Transmission of fertility pattern in mother-daughter relation – Bayesian view (a case study of Austria)
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Published:
May 13, 2013
Keywords:
fertility patterns, intergenerational transmission of fertility, Zero-Inflated Poisson, fertility modeling, Bayesian inference, fertility in Austria
Main Article Content
Abstract
The connection between fertility of parents and their children has been investigated many times over the past century. It seems to be insignificant among pre-transitional populations, but becomes more important over time, especially in developed countries. Following Pearson’s example, it was widely adopted to use simple correlation analyses in such studies. In this study we will present how to use more advanced statistical models and methods to determine the occurrence and strength of examined relationships. Thus, we aim to investigate the intergenerational transmission of fertility in contemporary populations (in the case of the motherdaughter relation in Austria) using the zero-inflated Poisson regression model. Using this model in fertility analysis allows us to treat childlessness as a qualitatively different state with possibly different determinants than parenthood (regardless of the number of children). Bayesian inference in this study enables us to obtain covariates’ distributions as well as distributions of covariates’ nonlinear functions (including their uncertainty) and allows us to incorporate our prior knowledge.
Article Details
How to Cite
Osiewalska, B. (2013). Transmission of fertility pattern in mother-daughter relation – Bayesian view (a case study of Austria). Studia Demograficzne, (1(163), pp. 3–35. https://doi.org/10.33119/SD.2013.1.1
Section
Original research papers & review papers
References
[1] Alho J.M., Spencer B.D., 2005, Statistical Demography and Forecasting, Springer, New York.
[2] Anderton D.L., Tsuya N.O., Bean L.L., Mineau D.G.P., 1987, Intergenerational Transmission of Relative Fertility and Life Course Patterns, “Demography”, vol. 24, 467–480.
[3] Bernardo J.M., Smith A.F.M., 1994, Bayesian Theory, J.Wiley, Chichester.
[4] Bijak J., Wiśniowski A., 2010,Bayesian forecasting of immigration to selected European countries by using expert knowledge, “Journal of the Royal Statistical Society”, Series A, Statistics in Society.
[5] Bijak J., 2011,Forecasting International Migration in Europe. A Bayesian View. Springer Series on Demographic Methods and Population Analysis, vol. 24.
[6] Bocquet-Appel J P., Jakobi L., 1993, A Test of a Path Model of Biocultural Transmission of Fertility,“Annals of Human Biology”, vol. 20, Art. 4, 335–347.
[7] Booth A.L., Kee H.J., 2009, Intergenerational Transmission of Fertility Patterns, “Oxford Bulletin of Economics and Statistics”, vol. 71, no. 2, p. 183–208.
[8] Bryant J., Graham P., 2013, Bayesian Demographic Accounts: Subnational Population Estimation Using Multiple Data Sources, “Bayesian Analysis”, 8(2): forthcoming.
[9] Bryant J., Graham P., 2011, Demographic Estimates and Projections Using Multiple Data Sources: A Bayesian Approach, ISI, Dublin.
[10] Buber I., Sobotka T., Prskawetz A., Engelhardt H., Gisser R., 2012, Austria: Stable and low fertility. Entry in the Online Handbook of Demography, Berlin, The Berlin Institute for Population and Development, http://www.berlin-institut.org/index.php?id=865&type=98
[11] Daponte B.O., Kadane J.B., Wolfson L.J., 1997, Bayesian Demography: Projecting the Iraqi Kurdish Population, 1977–1990,“Journal of the American Statistical Association”, vol. 92, no. 440, p. 1256–1267.
[12] Dommermuth L., Klobas J., Lappegard T., 2011, Now or later? The Theory of Planned Behavior and timing of fertility intentions, “Advances in Life Course Research”, no. 16, p. 42–53.
[13] Easterlin R.A., 1978, New Directions for the Economics Fertility [in:] Yinger J.M., Cutler S.J. [ed.], Major Social Issues. A Multidisciplinary View, The Free Press, New York.
