Parametric population projection and its usefulness for policy analysis

THE WORLD BANK Internal Discussion Paper AsIA REGIONAL SERIES Report No. IDP 93 Parametric Population Projection and its Usefulness for Policy Analysis Warren C. Sanderson April 1991 The views presented here are those of the author, and they should not be interpreted as reflecting those of the World Bank. :--;1-;-,(-;;-;-;-;-;-―、；-,-：》1-,(---,- イ larazetric Vapulation frojection and its usefulness for volicy analysis by Warren C. Sanderson Department of Economics SUNY - Stony Brook First Draft April, 1991 Acknowledgements: The research fok, this paper was done when I was a Visiting Research Follow at The World Bank. I would like to thank Jee-Peng Tan for her unflagging encouragement, helpful oomments, and her assistance in the selection of the projections presented here and Frances Plunkett who shared both bar materials and her deep knowledge of the Indian demographic scene with me. I would like also to thank Rodolfo Bulatao and Eduard Bos for interrupting their own busy schedules to produce the projections for me. Rizie Batia and Boubicar Sow contributed essential research assistance. Seminars at SUNY-Stony Brook and at The World Bank produced thoughtful comments,, some of which have been incorporated into this draft. None of these friends nor The World Bank as an institution should be considered to be accountable for any errors, omissions, or silly notions which appear here. The ideas in this paper are purely my own and do not represent the views of The World Bank in any way. Abstract This paper presents a now methodology for producing population projections based on interpretable parameters such as the contraceptive prevalence rate, contraceptive effectiveness rate, abortion rate and the mean age of women at marriage. It is designed to provide answers to the ##what if ... It type questions used in policy analysis. we demonstrate some of the features of the now framework by producing a parametric history of fer*'ility in India from 1981 to 1987 and a set of projections of the Indian population to the year 2050. The parametric history resolves the apparent contradiction betweea the rapid rise in contraceptive prevalance in India between 1981 and 1987 and the very slow progress made in reducing the rate of population growth. Changes in other fertility related behavior completely offset the effect of rising contraceptive use. The projections include a case where an improvement in the family planning program increases the rate of contraceptive prevalence by an average of about 6 percentage points over the period 1990-2004. The result is that, in the period 1990- 2010, the rate of Indian population growth would be reduced by only one-tenth of one percentage point. Both findings suggest that, in order to make faster progress toward reducing the rate of population growth, policies will need to be implemented which are targeted toward more than one dimension of fertility behavior. A C IOPULATION P* 32ON AMD XTS 8ULUB FOR POLICT RM8YIS Table of Contents Page No. 1. Introduction . . . . . . . . . . . . . . . . . . . 1 2. Indian Population Parameters in the 1980s . . . . 2 3. Examples of Paravetric Projections . . . . . . . . 12 4. PPP methodology ........... .. .. * 21 5. A Comparison Between Schedule-Based Projections and PPP . . . . . . . . . . . . . . . . . . . . . 35 6. Conclusions . . . . . . . . . . . . . . . . . . . 37 Appendix 1 . . . . . . . . . . . . . . 38 Appendix 2 . . . . . . . . . . a 6 . 40 Bibliography . .. .... . .. . .. .. .. .. 47 1. Introduction The basic ingredients of most population projections, today, are assumptions about the dynamic paths of schedules of age- specific fertility, mortality, and net immigration rates. Scheule-based projection is both easy and inexpensive, and agencies such as The World Bank, the United Nations and the U.S. Bureau of the Census use it routinely. This paper is about a different sort of projection methodology whose basic building blocks are not schedules, but understandable parameters like the contraceptive prevalence rate and women's mean age at marriage. Parametric population projection (PPP) provides decision-makers and researchers with the means to answer questions about the effects of various policies on the future size and age structure of a country's population. In this paper, we present the basic methodology of PPP and demonstrate some of its capabilities using India as an example. In the process, we show how PPP can be used to resolve an important puzzle about recent Indian fertility trends and to help in the formulation of population policy. PPP is designed to provide answers to the "what if ... type questions used in policy analysis. Suppose, for example, that decision-makers were considering a program which would cost $1 million dollars per year, and which would have the effect of raising the contraceptive prevalence rate in their country by 1 percentage point (over what it otherwise would have been) in each year of the project. In order to decide whether the expendituzes were 4orthwhile, the decision-makers would need to know what the population of their country would be at various future dates if the program were funded and if it were not. If the consequences for population size and structure were substantial, the decision- makers might push on with the project with increased enthusiasm. If the consequences were trivial, they might choose not to undertake it at all. The current schedule-based population projection methodology cannot answer that sort (f policy question because it has no way of translating the idea of "a 1 percentage point rise in the contraceptive prevalence rate" into its hypothesized age-specific fertility rates. PPP, on the other hand, is designed precisely to answer such questions. In order to understand the advantage of PPP as an analytic tool for policy analysis, it is necessary to examine briefly the nature of schedule-based projections. In concept and even in practice, the computation of population projections using schedules of fertility, mortality, and immigration rates is comparatively simple. The procedure 1 begins with an initial population distributed by age and sex. A set of survival rates is applied to that population to determine how many people would be alive in the next period. Birth rates, by age of mother, are applied to women to determine how many births there would be, and finally, net immigration rates are employed to calculate the net numbers of newcomers. The art of schedule-based population projection is in making plausible assumptions about the future fertility, mortality. and immigration rate schedules. Of course, all projection methodologies, including PPP, must make suppositions about what is likely to happen tomorrow and the next day, but these specifications are less interpretable when they pertain to entire schedules than when they are determined through the application of comprehensible, policy-relevant parameters. For example, during the 1980's a number of factors were changing simultaneously in India, the contraceptive prevalence rate was rising rapidly, the mean age at marriage for females was increasing, and the length of the period of protection against pregnancy offered by breastfeeding and traditional antinatal behaviors was diminishing. The first factor decreases fertility especially at older ages, the second factor decreases it chiefly at younger ages, and the third causes a Pore uniform increase. PPP takes these factors into account in the process of specifying plausible future paths of fertility. Schedule-based forecasts, on the other hand, ignore those underlying determinants of fertility behavior and focus on how the age-specific fertility rates themselves are apt to move over time. The future age- specific rates determined by these two methods may or may not turn out to be similar, but in the case of PPP we know what was assumed about the governing demographic behavior, whereas in the other case we do not. Following this Introduction, we show what happened to the Indian PPP parameters during the eighties and in the process, solve a demographic puzzle. In the third section, we take this history and use it to produce alternative projections. It is in these two sections where we provide a taste of what PPP can do in answering policy questions. Consumers of projections may wish to skip to the fifth section, where the relative merits of PPP and schedule-based projection procedures are discussed. Those who are curious abou the methodology of PPP and read onward will find all the details described there. The technicalities of the parameter estimation and a computer program for PPP written in the GAUSS programming language are to be found in the Appendix. 2 2. Indian Population Parameters in the 19809a The experience of India in the 1980's poses an intriguing demographic puzzle as can be seen immediately from Figure 1. The rate of population growth remained almost constant from 1980 through 1988, although toward the end of that period there was a slight decline. An important contributor to this pattern was the behavior of the total fertility ratel which was nearly invariant, at 4.4, from 1980 through 1984, after which it began to fall, reaching 4.0 in 1988. In contrast, the contraceptive prevalence rate2 rose rapidly throughout the 1980's, from 24.4 percent in 1980 to 35.6 percent in 1984 and to 46.7 percent in 1988. Indeed, the contraceptive prevalence rate rose almost as rapidly in the phase of total fertility rate constancy as it did during the period of falling fertility. Something certainly appears to be amiss in this figure. If the contraceptive prevalence rate was truly climbing as rapidly as pictured, how is it possible that the total fertility rate remained nearly constant from 1980 to 1984? Indeed, how is it possible that a rise in the contraceptive prevalence rate from 24.4 to 46.7 -- a 91 percent increase -- could have produced only a 10 percent decline in the total fertility rate? This is, indeed, an intriguing mystery and we would not want to spoil its dwnant by providing it so soon after its introduction. Instead, we will proceed slowly, first, assessing why it is important to solve it, and second, showing how PPP provides the essential clues. Understanding what happened to the fertility in India during the 1980's is no purely academic exercise; it is crucial to the formulation of appropriate policy. To see this, let us try to ascertain the degree of success experienced by the Indian family planning program? If the program's goal were to increase the contraceptive prevalence rate, the increase in that rate of 91 percent (22.3 percentage points) over 8 years should perhaps be considered not simply a success, but a triumph. on the other hand, if its goal were to reduce the rate of Indian population growth, the eighties must surely be a decace of disappointment. The population growth rate was 2.1 percent An 1980 and 2.0 percent in 1988. Should policy-makers be encouraged to expand 1 The total fertility rate measures the number of children an average women would bear over her reproductive life given the birth rates of the specified year. 2 The contraceptive prevalence rate is the proportion of married women of childbearing age who practiced contraception in the specified year. 3 Total Fertility Rate, Population Growth Rate, and Contraceptive Prevolence Rate: India 1 980-1988 4.50 - -- - e- - - - - 50 -4.05 total fertility rate -- 45 (: 3.60 40,9 1 3.15 -5 a ^*** oeOce (oe 10 tiePreva 0 2.70 contrac JO i2.25 -..t n 25 p. .population growth rate 20 *0 1.35 150 o 0.90 1O' 0.45 .5 0.00 so "' 1980 1981 1982 1983 1984 1985 1986 1987 1988 