Appraising the Financial Sustainability of a Pension System with Signal Processing
DOI:
https://doi.org/10.25115/eea.v33i3.3134Keywords:
Monte Carlo Simulation, Pyramid of Age, Pension System.Abstract
One key issue of the Spanish pension system is its financial sustainability in regard to slumping fertility rate and rising longevity of the Spanish population. The paper presents a versatile and robust model that may help pension managers gain insight into the future Spanish pyramid of ages, from which they will appraise cash inflows and outflows of the pension system. The model forecasts ninety years of the Spanish population for each cohort of the pyramid of ages. Borrowed from the signal processing discipline, the model relies on the Burg method which fits a pth order autoregressive (AR) model to the input signal by minimizing (least squares) the forward and backward prediction errors while constrai-ning the AR parameters to satisfy the Levinson-Durbin recursión, then uses an infinite impulse response prediction error filter. Results add better perspective and insight to the Spanish population projection forecasted by the United Nations Population Division.
Downloads
References
ALHO, J.M., JENSEN S.E.H. and LASSILA, J. (2008). Uncertain Demographics and Fiscal Sustainability. Cambridge: Cambridge University Press.
BOOTH, H. (2006). “Demographic forecasting: 1980 to 2005 in review“. International Journal of Forecasting, 22, pp. 547-581.
BOX, G. E. P. and JENKINS, G. M. (1976). Time Series Analysis: Forecasting and Control. Revised Edition, San Francisco: Holden Day.
BURG, J.P. (1975). “Maximum Entropy Spectral Analysis“. Available at: http://sepwww. stanford.edu/theses/sep06/ [May 12, 2015].
COHEN, J. E. (1999). “Should population projections consider "limiting factors" and if so how?“. In LUTZ, W., VAUPEL, J. W. and AHLBURG, D. A. (Eds.). Frontiers of Population Forecasting. New York: Population Council. A supplement to Population and Development Review, 24 (1998), pp. 118-138.
DURBIN, J. (1960). “The fitting of time series models“. Revue de l'Institut International de Statistique, 28, pp. 233-44.
HAUSER, R. M. and WILLIS, R. J. (2005). “Survey design and methodology in the Health and Retirement Study and the Wisconsin Longitudinal Study“. In WAITE, L. J. (Ed.). Aging, Health, and Public Policy: Demographic and Economic Perspectives, New York: Population Council, Supplement to Population and Development Review, 30 (2004).
LEE, R. D. (1990). “Long-run global population forecasts: a critical appraisal“. Population and Development Review, 16, pp. 44-71.
LEE, R.D. and TULJAPURKAR, S. (1994). “Stochastic population forecasts for the United States: Beyond high, medium, and low“. Journal of the American Statistical Association, 89(428), pp.1175-1189.
LEVINSON, N. (1946). “The Wiener RMS (root mean square) error criterion in filter design and prediction“. Journal of Mathematical Physics, 25, pp. 261-78.
LUTZ, W., SANDERSON W.C. and SCHERBOV S. (1998). “Expert-based probabilistic population projections“. Population and Development Review, 24, pp. 139-155.
METTLER, U. (2003). “Projecting Pension Fund Cash Flows“, ASTIN colloquia, IAA (International Actuarial Association), Zurich, Switzerland. www.actuaries.org/ASTIN/ Colloquia/Zurich/Mettler.pdf (Accessed on May 24, 2015).
MORA, F.E., MUÑOZ DE BUSTILLO LLORENTE, R. (2004). “Mitos y falacias populares en el debate acerca de los sistemas de pensiones“. Estudios de economía aplicada, 22(2), pp. 289-316.
OPPENHEIM, A. V. and SCHAFER, R. W. (1975). Digital Signal Processing, Upper Saddle River. New Jersey: Prentice Hall.
PEREZ, J.I.A. (2006). “La reforma de los sistemas de pensiones en Europa del Este y su impacto sobre la eficiencia y la equidad“. Estudios de economía aplicada, 24(2), pp. 783-814.
PRIEMER, R. (1991). Introductory Signal Processing. Singapore: World Scientific.
RAFTERY, A.E., LIB, N., ŠEVČÍKOVÁC, H., GERLANDB, P. and HEILIGB, G.K. (2012). “Bayesian probabilistic population projections for all countries“. Proceedings of the National Academy of Sciences, 109(35), pp. 13915-13921. doi:10.1073/pnas. 1211452109. Available at: http://www.pnas.org/content/109/35/13915.full.pdf+html [Accessed on May 12, 2015].
TULJAPURKAR, S. and BOE, C (1999). “Validation, probability-weighted priors, and information in stochastic forecasts”. International Journal of Forecasting, 15, pp. 259- 271.
U.S. Census Bureau (2014). “Methodology, Assumptions, and Inputs for the 2014 National Projections“. Available at: http://www.census.gov/population/projections/files/ methodology/methodstatement14.pdf [Accessed on May 12, 2015].
WHELPTON, P.K. (1936). “An empirical method for calculating future population”. Journal of the American Statistical Association, 31, pp. 457-473.
