Modeling the Diffusion of Private Pension Provision


  • Larysa Yakymova



voluntary pension system, diffusion mechanism, Rogers model, Bass model, CEE countries


The purpose of this paper is threefold: to adapt the innovation diffusion models to describe and predict the diffusion of private pension provision; to evaluate the suitability of diffusion models based on the historical data from the Romanian and Ukrainian voluntary pension systems; and to compare the diffusion parameters of private pension provision in these countries. The study proven that diffusion models, such as the Rogers model and the Bass model, can reproduce the diffusion of innovations in the field of pensions. The Rogers diffusion parameters for Romania and Ukraine are almost identical; this gives grounds for a conclusion about the similar behavioral patterns in post-socialist countries. However, some limitations on models use are noted. During the crisis and when using the nudge mechanism, models are not always well-fitting, but when new pension schemes are introduced or new pension funds are opened, models can be used in “guessing by analogy”.

JEL Codes - C51; G53


Administrator of the Pension Fund “Center of Personified Accounting”, 2017. Pension funds. from

Arza, C., 2008. Changing European welfare: The new distributional principles of pension policy. In C. Arza and M. Kohli (Eds.), Pension Reform in Europe: Politics, policies and outcome (pp. 109-131). New York: Routledge.

Baltac, A. G., and Dinca (Nicola), Z., 2013. Companies' Role in the Evolution of the Romanian Economy in the Period 2011-2013. Romanian Statistical Review, 61(4), 113-117.

Bass, F. M., 1969. A new product growth model for consumer durables. Management Science, 15(5), 215-227.

Brooks, S. M., 2005. Interdependent and domestic foundations of policy change: The diffusion of pension privatization around the world. International Studies Quarterly, 49(2), 273-294.

Brooks, S. M., 2007. When Does Diffusion Matter? Explaining the Spread of Structural Pension Reforms Across Nations. The Journal of Politics, 69(3), 701-715.

Bui, Q., 2015. A Review of Innovation Diffusion Theories and Mechanisms. Proceedings of the Twentieth DIGIT 2015 Workshop.

Chatterjee, R., and Eliashberg, J., 1990. The Innovation Diffusion Process in a Heterogeneous Population: A Micromodeling Approach. Management Science, 36(9), 1057-1079.

Chawla, M., Betcherman, G., and Banerji, A., 2007. From red to gray : the "third transition" of aging populations in Eastern Europe and the former Soviet Union. Washington, D.C.: The World Bank.

Countrymeters, 2017. Romania Population. from

Danich, V. M., and Yakymova, L. P., 2011. Modelyuvannya dynamiky rozpovsyudzhennya nederzhavnoho pensiynoho zabezpechennya u neodnoridnomu pensiynomu sotsiumi. Biznes Inform, 5(1), 81-83.

Ebbinghaus, B., and Gronwald, M., 2011. The Changing Public-Private Pension Mix in Europe: From Path Dependence to Path Departure. In B. Ebbinghaus (Ed.), Varieties of Pension Governance. The Privatization of Pensions in Europe. Oxford: Oxford University Press.

Financial Supervisory Authority, 2017. Evolution of Indicators. from

Freudenberg, C., Berki, T., and Reiff, A., 2016. A Long-Term Evaluation of Recent Hungarian Pension Reforms. MNB Working Papers, 2, 1-63.

Gilardi, F., Jordana, J., and Meseguer Yebra, C., 2006. The diffusion of regulatory reforms in pension systems: Latin America in comparative perspective. Documentos de Trabajo del CIDE, 136.

Guardiancich, I., 2010. Current pension system: first assessment of reform outcomes and output. Country Report, Germany. Research Project “Assurer une pension adequate dans un contexte europeen”.

Hennessy, A., and Steinwand, M. C., 2014. The Sources of Pension Reforms in Western Europe: Domestic Factors, Policy Diffusion, or Common Shock? International Interactions, 40(4), 477-505.

Holzmann, R., and Hinz, R., 2005. Old Age Income Support in the 21st century: An International Perspective on Pension Systems and Reform. Washington, DC: World Bank.

Islam, T., 2014. Household level innovation diffusion model of photo-voltaic (PV) solar cells from stated preference data. Energy Policy, 65, 340-350.

Jiang, Z., Bass, F. M., and Bass, P. M., 2006. Virtual Bass Model and the left-hand data-truncation bias in diffusion of innovation studies. International Journal of Research in Marketing, 23(1), 93-106.

