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An optimization model of retiree decisions under recursive utility with housing

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Abstract

We investigate both of analytical and numerical solutions of retirees’ spending and investment decisions. We use a dynamic and realistic recursive utility setting which includes the standard expected utility setting as a special case. We find that recursive utility is superior to expected utility in terms of predicting retirees’ consumption data. In addition to stock and bond investment decisions, we explicitly include housing decision. Our setting includes the setting without housing as a special case. We estimate retiree decisions numerically through simulations. We provide both of analytical and numerical comparative analysis which shows that some of the analytical dependencies are found to be weak numerically. For example, although marginal propensity to consume depends on the parameter of intertemporal substitution analytically, this dependence is found to be weak numerically. These differences show the importance of providing both of analytical and the numerical solutions. Our analytical solution could be useful for future studies to estimate some model parameters, to evaluate different elderly related policies, to quantify the welfare effects of different decisions and to analyze the parameter related issues such as the interchangeability of some parameters.

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Notes

  1. RU denotes recursive utility, EU symbolizes expected utility, C stands for consumption, B represents bond holdings and S denotes the stock holdings and EIS denotes the elasticity of intertemporal substitution throughout this paper.

  2. Epstein and Zin (1989), Weil (1989), Giuliano and Turnovsky (2003), Bansal and Yaron (2004), Rudebush and Swanson (2008), Guvenen (2009), Amisano and Tristani (2010), and Yao and Zhang (2012)

  3. Cocco (2005), Yao and Zhang (2005), Li and Yao (2007), and Fernandez-Villaverde and Krueger (2011).

  4. We assume equal lending and borrowing rates.

  5. e.g. Yao and Zhang (2005)

  6. e.g. Gomes and Michaelides (2005) and Yao and Zhang (2005)

  7. Yao and Zhang (2012) calculated the average stock proportion in liquid financial assets as 0.41 for the people aged 65-75. When we set β at 0.955, we obtain the value of 42% for the average stock proportion and this value lines up with the corresponding standard estimates.

  8. Yao and Zhang (2005) does not use recursive utility, thus it does not have the parameter 𝜖.

  9. Data refers to sample averages of key variables for households in the Survey of Consumer Finances between 1989 and 2001

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Acknowledgments

We are grateful to Fernando Zapatero and Selale Tuzel for their numerous helpful comments.

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Authors and Affiliations

  1. Department of Economics and Finance, Gulf University for Science and Technology, P.O.Box 7207, Hawally, 32093, Kuwait

    Asiye Aydilek

  2. Department of Mathematics and Natural Sciences, Gulf University for Science and Technology, P.O.Box 7207, Hawally, 32093, Kuwait

    Harun Aydilek

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  1. Asiye Aydilek
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  2. Harun Aydilek
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Correspondence to Asiye Aydilek.

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Aydilek, A., Aydilek, H. An optimization model of retiree decisions under recursive utility with housing. J Econ Finan 44, 258–277 (2020). https://doi.org/10.1007/s12197-019-09485-5

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