[14] Easterlin R.A., 1987, Birth and Fortune: The Impact of Numbers on Personal Welfare, University of Chicago Press, Chicago.
[15] Fisher R.A., 1930, The genetical theory of natural selection, Clarendon Press, Oxford.
[16] Geweke J., 1996, Monte Carlo Simulation and Numerical Integration [in:] H. Amman, D. Kendrick, J. Rust (ed.), Handbook of Computational Economics, North-Holland, Amsterdam.
[17] Greene W.H., 2003, Econometric Analysis, 5th edition, Macmillan, New York.
[18] Högnäs R.S., Carlson M.J., 2012, “Like Parent, Like Child?”: The intergenerational transmission of nonmarital childbearing,” Social Science Research”, Nov. 41(6), 1480–94.
[19] Hyppölä J., Tunkelo A., Törnqvist L., 1949, Suomen väestöä, sen uusiutumista ja tulevaa kehitystä koskevia laskelmia [Calculations Concerning the Population of Finland, Its Renewal and Future Development], “Tilastollisia tiedonantoja”, 38. Helsinki: Statistics Finland.
[20] Jansakul N., Hinde J.P., 2001, Score Tests for Zero-Inflated Poisson Models, “Computational Statistics & Data Analysis”, no. 40, 75–96.
[21] Jeffreys H., 1961, Theory of Probability, 3rd edition, Oxford University Press, Oxford.
[22] Kass R.E., Raftery A., 1995, Bayes Factor, “Journal of the American Statistical Association”, vol. 90, no. 90.
[23] Kolk M., 2013, Understanding Transmission of Fertility Preferences Across Multiple Generations Socialization or Socioeconomics?, “Stockholm Research Reports in Demography”, no. 4, available at: http://www.suda.su.se/SRRD/SRRD_2013_4.pdf
[24] Kolk M., 2011, Intergenerational continuities in family size – Multigenerational transmission of fertility in contemporary Sweden, “Stockholm Research Reports in Demography”, no. 14, available at: http://www.suda.su.se/SRRD/SRRD_2011_14.pdf
[25] Koop G., 2003, Bayesian Econometrics, Wiley, Chichester.
[26] Lambert D., 1992, Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing, “Technometrics”, vol. 34, no. 1,1–14.
[27] Land K.C., 1986, Methods for National Population Forecasts: A Review, “Journal of the American Statistical Association”, no. 81, 888–901.
[28] Langford C.M., Wilson C., 1985, Is There a Connection Between a Woman’s Fecundity and That of Her Mother?, “Journal of Biosocial Science”, no. 17, 437–443.
[29] Lenk P., 2009, Simulation pseudo-bias correction to the harmonic mean estimator of integrated likelihoods, “Journal of Computational and Graphical Statistics”, 18, 941–960.
[30] Lutz W., Skirbekk V., 2005, Policies addressing the tempo effect in low-fertility countries, “Population and Development Review”, 31(4): 699–720.
[31] Lutz W., Skirbekk V., Testa M.R., 2006, The low fertility trap hypothesis: Forces that may lead to further postponement and fewer births in Europe, “Vienna Yearbook of Population Research”, 4:167–192 (2006).
[32] Martin-Matthews A., Kobayashi K.M., Rosenthal C.J., Matthews S.H., 2001, Age-gapped and agecondensed lineages: Patterns of intergenerational age structure among Canadian families, “QSEP Research Report”, no. 363.
[33] Marzec J., 2008, Bayesowskie modele zmiennych jakościowych i ograniczonych w badaniach niespłacalności kredytu, Wydawnictwo Uniwersytetu Ekonomicznego w Krakowie, Kraków.
[34] Marzec J., Osiewalski J., 2012, Dwuwymiarowy model typu ZIP-CP w łącznej analizie zmiennych licznikowych, „Folia oeconomica cracoviensia”, vol. LIII.
[35] Murphy M., 1987, Differential family formation in Great Britain, “Journal of Biosocial Science”, no. 19, 463–485.