YEAR Pigure I the same programs which were associated with the substantial increase in contraceptive prevalence, but little decrease in the population growth rate or should they be encouraged to seek out additional approaches targeted toward increasing the impact of contraceptive use on population growth? In order to answer this question, we need a deeper understanding of what happened to fertility in India during the 1980's. Policy making and policy dialogue in an environment where we are unsure about linkages between contraceptive prevalence and population growth is much like shooting in the dark. You can still make a loud sound, but you would be lucky to hit your target. In the past, the assumption was commonly made 4 that increasing contraceptive prevalence, regardless of how it was done, was the key to lowering the rate of population growth. The experience of India in the 1980's teaches us that reality is not that simple, and that large increases in contraceptive prevalence can, under some circumstances, produce only small changes in the total fertility rate and in the population growth rate. It is crucial for decision-makers who are interested in lowering the rate of population growth to incorporate a grasp of what happened in India into their policies for the future. PPP can help in this process by contributing important clues toward an understanding of the patterns seen in Figure 1. PPP merges the analytic frameworks in Bongaarts and Potter (1983), Coale (1971), and Coale and McNeil (1972) to provide a history of demographic developments in terms of easily interpreted parameters3. These parameters are: 1. the earliest age at which a consequential number of women first marry, 2. the proportion of women who ever marry, 3. the mean age at marriage of women, 4. the mean age at marriage of men, 5. the contraceptive prevalence rate, 6. the contraceptive effectiveness rate, 7. the total marital abortion rate, 8. the average length of the interval of protection against pregnancy due to breastfeeding and other fertility-affecting behaviors not mentioned above, 9. the length of time it would take a woman who was continuously married from age 20 onward to bear an average of 2 children, 3 Something akin to this was suggested in Chidambaram (1984), but, to our knowledge, never implemented. 4 This parameter is one of those borrowed from the Bongaarts proximate determinants framework. In this paper, we have expanded its role. As measured here, the variable gauges not only the length of the period of nonsusceptibility due to breastfeeding and other fertility-influencing behavior such as post-partum abstinence, but it also incorporates the effects of approximation error. We discuss this in connection with Table 1 below and, in more detail, in Section 4. 5 10. the proportion currently remarried among 20 year old ever- widowed women, and 11.. the proportion currently remarried among 49 year old ever- widowed women. The parameters related to marriage, (1) through (4), (10), and (11), are used to construct an analytic schedule of proportions currently married. The others, (5) through (9) serve to produce a parameterized set of age-specific marital fertility rates. A full discussion of how these figures are employed to produce projections is contained in Section 4. We have estimated or observed all of these parameters for India in 1981, 1985, and 1987. These figures appear in Table 1. Together they provide an analytic history of fertility change in India during the previous decade and hold the clues we are seeking to the mystery in Figure ls. The contraceptive prevalence rate in India rose rapidly from 25.1 percent in 1981 to 37.2 percent in 1985, but the total fertility rate fell only from 4.4 to 4.2. From 1985 to 1987, the contraceptive prevalence rate rose from 37.2 to 42.8 percent and the total fertility rate fell from 4.2 to 4.1. Could there have been factors which changed in a pronatal direction, thus offsetting the expansion in the proportion contracepting'? Table 1 contains six parameters relating to marriage, the age when women start marrying in significant numbers, the proportion of women who ever marry, the mean ages of marriage for females and males, and the proportions of ever widowed women at ages 20 and 49 who are remarried at the time of observation. The only trend in these numbers appears in the women's mean age at marriage'. Indian women married at a mean age of 18.5 in 1981 5 Analytic descriptions and analytic histories have a long and honorable tradition in demography. The one we present here merges lines developed by Coale and by Bongaarts, along with some new mortar designed to help the building blocks fit together into a szable structure. 6 We can ignore the possibility that the data themselves are grossly in error. The population growth rate between the 1981 and 1991 Indian census was 2.1 percent, which is consistent with the growth rates in Figure 1 and the increase in contraceptive prevalence is confirmed by data from the Second and Third All-India Family Planning Surveys (ORG(1983 and 1991)). 7 The mean age at marriage for males is not estimated independently, but, for 1985 and 1987, by adding 4.4 years to the females' mean age at marriage. The 4.4 year figure refers to the year 1984 and comes from India (1989a). In 1981, the difference in the mean ages at marriage for males and females was 5.0 years (India (1990)). 6 and 19.3 in 1987. This rise has had a modest depressing effect on birth rates and it, therefore, certainly could not hold the explanation of why fertility fell so little. Table 1: Indian Fertility Parameters: 1980's 1981 1985 1987 Age When Women Start Marrying 12.4 13.0 12.9 Proportion Ever Married 0.99 0.96 0.96 Mean Age of Women At Marriage 18.5 19.1 19.3 Contraceptive Prevalence Rate 25.1 37.2 42.8 Contraceptive Effectiveness 0.9 0.9 0.9 Rate Total Marital Abortion Rate 0 0 0 Interval of Other Non- 25.5 19.7 17.8 contraceptive Protection Against Pregnancy (in months) Duration From Age 20 to an 7.2 7.0 7.1 Average of 2 Children (in years) Proportion Currently Remarried 0.75 1.00 0.99 Among Ever Widowed Women (at age 20) Proportion Currently Remarried 0.15 0.11 0.13 Among Ever Widowed Women (at age 49)_ There is a change in proportion currently remarried among ever widowed women at age 20 from 0.75 in 1981 to 1.00 in 1985. PPP uses this proportion and the analogous one at age 49 to interpolate all the intervening remarriage proportionss. The change from 0.75 to 1.00 in the proportion of currently remarried among the ever widowed at age 20 has a very small effect on fertility because so few women are widowed when they are young. 8 We interpolate between the proportion of ever-widowed women who were remarried at age 20 and the proportion at age 49 using a reverse S-shaped curve (logistic interpolation). The resultant age-specific proportions remarried among the ever-widoved are used in the computation of proportions currently married. A full explanation of how this works appears in Section 4. 7 Therefore, that change also cannot explain why fertility fell so little. There are also no trends in contraceptive effectiveness, the total marital abortion rate, or in the average time it would take a woman married continuocsly from age 20 to bear 2 children. Since these were all roughly constant, they could not have offset the rise in the contraceptive prevalence rate. From Table 1 we can see that the average interval of anti- natal protection due to breastfeeding and other factors such as the miscarriage rate, customs concerning postpartum abstinence, involuntary sterility, spousal separations, and coital frequency9 fell rapidly from 1981 through 1987. It is this factor which almost completely nullified the effect of rising contraceptive use. This can be easily seen by turning to equations (12) and (13) in Section 4. An increase in the contraceptive prevalence rate from 25.1 to 42.8 percent, given a contraceptive effectiveness rate of 0.9, would, other things being equal, cause the total fertility rate to fall by 21 percent. A decrease in the average interval of antinatal protection due to other factors from 25.5 months to 17.8 months would have, other things held constant, would cause fertility to rise by 21 percent, exactly offsetting the effect of increased contraceptive use. Most policy analysis has concentrated on increasing the contraceptive prevalence rate and ignored other influences on marital fertility. Changes in these other factors have completely compensated for the increase in contraceptive use. It is certainly time that decision-makers take them into consideration when formulating policylo. Because of the importance of the other factors which affect marital fertility, it is useful to pause for a consideration of what they are and how they enter into PPP. Bongaarts (1978) disaggregated the proximate determinants of the total fertility rate into factors measuring variation in marriage rates, contraceptive prevalence rates, contraceptive effectiveness rates, abortion rates, and the length of periods of post-partum protection against pregnancy due to amenorrhea, customs governing abstinence, and any other factors which cause the return to susceptibility to be delayed. There are proximate determinants which were explicitly omitted from this framework, such as coital 9 This interval does not include the time a woman is protected from pregnancy due to contraception nor to the months in which she did not have a child because of the antecedents or consequences of an induced abortion. 10 This is certainly not the first finding of important offsetting effects. See, for example, Easterlin and Criamins (1985, Chapter 4) and Casterline et al. (1984 pp. 45-46). 8 frequency, and sterility, because it was thought that the likely variations in these would result in only small changes in fertility. PPP, however, cannot be based on an incomplete accounting of factors which influence fertility. Therefore, the length of the period of post-partus protection due to other factors is not measured directly, but indirectly as a residual (see equation (20) in Section 4). Its value, then, is determined not only by the duration of postpartum amenorrhea, but by all other factors which influence fertility and by any approximation errors in the equations we use. The value of this new measure of the influence of all other fertility-influencing considerations is not so much in its level, but in its changes over time. Those changes tell us how the net effect of all the omitted fertility determinants altered with the passage of time. PPP shows us that changes in other fertility behavior massively offset the increase in contraception during the 1980's. This suggests four vital questions for future policy analysis: (1) which particular other factors changed, (2) by how much did they change, (3) why did they change, and (4) what policies could have been implemented to have mitigated those changes. We need answers to these questions in order to design improved programs, which, in the future, would translate more of the effect of increased contraceptive usage into a decrease in population growth. Without being constrained by any data which could help us answer these four questions, we can speculate freely on them, especially the third and the fourth. Changes in other fertility- related factors would have caused fertility to increase by 21 percent from 1980 to 1987. It seemp highly unlikely that such a large increase would have been possible without the occurrence of a simultaneous increase in contraceptive use. In other words, it seems plausible that the changes in contraceptive behavior and other fertility-related behavior were related