metadata: authors: 0: author: Bos, Eduard
1: author: Bulatao, Rodolfo
docna: 0: docna: Projecting fertility for all countries
docty: Policy Research Working Paper
subtopic: Population & Development,Demographics,Reproductive Health,Early Child and Children's Health,Law and Justice Institutions
teratopic: Gender
abstracts: cdata!: This paper reviews and updates the
            procedures for making fertility projections. It classifies
            countries as pre-transitional, transitional, and
            post-transitional on the basis of current fertility and
            recent trends. Three data sets are used to analyze the
            trends for countries or economies in the transition stage:
            (a) World Bank estimates of fertility in the lastest
            quinquennium; (b) survey, census, and registration-based
            fertility estimates; and (c) World Bank estimates
            corresponding to the two decades immediately following
            initial transition. The average rate of total fertility
            decline across all the data is subsequently used as the
            medium decline pattern. Regression analysis is used to
            estimate the relationship between the current rate of
            decline in fertility and a number of socioeconomic
            variables. Additional analyses of fertility patterns focus
            on the pre- and post-transitional stages. The result of the
            analysis are translated into rules for projecting future
            fertility rates. These rules allow future fertility trends
            to be defined from previous trends country by country. To
            allow long-run projections, the rules assume that all
            countries eventually converge to replacement fertility.
repnme: repnme: Projecting fertility for all countries
display_title: Projecting fertility for all countries
listing_relative_url: /research/1990/09/700176/projecting-fertility-all-countries
topicv3: Infant and Child Mortality m1326544 1446,Population, Aging and Health m1327736 640,Life Expectancy m1504363 2666,Mortality m1504365 3661,Population Projections m1504366 3662
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Gender
origu: Policy, Research & Ect Affairs
no_of_pages: 34
model_extractions: **Policy, Researcdi, and External Affairs**

K

**Population, Health, and Nutrition**

**WPS** 500

This paper -a product of the Population, Health, and Nutriiion Division, Population and Human - Resources Department is part of a continuing effort in PRE to produce sensible and fully documented population projcctions. Copies of this paper are available free from the World Bank, 1818 H Street NW, Washington DC 20433. Please contact Vivian Altfeld, room S6-065, extension 31091 (28 pages, with figures and tables).

As part of its worldwide population projections, the Bank annually provides projections of fertility in each country. This paper reviews and updates the procedures for making fertility projections.

Bos and Bulatao classify countries as pretransitional, transitional, and post-transitional on the basis of current fertility and recent trendsand examine trends separately for each group of countries. A basic assumption underlying the analysis is that fertility will fall in all countries from high levels during the pre-transitional stage, to declining levels during the transition, and to low levels during the post-transitional stage. The start of this fertility transition process is identified in the analysis by a decline in the total fertility rate of at least 0.5 points over five years.

Focusing on the transition stage, Bos and Bulatao analyze trends for countries or economies that experienced at least part of the fertility transition after 1955. They use three data sets: World Bank estimates of fertility in the latest quinquennium; survey, census, and registrationbased fertility estimates; and World Bank estimates corresponding to the two decades immediately following initial transition. The three data sets produce somewhat different estimates of the rate of decline. The average rate of total fertility decline across all the data, 0.12 annually, is subsequently used as the medium decline pattern. Slow and rapid fertility decline are defined as half and twice the medium decline rate.

Regression analysis is used to estimate the relationship between the current rate of decline in fenility and a number of socioeconomic variables. Differences in the rate of fertility change during the transition are partly explained by socioeconomic indicators, but the addition of the previous rate of change as a predictor improves the model significantly. Models with just the previous rate of change fit almost as well as those including the socioeconomic indicators.

Focusing on the pre- and post-transitional stages, the authors carry out additional analyses of fertility patterns. Pre-transitional fertility trends show little pattern. The start of the transition cannot be reliably predicted but appears, from previous analyses, to be subject to a mortality threshold. Post-transitional fertility trends also show little pattern. The shift from transitional decline to the post-transitional stage involves slower fertility decline, and alteriative pattems of slowing are distinguished.

The results of the analysis are translated into rules for projecting future fertility rates. These rules allow future fertility trends to be defined from previous trends country by country - and incorporate changes in total fertility with projected reductions in high levels of primary sterility. To allow loig-run projections, the rules assume that all countries eventually converge to replacement fertility.

The results of applying the rules are illustrated for eight countries and compared with previots World Bank projections and projections of the United Nations Population Division.

The PRE Working Paper Series disseminates the findings of work under way in the Bank's Policy, Research, and Extemal AffairsComplex. An objective of the scries is to get these findings out quickly, even ifpresentations are less than fully polished. The findings, interpretations, and conclusions in these papers do not necessarily represent official Bank policy.

Produced by the l'RE Dissemination Center
# CONTENTS

|World Bank population projections .<br>...............<br>1|
|---|
|Approaches to projecting fertility .<br>................<br>2<br>Previous World Bank projections ....<br>........<br>2<br> <br>|
|U.N. projections ......<br>................<br>2|
|U.S. Bureau of the Census projections ....<br>.....<br>3|
|National projections ......<br>..............<br>3|
|Proximate determinants of fertility approach ...<br>.. 4|
|Socioeconomic determinants approach ....<br>..... 4|
|Analysis of fevtifl y tends .....................<br>s|
|Stages in fertility transition ..................<br>s|
|Pre-nsitional countries .................<br>_s_<br>|
|Transitional countries .......<br>...........<br>8|
|Post-transitional countries .....<br>..........<br>13<br>|
|Movement between stages .......<br>...........<br>15|
|Application to population projections .....<br>.........<br>16<br>|
|Pre :.ansition ............<br>...........<br>16|
|Start and pace of transition .....<br>..........<br>16|
|Late and post-transition .................<br>17|
|Age-specific fertility ........<br>...........<br>18|
|Rapid and slow decline ......<br>...........<br>18|
|Mllustrative<br>projections ............<br>...........<br>20|
|Conclusion .............................<br>20|
|References ..............................<br>28|
This paper describes new procedures used to project<sup>fertility in World Bank population</sup> projections. The previous procedures were in use in the Bank<sup>for over a decade and underwent occasional</sup> modification. This comprehensive revision is based on a new review<sup>of data and provides a clear rationale</sup> for future trends. The methodology may be of use for other<sup>purposes, but its main application is to the</sup> annual update of Bank population projections for all countries<sup>or economies and regions of the world. The</sup> methodology does not depend on detailed country by country<sup>analysis of determinants of fertility; though</sup> this might yield better predictions of future fertility, it is<sup>increasingly cumbersome if one wishes to project</sup> more and more countries. An attempt to predict the future<sup>can never be a genuinely scientific exercise;</sup> OL: aim is limited to formulating heuristic rules that<sup>can be supported by past trends.</sup> Past trends are examined in the period total fertility<sup>rate (TFR) and used in the definition of</sup> future trends. Other fertility indicators (i.e., the gross<sup>reproduction rate and cohort fertility rates) have</sup> certain advantages, but TFRs tend to be available for more<sup>countries and are easily understood.</sup> For this review, countries or economies are classified on<sup>the basis of fertility level and recent</sup> trends as pre-transitional, transitional, or post-transitional.<sup>All countries are assumed to move from a</sup> pre-transitional stage of high fertility through the fertility<sup>transition to a post-transitional stage of low</sup> fertility. Trends in fertility are exami **n** i-rately mA for countries in each stage.

