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ARTICLE

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ABSTRACT

The primary objective of the work is to use Bayesian methods to investigate women fertility in Poland and identify key factors influencing it. Bayesian Poisson regression model has been used in the analysis. The model allows determining factors that have a significant impact on the number of children born. Moreover Bayesian approach makes it possible to incorporate a priori knowledge and improve the estimation of model parameters. The model has been estimated using Markov chain Monte Carlo method with Gibbs sampling.
The work has been based on the Polish study ”Family changes and Fertility Patterns in Poland” (1991). The following attributes have been considered in the analysis of women fertility: place of living, education, marital status, employment and religion. The results have been compared with the results of related research for Poland and other countries.

KEYWORDS

fertility, Poisson regression model, Bayesian inference, Markov chain Monte Carlo method

REFERENCES

[1] Adelman I., An Econometric Analysis of Population Growth. The American Economic Review, Vol. 54, No. 2, 314-339, 1963.

[2] Balicki J., Fratczak E., Nam Ch.B., Przemiany ludnosciowe. Fakty – Interpretacje – Opinie. Wydawnictwo Uniwersytetu Karola Stefana Wyszynskiego w Warszawie, 2007.

[3] Becker G.S., A treatise on the family. Harvard University Press, Cambridge, Mass. 1981.

[4] Becker G.S., Ekonomiczna teoria zachowan ludzkich. PWN, 1990.

[5] Becker G.S., Human capital: A theoretical and empirical analysis with special reference to education. The University of Chicago Press, 1993.

[6] Becker G.S., Barro R.J., A Reformulation of the Economic. Theory of Fertility. The Quarterly Journal of Economics, Vol. 103, No.1, 1-25, 1988.

[7] Bernardo J., Smith A., Bayesian Theory. A John Wiley & Sons, 2004.

[8] Bolstad W.M., Introduction to Bayesian statistics. A John Wiley & Sons, 2007.

[9] Brewster K.L., Rindfuss R.R., Fertility and women’s employment in industrialized nation. Annual Review of Sociology, 26, 271-296, 2000.

[10] Brookes S., Gelman A., General methods for monitoring convergence of iterative simulations. Journal of Computational and Graphical Statistics, 7, 434-455, 1998.

[11] Casella G., George E.I., Explaining the Gibbs sampler. The American Statistician, 46, 167-74, 1992.

[12] Coleman J.S., Foundations of social theory. Cambridge. Harvard University Press, 1990.

[13] Dellaportas P., Smith A.F.M., Bayesian inference for generalized linear models and proportional hazard models via Gibbs sampling. Applied Statistics, Vol. 42, No. 3, 443-459, 1993.

[14] Dey D.K., Ghosh S.K., Mallick B.K., Generalized Linear Models: A Bayesian Perspective, New York: Marcel Decker, 2000.

[15] Dobson A.J., An introduction to generalized linear models. Chapman & Hall, 1991.

[16] Doss H., Narasimhan B., Bayesian Poisson regression using the Gibbs sampler: Sensitivity analysis through dynamic graphics. Technical report, Penn State Erie, 1994.

[17] Easterlin R.A., The Economics and Sociology of Fertility: A Synthesis. Tilly Ch. (Red.) Historical Studies of Changing Fertility, Princeton, 1979.

[18] Easterlin R.A., Birth and fortune: the impact of numbers on personal welfare. Basic Books, 1987.

[19] El-Sayyad G.M., Bayesian and classical analysis of Poisson regression. Journal of Royal Statistical Society. Series B. Vol. 35, No. 3, 445-451, 1973.

[20] Fratczak E., Modelowanie cyklu zycia jednostki i rodziny teoria i praktyka. Oficyna Wydawnicza SGH, 1999.

[21] Fratczak E., Józwiak J., Paszek B., Zastosowania analizy historii zdarzen w demografii. Oficyna Wydawnicza SGH, 1996.

[22] Fratczak E., Kowalska I., G¨otz R., Drobniˇc S., Blossfeld H.P., Polish family and fertility survey. A user’ guide. Warsaw and Bremen, 1996.

[23] Fratczak E., Sobczak I. (Red.), Dzietnosc kobiet polskich w okresie transformacji ustrojowej. Polskie Towarzystwo Demograficzne, 2000.

[24] Gamerman D., Lopes H., Markov Chain Monte Carlo: stochastic simulation for Bayesian inference. Chapman & Hall (CRC Press), 2006.

[25] Gawryszewski A., Ludnosc Polski w XX Wieku. Instytut Geografii i Przestrzennego Zagospodarowania im. Stanisława Leszczyckiego, PAN, 2005.

[26] Gelman A., Carlin J.B., Stern H.S., Rubin D.B., Bayesian data analysis. Chapman & Hall/CRC, 2000.

[27] Gelman A., Rubin D., Inference from iterative simulation using multiple sequences. Statistical Science, 7, 457-72, 1992.

[28] Geman S., Geman D., Stochastic relaxation, Gibbs distributions and the Bayesian restoration of image. IEEE Transaction on Pattern Analysis and Machine Intelligence, 6, 721-741, 1984.

[29] Geweke J., Evaluating the accuracy of sampling-based approaches to calculating posterior moments. Bayesian Statistics, 4, 169-193, 1992.

[30] Gilks W., Best N., Tan K., Adaptive rejection Metropolis sampling with Gibbs sampling. Applied Statistics, 44, 455-472, 1995.

[31] Gilks W., Wild P., Adaptive rejection sampling for Gibbs sampling. Applied Statistics, 41, 337-348, 1992.

[32] Hardin J.W., Hilbe J.M., Generalized linear models and extensions. Stata Press, 2007.