to one another. Broadly speaking, there are two sorts of approaches to problems of this nature. The two types of behavior may have been: (1) independently caused by the sase underlying factors, or (2) simultaneous determined. The independent causation hypothesis holds that factors like education and modernization act on fertility through the adoption of contraception and through the modification of breast-feeding or other similar practices. The simultaneous causation framework does not deny that the same underlying factors may influence both sorts of behavior, but adds the possibility that contraceptive use may influence other fertility-related behavior and visa versa. In the case of independent causation, policies would need to be designed and implemented which change the structure of the relationship between the antecedent variables and the other fertility-related behaviors. In the case of simultaneous causation, the policies would need to be much more carefully 9 crafted, because they would affect both contraception and other related behavior. In this vein, one intriguing line of conjecture is that the family planning program itself may have indirectly caused offsetting changes in breastfeeding behavior. It is possible that one consideration in the decision eventually to become sterilized" was the desire currently to forego the rigors of longer breastfeeding. If this form of behavioral compensation were common in India, then the spread of sterilization itself would be the factor which is producing its countervailing effect. In this case, outreach programs which emphasized the desirability of longer breastfeeding intervals could have the unwanted consequence of reducing the acceptance of sterilization. PPP by itself does not provide any detailed insight into the type of family planning programs which are most likely to be successful, but it does provide some broad hints. Fertility behavior is complex and couples can substitute one form family limitation for another. Supply-side policies which focus narrowly on one aspect of fertility behavior may well produce offsetting changes in other dimensions of it. The intricacy of fertility decision-making suggests that consideration should be given to broader population programs, those which engage women simultaneously in a number of dimensions. Such programs might offer women advise on maternal and child health care, in addition to contraception both for spacing and stopping. In this way, women could be taught about the deleterious effects of short birth intervals on their own health and on the health of their babies and be given means of achieving longer intervals without prolonged breastfeeding or spousal separation. This multiphasic approach to family limitation programs seems to be especially warranted in the case of India, where the complexity of fertility behavior has limited the effectiveness of alternative approaches to the reduction of population growth. In the struggle against rapid population growth in India, the first seven years of the 1980's may go down in history as the period of The Great Pyrrhic Victory; the battle to raise contraceptive prevalence rates was a great success, but the campaign to reduce population growth got virtually nowhere. Did the family planning program explicitly or implicitly encourage this situation? Can elements be added to the family planning program which boost the impact of increases in -ontraceptive use on population growth? The prospects for the Indian population depend crucially on the answers to these questions. 11 Sterilization is the most common form of fertility control in India (see ORG (1991) p. 83). 10 PPP produces a clear message for policy-makers. If you are Interested in saking more progress In the campaign for lower population growth rates Ia Iadia, you will need to understand the relationship between what is happening in the family planning progran and what Is happening to other forms fertility- influeasing conduct and to act on that unferstanding. Good luck may help reduce the Indian population growth rate in the future, but, in case that did not happen, good policies based on knowledge would make an excellent substitute. We have used India as an example here and have briefly shown how the parametric framework of PPP can be used to inform policy- making. This is certainly not a substitute for a fuller analytic recounting of the recent demographic history of India. Further, it neither answers the four questions posed above nor does it provide detailed guidance on what sort of contraceptive programs would likely be most effective. In our view, such a study is vital for good policy-making. Those tasks, however, must be left to other papers. The next step in this one is to demonstrate how PPP can be used to produce informative population projections. 11 3. Bauples of Parametrio Projections In order to illustrate the capabilities of PPP, we present five population projections for India here2. The first two we label as "optimistic" and "pessimistic". The "optimistic" scenario envisions rapid increases in the mean age at marriage (for both women and men), the contraceptive prevalence rate, and average time it would take for a woman who married at age 20 to bear her second child. It also assumes a relatively slow decline in the interval of protection due to breastfeeding and other fertility-affecting behavior. The "pessimistic" projection assumes slower increases in the mean age at marriage# contraceptive prevalence rate, and the time it would take a woman married at age 20 to have her second birth. Analogously, it maintains a relatively rapid decline in the interval of non- contraceptive protection. The third projection illustrates an intriguing capability of PPP. The ability to provide us with some clues as to the sorts of implicit assumptions which are made in current projections. In particular, we took the most recent published World Bank projection for India (as of December, 1990)13 assumed (what we considered to be) plausible time paths of all the parameters except the contraceptive prevalence rate, and determined the latter's course so as match the total fertility rates used in that projection. In this way, we obtained a one set of parameters which are consistent with that projection. Of course, there are many others, but, nevertheless, this process of extracting the underlying assumptions can provide a test of the plausibility of the projection itself. The fourth and fifth examples both take the third or what we call the "matching" projection as their base. The fourth scenario is exactly the same as the third except that the increase in the contraceptive prevalence rate is slower in the 1990's than in the third, but more rapid in the first decade of the new century. Projections 3 and 4 taken together show the consequences on the size, growth rate, and age structure of the population of a postponement in some of the increass in contraceptive use. Policy-makers may wish to know how sensitive future population size is to various dynamic paths of family 12 We do not mean to imply that these are, in any way, the most informative or most policy-relevant projections which can be made. Our objective here is only to put PPP through a light work-out, not to provide a substantive analysis of the possible future facing India. 13 Bulatao et al. (1989). 12 planning use. These two projections give one illustration of how PPP can be employed to provide the needed information. The fifth projection deals with the impact of the mean age at marriage of women on population growth. The "matching" projectic assumes that the mean age at marriage increases gradually from 19.3 in 1987 to 22.9 in 2045-49. In this last example, we maintain all the other assumptions, but keep the mean age at marriage at 19.3 throughout the period. By comparing this projection with the third one, we can learn about the importance or unimportance of marriage age changes to future population dynamics. All of the projections use the same mortality rates as those assumed in Bulatao 2t al. (1989). ASSUMED PATHS OF THE CONTRACEPTIVE PREVALENCE RATES 0.80 0.72 o.48 .. W.. ......epessimistic case Q.0.40 4 program prob'i "' case 0.32 8 0.24 t 0.16 0 0.08 0.0 II I I I 1992.5 1997.5 2002.5 2007.5 2012.5 2017.5 2022.5 2027.5 2032.5 2037.5 2042.5 2047.5 Mid-point of 5 Year Interval Figure 2A Figures 2A, 2B, 2C, and 2D show the hypothesized temporal patterns of the main parameters for the five scenarios. Let us consider first Projection 1, an optimistic case, and Projection 2, a pessimistic case. In the optimistic forecast, the mean age at marriage for women rises from 19.3 in 1987 to 23.5 in 2015-19 and remains at that level. The contraceptive prevalence rate rises from 42.8 percent in 1987 to 73.0 percent in 2015-19 and also remains constant thereafter. our broad measure of the influence of other factors on fertility, decreases from an interval of 17.8 months in 1987 to 10 months in 2025-29 and the time it takes to achieve an average of 2 children beginning at 13 ASSUMED PATHS OF THE MEAN AGE AT MARRIAGE "matc ng" case 25.0 - 22.5 ---. - 20.0 pessimistic case S17.5 constant case .- o 1 5.0 L . 05.0 <12.5 4) <10.0 C a 4) 7.5 5.0 2.5 1992.5 1 697.5 2002.5 2007.5 2012.5 2017.5 2022.5 2027.5 2032.5 2037.5 2042.5 2047.5 Mid-point of 5 Year Interval Figure 23 age 20 rises from 7.1 years in 1987 to 13.0 years in 2045-49. In the pessimistic case, all the anti-natal changes happen must more slowly. It is important to notice, however, that the pessimistic outlook still assumes substantial change in the direction of lower fertility. The mean age at marriage is assumed to rise from 19.3 in 1987 to 21.7 in 2045-49 and the contraceptive prevalence rate to rise from 42.8 to 69.0 over the same period. In addition, the average time it would take for a woman married at age 20 to have her second birth is specified as rising from 7.1 to 9.3 years. These influences are offset, substantially, by the simultaneous decrease in the duration of non-contraceptive protecttan from 17.8 months to 8.0 months during the projection period. Figure 3 shows the projection results for the five cases. Let us again concentrate first on the first two. Both illustrations begin with aA]14AUAA*14AUAAon of 850 million in 1990. By the year 2010, the population under the optimistic scenario would grow to 1.146 billion as compared to 1.291 billion under the pessimistic scenario. In other words, the population would be about 13 percent higher in 20 years in the pessimistic situation as opposed to the optimistic one. By the year 2030, the population size would be 48 percent higher under the pessimistic forecast, and by 2050 it would be 93 percent higher (2.782 billion as compared to 1.443 billion). These three 14 PATHS OF INTERVAL OF NONCONTRACEPTIVE PROTECTION 0 .01,4.4 '0. h e 12.6 0-10.8+ .s 9.0+.. o 72 "matching" case pessimistic case o 5.4 C o 3.6 z o 1.8 2 1992.5 1997.5 2002.5 2007.5 2012.5 2017.5 2022.5 2027.5 2032.5 2037.5 2042.5 2047.5 .C Mid-point of 5 Year Interval Figure 2C percentages, 13 percent over 20 years, 48 percent over 40 years, and 93 percent over 60 years, can be interpreted as upper bounds on the effectiveness of any family planning policies to reduce population size, because it is highly unlikely that any strategy could cause the alteration of all the parameters simultaneously from their pessimistic values to their optimistic ones. In other words, over a 20 year period, it would be highly unlikely that any program could reduce the rate of population growth by more than an average of 0.6 percentage points. Over a 60 year period, the upper bound on the reduction in the population growth rate would be 1.1 percentage points. More likely, any program effects would be much smaller. From a policy perspective how should reductions of population growth rates of, for example, half the maxima above, an average of 0.3 percentage points over 20 years and 0.55 percentage points, be evaluated? Are these large changes in population growth rates or small ones? PPP cannot answer these questions, but by formulating them quantitatively it can help in the framing of appropriate policies. The average rates of population growth in the optimistic situation are 1.5, 0.7, and 0.4 percent per annum respectively over the periods 1990-2010, 2010-2030, and 2030-2050. For the same periods the average rates of population growth in the 15 PATHS OF THE AVERAGE INTERVAL FROM AGE 20 TO 2 KIDS 13.0 10t .7 *,se 210.4 s "matching" case o ..... . ....... ..... . ... 