Focusing on the transition stage, trends are analyzed<sup>for countries or economies that</sup> experienced at least part of the fertility transition after<sup>_1955._Three data set are used: World Bank</sup> estimates of past fertility since the stari of the decline;<sup>survey, census, and registration based TFR</sup> estimates; and World Bank estimates of fertility decline in<sup>the most recent period. The three data sets</sup> produce somewhat different estimates of the rate of decline.<sup>The average, around .12 annually, is used</sup> as the medium decline pattern. Regression analysis is employed<sup>to estimate the relationship between the</sup> current rate of decline in fertility, the rate of decline<sup>in the past quinquennium, and a number of</sup> socioeconomic indicators. Slow and rapid fertility decline<sup>are defined as half and twice the medium</sup> decline rate.

Focusing on the pre- and post-transitional stages, additional<sup>analyses of fertility patterns are</sup> carried out. Pre-transitional fertility trends are found<sup>to show little pattern. The start of the transition,</sup> defined as a decline of at least _.5_ points in TFR over a quinquennium,<sup>cannot be reliably predicted but</sup> appears, from previous analyses, to be subject to a mortality<sup>threshold. Post-transitional fertility trends</sup> also show little pattem. The shift from transitional decline<sup>to the post-transitional stage involves slower</sup> fertility decline, and altemative pattems of slowing are<sup>distinguished.</sup> The results of the analysis are translated into a number of<sup>rules to be applied in projecting</sup> future total fertility rates. A comparison of the results of<sup>applying these rules with previous World Bank</sup> projections and those made by the United Nations (U.N.)<sup>Population Division is provided.</sup>

# WORLD BANK POPULATION PROJECTIONS

Annually for the past 13 years, the World Bank has<sup>produced both short- and long-term</sup> population projections for all countries or economies,<sup>areas, and regions of the world. The short-term</sup> projections are used in Bank operations as relatively reliable<sup>forecasts of future population and other</sup> demographic indicators in the next 20 years or so. The long-term<sup>projections-up to 200 years-are useful</sup> primarily as illustrations of the long-lasting effects of<sup>current high population growth ("population</sup> momentum") rather than as projections of population size<sup>for applied purposes. Methodology for carrying</sup> out the projections must provide results for each country<sup>that are consistent with current trends and feasible</sup> in the long term. For example, even if current<sup>trends do not support a rise to replacement fertility in</sup> various Western countries any time soon, fertility cannot<sup>remain at current levels for more than a few</sup> decades, because extinction of national populations is not<sup>a credible scenario. Similarly, current Sub-</sup> Saharan African fertility levels would result in exponentially<sup>increasing populations that would soon</sup> number in the billions and cannot be maintained, even<sup>if current trends and conditions do not justify</sup>
immediate fertility d''ine. The requirement for reliable short-term projections and the need for longterm scenarios create ,Qeiad problems not encountered in many projection exercises. The U.S. Bureau of the Ces does make severd population projections with a 100-year horizon, but because of nearreplacement fertility and a low rate of population growth, the U.S. population is one of the least problematic for such long-term projections. More typically, projections involve a time horizon no longer than 20 to 40 years.

# APPROACHES TO PROJECTING FERTILITY

A review of approaches currently used to project national fertility levels indicates that the approaches used by international agencies appear serviceable but are not entirely transparent. More sophisticated approaches have been devised but have significant diawbacks. We review the approaches used in different population projections: in previous World Bank projections; in projections of the U.N. Population Division; in projections of the Center for Intemational Research of the U.S. Bureau of the Census; in projections of some national statistical offices; and two other general strategies of use in any projection.

Previous World Bank projections. In previous World Bank population projections (e.g., Zachariah and Vu 1988), fertility rates were projected by determining a future year (referred to as the replacement year) when fertility will reach replacement level, i.e., when the net reproduction rate (NRR) will equal 1. Estimates of the replacement year were obtained from a regression equation using as predictors family planning status (a categorical variable), projected expectation of life at birth for females in 1985-90, changes in the birth rate from 1970 to 1980, and the projected TFR for 1985-90. Th dependent variable was an initial guess of the replacement year, based on other projections, country and regional comparisons, and general information about the socioeconomic and demographic situation of each country. The predicted value from the equation was rounded to the nearest year ending in 0 or _5,_ and subjective adjustments were then made on the basis of regional consistency or country-specific information. For instance, Sub-Saharan African countries in the same region were assumed to reach replacement fertility 'at more or less the same **time'** (Zachariah and Vu 1986:xvi).

Between the current period and the replacement year, total fertility rates (TFR) for most countries were obtained by fitting a reverse geometric (accelerating) curve up to 1995-2000, and a geometric (decelerating) curve thereafter. Total fertility rates after the replacement year were assumed to stay at replacement, and therefore to vary solely in response to the mortality schedule. For SubSaharan Africa, a few countries in Asia, and all countries with fertility already below replacement, it was assumed that TFR would remain constant for one or more periods before moving toward replacement.

Several shortcomings of this methodology have been pointed out (Demeny 1985; Pressat 1986; Murray 1987). Abbreviated explanations were provided in some publications, makcing it difficult for readers to understand why some countries would reach replacement fertility earlier than others. The selection of independent variables for the regression equation appears arbitrary. No explanaton was given for choosing changes in the crude birth rate and current TFR rather than the current crude birth rate and changes in TFR. The family planning status variable was based on an arbitrary categorization of a continuous variable (percent using contraception) into three levels. And the predicted replacement years sometimes appeared unsatisfactory: for the 1988-89 Bank projections (the final run that made use of this methodology), subjective adjustments to replacement years were made for about 30 countries.

U.N. projections. The approach taken in the U.N. Population Division projections foUows several general pninciples (or basic assumptions') for above-replacement and below-replacement countries, rather than unambiguous rules.

For above-replacement countries, the assumptions are that fertility will decline with the timing 2
and **speed** of the decline related to socioeconomic development and population policy: Pat and current fertility trends are evaluated and placed within the social, economic and political context of the country. Trmds and anticipated changes in the socio-economic structure and cultur values of the society as well as policies and programmes directed towards family planning are considered vis-a-vis expected trends in fertility (U.N. 1986).

A sc,,&rate approach is applied to some Latin American countries, for which projections<sup>done by the</sup> Centro Latinoamericano de Demograffa (CELADE) are adopted.

For below-replacement countries, the U.N. considers "idiosyncratic characteristics of socioculturd changes' (U.N. 1989), making projections on a case-by-cas basis. 'Heavy emphasis' is actually placed on projections from national statistical offices, though some of these are modified in the ,Wterest of international comparability. These countries are assumed to follow some path back to replacermentlevel fertility, the level that produces an NRR of one when combined with the lowest mortalit) twsumed possible in the projection period.

