrows exactly enough from abroad to increase its domestic investment sufficiently to maintain the stipulated X% annual improvement in VIP. Alternatively, if domestic saving is more than enough to maintain this X% improvement, the excess domestic saving is used to repay international borrowings. The external liability for debt service includes a 5% interest charge on the current year's outstanding debt. See Reference [7].
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V. COMMENT
Studies of political economy cannot logically fail to study people and hence populations. Economic development largely concerns the develop- ment of people, which means investments in education and health as well as in physical capital, both of which are encouraged when lower birth rates make labour more scarce relative to capital. One of the distinguishing and surely significant characteristics of Less Developed Countries is their high fertility rates and their consequently high proportion of unproductive children. Reductions in fertility enable domestic capital to be accumulated more rapidly. Greater future savings of L.D.C.'s because of effective birth control programmes should render them more credit-worthy. The poverty induced by high fertility also affects commodity flows and terms of trade. The influences of population growth are so pervasive throughout all macro- economic relations that they should surely become a major concern of the economics profession.
STEPHEN ENKE
General Electric Company- TEMPO Santa Barbara, California.
REFERENCES
1. A. DeVany and S. Enke, Population Growth and Economic Development: Back- ground and Guide, Santa Barbara, TEMPO, 1968, No. 119.
2. R. Eckert and D. O'Hara, Manualfor the Calculation of Government Expenditures for Selected Social Services, Santa Barbara, TEMPO, 1968, No. 121.
3. S. Enke, " Birth Control for Economic Development," Science, May 1969, No. 164, pp. 798-802.
4. S. Enke, Economic Benefits of Slowing Population Growth: Charts and Notes, Santa Barbara, TEMPO, 1968, No. 122.
5. S. Enke, " The Economics of Having Children," Policy Sciences, June 1970, No. 1, Vol. 1, pp. 15-29.
6. S. Enke and R. G. Zind, " Effects of Fewer Births on Average Income," Journal of Biosocial Sciences, January 1969, Vol. 1, pp. 41-55.
7. S. Enke, " High Fertility Impairs Credit Worthiness of Developing Nations," (Festschrift in honour of Professor Edgar Hoover, title not chosen) (Gordon and Breach, 1971).
8. S. Enke, " Politico-Economic Global Systems," Macrosystems: Analysis, Instru- mentation, and Synthesis of Complicated Systems, Spring, 1971, Holt, (Reinhart and Winston).
9. S. Enke," Some Aspects of Slowing Population Growth," ECONOMICJOURNAL, March 1966, No. 76, pp. 44-56.
10. S. Enke, Zero US Population Growth-When, How and Why, Santa Barbara, TEMPO, 1970, No. 35.
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1971] ECONOMIC CONSEQUENCES OF RAPID POPULATION GROWTH 811
1 1. Bruce Herrick and R. Moran, " Economic Effects of Chilean Fertility Decline,' Santiago, Chile, Centro de Investigaciones Economicas, Universidad Catolica de Chile (to be published).
12. W. E. McFarland, Description of the Economic-Demographic Model, Santa Bar- bara, TEMPO, 1968, No. 120.
13. W. E. McFarland, Sensitivity Analysis of the Economic-Demographic Model, Santa Barbara, TEMPO, 1969, No. 52.
14. W. E. McFarland and D. O'Hara, Guatemala: The Effects of Declining Fertility Santa Barbara, TEMPO, 1969, No. 50, Vol. II.