[36] Murphy M., 1999, Is the relationship between fertility of parents and children really weak?, “Social Biology”, no. 46, 122–145.
[37] Newton M.A., Raftery A.E., 1994, Approximate Bayesian Inference by the Weighted Likelihood Bootstrap (with Discussion), “Journal of the Royal Statistical Society B”, vol. 56.
[38] Osiewalska B., 2012, Przejmowanie wzorca płodności matek przez generacje córek w Polsce – podejście bayesowskie [in:] J. Kurkiewicz (eds.), Przemiany demograficzne w Polsce – uwarunkowania i konsekwencje, Badania statutowe 12/KS/2/2012/S/012, Uniwersytet Ekonomiczny w Krakowie, Kraków (typescript).
[39] Osiewalski J., 2001, Ekonometria bayesowska w zastosowaniach, Wydawnictwo Akademii Ekonomicznej w Krakowie, Kraków.
[40] Osiewalski K., Osiewalski J., 2012, Missing observations in daily returns – Bayesian inference within the MSF-SBEKK model, “Central European Journal of Economic Modelling and Econometrics”, vol. 4, Issue 3, 169–197.
[41] Osiewalski K., Zając B., 2010, Krzywe cząstkowych współczynników zgonów – modele wygładzania [in:] Społeczne i Ekonomiczne Konsekwencje Zmian Procesów Demograficznych, „Zeszyt Sekcji Analiz Demograficznych”, no. 22/2010, part 1, 77–86.
[42] Osiewalski K., Zając B., 2011, Bayesowskie porównanie modeli zachowań prokreacyjnych [in:] Frątczak E., Sobczak I., Szreder M. (eds.), Prace i materiały Wydziału Zarządzania Uniwersytetu Gdańskiego. Wybrane problemy rozwoju demograficzno-społecznego Polski i metody ich badania (p. 21–39), Fundacja Rozwoju Uniwersytetu Gdańskiego, Sopot.
[43] Pajor A., 2003, Procesy zmienności stochastycznej SV w bayesowkiej analizie finansowych szeregów czasowych, Akademia Ekonomiczna w Krakowie, Kraków.
[44] Pajor A., 2010, Wielowymiarowe procesy wariancji stochastycznej w ekonometrii finansowej. Ujęcie bayesowskie, Wydawnictwo Uniwersytetu Ekonomicznego w Krakowie, Kraków.
[45] Pajor A., Osiewalski J., 2013, A Note on Lenk’s Correction of the Harmonic Mean Estimator, “Central European Journal of Economic Modelling and Econometrics”, 5: 271–275 (2013).
[46] Pearson K., Lee A., 1899,On the Inheritance of Mankind, “Philosophical Transactions of the Royal Society of London”, A 192.
[47] Pearson K., Lee A., Bramley-Moore L., 1899, Inheritance of fertility in man, and of fecundity in thoroughbred racehorses, “Philosophical Transactions of the Royal Society of London”, A 192.
[48] Pflaumer P., 1988, Confidence Intervals for Population Projections Based on Monte Carlo Methods, “International Journal of Forecasting”, no. 4, 135–142.
[49] Pipień M., 2006, Wnioskowanie bayesowskie w ekonometrii finansowej, Wydawnictwo Akademii Ekonomicznej w Krakowie, Kraków.
[50] Raftery A.E., Li N., Ševčíková H., Gerland P., Heilig G.K., 2012, Bayesian probabilistic population projections for all countries, Proceedings of the National Academy of Sciences USA, 109(35): 13915–13921.
[51] Raftery A.E., 1995,Bayesian Model Selection in Social Research, Sociological Methodology, no. 25, p. 111–163
[52] Robert C.P., Casella G., 2005, Monte Carlo. Statistical Methods, Springer, New York.
[53] Spielauer M., 2005, Concentration of reproduction in Austria, General trends and differentials by educationattainment and urban–rural setting, “Vienna Yearbook of Population Research”, 2005–012, p. 171–195.