Besides the medium variant, or most likely scenario, developed according to these principles, high and low variants are also developed. The high variant assumes stabilization with TFR at about<sup>2.5-</sup> 2.6, and the low variant assumes stabilization with TFR at 1.5-1.6 (except for countries<sup>in Latin Amnerica,</sup> for which the CELADE projections are adopted). These variants are meant to provide<sup>a range of</sup> projectioes but not statistical confidence intervals like those proposed by Cohen (1986). In<sup>many cases,</sup> the high ; low variants for the current period are estimates made by national statistical offices; occasionaly, they are estimates made by the World Bank or the U.S. Bureau of the Census.

Fertility levels are expressed in terms of the total fertility rate or the gross reproduction rate, and other fertility measures are derived from it. Fertility levels for projection periods between the<sup>current</sup> and the stable fertility period appear to be derived from models; however, these are not discussed.

U.S. Bureau of **the** Census international projections. The Center for International Research at the Bureau applies separate procedures for low fertility zountries, with TFRs of 2.2 or lower, and high fertility countries. Low fertility countries ar- assumed to have TFRs in 2000 between 1.5 and 1.8 (depending on how low TFR is currently) and in 2050 of exactly 1.7. For intermediate periods, TFRs are obtained by linear interpolation. Age-specific fertility patterns are taken from the latest<sup>empirical</sup> esimates and adjusted proportionally as TFR changes.

These projected TFRs are considerably below World Bank and U.N. medium fertility projections. Applied in combination with World Bank assumptions for mortality and migration,<sup>the</sup> Bureau of the Census procedures would result in some low fertility countries having substantially smaller populations in 2050 than they have currently. Another unit of the bureau makes national projections for the U.S., to be described below. These projections assume that TFR stabilizes early in the next century around 1.9 (with the low and high variants being 1.6 and 2.3).

High fertility countries are assumed to follow a logistic path to lower fertility. Logistic functions are estimated country by country from past data, assuming an upper asymptote equal to one point above the highest recorded TFR in the data (but no lower that 6.0) and a lower asymptote<sup>of 2.0. The</sup> resulting estimats for the year 2000 from applying these functions are required to 'make sense' in relation to 'levels of modern contraception, education among women in the childbearing<sup>ages, and urbanization</sup> **trends"** (U, S. Bureau of the Census 1990). For each country where they do not, an alternative logistic fun.ction is estimated using an assumed TFR for the year 2000, sometimes based on experience of similar countries. Furt} er adjustments may subsequently be made to ensure consistency within regions.

Nadonal projections. Some representative approaches used by national statistical offices or 3
plsnning agencies in population projecti ns in industrial countries will be reviewed. Approaches used in developing countries, when such project.ons are made, tend to be similar.

A survey of approaches used by the statistical offices of the 12 member states of the European Community, which have some of the most complete and detailed vital statistics available, shows few advantages over the approaches of the U.N. or the World Bank (Eurostat 1988). Generallv, the period TFR is used as a measure to express future fertilitv rates. In most cases, fertility is assumed either to remain constant at the current level or to increase somewhat for the next decade or so and to remain constant thereafter. The Federal Republic of Germany and Luxembourg make different assumptions for fertility trends of two subgroups. citizens and foreigners. In some Eastern European countries, larger increases in fertility have been projected, reflecting a belief that pro-natalist population policies will be effective (Isupov 1981), despite the lack of confirmatory evidence (Monnier 1989). Most of the statistical offices prepare several, or even mnany, different projection variants.

Some of the most detailed projections are made by the U.S. Bureau of the Census. No fewer than 27 projection variants till 2080 are provided, representing all possible combinations of three different assumptions each for fertility, mortality, and migration, assumptions specific to Whites and Blacks separately (U.S. Bureau of the Census 1989). The fertility assumptions are cc npler.. Trends in agespecific fertility rates are projected, from which other fertility measures are derived. The middle set of fertility assumptions includes no changes in age-specific fertility rates, which means that at first TFR **will** actually increase somewhat, then drop slightly below its current level. High and low assumptions are based partly on birth expectations data from surveys, and are gradually phased in by birth cohort, not taking full effect until about 2015, after whicb they remain constant. The process appears more careful and elaborate than that of other dtatistical offices but does require considerably more data.

Proximate deterninants of fertility approach. Changc in aggregate fertility measures are caused by changes in individual attributes and behavior, namely fecundity, coia-I frequency, postpartum infecundability, contraceptive practice, and abortion. The effects of these proximate dctterminants can be wodeled following a strategy proposed by Bongaarts (1978, 1982), in which the attributes or *,ehrviors are expressed as indices of the prevalence of pathological sterility, the proportion married, the duration of breastfeeding and postpartum abstinence, contraceptive prevalence, and the prevalence of abortion. The model shows the contribution that each proximate determinant makes toward reducing actual fertility below the biological maximum, and is useful especially for explaining current levels and differentials and past trends in fertility (Freedman 1987). Because fertility can change only when one or more of the proximnate determinants changes, extrapolations for levels of these determinants could provide projections of fertility (Chidambaram 1984).

However, extrapolated trends in proximate determinants are as uncertain as, if not more uncertain h'n, directly extrapolated fertility trends. The most important factor in the fertility transition has been the use of contraception, but predicting the start of widespread use appears very difficult. Breastfeeding has been declining in many developing countries, but the fertility-increasing effect of this trend may be offset by declining sterility. Another problem is that the method is not very robust with regard to the initial estimate of total fecundity; consequently, the estimates of actual total fartility in the presence of proximate determinants are likely to be uncertain. Although models for incorporating proximate determinants into projections exist (Chidambaram 1984), we are not aware of any national projection that has made explicit use of this approach.

Socioeconomic determinants approach. Macroeconomic models with endogenous demographic variables might be used for fertility projection. Such economic-demographic models have been used most often for regional or small-area projections in the U.S. (National Academy of Sciences 1980; Murdock et al. 1984). However, in most econometric models, demographic variables receive limited attention because they are not the primary aim of the forecasts, and consequently are not modeled with much care (Pittinger 1977). Isserman (1986) discussed a model in which fertility for states in the 4
U.S. was modeled with a number of sowe.conomic characteristics, among which are female labor force participation rates, male and female incomes, percent rural, percent Mormon, percent Hispanic, and net migration rates. Although regression equations with these variables were found to capture most of the variation in White fertility rates, this approach was termed 'virtually useless' for projecting fertility, because forecasting changes in these variables proved more difficult than projecting fertility itself (Isserman 1986). So far, such macroeconomic models have been most useful to project future migration rates (American Statistical Association 1977).

# ANALYSIS OF FERTILITY TRENDS

A description and analysis of fertility trends in various countries will be provided to serve as the basis for a revised approach to projecting fertility. The first step in analyzing trends is to distinguish different stages io fertility transition and to classify countries by stage. The second step is to provide a representation of trends within each stage. Then we consider the question of when countries move from one stage to another.

The fertility data used are World Bank estimates for the period 1955-85, derived from a number of sources, such as the U.N. _World Population Projections, 1988 Revision,_ national statistical offices (mainly for developed countries), fertility surveys, and the Demographic and Health Surveys. Many of the TFR estimates from the U.N. are obtained through backward projection, and are therefore influenced by estimates of mortality and age structure. To complement the examination of these data, survey or census-based estimates are used exclusively in some- parallel analyses.