7.8 .... ... . ****. . * pessimistic case 0 6.5 E 5.2 3.9 2.6 -1.3 0.0 1992.5 1997.5 2002.5 2007.5 2012.5 2017.5 2022.5 2027.5 2032.5 2037.5 2042.8 2047.5 Mid-point of 5 Year Interval Pigure 2D pessimistic scenario are 2.1, 2.1, and 1.7 percent per annum respectively. The average rate of population growth in India over the period 1981-87 was close to 2.1 percent per annum, so the time paths of the parameters from 1990 to 2030 provide an example of what would need to happen in India to keep population growth rates from rising given the assumed pessimistic changes in the duration of noncontraceptive protection. In other words, if the mean age at marriage for women increased gradually from 19. 3 in 1987 to 20.9 in 2025-29, the contraceptive prevalence rate increased regularly from 42.8 percent to 59.0 percent, contraceptive efficiency remained high at 0.90, and the average time it took for a woman married at age 20 to have 2 children increased from 7.1 years to 8.5 years, the. nonlation axyth rate would remain unaffeActedl All those changes would do nothing more than offset declines in mortality and in the duration of noncontraceptive protection. The pessimistic projection, then, is, in one sense, a continuation of the situation in the 1980's where there were changes in demographic behavior which were not sufficient to produce a consequential change in population growth rates. The pessimistic projection illustrates a powerful feature of PPP, its ability to retrieve parameters, such as the contraceptive prevalence rate, which are needed, under a set of 16 specified conditions, to obtain a desired rate of population growth. We use this same ability in our next example. Five Examples of Indian Parametric Population Projections 3Mo 0 proj.1 2700 a proj. 2 A proj. 3 '-2400 * ro. C + proj.5 .22100prj5 proj. 5 o proi. 3 0 1200 * ~9W ti. 600 300 0 1 1 1 1 1 1 1 1 1 1 1 1990 1995 2000 2005 2010 2015 2020 2025 2030 2035 2040 2045 2050 YEAR Figure 3 17 Figures 2A, 23, 2C. and 2D also contain the parameters for the case in which we match the total fertility rates used in the 1989 World Bank projection for India. In this instance, we specified the time profiles of the mean age at marriage for women, the contraceptive effectiveness rate, the total marital abortion rate, duration to 2 children for a marriage which begins at age 20, and the period of other noncontraceptive protection which were generally between the optimistic and pessimistic ones used in the first two examples. We, then, chose the contraceptive prevalence rate which produced the same total fertility rate for each quinquenium from 1990-94 to 2045-49 as was used in the World Dank0s projection. in essence, this exercise produces a set of parameters consistent with the Bank's projectioO4. The numbers for the contraceptive prevalence rate in Projection 3 are those which, given the other parameters, were implicit in the Bank's projection"5. These implied prevalence rates present a portrait of continuity. They begin by showing a diminution of the rapid rate of progress made in the 1980's6, and, progressively ever slower rates of increase until a stable figure of around 73 percent is attained in 2010-14. In roughly two decades, then, the fertility transition in India is expected to be complete"7. What would happen to Indian population growth, though, if the matched contraceptive prevalence rates were overly optimistic in the short-run? Suppose for a moment that,, in the period from 1987 to 1990-94, the Indian family planning program experienced difficulties and that progress in increasing the contraceptive 14 Matching the total fertility rates does not guarantee that the projected population sizes match exactly, because population growth depends on both the total fertility rate and the mean age at childbearing. The mean ages are childbearing are somewhat different between PPP and the World Bank projection, but the effects of this on population size are inconsequential. 15 Note that the implicit contraceptive prevalence rates are initially higher than those in our optimistic case, yet our optimistic population projection is lower. This is because our optimistic scenario is optimistic on all the fertility determinants not just the contraceptive prevalence rate. 16 From 1981 to 1987 the contraceptive prevalence rate grew at about 3 percentage points per year. Over the period 1987 to 1995-99, the implicit rates grow by about 1.6 percentage points per year. ITWe actually do not need the contraceptive prevalence rates to see this. The World Bank's projection is hypothecated upon India reaching replacement level fertility in 2015-19. 18 prevalence rate came to a virtual halt". Let us further mgine that the program eventually becomes rejuvenated and that by 2005-09 the contraceptive prevalence rates returned to the level in Projection 3 and remain essentially identical to those rates through 2045-49. What would be the effect of that period of programatic distress on size of the Indian population? We will see in a moment, but for now let us put the question more precisely. The alternative contraceptive prevalence rates, which assume almost no progress between 1987 and 1990-94 and full recovery by 2005-09, are shown as Projection 4. All the other time paths of parameters remain as in the third projection. In 1990-94, the contraceptive prevalence rate would be 45.0 percent instead of 50.5 percent. In 1995-99, it would be 50.0 percent instead of 58.0 percent and in 2000-04, it would be 58.0 percent instead of 63.0 percent. The problems experienced by the program, in this scenario, reduce the contraceptive prevalence rate by an average of slightly over 6 percentage points each year during the 1990- 2004 period. The effect of the fifteen year period of lower contraceptive prevalence rates can be seen in Figure 3. The Indian population would be 3 percent higher in 2010 with the lower contraceptive prevalence rates as compared with the higher ones. By the year 2050, the population would be 5 percent larger. Over the period from 1990 to 2010, the weaker program would result in the rate of population growth increasing from 1.60 percent per year to 1.76 per year. In a technical sense, we could have told this story in reverse just as well. We could have begun with the lower contraceptive prevalence rates and asked about the quantitative effect of a program which increased contraceptive prevalence rates around 6 percentage points per year in the 1990-2004 period. The answer, given the assumptions presented in Figure 2, would have been that India's population size would have been reduced by 3 percent by 2010 and 5 percent by 2050. This is an example of how PPP could be used in cost-benefit type analyses of population programs. Suppose that policy-makers were proposing a project which was designed to raise contraceptive prevalence rates from those in Projection 4 to those in Projection 3 and which cost $100 million. PPP would show that the effect of the program would be a 3 percent decrease in the population size over 20 years and a 5 percent change over 18 Fortunately, this is very far from being the case. Quite to the contrary, recent data show continuing declines in fertility through 1989. 19 60 years. Policy-makcers could, then, decide whether that effect were large enough to justify the $100 million expenditure. The final projection shows the effect of changes in the mean age at marriage for women on population growth. The parameters are the same as those for the matched projection in Figure 2, except that the mean age at marriage is assumed to remain constant at 19.3. The effect is shown in Figure 3. In 2010, the population with the lower age at marriage would be 2 percent larger. By 2030t it would be 9 percent larger and by the mid- 21st century, it would be 21 percent higher. over the 2 decades, 1990-2010, the lower age at marriage would cause an increase in the rate of population growth from 1.60 to 1.72 percent per annum. Over the entire period from 1990 to 2050, the corresponding growth rates would be 1.09 and 1.42 percent per annum. To put these same figures in a somewhat different perspective, note that under Projection 3, the Indian population would grow by 70 percent between 1990 and 2030; if the mean age at marriage did not change, the population would grow by 84 percent. in this section, we have illustrated how PPP could be used to provide an additional quantitative dimension to policy analysis and dialogue. These examples provide neither a badly needed analytic inquiry into future Indian population trends nor do they exhaust the possibilities of MPP. They are meant only as appetizers. Appropriate main courses, full-scale country analyses using PPP, must,, unfortunately, await another sitting, but some meat does remain to be served. in the following section, we discuss the methodology of PPP. For those who are not hungry for that kind of detail or who do not like the flravor of methodological discussions, we recommend that you go directly to the dessert in Section 5. There you will find a light discourse on the advantages and disadvantages of PPP as compared with conventional schedule-based projections. 19 An analytic inquiry into future population trends would need to be based on assessment of how the proximate determinants influence one another, are influenced by factors such as changes in literacy rates, and how they are influenced by various sorts of government policies. In other words, it would move back one step to a formulation of a model of the causal antecedents of the proximate determinants. Such a model could be used to ascertain what the effects of a multidimensional family planning program, such as the one suggested in Section 2, would be. 20 4. PP Kethodology In this initial version of PPP, we parameterize only age- specific fertility rates. In practice, we utilize future mortality rate, and net immigration rate projections kindly provided to us by The World Bank. The mortality rates are themselves parameterized and depend on an infant mortality rate and an adult liZe expectancy. Age-specific fertility rates may be written as the product of two terms: (1) age-specific proportions currently married, and (2) age-specific marital fertility rates". We write: * (a) -X(a) -p(a)() where *(a) = the age-specific fertility rate at age a, x(a) = the proportion of women of age a who are currently married, and p(a) = the marital fertility rate at age a. In PPP there are separate parameterizations for the age- specific proportions currently married and for the age-specific marital fertility rates. 4.1 Parameterisation of the Age-Specific Proportions Currently Married We write the proportion of women currently married as follows: X (a) - [y (a) - 8 (a) I [1 - w (a)] + [y (a) -(a) ] * (a) *p (a) (2) 2 This formulation impli*s that nonmarital fertility is small enough to ignore. Where informal marriages are common, we include women in those arrangements as being currently married. Where there is a consequential amount of childbearing outside of both formal and informal marriage, PPP should include a parametric representation of nonmarital fertility. 