[54] Tanaka C.M., Iwasa Y., 2012, Cultural evolution of a belief controlling human mate choice: Dynamic modeling of the hinoeuma superstition in Japan, “Journal of Theoretical Biology”, no. 309, 20–28.
[55] Tymicki K., 2006,Intergenerational transmission of fertility, review of up to date research and some new evidence from Bejsce parish register reconstitution study, 18th – 20th centuries, Poland, European Population Conference 2006 Liverpool Paper.
[56] Yu B., Mykland P., 1994, Looking at Markov Samplers Through Cusum Path Plots: A Simple Diagnostic Idea, Technical Report no. 413, Department of Statistics, University of California at Berkeley.
[57] Zellner A., 1971, An Introduction to Bayesian Inference in Econometrics, John Wiley, New York.
[2] Anderton D.L., Tsuya N.O., Bean L.L., Mineau D.G.P., 1987, Intergenerational Transmission of Relative Fertility and Life Course Patterns, “Demography”, vol. 24, 467–480.
[3] Bernardo J.M., Smith A.F.M., 1994, Bayesian Theory, J.Wiley, Chichester.
[4] Bijak J., Wiśniowski A., 2010,Bayesian forecasting of immigration to selected European countries by using expert knowledge, “Journal of the Royal Statistical Society”, Series A, Statistics in Society.
[5] Bijak J., 2011,Forecasting International Migration in Europe. A Bayesian View. Springer Series on Demographic Methods and Population Analysis, vol. 24.
[6] Bocquet-Appel J P., Jakobi L., 1993, A Test of a Path Model of Biocultural Transmission of Fertility,“Annals of Human Biology”, vol. 20, Art. 4, 335–347.
[7] Booth A.L., Kee H.J., 2009, Intergenerational Transmission of Fertility Patterns, “Oxford Bulletin of Economics and Statistics”, vol. 71, no. 2, p. 183–208.
[8] Bryant J., Graham P., 2013, Bayesian Demographic Accounts: Subnational Population Estimation Using Multiple Data Sources, “Bayesian Analysis”, 8(2): forthcoming.
[9] Bryant J., Graham P., 2011, Demographic Estimates and Projections Using Multiple Data Sources: A Bayesian Approach, ISI, Dublin.
[10] Buber I., Sobotka T., Prskawetz A., Engelhardt H., Gisser R., 2012, Austria: Stable and low fertility. Entry in the Online Handbook of Demography, Berlin, The Berlin Institute for Population and Development, http://www.berlin-institut.org/index.php?id=865&type=98
[11] Daponte B.O., Kadane J.B., Wolfson L.J., 1997, Bayesian Demography: Projecting the Iraqi Kurdish Population, 1977–1990,“Journal of the American Statistical Association”, vol. 92, no. 440, p. 1256–1267.
[12] Dommermuth L., Klobas J., Lappegard T., 2011, Now or later? The Theory of Planned Behavior and timing of fertility intentions, “Advances in Life Course Research”, no. 16, p. 42–53.
[13] Easterlin R.A., 1978, New Directions for the Economics Fertility [in:] Yinger J.M., Cutler S.J. [ed.], Major Social Issues. A Multidisciplinary View, The Free Press, New York.
[14] Easterlin R.A., 1987, Birth and Fortune: The Impact of Numbers on Personal Welfare, University of Chicago Press, Chicago.
[15] Fisher R.A., 1930, The genetical theory of natural selection, Clarendon Press, Oxford.
[16] Geweke J., 1996, Monte Carlo Simulation and Numerical Integration [in:] H. Amman, D. Kendrick, J. Rust (ed.), Handbook of Computational Economics, North-Holland, Amsterdam.
[17] Greene W.H., 2003, Econometric Analysis, 5th edition, Macmillan, New York.
[18] Högnäs R.S., Carlson M.J., 2012, “Like Parent, Like Child?”: The intergenerational transmission of nonmarital childbearing,” Social Science Research”, Nov. 41(6), 1480–94.