## **_Stages In fertility_** _transition_

Current total fertility rates around the world range from around 8 (Rwanda, Yemen Arab Republic) to around 1.4 (Federal Republic of Germany, Italy, Luxembourg). Depending on the TFR level and its recent trend, countries can be categorized into three grolvns. Countries or economies with high fertility in whic a fertility has not yet declined in a significant way (to be -rined below) are said to be pretransitional; those in which fertility is currently declining in a significar. y are said to be transitional; and those in which fertility has reached low levels (near or below replacement) are said to be posttransitional. A fundamental tenet of demographic trans;tion theory, which defines these stages, is that all countries sooner or later move from the pre-transitional stage through the transitional stage to the posttransitional stage; once countries have made the transition, they remain at relatively low levels of fertility.

The first versions of demographic transition theory (Notestein 1945; Davis 1963) did not make explicit how a demographic transition is identified. Not every fertility decline can be called transitional: pre-transitional countries often experience small changes in TFR, but declines are usually not sustained; they remain therefore pre-transitional. Thus, it is necessary to specify what type or quantity of fertility decline is transitional. In this paper, we use a decline of at least .5 points in TFR over a quinquennium as identifying the start of fertility transition. Additionally, we assume that any country with a TFR below 4.5 has begun the transition (Bulatao and Elwan 1984:62-66). Table 1 classifies countries by fertility stage using this definition.

Pre-transitional countries. These differ widely in their level of fertility, with TFRs ranging from 8 to 5. There is little intentional control of fertility through contraceptive use; fertility differentials are the result of different marriage pattems, different durations of breastfeeding and postpirtum abstinence, and the level of sterility. Pre-transitional fertility trends are sometimes downward, sometimes upward. Figure la shows fertility levels and trends in a number of typical pre-transitional countries. These data have been smoothed by backward projection but nevertheless illustrate the variability among pretransitional countries. Some of the upward trends are believed to result from declining sterility and reduced breastfeeding.

5
# Table 1. Countries and economies classified by fertility transition status as of **1980**

# **1.** Pre-transitional

Anuc ANGOLA BENIN BURKINA FASO BURUNDI CAMEROON CAPE VERDE CENTRAL AFRICAN REP. CHAD COMOROS CONGO. PEOPLE'S REP. COTE D'IVOIRE DlIBOUTI EQUATORIAL GUINEA ETHIOPIA GABON GAMBLA. THE GHANA GUINEA GULINEA-BISSAU KENYA LESOTHO AllCA MALATINAME SA C UBERA AFGHANISTAN BOLIVIA LIBYA BANGLADESH GUATEMALA MADAGASCAR BHUTAN NICARAGUA MALAWI GAZA STRIP MAUI IRAN, ISLAMOC REP. **OCIANLV** MAURITANIA IRAQ PAPUA NEW GUINEA MOZAMBIQUE JORDAN SOLOMON ISLANDS NAMIA CAMBODIA VANUATU NIGER LAO PEOPLE'S DEM. REP. NIGERIA MALDIVES RWANDA MONGOUA SAO TOME AND PRINCIPE NEPAL SENEGAL OMAN SIERRA LEONE PAWUSTAN SOMALIA QATAR SWAZILAND SAUDI ARABIA TANZANIA SYRIAN ARAB REP. TOGO WEST BANK UGANDA YEMEN, PEOPLE'S DEM. REP. ZAIRE YEMEN ARAB REP. ZA.MBIA

# **1.** Transitional

AFRh;A ALGERIA BOTISWANA EGYPT MOROCCO SOUTH AFRICA SEYCHELLES TUNISIA ZIMBABWE XEANLi F1;1 FRENCH POLYNESIA KIRIBATI NEW CALEDONIA PACIRIC ISLANDS TONGA WESTERN SAMOA ASIA LATIN AMERICA AND THE CARIBBEAN BAHRAIN ARGENINA PANAMA BRUNEI BAHAMAS PARAGUAY MYANMAR BEUZE PERU INDIA BRAZIL ST. KrTES AND NEVIS INDONESIA CHILE ST. LUCIA ISRAEL COLOMBIA ST. VINCENT KOREA, DEM. P. REP. COSTA RICA SURINAME KUWAIT DOMINICA TRINIDAD AND TOBAGO LEBANON DOMINICAN REP. URUGUAY MALAYSIA ECUADOR VENEZUELA PHIIPPINES EL SALVADOR SRI LANKA GRENADA THAILAND GUYANA TURKEY HAM VIET NAM HONDURAS JAMAICA EUROPE MEXICO ALBANIA MONTSERRAT

# III. Post-transitional

AFRICA MAURITIUS REUNION OCEANI AUSTRALIA GUAM NEW ZEALAND NORTH AMERIC, CANADA U.S.A.

ASIA CHINA HONG KONG JAPAN KOREA. REP. MACAO SINGAPORE TAIWAN. CHINA FRANCE EUROPE EUROPE AUSTRIA POLAND BELGIUM PORTUGAL BULGARIA ROMANIA CHANNELIS. SPAIN CYPRUS SV'EDEN CZECHOSLOVAKaA SWITZERLAND DENMARK UNITED KINGDOM FINLAND U.S.S.R. YUGOSLAVIA GERMAN DEM. REP. GERMANY. FED. REP. LATIN **AMERICA AND** GREECE THE CARIBBEAN HUNGARY ANlTGUA AND BARBUDA ICELAND BARBADOS IRELAND CUBA ITALY GUADELOUPE LUXEMBOURG MATNQUE MALTA NETHERLANDS ANTlILS NElHEREANDS PUERTO RICO NORWAY VIRGIN IS. (U.S.A.) 6
<!-- Start of picture text --> Figure la Trends in Total Fertility<br>PRE-TRANSIT IONAL CO.INTA IES<br>7 7 7=<br>2<br>1955 1990 1995 19I70 1975 1990 1995<br>Figure It. Trends in Total Fertility<br>TRANSIT ONAL rOtaNfQIS<br>7<br>__ 3 , .3 ,<br>4 2 -,<br>S<br>19S 1960 1965 1970 1975 19B0 1995<br>YEAR<br><!-- End of picture text --> <!-- Start of picture text --> Figure Ic. Trer,c;-. in Total Fertility<br>POST-TRANSITIONAL COrNITQIS<br>2.4 39<br>2.5<br>Sa4d<br>1 4<br>195 1 960 . .1S5 . 1..70. 1S75 19e0 19e<br>,e^o<br><!-- End of picture text --> 7
Pre-transitional countries are found mustly in Africi, with some others in South Asia, the Middle East, Oceania, and Latin America. Life expectancy is generally low; in this group, it surpasses 60 years only in a few Middle Eastern and North African countries. With a few exceptions, the countries in this group are classified by the World Bank as low- and lower-middle iacome countries.

Transitional countries. Current fertility in countries in transition vanies considerably because fertility decline may have just started or may be continuing a trend started as long as two decades ago. Figure lb portrays representative countries over the period 1950-85, &'- wing the decline from a-gh levels of fertility to transitional fertility. TFRs at the start of the transition were quite dissimilar, from 7.2 (Algeria) to 5.0 (Trinidad and Tobago), and cfrrent TFRs continue to show a wide spread. This grapn also shows that the rate of fertility decline varies: the average annual change for Trinidad and Tobago (-.006) for the period 1975-85 is considerably snaller than the annual change for Algeria (-.017).

