Probabilistic projection of subnational total fertility rates

BACKGROUND We consider the problem of probabilistic projection of the total fertility rate (TFR) for subnational regions. OBJECTIVE We seek a method that is consistent with the UN’s recently adopted Bayesian method for probabilistic TFR projections for all countries and works well for all countries. METHODS We assess various possible methods using subnational TFR data for 47 countries. RESULTS We find that the method that performs best in terms of out-of-sample predictive performance and also in terms of reproducing the within-country correlation in TFR is a method that scales each national trajectory from the national predictive posterior distribution by a region-specific scale factor that is allowed to vary slowly over time. CONCLUSIONS Probabilistic projections of TFR for subnational units are best produced by scaling the national projection by a slowly time-varying region-specific scale factor. This supports the hypothesis of Watkins (1990, 1991) that within-country TFR converges over time in response to country-specific factors, and thus extends the Watkins hypothesis to the last 50 years and to a much wider range of countries around the world. CONTRIBUTION We have developed a new method for probabilistic projection of subnational TFR that works well and outperforms other methods. This also sheds light on the extent to which within-country TFR converges over time.

[1]  Richard Lachmann Book Review:From Provinces into Nations: Demographic Integration in Western Europe, 1870-1960. Susan Cotts Watkins , 1992 .

[2]  Rele Fertility levels and trends in India 1951-81. , 1987 .

[3]  Nan Li,et al.  Bayesian probabilistic population projections for all countries , 2012, Proceedings of the National Academy of Sciences.

[4]  C. Mosk From Provinces into Nations: Demographic Integration in Western Europe, 1870–1960. By Susan Cotts Watkins. Princeton: Princeton University Press, 1991. Pp. xvii, 235. $42.50 , 1991, The Journal of Economic History.

[5]  S. Klüsener,et al.  Spatial Aspects of the Rise of Nonmarital Fertility Across Europe Since 1960: The Role of States and Regions in Shaping Patterns of Change , 2012 .

[6]  Srinivas Goli,et al.  Fertility Convergence in the Indian States: An Assessment of Changes in Averages and Inequalities in Fertility , 2012 .

[7]  S. Poedjastoeti Levels and trends of fertility in Indonesia based on the 1971 and 1980 population censuses : a study of regional differentials , 1987 .

[8]  H. Hersbach Decomposition of the Continuous Ranked Probability Score for Ensemble Prediction Systems , 2000 .

[9]  Susan Cotts Watkins From Provinces into Nations: Demographic Integration in Western Europe, 1870-1960 , 1990 .

[10]  J. Muscat Convergence and Continuity , 2014 .

[11]  F. Shorter,et al.  Trends in fertility and mortality in Turkey, 1935-1975 , 1982 .

[12]  J. P. Cole,et al.  Proyecciones de la población de México , 1974 .

[13]  J. Tayman Assessing Uncertainty in Small Area Forecasts: State of the Practice and Implementation Strategy , 2011 .

[14]  Stanley K. Smith,et al.  Empirical Prediction Intervals for County Population Forecasts , 2009, Population research and policy review.

[15]  Chao Qian,et al.  Population , 1940, State Rankings 2020: A Statistical View of America.

[16]  A. Kalwij The impact of family policy expenditure on fertility in western Europe , 2009, Demography.

[17]  M. O'connell Regional Fertility Patterns in the United States: Convergence or Divergence? , 1981, International regional science review.

[18]  A. Raftery,et al.  Strictly Proper Scoring Rules, Prediction, and Estimation , 2007 .

[19]  Andrei Rogers,et al.  Does Specification Matter? Experiments with Simple Multiregional Probabilistic Population Projections , 2012, Environment & planning A.

[20]  Stanley K. Smith,et al.  Stability over time in the distribution of population forecast errors , 1988, Demography.

[21]  Chris Wilson,et al.  On the scale of global demographic convergence, 1950-2000. , 2001, Population and development review.