[19] Hyppölä J., Tunkelo A., Törnqvist L., 1949, Suomen väestöä, sen uusiutumista ja tulevaa kehitystä koskevia laskelmia [Calculations Concerning the Population of Finland, Its Renewal and Future Development], “Tilastollisia tiedonantoja”, 38. Helsinki: Statistics Finland.
[20] Jansakul N., Hinde J.P., 2001, Score Tests for Zero-Inflated Poisson Models, “Computational Statistics & Data Analysis”, no. 40, 75–96.
[21] Jeffreys H., 1961, Theory of Probability, 3rd edition, Oxford University Press, Oxford.
[22] Kass R.E., Raftery A., 1995, Bayes Factor, “Journal of the American Statistical Association”, vol. 90, no. 90.
[23] Kolk M., 2013, Understanding Transmission of Fertility Preferences Across Multiple Generations Socialization or Socioeconomics?, “Stockholm Research Reports in Demography”, no. 4, available at: http://www.suda.su.se/SRRD/SRRD_2013_4.pdf
[24] Kolk M., 2011, Intergenerational continuities in family size – Multigenerational transmission of fertility in contemporary Sweden, “Stockholm Research Reports in Demography”, no. 14, available at: http://www.suda.su.se/SRRD/SRRD_2011_14.pdf
[25] Koop G., 2003, Bayesian Econometrics, Wiley, Chichester.
[26] Lambert D., 1992, Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing, “Technometrics”, vol. 34, no. 1,1–14.
[27] Land K.C., 1986, Methods for National Population Forecasts: A Review, “Journal of the American Statistical Association”, no. 81, 888–901.
[28] Langford C.M., Wilson C., 1985, Is There a Connection Between a Woman’s Fecundity and That of Her Mother?, “Journal of Biosocial Science”, no. 17, 437–443.
[29] Lenk P., 2009, Simulation pseudo-bias correction to the harmonic mean estimator of integrated likelihoods, “Journal of Computational and Graphical Statistics”, 18, 941–960.
[30] Lutz W., Skirbekk V., 2005, Policies addressing the tempo effect in low-fertility countries, “Population and Development Review”, 31(4): 699–720.
[31] Lutz W., Skirbekk V., Testa M.R., 2006, The low fertility trap hypothesis: Forces that may lead to further postponement and fewer births in Europe, “Vienna Yearbook of Population Research”, 4:167–192 (2006).
[32] Martin-Matthews A., Kobayashi K.M., Rosenthal C.J., Matthews S.H., 2001, Age-gapped and agecondensed lineages: Patterns of intergenerational age structure among Canadian families, “QSEP Research Report”, no. 363.
[33] Marzec J., 2008, Bayesowskie modele zmiennych jakościowych i ograniczonych w badaniach niespłacalności kredytu, Wydawnictwo Uniwersytetu Ekonomicznego w Krakowie, Kraków.
[34] Marzec J., Osiewalski J., 2012, Dwuwymiarowy model typu ZIP-CP w łącznej analizie zmiennych licznikowych, „Folia oeconomica cracoviensia”, vol. LIII.
[35] Murphy M., 1987, Differential family formation in Great Britain, “Journal of Biosocial Science”, no. 19, 463–485.
[36] Murphy M., 1999, Is the relationship between fertility of parents and children really weak?, “Social Biology”, no. 46, 122–145.
[37] Newton M.A., Raftery A.E., 1994, Approximate Bayesian Inference by the Weighted Likelihood Bootstrap (with Discussion), “Journal of the Royal Statistical Society B”, vol. 56.
[38] Osiewalska B., 2012, Przejmowanie wzorca płodności matek przez generacje córek w Polsce – podejście bayesowskie [in:] J. Kurkiewicz (eds.), Przemiany demograficzne w Polsce – uwarunkowania i konsekwencje, Badania statutowe 12/KS/2/2012/S/012, Uniwersytet Ekonomiczny w Krakowie, Kraków (typescript).
