Retirement date effects on saving behavior: Endogenous labor supply and non‐separable preferences

• Date: 01 September 2017
• Published date: 01 September 2017
• DOI: http://doi.org/10.1111/ijet.12132
• Author: Aylit Tina Romm

doi: 10.1111/ijet.12132

Retirement date effects on saving behavior: Endogenous labor

supply and non-separable preferences

Aylit Tina Romm∗

This paper analyzes the effect of changing retirement dates on pre-retirement saving, looking

at the effect of a negative cross derivative of the utility function with respect to consumption

and leisure. This effect is analyzed in the contexts of both exogenous and endogenous labor

supply before retirement. In the case of exogenous labor supply, the relative decrease in saving

in response to an increase in the expected retirement age is larger in the case of a negative cross

derivative of the utility function (non-separable preferences) than in the case of a zero cross

derivative (separable preferences). However, in the case where labor supply before retirement

decreases at the intensive margin in response to an increase in the retirement age, the relative

decrease in saving in response to an increase in the expected retirementage is smaller in the case

of a negative cross derivative than in the case of a zero crossder ivative.

Key wor ds non-separable preference, retirement date, saving, endogenous labor supply

JEL classification D91, J26

Accepted 18 May2016

1 Introduction

An implication of the standard life-cycle model of consumption and saving (Modigliani and Brum-

berg 1954; Friedman 1957) is that the effect of later expected retirement dates is the same as any

increase in lifetime wealth, where for utility maximizers, the relative increase in consumption in

every time period is equal to the relative increase in lifetime wealth. Such an implication is based on

two assumptions. Firstly, standardlife cycle models assume that individuals receive utility from con-

sumption only.Secondly, there is no change in labor supply at the intensive margin before retirement,

that is, the amount of labor hours supplied by each individual before retirementis exogenously given.

Under the assumptions, however, that an individual’s utility is affected by consumption as well as

leisure, and that the amount of labor hours an individual supplies before retirement is endogenously

determined by the agent, the impact of a change in the expected retirementdate on saving behavior is

not so simple. In this paper, we studythe implications of changes in individuals’ expected retirement

dates for consumption/saving behavior, relaxingthese two assumptions inherent in the standard life

cycle model.

As our main contribution, we demonstrate that the magnitude of the reaction of saving behavior

to a change in the retirement date is largely determined by the sign and magnitude of the cross

∗School of Economics and Business Sciences, and African Microeconomic Research Unit (AMERU), University of the

Witwatersrand, Johannesburg, South Africa. Email: aylit.romm@wits.ac.za

The author would like to thank Economic ResearchSouther n Africa (ERSA) for valuable financial support. Thanks also

to Alexander Zimper and Martin Wittenberg for valuable comments.

International Journal of Economic Theory 13 (2017) 327–346 © IAET 327

International Journal of Economic Theory

Retirement date effects AylitTina Romm

derivative of the utility function with respect to consumption and leisure, and by the degree to which

labor supply before retirement reacts to such a change in the retirement date.

Starting with Heckman (1974), many authors have suggested that preferences are non-separable

in consumption and leisure. The testing of separability between consumption and leisure was first

addressed by authors such as Jorgenson and Lau (1975), Ghez and Becker (1975), Abbotand Ashen-

felter (1976, 1979), Blackorby et al. (1978), Barnett (1979, 1981), Atkinson et al. (1981), Deaton

(1982), Browning et al. (1985), Murphy and Thom (1987), Browning and Meghir (1989), Kaiser

(1993), and more recently by authors such as Basu and Kimball (2002), Ham and Reilly (2002),

French (2005), Laitner and Silverman (2005), Ziliak and Kniesner (2005), and Kiley(2007). All these

studies conclude that preferences are non-separable in consumption and leisure, and in particular,

that the marginal utility of consumption is negatively related to leisure, that is, the cross derivativeof

the utility function is negative. Given this empirical evidence, it is thus fitting that we analyze the ef-

fect of changing retirement dates on saving behavior in the case where preferencesare non-separable

in consumption and leisure.

We show that while, as would be expected, younger individuals save less in response to a later

anticipated retirement date, in the case of exogenous labor supply before retirement, the relative

decrease in saving would be larger the more negative the cross derivativeof the utilit y function with

respect to consumption and leisure. Key to our finding is that if preferences are non-separable in

consumption and leisure, and if the marginal utility of consumption is negatively related to leisure

(the cross derivative of the utility function is negative), the positive effect on consumption of an

increase in lifetime resources induced by a later anticipated retirement date1is dampened by a

negative effect on consumption caused by a decrease in the ratio of future leisure to current leisure.

The fact that a later expected retirement date is accompanied by a decrease in future leisure relative

to current leisure is not significant for preferences that are separable in consumption and leisure,

that is, when the cross derivative of the utility function is zero, where a change in the expected date

of retirement will induce changes in consumption, and hence saving, analogous to if utility were a

function of consumption alone. If, however, the cross derivative of the utility function is non-zero,

our model shows that this nuance changes the analysis in a non-trivial manner. This is so, since

while in the case of separable preferences, optimal consumption and hence saving is completely

independent of current or future leisure, in the non-separable case, optimal consumption and saving

depend on the ratio of current to future leisure, which in turn is dependent on the date of retirement.

In particular,in the case of a negative cross derivative, optimal consumption decreases with a decrease

in the ratio of future leisure to current leisure.

Secondly, we examine the implication of agents decreasing their labor supply at the intensive

margin before retirement in response to a later expected retirementdate. The expectation of retiring

later corresponds to an expected increase in lifetime wealth. The literature has shown that increases

or expected future increases in wealth lead agents to reduce the hours they work (Joulfaian and

Wilhelm 1994; French and Cheng 2000; Imbens et al. 2001; Disney and Gathergood 2013. We show

that when individuals reduce the hours worked before retirement in response to an increase in the

expected age of retirement, for zeroor small negative cross derivatives of the the utility function with

respect to consumption and leisure, the decrease in saving is far larger than if they worked the same

hours as before. This results from the fact that a decrease in hours worked before retirement will

offset the increase in lifetime wealth implied by the later retirementage. At the extreme, agents happy

with their existing level of lifetime wealth will reduce hours worked to the extent that lifetime wealth

1Such an increase in lifetime wealth will certainly occur if later retirementages are not accompanied by a decrease in labor

supply at the intensive margin before retirement.

328 International Journal of Economic Theory 13 (2017) 327–346 © IAET