[22]  E. Spratley Birth and fertility rates for states and metropolitan areas: United States. , 1977, Vital and health statistics. Series 21, Data from the National Vital Statistics System.

[23]  D. Reher The demographic transition revisited as a global process , 2004 .

[24]  R. Tomlinson The ‘Disappearance’ of France, 1896–1940: French Politics and the Birth Rate , 1985, The Historical Journal.

[25]  O. Thévenon,et al.  The Impact of Family Policies on Fertility Trends in Developed Countries , 2011 .

[26]  Chris Wilson Fertility Below Replacement Level , 2004, Science.

[27]  Adrian E Raftery,et al.  bayesTFR: An R Package for Probabilistic Projections of the Total Fertility Rate. , 2011, Journal of statistical software.

[28]  A. Gauthier The impact of family policies on fertility in industrialized countries: a review of the literature , 2007 .

[29]  A. Raftery,et al.  Probabilistic Projections of the Total Fertility Rate for All Countries , 2011, Demography.

[30]  V. R. Enderica Dinámica y Estructura de la Población , 2017 .

[31]  P. Rees,et al.  Sub-national projection methods for Scotland and Scottish areas: a review and recommendations , 2015 .

[32]  S. Watkins From local to national communities: the transformation of demographic regimes in Western Europe 1870-1960. , 1990 .

[33]  Tom Wilson,et al.  Probabilistic regional population forecasts: The example of Queensland, Australia , 2007 .

[34]  A. Raftery,et al.  Regional Probabilistic Fertility Forecasting by Modeling Between-Country Correlations. , 2012, Demographic research.

[35]  Andreev Em,et al.  [Demographic history of Russia: 1927-1959] , 1998 .

[36]  中華人民共和国国家統計局 Fertility estimates for provinces of China, 1975-2000 , 2007 .

[37]  E. Pantelides,et al.  La fecundidad adolescente en la Argentina al comienzo del Siglo XXI , 2007 .

[38]  Nathan Keyfitz,et al.  The limits of population forecasting. , 1981 .

[39]  A. W. Hedrich Vital Statistics Rates in the United States: 1900-1940 , 1944 .

[40]  A. Gullickson The Use of Stochastic Methods in Local Area Population Forecasts 1 , 2022 .

[41]  Patrick Gerland,et al.  Bayesian Population Projections for the United Nations. , 2014, Statistical science : a review journal of the Institute of Mathematical Statistics.

[42]  J. Chamie Trends, Variations, and Contradictions in National Policies to Influence Fertility , 1994 .

[43]  J. R. Rele 70 years of fertility change in Korea: new estimates from 1916 to 1985. , 1988, Asia-Pacific population journal.

[44]  Tim Miller,et al.  SPECIAL REPORT: The Growth and Aging of California's Population: Demographic and Fiscal Projections, Characteristics and Service Needs , 2003 .

[45]  C. Hirschman,et al.  Why fertility changes. , 1994, Annual review of sociology.

[46]  D. Reher Towards long-term population decline: a discussion of relevant issues , 2007 .

[47]  T. Wilson Quantifying the uncertainty of regional demographic forecasts , 2013 .

[48]  L. Carter,et al.  The role of population size in the determination and prediction of population forecast errors: An evaluation using conifidence intervals for subcounty areas , 1998 .

[49]  P. McDonald,et al.  NATIONAL AND PROVINCIAL-LEVEL FERTILITY TRENDS IN IRAN, 1972-2000 , 2005 .

[50]  Chris Wilson Understanding global demographic convergence since 1950 , 2011 .

[51]  M A Stoto,et al.  The accuracy of population projections. , 1983, Journal of the American Statistical Association.

[52]  Shawn F. Dorius Global Demographic Convergence? A Reconsideration of Changing Intercountry Inequality in Fertility , 2008 .

[53]  J. Beer,et al.  An Explanatory Model for Projecting Regional Fertility Differences in the Netherlands , 2007 .

[54]  S. Basten,et al.  Spatial Variation of Sub-national Fertility Trends in Austria, Germany and Switzerland , 2012 .