For these transitional countries, v- .irst attempted to determine the average annual fertility decline. Second, we examined trends to determine whether these declines were linear. Third, we looked at the deterninants of the pace of fertility decline.

Three alternative data sets were used to determine average decline. Of the 59 transitional countries in Table 1, we initially selected those 49 w;th total fertility of three or higher in 1985-90. The lower-fertility countries were left out with the intention of treating separately the slowing of ferility decline toward the end of transition. The mean annual decline in total fertility in these countries from 1980-85 to 1985-90, using World Bank estimates, was .09 points.

An attempt was made to validate this result with a second data set. For 32 countries that started fertility transition at least ten years previously, survey, census, or registration data were assembled from U.S. Bureau of the Census (1979), World Fertility Surveys, contraceptive prevalence surveys, or Demographic and Healt. Surveys, covering at least three time points-and often many more-after the start of fertility transition. Average annual declines in fertility were obtained for each country by linear regression. Across countries, the mean annual decline was .15, substantially higher than the first figure.

In an attempt to reconcile the two figures, we carefully examined the Bank fertility estimates. Instead of using the quinquennial estimates, we interpolated to obtain total fertility rates in the years that fertility transition started, as well as exactly 10, 15, or 20 years later (depending on how long ago fertility transition started). This procedure was applied to the 32 countries covered in the previous procedure, as well as to 10 other countries with sufficiently early transitions but insufficient data to be included in the previous data set. In this set of estimates, the largest fertility declines, of close to .20 points annually over 15 to 20 years, were for Singapore, and Mexico. The smallest declines, of .05 to .08 points annually, were for Fiji, the United Arab Emirates, and Sri Lanka. The mean annual decline across countries was .13 for all 41 countries, or .14 for the 32 countries in the previous data set.

Figure 2 shows the distribution of countries ' heir average declines in the third data set, as well as the distribution of declines recorded in the first and second decades after the start of transition. Declines in the second decade tend to be slightly slower. (Particularly for countries with very rapid initial declines, two decades is enough to bring TFR within one point of .eplacement fertility.) This may partly explains the discrepancies among the results. The first data set, with the mo,st recent data, has proportionally more cases of late transition and therefore has a lower avenge. The estimates from the three data sets may also differ for a variety of other reasons, including selectivity, differences in typical declines in different decades, and differences in the specific years covered by estinates. The results from the latter two data sets agree in the aggregate, and, as Figure 3 shows, tend to roughly agree for individual countries. In this figure, average declines estimated from the two data sets are plotted against each other. Most points cluster around the line along which estimates are equal. However, declines based on Bank estinates tend to be slightly more moderate, less extreme in either direction.

8
Figure 2. Percentage distribution of countries by average annual TFR decline, and of declines in first and second decades after transition started <!-- Start of picture text --> Percent<br>40<br>I Country estimates<br>-4- First decade<br>30 - - Second aecade<br>2 0-<br>10 '<br>0 038 0 063 0.088 0.113 0 138 0 163 0.188 0.212 0.238<br>Annual decline (groun midpoints)<br><!-- End of picture text --> The estimates from the three data sets are summarized in Table 2, which provides medians and 'ercentiles, as well as the means across data sets. The typical annual decline in TFR might be said to he roughly .12 points. Using the tenth iad ninetieth percentiles, one could assign half this raue as roughly indicating slow fertility decline and double this rate as roughly indicating rapid fertility decline. A rapid decline estimate of .24 is slightly above the annual rapid decline of .2164 estimated in previous work (Bulatao and Elwan 1985), but appears appropriate in comparison to recent declines in Africa not considered in that work: .20 points a year in 1984-89 in Keniya, .25 points a year in 1980-86 ie Figure 3. Estima.ed annual TFR change from two data sets: 32 countries <!-- Start of picture text -->
-0 02<br>-o  04  -<br>-0.06  0<br>-0.08  0<br>-0 10  0  1<br>§ 0 12  -0  w  °<br>8 _  - O 19 O  w  0  0  a  0<br>-0120  _  o<br>-0.22  -<br>-0.24  -<br>-0 26-<br>-o.2as<br>-2  -0 2S -A  -0 21 -0 19 -o 17 -0 15 -0 13 -0 11 -o  09  -0 07 -0 05 -0 03<br>SLrvey, cernus.  cr  regtsatia7..-  c.?tO<br><!-- End of picture text -->

9
Table 2. Annuwl decline in TFR: Percectiles across countries obtained from three data set

|Percentile|A|B|C|Mean|
|---|---|---|---|---|
|10|-0.160|-0.224|-0.176|-0.187|
|25|-0.116|-0.176|-0.163|-0.151|
|_50_|-0.084|-0.150|-0.136|-0.123|
|75|_-0.055_|-0.104|-0.111|-0.090|
|90|-0.022|-0.085|-0.089|-0.066|
|(Number of<br>countries)|(49)|(32)|(41)||

Note: Data set A uses 1980-85 and 1985-90 Bank estimates. Data set B uses survey, census, or registration data from the date of transition. Data set C uses Bank estimates adjusted to start at the date of transition.

# Botswana, and .29 points a year in 1981/82-86 in Zimbabwe.

One question this analys.; raises is whether TFR decline should be represented as linear. We examined the shape of the TFR curve over the entire transition period, regressing TFR on number of years since the start of the transition for a selection of countries with frequent survey-based data. A linear formulation fit quite well, with R<sup>2</sup> ranging from .86 to .96. Little improvement was obtained from modeling the decline with a quadratic or cubic term. Figure 4 shows six representative countries with linear and quadratic curves fitted to fertility rates. For the Republic of Korea, Mauritius, Thailand, Taiwan, and Trinidad and Tobago, a stiaight line fits the data well. Only for Sri Lanka does a quadratic formulation give a slightly better fit, because of a stall in fertility decline. Stalls present an obstacle to modeling fertility decline for two reasons. First, their occurrence is hard to predict, partly because they occur for a variety of different reasons (Gendel! 1984; Bongaarts 1986). Second, they are of variable duration: Korea's stall in fertility decline was a brief interlude before rapid fertility decline resumed, whereas Costa Rica's and Fiji's have lasted much longer. In general, many of the countries that have experienced stalls in fertility have resumed fertility decline after a variable number of years. For thes reasons, modeling fertility decline as a simple linear process that does not attempt to repre.sent stalls (but takes them into account in determining the general pace of decline) appears justified. However, during the late stages of the tmnsition, when TFR has dropped below 3, fertility decline slows down and becomes nonlinear. The level at which this happens depends on how far fertility will ultimately fall, which varies from country to country. This segment of the transition might be treated separately if a linear formulation is applied.