21 where x(a) is the proportion of married women at age all in the specified year, y(a) is the proportion of ever married women at age a in the specified year, 6(a) is the roportion of women at age a who are either divorced or separated in the specified year, w(a) is the proportion of women of age a who were ever widowed prior to or including the specified year, and p(a) is the proportion of ever-widowed women of age a, who are remarried as of the specified year. We proceed by showing how each of these age-specific schedules can be parameterized. Coale and McNeil(1972) provides a parametric specification of the age-specific proportions of women ever married. This formulation has been thoroughly tested and found to fit the data quite well in a large number of cases. We use this as the basis of the PPP schedule of the proportions currently married. According to Coale and McNeil, the age-specific proportions currently married can be expressed as: a y(a) - 0.1946cfr(a) da (3) 0 where r(a( ) (&-ao-6. 06k)* a0 is the earliest age at which a consequential number of women first get married, 21 It is important to recall that our definition of marriages includes women who are living in informal unions as well as formal ones. n If appropriate data are not available, it may occasionally be necessary to just use the proportions currently divorced here. 22 c is the proportion of women ever married, k= smam - ao 11.37 and, smamf is the singulate mean age at marriage for females2, Equation 3 allows us to express the proportion ever married by age using three parameters, the age at which a consequential number of women first marry an, the mean age at marriage, smam, and the proportion of women who ever marry, c. Widowhood is a more complex phenomenon because it depends on the path of past sale mortality rates. To our knowledge there are no parametric models of female widowhood as a function of male mortality rates, but there do exist methods for the estimation of male mortality based on the proportions of women ever widowed. One such method, which appears in United Nations (1983, pp. 122-126) suggests the use of the following equation for the estimation of male mortality: s (a, 20) - &o (a) + a, (a) *swmf + a (a) *Smam, + a3 (&) * (a-5) (4) where s,(a,20) is the probability of a male surviving from age 20 to age a, smamf is the singulate mean age at marriage of females, smam is the singulate mean age at marriage of males, and 23 The singulate mean age at marriage is just what the mean age at marriage would be given a fixed set of age-specific marriage rates and a population with the same number of women at each age. The singulate mean age at marriage is utilized here instead of the mean age at which women marry in a given year because it removes the influence of the age structure of the female population. 24 This survival rate has a different reference date from the three right- hand side variables. As age increases the reference date for the survival rate recedes further back in time. A full discussion of this appears in United Nations (1983, pp. 111 - 114). 23 w(a) is the proportion of ever-married women of a who have ever been widowed, and the af (a-5) are sets of age-specific constantsa. Since the w(a) are exactly what we need for equation _2) and the s (a,20) can be computed from past male survival rates?, it is natural just to rearrange equation (4) to obtain: w (a) - s.(a, 20) - a0 (a) - a1 (a) Mam - az (a) SMam (5) a3(a) Equation (5) allows us to express the proportions ever- widowed as a function of two parameters, the singulate mean ages at marriage of females and males. The age-specific proportions of ever-married women who are currently remarried in the period in question, the p (a), are bounded between 0 and 1. They are likely to be higher for younger women and lower for older women. We postulate, therefore, that these remarriage rates follow a logistic pattern with respect to age, and so we write: AL.*(a - Az1)(6 p (a) - e*( 1 1 + eA*a- Az) where p (a) is the proportion of ever-widowed women of age a who are currently remarried, and A, and A. are the logistic parameters. 25 These age-specific constants appear in United Nations (1983), Table 97, p. 112. 2 The "past" male survival dates are rates which predate the poriod of interest. Suppose, for example, that we were making a projection for 2010-14. The *past" male survival rates would be those experienced before 2010-14. Those rates would still be in the future as of this writing, but they are in the past with respect to the reference year of the projection. 24 It would not be appropriate to use the two A parameters in PPP because they have no direct interpretation. So, we take one more step and express the A's as a function of p(20) and p(49). A little algebra is all that is necessary to see that: p (49) . - 1 p(20) 1o i 1 2p(49)] 19 - p(20)] (7) 29 and 20*1 p(49) - 49*14 p(20) . 1 - p(49) 1 - p(2o)] 8 1 p(49) - 1 p(20) q1 - p(49) -1 n1 - 0(20)] Equations (6), (7), and (8) allow us to obtain all the necessary age-specific remarriage rates from two parameters, the values of those rates at ages 20 and 49. In the case of the 6(a), we deviate from our standard procedure. Instead of formulating a method for parameterizing the 6(a), we simply use a convenient $(a) schedule27. As a practical matter, the 6(a) tend to be small, usually less than 5 percent, and in this range, they have little impact on the projections. It would have been a very simple matter to parameterize the 6(a), but we did not see the point in it. In summary, the parameters for the age at which women first start getting married in appreciable numbers, their mean age at marriage, and the proportion of them who ever marry is sufficient to determine all the y(a)'s, the age-specific proportions of women ever married. The parameters for the mean ages at marriage for females and males, along with past male mortality rates is enough to produce the w(a)ls, the age-specific proportions of women ever vidowed. The proportion of ever widowed women remarried at ages 20 and 49 is what is required to produce all the p(a)'s, the age-specific remarriage rates. These schedules along with the 6(a)'s enter into equation (2) to produce our parametric age-specific proportions currently married. In general, we use the latest available data. 25 4.2 Parameterisation of the age-speoifti Marital Fertility Rates For our purposes, the best analytic representation of age- specific marital fertility rates is due to Coale (1971) and Coale and Trussell (1974) . They write: P (a) M*q (a) *e (a) (9) where p(a) is the marital fertility rate at age a, q (a) is the "standard" age-specific marital fertility rate at age a in the case of no parity-specific fertility control, a(a) is a set of constants reflecting the differential age- specific effects of contraception:, and M and n are the two parameters. Differences in N values capture variations in age-specific fertility rates which are due to dissimilarities in factors such as the length of breastfeeding and to the practice of contraception at young ages. Variations in the a's are caused by differences in the extent to which the practice of contraception increases with age. The parameters N and m are not of direct usefulness to PPP because they lack easy interpretability. Our approach, then, it to find a set of easily understood and policy- relevant parameters which can be mapped into M and m. The Bongaarts proximate determinants approach (see Bongaarts (1978) and Bongaarts and Potter (1983)) has been frequently used to decompose changes in the total fertility rate. It is of interest here because it incorporates variables such as the contraceptive prevalence rate and the contraceptive efficiency rate and so includes factors which may be of concern to decision- makers. An alternative would be to use the formulation in Page (1977). In the Page approach, age-specific marital fertility rates depend on the duration of marriage as well as age. Incorporating duration of marriage into our framework would make it considerbly more cumbersome, and would make analyses of countries like India, which do not make the micro-level data from fertility surveys available to the research community, impossible. 2 The values of r9(a) and v(a) can be found in United Nations (1983) p. 24. 26 Bongaarts and Potter (1983) suggest a simple approximation to the total fertility rate: ef - C- C,* CO Ca * 15.3 (10) where C, C C^ ^ and C are a set of indices which range between 0 and MadWich reflect the proportionate decreases from the maximum possible level of fertility due to marriage, the period of post- partum nonsusceptibility, contraception, and induced abortion respectively, and 15.3 is the maximum possible fertility levels. They also offer the following specifications for the C3, Cir Co, and C,: 49 9 X (a) -p(a) E P (a) a-ls where C, is the proportionate decrease in fertility resulting from marriage rates of less than 100 percent at each age, x(a) are the age-specific proportions of women of age a who are currently married, and p(a) are the age-specific marital fertility rates. C, a 20 (12) 18.5 + ( 3 Bongaarts and Potter (1983) use the 15.3 figure in their empirical work, but stress that this figure, which they call TF, is best considered to lvave a range between 13 and 17 (see pp. 87-99 for example and Bongaarts(1978)). 27 where C1 is the proportionate decrease in fertility resulting from any breastfeeding, postpartum abstinence, or any other factor which lengthens the period of nonsusceptibility between births, and i is the length of the period of postpartum nonsusceptibilityl. Cc - 1 - 1.08*u*e (13) where C is the proportionate decline in the total fertility rate due to the use of contraception, * is the contraceptive prevalence rate, and e is the contraceptive effectiveness rate. Catfz (14) tfr + 0.4(1 + u)*Ca where C is the proportionate reduction in the total fertility rate due to induced abortions, ta is the total abortion rate:, tfr is the total fertility rate, and u is the contraceptive prevalence rate. Combining equations (10) through (14), we have 31 The standard notation is a trifle confusing here. The subscript I in C1 differentiates it from the other C's. The value of I in equation (12) is the length of the period of nonsusceptibility. 32 The total abortion rate is defined analogously to the total fertility rate. It is the number of induced abortions that a woman would have over her lifetime if she experienced a given set of age-specific abortion rates (usually those for a particular year). 28 49 t a-a (a 20 *(-108e)r*5 ( f9 18.5+f tfr+0.4(1+u)tal a-15 where all the variables have been defined above. 49 Since E Z(a) *p (a) is, by definition, the total fertility a-15 49 rate,and p p(a) is, by definition, the total marital fertility a-15 rate, we can rewrite equation (15) as: tmfr ( 20 *(1-1.08ue) fr *15.2 (16) 18.5+i efr+0.4 (1+u)ta) Equation (16) has four multiplicative terms. The first can now be interpreted as the proportional decrease in the total mrital, fertility rate due to the period of nonsusceptibility, the second, the proportional decrease in the total marital fertility rate due to contraception. The third term, in contrast, is anomalous. It clearly refers to the proportionate decline in the total fertility rate (not the total marital fertility rate) due to the presence of induced abortions. In order to make equation (16) consistent, we rewrite the third term to obtain: tmfr ( 20 (1-108ue)1 *15.3 (17) 18.5+1 ftmfr+0 .4(1+u) tea where tma is the total marital abortion rate3. 