15. W. E. McFarland and D. O'Hara, Turkey: The Effects of Falling Fertility Santa Barbara, TEMPO, 1969, No. 50, Vol. I.
This content downloaded on Wed, 13 Feb 2013 15:43:53 PM All use subject to JSTOR Terms and Conditions
- Article Contents
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- Issue Table of Contents
- The Economic Journal, Vol. 81, No. 324 (Dec., 1971), pp. 741-1061+i-xv+i-xii
- Volume Information [pp. i - xii]
- Front Matter
- The Concept of Economic Surplus and Its Use in Economic Analysis [pp. 741 - 799]
- Economic Consequences of Rapid Population Growth [pp. 800 - 811]
- Richard Cantillon, Financier to Amsterdam, July to November 1720 [pp. 812 - 827]
- A Theory of the Economics of Time [pp. 828 - 846]
- Rosa Luxemburg and the Impact of Imperialism [pp. 847 - 862]
- Hypothesis and Paradigm in the Theory of the Firm [pp. 863 - 885]
- The Exchange Constraint on Development--A Partial Solution to the Problem [pp. 886 - 903]
- Tariffs, Economic Welfare and Development Potential [pp. 904 - 915]
- Notes and Memoranda
- Hicks on Ricardo on Machinery [pp. 916 - 922]
- A Reply to Professor Beach [pp. 922 - 925]
- Competitiveness of Exports: A Micro-Level Approach--A Comment [pp. 925 - 927]
- Competitiveness of Exports: A Micro-Level Approach--A Reply [p. 928]
- The Integration of Equity and Efficiency Criteria in Public Project Selection: A Comment [pp. 929 - 931]
- Reply to Dr. Mathur [pp. 931 - 933]
- Recent Contributions to the Theory of Marginal Cost Pricing: The Problem of Peak Loads [pp. 934 - 936]
- Keynes on Lloyd George [pp. 936 - 937]
- Current Topics [pp. 938 - 942]
- Reviews
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- New Books [pp. 1027 - 1061]
- Back Matter [pp. i - vi]
Week 3 Assignment Instructions and Sample R codes
This assignment is to give you the hands-on experience using R for conducting logistic regression in real world data set. Please refer to the Example 10.3 and 10.5 in Chapter 10 in the reference textbook for details about how to generate logistic regression models and the evaluate the model performances. Then open this website, go over the Satisfaction example and use the same R codes to reproduce the results, study the way to explain the model and evaluate the results.
Now open this file Satisfaction2.csv (slightly different from the sample dataset) and repeat the same analysis as in the website to conduct a logistic regression analysis.
Hints:
Use getwd(), setwd() and dir() to save and retrieve dataset in R with much convenience
Don’t forget to use install.packages("") for prediction or ROCR if that packages are not installed
Reference
https://www.kaggle.com/arpina/logistic-regression-analysis/notebook
Satisfaction <-read.csv("Satisfaction2.csv")
summary(Satisfaction)
str(Satisfaction)
#Making appropriate corrections regarding variable classes.
Satisfaction$Seat.comfort <- factor(Satisfaction$Seat.comfort, ordered = TRUE)
Satisfaction$Departure.Arrival.time.convenient <- factor(Satisfaction$Departure.Arrival.time.convenient, ordered = TRUE)
Satisfaction$Food.and.drink <- factor(Satisfaction$Food.and.drink, ordered = TRUE)
Satisfaction$Inflight.wifi.service <- factor(Satisfaction$Inflight.wifi.service, ordered = TRUE)
Satisfaction$Inflight.entertainment <- factor(Satisfaction$Inflight.entertainment, ordered = TRUE)
Satisfaction$Leg.room.service <- factor(Satisfaction$Leg.room.service, ordered = TRUE)
Satisfaction$Baggage.handling <- factor(Satisfaction$Baggage.handling, ordered = TRUE)
Satisfaction$Checkin.service <- factor(Satisfaction$Checkin.service, ordered = TRUE)
Satisfaction$Cleanliness <- factor(Satisfaction$Cleanliness, ordered = TRUE)
Satisfaction$Online.boarding <- factor(Satisfaction$Online.boarding, ordered = TRUE)
library(prediction) #install.packages("prediction") if not installed
library(ggplot2)
library(lattice)
library(caret)
library(gplots)
library(ROCR) # need to use install.packages("ROCR") if ROCR is not installed
#Plotting graphs.
Probs_1 <- as.data.frame(prop.table(table(Satisfaction$satisfaction_v2, Satisfaction$Class), 1))
ggplot(Probs_1, aes(x = Var2, y = Freq, fill = Var1)) + geom_bar(stat = "identity", position = "fill", color = "black") + theme_bw() +
scale_fill_brewer(palette = "Dark2") + labs( x = "Class", y = "Satisfaction", fill = "Satisfaction", title = "Relationship between satisfaction and customer class")
#Based on the barplot constructed we can conclude that most satisfied passengers we passengers from Business class, followed by eco plus and then with eco class.
#This makes sense since the more expensive a ticket is, the better should be service and satisfaction.
Probs_2 <- as.data.frame(prop.table(table(Satisfaction$satisfaction_v2, Satisfaction$Food.and.drink), 1))
ggplot(Probs_2, aes(x = Var2, y = Freq, fill = Var1)) + geom_bar(stat = "identity", position = "fill", color = "black") + theme_bw() +
scale_fill_brewer(palette = "Dark2") + labs( x = "Food and drinks", y = "Satisfaction", fill = "Satisfcation", title = "Relationship between satisfaction and Food and drink")
#From the barplot constructed what can generally be concluded is that passenger rating on food and drinks has not much relationships with passenger satisfaction
#as both in the case of rating 0 and 5 satisfaction is almost equal.