[33] Heidelberger P., Welch P., A spectral method for confidence interval generation and run length control in simulations. Communication of the ACM, 24, 233-245, 1981.

[34] Heidelberger P., Welch P., Simulation run length control in the presence of an initial transient. Operation Research, 31, 1109-1144, 1983.

[35] Hilgeman Ch., Butts C.T., Women’s employment and fertility: A welfare regime paradox. Social Science Research, Vol. 38, Issue 1, 103-117, 2009.

[36] Holzer J.Z., Demografia. Polskie Wydawnictwo Ekonomiczne, Warszawa, 2003.

[37] Holzer J.Z., Kowalska I., Fertility and family surveys in countries of the ECE region. Standard country report, Poland, UNECE, UNPF, 1997.

[38] Ibrahim J.G., Laud P.W., On Bayesian analysis of generalized linear models using Jeffreys’s prior. Journal of the American Statistical Association, Vol. 86, No. 416, 981-986, 1991.

[39] Jeffreys H., An invariant form for the prior probability in estimation problems. Proceedings of the Royal Society of London, Ser. A 186, 453-461, 1946.

[40] Jeffreys H., Theory of probability. New York: Oxford University Press, 1961.

[41] Kaplan H., Evolutionary wealth flows theories of fertility: empirical test and new models. Population and development Review, 20 (4), 1994.

[42] Klasen S., Launov A., Analysis of the Determinants Fertility Decline in the Czech Republic. Journal of Population Economy, Vol. 19, 25-54, 2006.

[43] Kotowska I.E. (Red.), Przemiany demograficzne w Polsce w latach 90.w swietle koncepcji drugiego przejscia demograficznego. Oficyna Wydawnicza SGH, 1999.

[44] Kotowska I.E., Józwiak J., Matysiak A., Baranowska A., Poland: Fertility decline as a response to profound societal and labour market changes? Demographic Research, Vol.19, Article 22, 795-854, 2008.

[45] Kurkiewicz J., Modele przemian płodnosci w wybranych krajach europejskich w swietle drugiego przejscia demograficznego. Wydawnictwo Akademii Ekonomicznej w Krakowie, 1998.

[46] Leibenstein H., Rozwój i zacofanie gospodarcze. Studia z teorii rozwoju gospodarczego, 1963.

[47] Lesthaeghe R., A century of demographic and cultural change in Western Europe, an exploration of underlying dimensions. Population and Development Review, 9 (3), 411-435, 1983.

[48] Lesthaeghe R., The second demographic transition in Western Countries: An interpretation. Interuniversity Programme in Demography. Working Paper, No. 2, 1991.

[49] Lesthaeghe R., Surkyn J., Cultural dynamics and economic theories of fertility change. Population and Development Review, 14 (1), 1-45, 1988.

[50] Lynch S.M., Introduction to applied Bayesian statistics and estimation for social scientists. Springer, 2007.

[51] McCullagh P., Nelder J.A., Generalized linear models. Chapman & Hall, 1989.

[52] Montgomery M.R., Casterline J.B., Social Influence, Social Learning and New models of fertility. Population and Development Review, Vol. 22, 151-175,1996.

[53] Nelder J.A., Wedderburn R.W.M., Generalized linear models. J. R. Statist. Soc. A, 135, 370-384, 1972.

[54] Ol´ah L.Sz., Fratczak E., Becoming a Mother in Hungary and Poland during State Socialism. Demographic Research, Special Collection 3, Article 9, 211-244, 2004.

[55] Osiewalski J., Ekonometria bayesowska w zastosowaniach. Wydawnictwo Akademii Ekonomicznej w Krakowie, 2001.

[56] Raftery A., Lewis S., One long run with diagnostics: implementation strategies for Markov Chain Monte Carlo. Statistical Science, 7, 493-497, 1992.

[57] Raftery A., Lewis S., The number of iterations, convergence diagnostics and generic Metropolis Algorithms. In Gilks W., Spiegelhalter D., Richardson S., editors, Practical Markov Chain Monte Carlo, London, UK: Chapman & Hall, 1995.

[58] Robert C., Casella G., Monte Carlo statistical methods. Springer Texts in Statistics, 2004.

[59] Silvey S.D., Wnioskowanie statystyczne, PWN, 1978.

[60] Skirbekk V., Fertility trends by social status. Demographic Research. Vol. 18, Article 5, 145-180, 2008.

[61] Sleebos J.E., Low fertility rates in OECD countries. Facts and Policy Responses. Organization for Co-operation and Development, 2003. http://www.oecd.org/dataoecd/13/38/16587241.pdf

[62] Stanisz A., Przystepny kurs statystyki z zastosowaniem STATISTICA PL na przykładach z medycyny. Tom 2. StatSoft, 2007.

[63] Szołtysek M., Rozrodczosc w perspektywie ekonomicznej i demografia przeszłosci. Roczniki Dziejów Społecznych i Gospodarczych. Vol. 65, 25-53, 2005.

[64] Szreder M., Informacje a priori w klasycznej i bayesowskiej estymacji modeli regresji.Wydawnictwo Uniwersytetu Gdanskiego, 1994.

[65] Szreder M., Osiewalski J., Przykład bayesowskiej estymacji modelu rynku w nierównowadze z wykorzystaniem subiektywnych rozkładów a priori. Przeglad Statystyczny, Nr 3-4, 1991.

[66] Van de Kaa D.J., Europe’s second demographic transition. Population Bulletin, Vol. 42, No. 1, 1987.

[67] Van de Kaa D.J., Post modern fertility preferences: from changing value orientation to new behaviour. Population and Development Review (supplement), Vol.27, 290-331, 2001.

[68] Wang W., Famoye F., Modeling household fertility decisions with generalized Poisson regression. Journal of Population Economics, 10, 273-283, 1997.

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