Kalish, S., 1985. A new product adoption model with price, advertising, and uncertainty. Management Science, 31(12), 1569-1585.

Kamakura, W. A., and Ealasubramanian, S. K., 1987. Long-term forecasting with innovation diffusion models: The impact of replacement purchases. Journal of Forecasting, 6(1), 1-19.

Kumar, A., Baisya, R. K., Shankar, R., and Momaya, K., 2007. Diffusion of mobile communications: Application of bass diffusion model to BRIC countries. Journal of Scientific and Industrial Research, 66, 312-316.

Leigh, L., and Yorke-Smith, N., 2011. An adaptation of the Bass new product diffusion model for multiple purchases of capital Items. Proceedings of 10th International Marketing Trends Conference.

Mahajan, V., Muller, E., and Bass, F. M., 1990. New Product Diffusion Models in Marketing: A Review and Directions for Research. Journal of Marketing, 54(1), 1-26.

Massiani, J., and Gohs, A., 2015. The choice of Bass model coefficients to forecast diffusion for innovative products: An empirical investigation for new automotive technologies. Research in Transportation Economics, 50, 17-28.

National Commission for Regulation of Financial Services Markets, 2017. Information on the state and development of non-state pension provision of Ukraine. from

OECD, 2017. Pensions at a Glance 2017: OECD and G20 Indicators. Paris: OECD Publishing.

Orenstein, M. A., 2003. Mapping the diffusion of pension innovation. In R. Holzmann, M. A. Orenstein and M. Rutkowski (Eds.), Pension Reform in Europe: Process and Progress (pp. 171-193). Washington: The World Bank.

OtpPension, 2017. Activity results. from

PensionMarket, 2017. Pension funds (NPF). from

Philippas, D. T., 2011. A mathematical model for financial innovation: empirical evidence from financial markets. (doctoral), University of Patras, Patras. Retrieved from

Ratcliff, R., and Doshi, K., 2016. Using the Bass Model to analyze the diffusion of innovations at the Base of the Pyramid. Business & Society, 55(2), 271-298.

Rogers, E. M., 1983. Diffusion of Innovations. New York: The Free Press.

Rust, S., 2016. German insurance association defends Riester-Rente amid failure claims. IPE. from

State Statistics Service of Ukraine, 2017. Population. from

Strang, D., and Soule, S. A., 1998. Diffusion in Organizations and Social Movements: From Hybrid Corn to Poison Pills. Annual Review of Sociology, 24(1), 265-290.

Tarde, G., 1903. The laws of imitation New York: Henry Holt and Company.

Tosa, C., Miwa, T., and Morikawa, T., 2015. Modelling and forecasting car ownership in Romania’s counties using Bass diffusion model. Paper presented at the European Transport Conference 2015, Frankfurt, Germany.

Weyland, K., 2005. Theories of Policy Diffusion: Lessons from Latin American Pension Reform. World Politics, 57(2), 262-295.

Weyland, K., 2007. Bounded Rationality and Policy Diffusion: Social Sector Reform. Princeton, NJ: Princeton University Press.

Wright, M., Upritchard, C., and Lewis, T., 1997. A Validation of the Bass New

Product Diffusion Model in New Zealand. Marketing Bulletin, 8, 15-29.

Xie, J., Song, M., Sirbu, M., and Wang, Q., 1997. Kalman filter estimation of new product diffusion models. JMR, Journal of Marketing Research, 34(3), 378-393.

Yakimova, L., 2018. Modeling the Impact of Crises on Evolution of Pension Systems. In I. Nekrasova, O. Karnaukhova and B. Christiansen (Eds.), Fractal Approaches for Modeling Financial Assets and Predicting Crises (pp. 115-138). USA: IGI Global.

Yakymova, L. P., 2013. Modelyuvannya prostorovo-chasovoyi dynamiky pensiynoho sotsiumu. Biznes Inform, 9, 84-89.

Young, H. P., 2009. Innovation Diffusion in Heterogeneous Populations: Contagion, Social Influence, and Social Learning. The American Economic Review, 99(5), 1899-1924.

Zabkar, V., and Zuzel, B., 2002. Bass new product diffusion model: estimation and findings. Metodoloski zvezki, 17, 209-219.




How to Cite

Yakymova, L. (2018). Modeling the Diffusion of Private Pension Provision. Scientific Annals of Economics and Business, 65(4), 385–405.