Probs_3 <- as.data.frame(prop.table(table(Satisfaction$satisfaction_v2, Satisfaction$Type.of.Travel), 1))
ggplot(Probs_3, aes(x = Var2, y = Freq, fill = Var1)) + geom_bar(stat = "identity", position = "fill", color = "black") + theme_bw() +
scale_fill_brewer(palette = "Dark2") + labs( x = "Type of travel", y = "Satisfaction", fill = "Satisfcation", title = "Relationship between satisfaction and type of travel")
#From the barplot constructed we can s ay that business travel passengers on average had higehr satisfaction rates.
#Splitting the data into Test and Train
set.seed(1)
trainingIndex <- createDataPartition(Satisfaction$satisfaction_v2, p = 0.8, list = FALSE)
Train <- Satisfaction[trainingIndex,]
Test <- Satisfaction[-trainingIndex,]
#Building the initial model using Logistic regression.
model1 <- glm(satisfaction_v2 ~., data = Train, family = "binomial")
summary(model1)
#Removing the insignifcant variables from the model.
model2 <- glm(satisfaction_v2~. -Seat.comfort- Gate.location - Online.boarding - Checkin.service- Cleanliness, data = Satisfaction, family = "binomial" )
summary(model2)
#Since the variables seat comfort, gate location, online support, on board service, online boarding, id, checkin sevices and cleanliness were shown to be insignificant in the summary
# of the first model i decided to not use them in the second model to improve the reliability of it.
coef(model2)
#One year increase in age decreases the log odds of satisfaction by 5.280300e-03.
#One extra minute of arrival delay decreases the log odds of satisfaction by 9.209865e-03.
#One extra minute of departure delay decreases the log odds of satisfaction by 3.696267e-03.
#The log odds of satisfaction given that the passenger is male is by 0.9% less than the likelihood of satisfaction of a female passanger.
#The log odds of satisfaction for a passenger doing a personal travel is by -8.617104e-01 less than the log odds of satisfaction for a customer doing a business type of travel.
#The log odds of satisfaction for a loyal passenger is by 1.994355 more than for a disloyal passenger.
exp(coef(model2))
#For a one-unit increase in age, we expect to see about 1% decrease in the odds satisfaction.
#One extra minute of arrival delay decreases the odds of satisfaction by 1%.
#One extra minute of departure delay increases the odds of satisfaction by 0.4%(this doesn't make sense).
#The odds of male satisfaction is 39% of the odds of female satisfaction.
#If we select loyal passengers the odd ratio of satisfaction would increase by 14 times from the odd ratio fo disloyal passengers.
#If we select passengers who were traveling for personal reasons the odd ratio of satisfaction would decrease by 2.36 times
# compared to choosing passengers doing business travel.
#Building a confusion matrix based on predictionis of the second model.
predict <- predict(model2, newdata = Test, type = "response" )
predict_class <- factor(ifelse(predict > 0.5, "satisfied", "neutral or dissatisfied"))
confusionMatrix(predict_class, Test$satisfaction_v2, positive= "satisfied")
#based in the confusion matrix, we can conclude that the model is pretty reliable in terms fo making predictions due to a high accuracy level and very small p-value.
#Sensitivity ratio shows that given that the customer was satisfied the model correctly predicted it in 88% of the cases.
#Specificity ratio shows that given that the customer wasn't satisfied the model did correct predictions in 85% of the cases.
#Out of all the predictions of a customer being satisfied the model was in fact correct in 88% of the cases.
#Out of all the times that the model predicted for a customer to not be satisfied , the customer in fact wan't satisfied in 85% of the cases.
#All the ratios show that the model was good in making predictions and is useful.
P_Test <- prediction(predict, Test$satisfaction_v2)
perf <- performance(P_Test, "tpr", "fpr")
plot(perf)
performance(prediction.obj = P_Test, "auc")@y.values
#The AUC curve which shows tha tradeoff between sensitivity and specificity has an auc of 94% . This again is a good indicator of a reliable model.
#To sum up the logistic regression model is well suited for the dataset, as the model built had above average accuracy measures, had a large AUC,
# and fairly good sensitivity, specificity, npv and ppv measures.

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