We attempted to predict the rate of decline in the three quinquennia following the start of the fertility transition with regression analysis, using as explanatory variables the following socioeconomic indicators from World Bank data: (a) year of start of the transition; (b) infant mortality rate (IMR) at the start of the tasition; (c) the rate of change in the IMR in the preceding quinquennium; (e) secondary school enrollment of women at the start of the transition; (f) TFR at the start of the transition; (g) region (Asia, Latin America, and other regions); and (h) percent of population living in urban areas. (lif expectancy was initially included but was dropped because of a strong correlation with the IMR.) Table 3 shows the characteristics of the sample countries and the correlations between rate of change in each quinquennium since the start of the transition and the predictor variables. Table 4 presents the results of multiple regression analyses. Models are presented with the mte of change in TFX for each of the quinquennia following the start of the fertility transition as the dependent varia',le. Two models are given 10
_IA_ <!-- Start of picture text --> . * a a a * .. .. . 4~~..<br>* - I:~~~~~~~~~~~~~~~~~~~G<br><!-- End of picture text --> <!-- Start of picture text --> £ ~~~~~~o *'<br><!-- End of picture text -->
Figure 4 (continued). Linear and quadratic regressions for<sup>TFR trend from start of fertility transition:</sup> Taiwan, Trinidad and Tobago, and Thailand Taiwan, linear regression, R<sup>2</sup> = .98 Taiwan, quadratic regression, R<sup>2</sup> = .99 <!-- Start of picture text --> 6<br><!-- End of picture text --> <!-- Start of picture text --> a<br><!-- End of picture text --> Trinidad and Tob., linea- **r** egr., R2=.93 <!-- Start of picture text --> 56 11 1 3II<br>Triiad and Tb, linear regresio , R 2 = .98<br>2 S<br>2 , 2 X S 6 7 * I 10 11 1Z 13 1* 15 w *7 1 1X<br><!-- End of picture text --> <!-- Start of picture text --> Trinidad and Tob., quadratic regr. R2=.96<br>5s~~~~1 . 5 011 aI S4<br>Triiadland Tb, quadratic regr.sin,R = .96<br>*0 0 9 *1 *2 U 14 15 *7 IS<br><!-- End of picture text --> 12
for the rate in the second and third quinquennia, one with and one without the rate of fertility change in the previous quinquennium as a predictor.

Differences in the rate of ferti!ity change during the transition are indeed partly explained by socioeconomic variables, but the addition o0 the previous rate of fertility change as a predictor improves the model significantly. In fact, models with just the rate of previous change fit almost as well as those also including the socioeconomic indicators.

Socioeconomic variables are often good predictors of fertility levels across countries (Richards 1983). However, these regressions indicate that initial socioeconomic levels are at best weak predictors of future fertility trends. Conceivably, trends in socioeconomic variables might predict simultaneous or lagged trends in fertility. We have not used lagged socioecouomic trend data in these regressions (except for the infant mortality trend) because the data are weak, and have avoided simultaneous trend data because projections of future fertility using such variables would require prior socioeconomic projections.

Post-transitional countries. There is no objective criterion by which to judge when a fertility transition has run its course. Fertility in some countries declines well below replacement level; in others, it bottoms out just above replacement. The experience of countries that have reached this stage shows the lowest level reached ranging between 1.3 and 2.4. Figure Ic shows representative posttransitional countries. Minimum TFRs differ by up to one point, and current fertility may be rising or falling. The speed of fertility decline does not determine the minimum TFR that is reached (Table 5): the correlation between these variables is weak and not significant.

Fertility in post-transitional countries fluctuates like fertility in pre-transitional countries. With the exception of a brief period in the 1950s, fertility in post-transitional countries has stayed in a narrow range. During the 1980s, many of these countries have experienced below-replacement fertility, though most of them still have positive rates of natural increase because of a proportionally large number Table 3. Sample characteristics and correlations between rate of fertility decline and other indicators: 42 countries

|VibL||||Correlation<br>TFR durin<br>after<br>|withrate o<br>g specified<br>q<br>start of tra<br>|f change in<br> <br>uinquennium<br>nsition<br>|
|---|---|---|---|---|---|---|
|arae|Mean|Minimu|Maximum|First|Second|Third|
|Year of start<br>of transition<br>|1964.6<br>|<br>1956<br>|1978<br>|-0.10<br>|-0.33<br>|-0.27|
|INR at start<br>|77<br>|37<br>|141|-0.31|-0.48|-0.38|
|etO) at start<br> <br>|59.3<br>|51<br>|67<br>|-0.00|0.24|0.17|
|Accrued<br>rate of change<br>in IMR<br>|-0.04<br>|-0.01|-O.C7|0.30|0.46|0.38|
|TFR at start<br> <br> <br>|6.1<br>|4.4<br>|7.7|-0.61|-0.36|-0.29|
|Latin<br>America<br>region<br>|0.19<br>|0<br>|1|0.18|0.15|0.16|
|Asia region<br>|0.50<br>|0<br>|1|0.03|0.16|0.07|
|Female secondary<br>school enroltment(X)<br> <br>|23.1<br>|3<br>|54<br>|-0.00|0.24|0.17|
|Percent<br>urban<br>|44.6<br>|13<br>|100<br>|-0.11|-0.19|-0.21|
|Rate of change in TFR, first<br>quinquenniun<br>after start<br>|-0.11<br>|-0.06<br>|-0.16<br>|1.00<br>|0.45<br>|0.39|
|Rate of change in TFR,<br>second<br>quinquennfum<br>|-0.14<br>|-0.06<br>|-0.29<br>|0.45|1.00|0.57|
|Rate of change in TFR.<br>third qufnquerwnium|-0.08|-0.02|-0.21|0.39|0.57|1.00|

13
Table 4. Regressions for nte of change in TFR in dute quinquenia folowing sta of fertlity transition

|Period and predictors|(1<br> <br>B|)<br>(t)|(2<br>8|)<br>(t)|
|---|---|---|---|---|
|First quinquennium|||||
|Constant|-1.45E-01|-8.57|||
|Female enrollment|5.26E-04|1.81|||
|Urban|9.90E-05|0.61|||
|IMR|1.36E-04|1.05|||
|IMR change|-1.85E-04|-0.94|||
|Asia region|-9.25E-04|-0.10|||
|<br>LAC region|-5.60E-03|-0.79|||
|Start year|-8.51E-04|-1.12|||
|TFR at start<br>|1.36E-02|3.27|||
|R<sup>2</sup>|0.37||||
|Second quinquennium|||||
|Constant|-3.34E-01|-5.56|-3.39E-01|-5.55|
|Female enrollment|-8.68E-05|-0.08|-6.77E-05|-0.06|
|Urban|-8.67E-04|-1.52|-8.633-04|-1.48|
|IMR|5.23E-04|1.15|5.28E-04|1.11|
|IMR change|-1.04E-03|-1.51|-1.05E-03|-1.47|
|Asia region|-1.60E-02|-0.48|-1.60E-02|-0.47|
|LAC region|-3.04E-02|-1.22|-3.06E-02|-1.19|
|Start year|2.75E-03|1.02|2.72E-03|0.97|
|TFR at start|4.87E-03|0.33|5.36E-03|0.30|
|Previous change|--|--|3.24E-01|9.68|
|R2|0.30||0.55||
|Third quinquennium|||||
|Constant|-2.99E-01|-4.25|-6.59E-02|-1.15|
|Female enrollment|3.05E-04|0.25|3.65E-04|0.37|
|Urban|-1.02E-03|-1.53|-4.162-04|-0.73|
|IMR|5.11E-04|0.95|1.45E-04|0.32|
|IMR change|-8.94E-04|-1.10|-1.64E-04|-0.24|
|<br>Asia region|-8.31E-04|-0.02|1.03E-02|0.32|
|LAC region|-2.87E-02|-0.98|-7.39E-03|-0.30|
|Start Year|2.52E-03|0.80|5.93E-04|0.23|
|TFR at start|4.23E-03|0.25|8.22E-04|0.06|
|Previous change|--|--|6.99E-01|3.86|
|R<sup>2</sup>|0.22||0.56||