33 The total marital abortion rate is the number of abortions a woman married at age 15 would have is she remained married to age 49 and experienced a given set of age-specific marital abortion rates (usually those for a particular year). Non-marital abortions have never played a role in the Bongaarts framework (see Bongaarts and Potter (1983, p. 85)), so the transformation here of the total abortion rate to the total marital abortion rate makes that structure more consistent. If fertility outside of formal and informal unions is significant and nonmarital abortions play a consequential role 29 Solving equation (17) for the total marital fertility rate, tafr, yields: tmfr _ 20 1 - 1.08*ue) 15.3 - 0.4*(l - u) *tma (18) 18. 5 + i There are two practical problems which must be solved before equation (18) can be used here. The first issue is how to treat the marital fertility rates of 15-19 year olds and the second is how to compensate for imprecision and incompleteness of the Bongaarts framework. The marital fertility rates of women 15-19 are often suspiciously high. Because of adolescent subfecundity, we would expect to find the rates lower for 15-19 year olds than for 20-24 year olds, but in the data this is frequently reversed3. This inversion is probably caused by a combination of two factors. First, in countries where the mean age at marriage is relatively high, say above 23, most of the women who are married at age 15- 19 have been in that status only a short time. Virtually all of those women, except the pregnant ones, are at hazard of conceiving; almost none of them are breastfeeding a child or practicing post-partum abstinence. Therefore, the number of woman years of susceptibility per woman year of calendar time is higher for these women than it is for their older sisters. The second factor is pre-nuptial pregnancies. In some countries, a fairly substantial number of brides in the 15-19 age group are already pregnant at marriage and, since they have a birth shortly after marriage, the age-specific marital fertility rates are inflated. The importance of pre-nuptial pregnancies for the marital fertility rates of 15-19 year olds varies across countries and over time and it is not captured by any of the Bongaarts parameters. Our solution to this problem is an adthoc one. First, we revise equation (18) so that it refers to women 20-49, and second, we introduce a parameter which reflects the extent to in reducing it, both the Bongaarts approach and PPP would need to be modified accordingly. 3 For example, the marital fertility rates for 15-19 and 20-24 year old Indonesian women were recorded as 0.419 and 0.307 respectively in the 1987 Indonesian DHS (Indonesia (1989)). 30 which the age-specific marital fertility rate is above what we would expect it to be3s. Modifying equation (18) so that the 15-19 years olds are removed is not a straightforward task. The first and only obvious step is to convert the constant term at the end of the equation to one which is appropriate for the truncated age span. That figure standardizes the level of fertility such that women who married at age 15, lived continuously with her husband through age 49, never breastfed, and never practiced any form of fertility control would have an average of 15.2 children. Similar women who married at age 20 would have an average of 12.8 children6, so the 15.3 in equation (18) needs to be replaced by 12.8. The bothersome question is what else should we do. There is no clear need to alter the constants in the equation. They reflect empirical approximations, which are not likely to be much worse for 20-49 year olds than for 15-49 year olds. The problem is whether we ought to change the interpretation of the parameters i, u, e, and tma, so that each one of them referred to the age group 20-49. For example, ought u now be construed to be the contraceptive prevalence rate among 20-49 year old women? At first glance, it seems evident that the answer ought to be in the affirmative, but, on second thought, it is not so obvious. The existence of the contraceptive prevalence rate as a variable in equation (18) is itself anomalous. The total marital fertility rate and the total marital abortion rate are measures from which all influences of the age structure of the population have been eliminated. The contraceptive prevalence rate, on the other hand, is affected by the age structure because we would expect the age-specific contraceptive prevalence rates not to be constant. The comparable variable to have in the ernation is the total contraceptive prevalence rate for women 20-49 , but this figure rarely occurs in the literature on family planning and in some cases may be impossible to compute because of lack of data8. So, we are faced with a trade-off here. The contraceptive prevalence rate for 15-49 year olds is easy to 3 The concept "above what we expect it to be" is certainly vague. We beg the pardon of the reader. Below, we will show precisely how we determine "what we expect it to be" and how the parameter comes into play. 36 The 12.8 figure is computed from data in Bongaarts and Potter (1983) footnote 3, p. 115. 3 This is defined as the sum of the age-specific contraceptive prevalence rates from age 20 to 49. 3 This would be the case for India in 1985, for example. 31 understand and readily available, but its use entails some approximation error. The contraceptive prevalence rate for 20-49 year olds is easy to understand, but not as readily available. The use of this variable would possibly involve less error. Probably the best variable to use would be the total contraceptive prevalence rate. This is less easy to understand and much more difficult to obtain. PPP is designed to be of use to policy-makers and so we have adopted the approach of Bongaarts to emphasis interpretability and simplicity at the expense of exactness. In this implementation, therefore, we have left the parameters u and e as they are most commonly defined, that is, referring to all married women of reproductive age. We do not expect the approximation error entailed in this decision to be consequential, because even in the case of India, where the marriage age is still relatively low, around 95 percent of all currently married women of reproductive age are between the ages of 20 and 49. Further, it would have been very confusing, given the use of the Bongaarts framework here, to have the major variables defined differently. Indeed, it is one aspect of the simplicity of PPP that it is immediately accessible to those familiar with the proximate determinants approach. In the case of India, age- specific contraceptive use rates are not available for 1985 and 1987, so the history presented in Section 2 would not have been possible with anything other than the contraceptive prevalence rate for women 15-49. These considerations lead us to the following revised version of equation (18): tmfro2 ( 20 )(1 - 1.08*ue)#12.8 - 0.4*(1 - u)*tma (19) (18.5 + I where tafr is the total marital fertility rate defined from age 20 onwards, and all the other variables are as defined above. The genius of the Bongaarts framework is its simplicity and interpretability. The cost of this is in precision. The lack of exactness arises because the formula for the decomposition of the total fertility rate is approximate, there are omitted fertility- affecting factors, the formulae for the included determinants are approximations, and because some of the determinants are themselves measured with error. The error is not large. Bongaarts and Potter (1983, Tables A:.2 and 4.3, pp. 88 - 91) show that it is generally smaller than 10 percent for a wide variety 32 of countries, although Casterline &al... (1984) indicates the errors are somewhat larger'. For our purposes, the existence of the error is not nearly as worrisome as the possibility that the error could vary over time. This might occur for a number of reasons. In any event, we would be left with a predicament. If some fertility-influencing component like the length of breastfeeding or coital frequency is varying over time or it the approximation error is changing, this too must be projected into the future, but how can we project what we cannot measure? The answer to this conundrum is to establish a residual category which encompasses all unmeasured factors and approximation errors, to measure how this value varies historically, and to use that information in the projections. We do this by reinterpreting, the Bonqaarts variable J. In the estimation phase (see Section 2 for example) instead of attempting to measure L directly, exploiting information on breastfeeding and perhaps on post-partum abstinence, we treat 1 as residual. The parameter J, measured in this way, not only captures the effects of changes in breastfeeding and patterns of post-partum abstinence, but it also incorporates variations in unmeasured fertility influences and in the degree of approximation error. The history of the parameter L, determined by this procedure, provides us clues as what to expect in the future even from factors which cannot be directly measured. In the estimation portion of PPP, we determine J by rewriting equation (19) to obtain: 256.*(1 - 1.08*u*e) - 18.5 (20) tmfrao + 0.4*(1 + u) *tma We use this equation to determine the time path of J, given the values of the other parameters and the observed tafr. Once we know the recent history of the parameters, including J, we use them to compute future values of the total marital fertility rate. Now let us return to our task of showing how a set of easily interpretable policy-relevant parameters can be mapped into the two Coale parameters N and m. Since the total marital fertility 49 rate in equation (19) is E p(a) , combining it with equation a-20 (9) produces one equation in the two unknowns, 1 and a: 39 Casterline et al. (1984) contains a detailed description of the sources of approximation in the Bongaarts framework. 33 ,820 (*(21) To complete the task of determining the N and a, we need a second equation. Our choice here is determined by what we perceive to be an important policy issue in program design. In some countries, like India, the family planning program concentrates on providing sterilization. Programs of this variety influence fertility later in the reproductive span and have little direct impact on tLe fertility of younger women. Other family planning programs offer couples more choice of contraceptive techniques and try to aid younger couples who nee' a temporary form of contraception in order to space their children. We try to capture this kind of difference in program emphasis by introducing a parameter which is the time is takes women married at age 20 to achieve an average of 2 children. We denote this time by T. This provides us with our second equation in N and m: E M-q(a)*esrote) - 2 (2 8-20 Equations (21) and (22) are two nonlinear equations in the two parameters X and m. Given i, u, e, tma, and T, they are easily solved for N and a on personal computers". From equation (9), the X and a immediately generate the age-specific marital fertility rates which are consistent with those parameters. We are now left with only one loose-end to attach to our exposition, the determination of age-specific marital fertility rate at age 15-19. Since v(15-19) is zero in the Coale age- specific marital fertility specification, the N value determined above can be entered into equation (9) to determine the "expected" age-specific marital fertility rate at age 15-19. We compute the ratio of the observed age-specific marital fertility rate at 15-19 to the "expected" one for the most recent possible date and apply it to future "expected" rates in order to determine the projected age-specific marital fertility rate at age 15-19. 