[39] Osiewalski J., 2001, Ekonometria bayesowska w zastosowaniach, Wydawnictwo Akademii Ekonomicznej w Krakowie, Kraków.
[40] Osiewalski K., Osiewalski J., 2012, Missing observations in daily returns – Bayesian inference within the MSF-SBEKK model, “Central European Journal of Economic Modelling and Econometrics”, vol. 4, Issue 3, 169–197.
[41] Osiewalski K., Zając B., 2010, Krzywe cząstkowych współczynników zgonów – modele wygładzania [in:] Społeczne i Ekonomiczne Konsekwencje Zmian Procesów Demograficznych, „Zeszyt Sekcji Analiz Demograficznych”, no. 22/2010, part 1, 77–86.
[42] Osiewalski K., Zając B., 2011, Bayesowskie porównanie modeli zachowań prokreacyjnych [in:] Frątczak E., Sobczak I., Szreder M. (eds.), Prace i materiały Wydziału Zarządzania Uniwersytetu Gdańskiego. Wybrane problemy rozwoju demograficzno-społecznego Polski i metody ich badania (p. 21–39), Fundacja Rozwoju Uniwersytetu Gdańskiego, Sopot.
[43] Pajor A., 2003, Procesy zmienności stochastycznej SV w bayesowkiej analizie finansowych szeregów czasowych, Akademia Ekonomiczna w Krakowie, Kraków.
[44] Pajor A., 2010, Wielowymiarowe procesy wariancji stochastycznej w ekonometrii finansowej. Ujęcie bayesowskie, Wydawnictwo Uniwersytetu Ekonomicznego w Krakowie, Kraków.
[45] Pajor A., Osiewalski J., 2013, A Note on Lenk’s Correction of the Harmonic Mean Estimator, “Central European Journal of Economic Modelling and Econometrics”, 5: 271–275 (2013).
[46] Pearson K., Lee A., 1899,On the Inheritance of Mankind, “Philosophical Transactions of the Royal Society of London”, A 192.
[47] Pearson K., Lee A., Bramley-Moore L., 1899, Inheritance of fertility in man, and of fecundity in thoroughbred racehorses, “Philosophical Transactions of the Royal Society of London”, A 192.
[48] Pflaumer P., 1988, Confidence Intervals for Population Projections Based on Monte Carlo Methods, “International Journal of Forecasting”, no. 4, 135–142.
[49] Pipień M., 2006, Wnioskowanie bayesowskie w ekonometrii finansowej, Wydawnictwo Akademii Ekonomicznej w Krakowie, Kraków.
[50] Raftery A.E., Li N., Ševčíková H., Gerland P., Heilig G.K., 2012, Bayesian probabilistic population projections for all countries, Proceedings of the National Academy of Sciences USA, 109(35): 13915–13921.
[51] Raftery A.E., 1995,Bayesian Model Selection in Social Research, Sociological Methodology, no. 25, p. 111–163
[52] Robert C.P., Casella G., 2005, Monte Carlo. Statistical Methods, Springer, New York.
[53] Spielauer M., 2005, Concentration of reproduction in Austria, General trends and differentials by educationattainment and urban–rural setting, “Vienna Yearbook of Population Research”, 2005–012, p. 171–195.
[54] Tanaka C.M., Iwasa Y., 2012, Cultural evolution of a belief controlling human mate choice: Dynamic modeling of the hinoeuma superstition in Japan, “Journal of Theoretical Biology”, no. 309, 20–28.
[55] Tymicki K., 2006,Intergenerational transmission of fertility, review of up to date research and some new evidence from Bejsce parish register reconstitution study, 18th – 20th centuries, Poland, European Population Conference 2006 Liverpool Paper.
[56] Yu B., Mykland P., 1994, Looking at Markov Samplers Through Cusum Path Plots: A Simple Diagnostic Idea, Technical Report no. 413, Department of Statistics, University of California at Berkeley.
[57] Zellner A., 1971, An Introduction to Bayesian Inference in Econometrics, John Wiley, New York.