14
of women of childbearing age. The lowest observed fertility in recent years has been in the Federal Republic of Germany, where TFR has been just below 1.3 for most of the past decade. By contrast, fertility in the U.S.S.R. has remained above replacement for the past 25 years. As a result of low fertility, negative rates of natural increase are now observed in Denmark, Belgium, the Federal Republic of Germany, the German Democratic Republic, and Luxembourg. In most other countries in this group, population decline should start, barring unexpected reversals in fertility, sometime in the next 30 years.

# _Movement between stages_

We will now consider the movement of countries from one stage in the fertility transition to another. Early and late starts for the transition have occurred on all continents, and no clear regional pattern arises. Two socioeconomic variables were examined as potential predictors of the start of fertility decline in developing countries: female secondary school enrollment and life expectancy at birth. Regression analysis showed weak relationships between these indicators at particular years and the year fertility decline started. More in-depth analysis of a limited number of countries might consider the lagged effect of education on the start of fertility decline, however, the scarcity of required data made such an analysis impractical here. Bulatao and Elwan (1986) observed no fertility transition to have started in developing countries until life expectancy at birth had stayed above 53 for at least five years. They described this threshold as a necessary but not sufficient condition for fertility transition. Stolnitz (1984) reported a life expectancy threshold of 50 for fertility decline in Asia, and of 55 in Latin America. Fertility declines have taken place at life expectancy levels as low as 53 (Republic of Korea, Tunisia, Indonesia) and have not taken place in countries with a life expectancy of 63 (Saudi Arabia, Syria, Jordan). Biological and behavioral mechanisms, such as the replacement hypothesis (that couples replace a child who has died by having another) may operate at the individual level, but how such factors trigger or prevent a societal fertility transition has not been explained. Nevertheless, this is a useful finding, because projecting life expectancy into the future is feasible (Bulatao and Bos 1989).

The progression from the transitional to post-transitional stage may be less remarkable than the start of the fertility transition but is not necessarily easier to project. No relationship appears between Table _5._ Mean annual TFR decline from one point above replacement and minimum TFR level reached, for countries below replacement fertility

|Country|Annual<br>decline|Minimum<br> <br>TFR|Country|Annual<br>decline|Minimum<br> <br>TFR|
|---|---|---|---|---|---|
|Singapore|0.10|1.69|Iceland|0.07|1.93|
|Martinique|0.10|2.11|New Zealand|0.07|1.93|
|Finland|0.09|1.50|Australia|0.07|1.94|
|Spain|0.09|1.75|Romania|0.07|2.00|
|Cuba|0.09|1.84|Germany, Fed.|Rep. 0.06|1.34|
|Netherlands|0.07|1.46|Italy|0.06|1.46|
|Switzerland|0.07|1.49|Austria|0.06|1.48|
|Portugal|0.07|1.71|Norway|0.06|1.66|
|U.S.A.|0.07|1.76|Canada|0.06|1.69|
|France|0.07|1.83|Taiwan, China|<br>0.06|2.26|
|Barbados|0.07|1.83|Belgium|0.05|1.52|
|Hong Kong|0.07|1.87|Malta|0.05|1.74|

15
the speed of the decline in TFR during the transition and the level at which fertility ultimately stabilizes. Table S shows countries which appear to have bottomed out below replacement fertility, i.e., where no further fertility decline was measured for a quinquennium. Regressing the minimum TFR level on the rate of decline from one point above the minimum level shows a weak, nonsignificant relationship (R<sup>2</sup> equal to .35). Each country seems to have an unpredictable minimum TFR level to which it declines at a pace that is unrelated to this level. Once the minimum level has been reached, TFRs fluctuate within a narrow range. For example, this country-specific minimum fertility level is about 1.5 in Switzerland, where it has ranged between 1.49 and 1.60 for the past 12 years, and 1.8 in the U.S., where it has ranged between 1.74 and 1.88 for two decades. In some countries, such as Poland and the Soviet Union, the minimum Irvel TFR has been above replacement, varyung between 2.2 and 2.4 for some time now.

# APPLICATION TO POPULATION PROJECTIONS

This section attempts to formulate heuristic rules for projecting future fertility based on the findings in the previous section. In particular, rules are needed to determine the course of fertility before the pre-transitional stage; the timing of the start of fertility transition; the speed of fertility decline during the transition, both for countries that are already experiencing transition and for countries that have not yet started; and the course of fertility during the post-transitional stage, both for countries which are already post-transitional and for other countries. Table 6 summarizes the recommended rules. Application of the .ules requires that estimates are available or can be made of current TFR, TFR five years earlier, current life expectancies, and the percent of women of reproductive age who are sterile.

Pre-transition. Pre-transitional fertility was found in the analysis to fluctuate erratically at high or moderately high levels. In the absence of any convincing approach to predicting such fluctuations, we will use the rule that pre-transitional fertility is constant. We make an exception for countries where primary sterility is high. Such sterility appears to be due mainly to preventable sexually transmitted diseases (Frank 1983; Larsen 1985; Farley and Belsey 1988). As sterility declined in a number of countries, there have been increases in TFR over the past decade: in Gabon, for instance, TFR increased from 4.5 in the mid-1970s to 5.5 in the mid-1980s. Frank (1983) found that, for each percentage point increase in primary sterility, TFR fell .11 points. Many countries have sterility levels in the 3 to 6 percent range (Europe averages 5.4. Latin America 3.1, and North America 6.0); we take 6 percent as a lower limit below which the effect of sterility on fertility can be ignored. We assume that sterility, where it is high, will decline linearly to 6 percent by 2005 and, following Frank, adjust TFR by adding the quantitr

## .11 [(percent sterile - 6) / 3]

## to predicted TFR in each of the three quinquennia between 1990 and 2005.

Start and pace of transition. The start of the transition in countries where no fertility transition has been observed was not predictable from socioeconomic indicators. We rely, therefore, on previous studies showing a life expectancy threshold for fertility transition. We impose as a necessary condition for fertility decline that life expectancy must be at least 50 years and propose the following rule: where the fertility transition has not started, it will do so in the next quinquennium (1990-95), unless life expectancy at birth is below 50 years. In that case, the start of the transition will be postponed until projected life expectancy reaches 50 years. (How life expectancy is projected is discussed in Bulatao and Bos 1989.) A few pre-transitional countries are not projected to reach a life expectancy of 50 for as long as 30 years, often because of current conditions like war and famine. In these few cases, we allow fertility transition to start by 2005.