40 All our computer work including the solutions of these simultaneous nonlinear equations for each projection period was done using the GAUSS programming language. 34 5. A Compariso Between schedule-Sed Projections and PP Zs it a good idea to stop producing schedule-based projections and replace them with parametric projections? To answer this question, let us compare the two methodologies in three dimensions (1) accuracy, (2) ease of computation, and (3) ease of interpretability. Population projections are notoriously inaccurate itt the medium term and beyond and sometimes in the short-run as well". For example, the total fertility rate in Bangladesh has fallen so rapidly in the latter half of the 19800s that population projections made in the middle 19800s now appear to be dramatically too high. Unanticipated changes in underlying demographic factors will always play havoc with projections regardless of whether they are schedule-based or parametric. Although parametric and schedule-based projections have different methodological strengths and weaknesses, overall neither can be said to be superior to the other. The strength of the parametric approach is that it can predict more flexible, and possibly more accurate age patterns of fertility. The corresponding weakness is that it is possible that this flexibility is carried to an extreme and that unlikely age profiles are produced. The strength of the schedule-based approach is that the schedules could embody implicit interactions between the fertility determinants which would be difficult to embed into an analysis in which all the components were projected separately. The corresponding weakness is that it is there is no natural avenue available to employ insights about the course of the separate components. Therefore, at this time, there is no way assessing which method would produce more accurate results. Schedule-based projections are less burdensome to compute than are parametric ones. The analysis of how a single schedule might change in the future may be easier than the investigation of how 3 or 4 major parameters could change. In addition, the schedule-based projection model is basically a linear one which needs no special estimation techniques. The parametric technique, on the other hand, requires the simultaneous solution of two nonlinear equations for each projection period. Although this is not difficult nowadays, it is more troublesome than the simple calculations required by the schedule-based approach. On the other hand, the parametric procedure is strikingly more informative and much more easily interpreted than the 41 See for example Ahlblrg (1987), Ahlburg and Vaupel (1990), Cohen (1986), Keyfitz (1981), and Soto (1983). 35 schedule-based one. All sorts of policy-relevant investigations, such as those discussed in Sections 2 and 3, can be carried out with parametric projections, but cannot be performed using schedule-based projections. The basic axis of tradeoff, then, is between ease of computation and informational content. Schedule-based projections are easier to compute, but provide less policy guidance. Parametric projections provide more scope for analysis, but are more difficult to calculate. Someone running a shop in which a large number of projections are regularly produced would probably wish to remain with schedule-based projections. Someone interested in policy issues related to the family planning program of a given country would probably find parametric projections more useful. 36 6. Conclusions In this paper we have developed a new methodology for making population projections and have shown its usefulness for policy analysis by studying the case of India. In Section 2, PPP shows that factors normally excluded from family planning programs have varied enough in India during the period from 1980 to 1987 to offset virtually all the gains due to the increased use of contraception. Almost none of the very substantial increase in contraceptive use was translated into decreases in the population growth rate. It appears that the family planning program has been too narrowly constructed. In order for more of the gain in the use of contraception to be transformed into reductions in population growth, the program must be able to affect more aspects of reproductive behavior than it currently does. Unfortunately, our knowledge of the interrelationships between various forms of fertilty-related behavior is weak, especially in India, where the basic micro-level data have never, to our knowledge, been analyzed from this perspective. This lack of understanding produces severe limitations on the formulation of effective policies to reduce the rate of population growth. Further, we see in Section 3, that population policies which influence only the contraceptive prevalence rate have limited effect on the population growth rate in any case. There we learned that a family planning program, which increased the contraceptive prevalence rate by an average of 6 percentage points per year in the 1990-2004 period, would only decrease India's population in 2010 by 3 percent. Again, it appears that effective policies to reduce the growth rate are most likely to be those which affect more than one of the proximate determinants of fertility. What appears to be needed is a broad multiphasir. population program. We have used PPP to analyze the demographic situation in India from a policy perspective and to suggest approaches to reducing the rate of population growth. In the process, we have shown that PPP has produced insights which were not available elsewhere. Applications of PPP to other countries in Asia are now being prepared. 37 Appeais I The Coale-McNeil nuptiality function (equation 3) is used to estimate the three parameters: a0, the age at which a consequential number of women first get married, c, the proportion of women who ever marry, and smamf, the singulate mean age at marriage for females. Let us define: 45-49 G - E (y(a)-yo(a))a (Al) a-3.5-19 where 1(a) is the proportion ever married at age a from equation (3), and, ,o(a) is the observed proportion ever married at age a. For 1981, we determined the three parameters by minimizing G, the residual sum of squares. The data for this is found in India (1990, Table A-10, p. 90) and comes originally from the 1981 Census of India. For 1985 and 1987, the observed proportions ever-married by age are not available. For those years, we estimated the three parameters using equation (Al) for the ages 15-19, 20-24, and 25-29, replacing the observed proportions ever married at age a with observed proportions currently married at age a. We tested this procedure on the 1981 data, where we know both the age-specific proportions currently married and ever married and found that the resulting parameters were nearly identical. It works because in India, at ages below 30, there are very few widows who are not remarried. The data for proportions currently married are computed by dividing age- specific fertility rates by age-specific marital fertility rates. The data come from India (1987 and 1989). The two p parameters in equations (7) and (8) are determined by minimizing H, where 38 45-49 r Q-1 ((a) - 0a)2 (A2) 8*5_19 x(a) is the proportion of women of age a who are currently married, from equation (2), and xo(a) is the observed proportion of women of age a who are currently married. These proportions are found in the three sources cited above. The parameter L in equation (20) is computed directly from equation (20), given values of the contraceptive protection rate, the contraceptive effectiveness rate, the total marital abortion rate, and the total marital fertility rate from age 20 onward. The contraceptive prevalence rate is from India (1990, Table E-1, p. 216). The contraceptive effectiveness rates come from the application of U.N. medium method-specific effectiveness rates to the method mix in India in 1987. Since there has been little change in the method mix, we did not recompute it for each of the years. The total marital abortion rates were assumed to be zero in the 1980's. We know that the rate was above zero, but it was probably small enough to ignore. The total marital fertility rates and associated age-specific marital fertility rates come from India (1983, 1987, and 1989). In order to compute the time it took a woman married at age 20 to have an average of two children, we had to estimate the M and m parameters in equation (9). Since the g(a) are observed in the sources cited above, the N and a parameters were estimated using a weighted linear regression after taking logarithms on both sides of equation (9). The weights were the observed age- specific proportions currently married. In the estimation of M and m, we used only observations from women 20-24 through 40-44. Given M and m, the parameter T, the time it took a woman married at age 20 to have an average of two children, is determined from equation 22. 39 Appendix 2: The Program Used to Compute the Age-Specific Fertility Rates /*This program takes the parameters and produces age-specific fertility rates to be used in The World Bank's population projection model. We will use 12 quinquennia from 1990-95 through 2044-49. THIS PROGRAM IS WRITTEN IN THE GAUSS PROGRAMAING LANGUAG8. CAUSS IS A PRODUCT OF APTECH SYSTEMS INC. 26250 196TH PLACE SOUTHEAST KENT, WASHINGTON, 98042 (206) 631-6679 The program is reproduced here for the -purpose of historical documentation. If you wish information on how to run it, please phone or write: Warren Sanderson Department of Economics SUNY Stony Brook Stony Brook, New York, 11794-4384 U.S.A. (516) 632-7550 Warren C. Sanderson 12/5/90 */ new; use optmm; library optaum; output file - out4.out reset; output on; screen on; printl-O; x0 - 0.65011.00; Qthese are the starting values; they may have to be changed in case the optimisation does rc. : work INPUT AMA INPUT ARTA INPUT AREA Q ,coode s "indi*; Q this is a four letter code for the country@ oname - "India - implicit Bank scenario *; @ run title 6 fage at which a consequential number of women first marry Q let aO - 12.9 12.9 12.9 12.9 12.9 12.9 12.9 12.9 12.9 12.9 12.9 12.9; Qproportion of women who ever marry Q let a - 0,96 0.96 0.96 0.96 0.96 0.96 0.96 0,96 0.96 0.96 0.96 0.96; 40 Ccan ag at marriage for wonen f ist sast - 19.6 19.9 20.2 20.5 20.8 21.1 21.4 21.7 22.0 22.3 22.6 22.9; Qte dIfferenoe betwen the aean ego at marriage for men and for woen ( lt dit - 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4; oontruaceptive prevalonce rat e let u - .505 0.58 0.53 0.67 0.72 0.73 0.73 .725 0.73 0.73 0.73 0.73; Qoontraeoptive effectivenss rat* @ lat o - 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90; etotal marital abortlon rate @ lea tsa m 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00; @length of the period of protoction duo to other forma of family limitation 6 let £len - 15.0 14.0 13.0 12.0 11.