The pace of fertility decline in countries where transition has started was found to be countryspecific. It was also found to be poorly explained by other demographic or socioeconomic variables. A quinquennial decline in fertility was found to be strongly correlated with the decline in the preceding 16
Table 6. Alternative patterns for future fertility trerds

||Defi<br>|nin<br>Ste<br>|g<br>charac<br>rility<br>|teristics<br> <br>Transitio<br>|n<br> <br> <br>|
|---|---|---|---|---|---|
|Pattern|NR|(p|ercent|E(0) started|Projected<br>fertitity<br>trend|
|1 Pre-transition,<br>high sterility<br>|*2<br>||26<br>|<50<br>No<br> <br>|TFRrises<br>with reduced<br>sterility<br>|
|2 Pre-transition,<br>Low sterility<br>3 ii<br>|>2<br>||'6<br>|'50<br>No<br> <br>|TFRconstant<br> <br> <br>|
|Transton<br>starting,<br>high sterility<br>4Titi i|>2<br>'||>6<br>|tS0<br>No<br> <br>|Transition<br>starts;<br>mediumTFRdecline<br>(reduced<br>by half in first<br>quinquenmium)<br>adjusted for reduced sterility<br>|
|ranson startng,<br>low sterility<br> <br>|>2<br> <br>||<6<br>|S0<br>No<br> <br>|Transition starts; medium TFR decLine<br>(reduced<br>by half in first<br>quinquennium)<br>|
|5 Transition<br>continuin<br>high sterility<br> <br>|g,<br>>2<br> <br>||6<br>|>50<br>Yes<br> <br>|TFR decline based on previous decline,<br>adjusted<br>for reduced<br>sterility<br> <br> <br>|
|6 Transition<br>continuin<br>low sterilits<br> <br>|g,<br>>2<br>||6<br>|50<br>Yes<br> <br>|TFRdecline<br>based on previous<br>decline<br> <br> <br> <br>|
|7 Transition<br>ending<br>|)1 a<br>52<br>|nd|any<br>value|>50<br>Yes<br> <br> <br>|TFRdecline<br>follows<br>geometric<br>path to<br>replacement<br> <br>|
|8Post-transition,<br>at replacement<br>9 Pttiti|=I<br>||any<br>value<br>|>50<br>Yes<br> <br>|TFRstays at replacement<br>(if drop is<br>recent, it may fall below for I period)<br>|
|os-ranson,<br>below reptacement|<1||any<br>value|>50<br>Yes|TFR constant for 3 periods, then recovers<br>to replacement by 2030 (recent drop may<br>continue for 1 period)|

quinquennium, and this relationship can therefore be used to project future fertility decline during the transition. We estimated a simple model of annual TFR change: 4,TFR = _-.05_ + _.5_ (A4TFR), where 4A.TFR is the average annual rate of change in TFR in the preceding quinquennium. On the assumption that exceptionally slow or rapid TFR decline is unlikely to be sustained for long, we require that projected declines should be no slower than half the medium annual rate of decline (using .12 points as the medium) and no faster than twice the medium annual rate of decline, giving a lower bound of .06 and an upper bound of .24.

No indicators were found for the pace of future transitional decline where transition has not started. We therefore apply to such countries the average decline in past data, of .12 TFR points annually. For the first quinquennium, however, we apply only half this rate, assuming that, on average, the decline should start in the middle of the period. Figure _5_ shows the medium trend applied in such cases, as well as the upper and lower bounds within which all declines must fall.

Late and post-transition. We noted that TFR decline usually slows down when countries **are** in the late stages of the transition, i.e., when TFR drops below 3. The level at which TFR stops falling cannot be predicted from the trend in fertility at higher levels; it has been anywhere from 1.3 to 2.4. For long-term projections, we must assume that each country reaches replacement fertility at some point, in order to avoid extinction, on one hand, and unending population growth, on the other. Fluctuations around replacement fertility would of course be an alternative, but no basis exists for projecting such fluctuations. We assume, then, that the fertility transition ends in replacement fertility, and that the last point of TFR decline takes 15 years along a geometric (decelerating) path. For countries with data, the last point of TFR decline actually took 14.4 years on average (implying an annual rate of geometric change of -.0254). An exception is made for countries experiencing very slow fertility 17
transition. Where the annual geometric decline in TFR over the past five years, as well as over the past 15 years, is -. 019 or slower, a country may be assigned 20 rather than 15 years to fal the last point to replacement Applying these rules is somewhat complicated. First, an approximate year for reaching replacemeat has to be estimated. Given the year when a TFR of 3.15 will be reached, this is estimated with the formula

- Replacement year = 15 _[1_ In(TFR / 3.15) 1 In (2.15 / 3.15)].

SecorAd, female life expectancy (e(f) has to be projected to that year and the replacement-level TFR estimated, using the approximation TFRX,,R, = 6.702 - .1107 e,, + .0006592 efn2.

Then the replacement year can be reestimated.

Generally, countries with TFRs at 2.15 or below are assumed to stay at that level for ten more years, and then to return gradually to replacement by 2030. The choice of this year is arbitrary, but it does coincide with the quinquennium that these countries together would start experiencing negative rates of natural increase. Countries with TFRs in the 1.75 to 3.15 range that have experienced relatively rapid declines are assumed to decline further in the next quinquennium. Rapid declines, for this purpose, are declines equivalent to taking 12.5 years or fewer to fall from 3.15 to 2.15 (or a geometric rate of of - .0305 or faster). How far these countries decline is determined by applying a slightly revised normal decline pattern for one quinquennium, with the proviso that the minimum cannot be below 1.75. The equation is

# TFR = exp[ln(TFR) + _5_ * ln(1.75 _I_ 2.75) / _151._

After declining for one quinquennium, TFR for these countries is assumed to stay stable in the next period and then to begin to return to replacement. Figure 6 shows the assumed patterns of TFR at low levels of fertility.

Age-specific fertility. Age-specific rates are determined from a model that takes the overall level of fertility into account. This aspect of the fertility projections has not been changed from previous practice. Two basic schedules of age-specific fertility are defined: for total fertility levels greater than six and for total fertility levels of three and lower (Figure 7). In between, age patterns are obtained by interpolation between the two schedules. At a TFR of 6, a greater proportion of births are at younger and older ages of the reproductive span, and the mean age of childbearing is 28.9 years. At a TFR of 3, births are concentrated in a narrower band of ages, and the mean age of childbearing is 28.0.

Rapid and slow fertility dedine. We suggested above that rapid decline might be defined as an annual fal of .24 in TFR during the transition, and slow decline as an annual fall of .06. (If it is desirable to define such declines in a relative rather 'man absolute sense, one might use instead twice or half the country-specific annual rate of change.) In addition, rules for the start and end of the transition may be modified. For rapid decline, assume that countries that have not started transition start immediately, regardless of mortality level. For slow decline, assume that the mortality threshold is a life expectancy of 53 rather than 50, which delays the transition in some but not al cases. For slow decline also, assume that 20 rather than 15 years are required for the TFR to decline the last point to replacement. These modifications provide more consistent rapid-decline and slow-decline scenarios.

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