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0; *1.ength of the period from ap 20 to an average of 2 children Q 1t durm2 - 7.5 8.0 8.5 9.0 9.5 10.0 10.0 10.0 10.0 10.0 10.0 10.0; etatio of ourZntly divorced to ever married by age l dratio - ( 0.010 0.010 0.009 0.009 0.008 0.008 0.007 ); massumed constant ove: time @ fproportiong of ever vidowed who are remarried at age 20 and at age 49 @ let raate e 0.99 0.13; asaumd contant over time Q @rat1o of merital fertility at age 15-19 to mrital fertility at age 20-24Q r1520 m 0.7969; 05 male ~urvival rates for each projection period @ sr - ( 0.98650 0.97148 0.95358 0.93033 0.89814 0.85154, 0.98831 0.97522 0.95953 0.93885 0.90974 0.86765, 0.98939 0.97793 0.96467 0.94696 0.92086 0.88204, 0.99022 0.97979 0.96774 0.95211 0.92969 0.89567, 0.99107 0.98152 0.97037 0.95589 0.93520 0.90318, 0.99191 0.98324 0.97301 0.95952 0.94002 0.90954, 0.99257 0.98497 0.97566 0.96316 0.94485 0.91593, 0.99360 0.98670 0.97831 0.96680 0.94971 0.92236, 0.99396 0.98774 0.98063 0.97046 0.95459 0.92883, 0.94492 0.98857 0.98172 0.97249 0.95851 0.93534, 0.99538 0.99000 0.98341 0.97445 0.96108 0.93923, 0.99606 0.99147 0.98583 0.97766 0.96464 0.94285 ); * END OF INFUT R EEND OF INPUT ARE END OF INPUT ARE N0TRING SLOV TMIS LINE SHOUW BE ~KANGED!! II! 41 • ass a na 3'a •$crna; 4tato -søros(3,1)|ato'..ns(,) = (aaaaO)./11.37; n note that k is a 12 x 1 vector * g~ bb ••(1n2-lnl)./29; c4 (20.*1n2 - 49.*1n1)./(1n2-n); r~r ones(B,1) (1./(1+ep(bb.*(aget-c))); let cof (0.1082 -0.00209 0.00072 0.9136, -0.0284 -0.00465 0.00157 1.0822, -0.0159 -0.00638 0.00253 1.0831, 0.0041 -0.00784 0.00395 1.0596, 0.0152 -0.00953 0.00611 1.0324. 0.0087 ••0.01189 0.00925 1.0144); let n - 0.460 0.431 0.395 0.322 0.167 0.024; let v t 0 0.279 0.667 1.042 1.414 1.671; vGD-v; outtI-0; outt2-0; let n5 - 0.411 0.460 0.431 0.393 0.322 0.167 0.024; lot v5 - 0 0 -0.279 -0.667 -1.042 -1.414 -1.671; let n - 0.325 0.375 0.421 0.460 0.475 0.477 0.475 0.470 0.465 0.460 0.435 0.449 0.442 0.435 0.428 0.420 0.410 0.400 0.389 0.375 0.360 0.343 0.325 0.305 0.280 0.247 0.207 0.167 0.126 0.087 0.055 0.035 0.021 0.011 0.003; sume(n[6:35,11); 8so(n(21:25,1))-sumo(n[26:43,1))-si.me(n[31:35,13); ay./5; n'; lot v 0.00 0.00 0.00 0.00 0.00 .004 0.03 0.06 0.10 0.15 0.20 0.25 0.31 0.37 0.44 0.52 0.60 0.68 0.76 0.83 0.90 0.97 1.04 1.11 1.18 1.25 1.32 1.39 1.46 1.53 1.59 1.64 1.67 1.69 1.70; i- 1; proc coe (a); local g; g - (0.1946.*c[1,1)./k[,1).*extp((.-0.174./k[,1).*(a-.a0[t1,1)-6.06.*k[,1.)) p ., *, 0,13)); 42 uppi - seqa(12.5,1,38)*; lowl m 9-~eqa(12.5,1,37) Lntord - 12; £ - 0; do Utll 1 .80 I2; t. - 1+1; **w *************** TOE RZOD ZI " 1990+(P-D).*8 "TOR 1990+(1-1).*5+4; "the sngulate man age at marrage for females ta : smamf[i,1; Odh proportion ho evrmary la : "[,13; 'th* cottraceptive prevalence rao : " u(£,11; *the contraceptive effectiveness rate ta : . ([11; Othe total =Ita abortIon rate ta :[ "thO duration from age 20 to 2 öhildren Ls : " durM2[1,13; "ths interval of pos-partum nonausoeptibility la: " £11en[,1); asa-1m2.8.*(20./(18.5+1en[IL,13)))./9.122; y - Lntquad1(öcoale,uppIllow'); y are age-speciftc marrUg rates from age 12.5 through age 49.5 Q Oth. age-specifte marrge rate* are : ; y f* 0 the proportion ever marrtd through age 49.5 la : sum(y); ,THE PROPORTIONS ZVE ARIED AR: '; divroed a y .* dratio; @divroed ta the proportion of divorced women by age from 12,5 through 49.5 Q m ar Ls the proportion now vidowed In the 6 age group 20-24 through 4$-49 ni, - (sr[L,,) - oof[.,1) - cof[.,2].*smaaf[i,1] cof[.,3).*sma mm[,13)./cof[.,4); "the predieted proportlon never vidowed are: ; agel seqa(22.55,6)./35; ag*2 - age1^2; age3 - agel^3; age4 - agel^4; age - age1~.aga2~-age3~.age4; b m w/(ones(6,)-age); anglagel - seqa(20.5.1,30)./35; 43 .sglagle - 8uglage1^2; snglageS - sagaa1^3; anglage4 - snglag,1^4; anglage •• siagage1~øsg1age2-saig1age3~s.ng1age4; nwang1. • ones(8.1) I(one(30,1)-snglage)*b; "thls La the predicted proportion never widowed from age 12 through 49 : ø; ******* ************************* NOW UI C==JT =11 ~POTION CMSMTY K~EUD *1 W - CUKS~(Y); C - Y.*(1-DAT10).*MS0GL + .- *PROROTION CÉRRETLY CARRIED FOR VOMEN fR0M ÅG 12.5 THROUGH 49.5 "; CK'; Q tafr * 12.8.*(20./(18.5+ile,n[l,1))*(1 - 1.08.*u[i,1).*e[L,)) THE COM ED TM (from age 20 to 49) • toft; if taftr le 2.0; ******armao ALelr *********emnto A1ert***LsA*LAs*** U; "ths total marital førtiltty rat* fxom age 20 is less or equal to than thi& is a prýoble"; *we stop herst break; endif; =sa - saaf[i,1 -14; dur :' dom2[i,1l; isma~u-ee8l(sma); isaaml-floor(am) ; fract1--saam-isaal; proc mand(m); local asfr,asdur,tafri,c=tmfrl,e,yrl,yrO,yr,z aste - (a[1,1)).*tn.*xp(-(m[2,1)).*v); if printl .øq 1; "m-s are " ; "asfr - astr'; * now we comp4te &ge-specific marital fertility by duration øf aarrLage beginning with the mean age at marriage 44 * Lf isaami .eq isaamu; asdur - ösfr[Lsma:l35,11# else; asdur - (1.-frat1).*astr[iamam1:35,1) + fractl.*(asfr[Lsaamu:SS,1)10O); endif; asdur - asfr[6:35,11; if printl .eq 1; "asdur endif; tafri - sumc(asfr[6:35,11) outti - tmfri; cutafrI - cum~sc(asd~x); if printi .8q 1; ncuxtafri m a eumtafri'; endif; S(cutafri -2) .gt 0; yrl-2; yrl-maxindc(e); if rows(yrl) .ne 1; yrl - 2; endif; if yrl .eq 1; yrl-2; endif; if print1 .eq 1; "yrj 9 a yrl; endif; yrO-yrl-1; s-0; z - cuatafr1[yr1,13-cutafr1[yro,l); if rovsz) .no 1; z - 0: endif; if z .1 0; z - 0.01; endif; yr - yrO + (2.0 - cuatmfrl[yrO.11)./z; outt2 - yr; "tafrl - frI tafr fr yr - yr dur - dur; " m11,1) ,a- [21; *rwturn value equal (tafr-tofr)^2+(yr-du) ^2; Sretp( (tmfr-tafr)^2 + (yr-dur)^2 ); ändp; delta - 4; icounti - 0; 11:output off; _algr-4; _stop-2; hss0o-; Icountl - icount + 1; (x,4,g,h)-optprtoptma<ux0,4ndn)); output on; if [1,1) .go 0 .and x[1,1) .la 1,0 .and x(213 .go 0 ,and 4[2,1) .1e 10; x0-x; endif; tf f .ge 0.000001; * C00VERENCE ON n TIS RUN IS ~00R. DO NOT TRUST THE RESMTS 45 "shall we continue? answer 1 - yes any other - no no Icontin - con(1,1); if Icontin .ra 1; break; endif; endif; um - (x[1,13); *M - * u - " ([2,1)); "durattoft - dur; delta-delta./2; If u .ge =ax; dur - dur + delta; delta - delta .* 2; soto 11; elseif <Icountl .eq 1 .or delta le 0.01); goto 12; else; dur - dur - delta; go.-,o 11; 12: enditf; if um .ge 1; "************* M ts greater than or equal to 1. This is not acceptabla endif: ri--r1520.*iueanc(af[6:10,11)}./meane(af[1:5,1)); aft1:S,1) - mf[1:5,l1.*rl; "the marital fertility ratss are: " af'; m "the total marital fertilty rate s u &dur - round(smam+dur); ramm - round(Smam) " rounded mean age at »a£ags U rsamm+14; rounded mean age at 2 children " adur+14; f,stimated tfr from age 20 - outtl "estimate duration - " outt2; asfr - zf.*c=[4:38,11; tfr sum(astr); asfr5 •• ieane(asfn[1:5,1))Imeanc(asfr[6:l0,1])tmeanIc(aSfr[11:15,l))| meanc(asftl6:20,1))>Iaeancasr(21:2$,11)jaeano(asft[26:3,1)l meana(asr[31:3S,1I); "the total fertilty rat* ts : tfr; "the age-speciftc fertility rates are asfrS'; tf - eq 1; tempi - asfr5'; else; tempi - templi asfrS': endif; age2 - seqa(15,1,35); ma - sume(asfr.*age2)./zu~o(asfr); a "the mean age at childbearing is : endo; output on; tempi; coodel - coode $+ "asfr"; save ^ceodel - templ; output off; end; 46 Bibliography Ahlburg, Dennis A. "Population Forecasting." In The Handbook of forecasting (second edition). eds. S. Makridakis and S. Wheelwright. New York: Wiley. pp. 135-49. Ahlburg, Dennis A. and James W. Vaupel. 1990. "Alternative Projections of the U.S. Population. Demograpby. 27(4). pp. 639-652. Bongaarts, John. 1978. "A Framework for Analyzing the Proximate Determinants of Fertility," Population and Develoment Review 4(1). Bongaarts, John. 1982. "The Fertility-Inhibiting Effects of the Intermediate Fertility Variables," Studies in Family Planning. 13: (6/7). Bongaarts, John and Robert G. Potter. 1983. Fertility. Biolov,y and Behavior. New York: Academic Press. Bulatao, Rodolfo A., and Eduard Bos. 1989. Projecting Mortality for all Countries. Policy, Planning, and Research Working Papers, No. 337. Washington, D.C.: The World Bank. Bulatao, Rodolfo A., Eduard Bos, Patience W. Stephens, and My T. Vu. 1989. Asia Reaion Population Prolections. 1989-90 Edition. Policy, Planning and Research Working Papers. WPS 331. Bulatao, Rodolfo A., and Eduard Bos. 1990. Projecting Fertility for all Countries. Policy, Research, and External Affairs Working Papers, No. 500. Washington, D.C.: The World Bank. Casterline, John B., Susheela Singh, John Cleland, and Hazel Ashurst. 1984. "The Proximate Determinants of Fertility." Comoparative Studies: Cross National Snamaries. Voorburg: International Statistical Institute. Number 39. Chidambaram, V.C. 1984. "Use of Intermediate Factors in Fertility Projections." In Poulation Prolections: MethodoloMv of the United Nations. Papers of the United Nations Ad Hoe Expert Group on Demographic Projections, November 16-19, 1981. New York: United Nations. pp. 39-48. Coale, Ansley J. 1971. "Age Patterns of Marriage." Population Studies. 25(2). pp. 193-214. 47 Coale, Ansley J. and Ronald R. McNeil. 1972. "The Distribution by Age of the Frequency of First Marriage in a Female Cohort." Journal of the American Statistical Association. 67(340). pp. 743-749. Coale, Ansley J. and T. James Trussell. 1974. "Model Fertility Schedules: Variations in the Age Structure of Childbearing in Human Populations." Poulation Index. 40(2). pp. 185-258. Cohen, Joel E., 1986. "Population Forecasts and Confidence Intervals for Sweden: A Comparison of Model-Based and Empirical Approaches." DeoaraRhy. 23. pp.105-126. Easterlin, Richard A. and Eileen M. Crimmins. 1985. Te Fertility Revolution: A Supv-Demand Analysis. Chicago: The University of Chicago Press. Freedman, Ronald. 1987. "Fertility Determinants." In John Cleland, Chris Scott, and David Whitelegge, eds. MM World Fertility Survey: An Assessment. Oxford: Oxford University Press. pp. 773-95. Hill, Kenneth. 1977. "Estimating Adult Mortality Levels from Information on Widowhood." Population Studies. 31(1). pp. 75-84. Hill, Kenneth and T. James Trussell. 1977. "Further Developments in Indirect Mortality Estimation." Population Studies. 31(2). pp. 313-33. India. 1989. Ministry of Home Affairs. Office of the Registrar General, India. Vital Statistic Division. Samle Registration System 1987. New Delhi. India. 1990. Ministry of Health and Family Welfare. Department of Family Welfare. Family Welfare Proaram in India: Year Book 1988-89. New Delhi. Indonesia. 1989. Central Bureau of Statistics and National Family Planning Coordinating Board. Institute for Resource Development/Westinghouse. National Ingonesia Contraceptive Prevalence Survey 1987. Jakarta. Keyfitz, Nathan. 1981. "The Limits of Population Forecasting." PoDulation and DeveloDment Review. 7. pp. 579-593. Land, Kenneth C. 1986. "Methods for National Population Forecasts: A Review." Journal of the American Statistical Association. 81. pp. 888-901. 48 Long, John F. and David B. McMillen. 1987. "A Survey of Census Bureau Population Projection Methods." Cliatic Change. 11. pp. 141-177. Page, R. J. 1977. "Patterns Underlying Fertility Schedules: A Decomposition By Both Age and Marital Duration," ennation atuiesg. 31(3). pp. 85-196. Stoto, Michael A. 1983. "The Accuracy of Population Projections." Jomal of the American Statistical Association. 78. pp. 13-20. United Nations. 1983. Department of International Economic and Social Affairs, Manual _X Indirect Techniques for DeMo=raphig_Ratiati2n, Population Studies, No. 81. ST/ESA/SR.A/81. New York: United Nations. United Nations. 1989. Department of International Economic and Social Affairs. World Population Prosoeots 1988. New York: United Nations. 49 ASIA REGION DISCUSSION PAPER SERIES Titie Date OriRinator IDP74 A Case Study of a Gradual Approach to Eonomxnc Reform: The Viet Nam ~ ~xperienc of 1985-88 Z. Drabek September 1990 Z. Drabek (80504) IDP85 On Einmaing Inadequacy of Energy Intakm: Reveuled Pood Consumption Behavlor versus Nutritional Norms B.S. Minhas September 1990 8. Jayantb (81419) IDP88 Asia Regim, PeinSa on Policy Cn1ien8 n Inda October 1990 C. Chamberuln (81409) IDP93 Paramotric Poplan Projecton and Its Usefulness for Policy Analysia W. Sanderson Apri 1991 Jeo-Peng Tan (81408) Note: Extra copies may be obtuned from the Aska Information Service Center.