Understanding joint retirement

Abstract

Evidence from different sources shows that spouses’ retirement decisions are correlated. Retirement policies affecting individuals in couples are therefore also likely to affect behavior of their spouses. It is therefore important to account for joint features in modeling retirement. This paper studies a structural collective model of labor supply and retirement of both partners in a couple with interdependent preferences, imperfect knowledge of preferences of the spouse, and subjective expectations about the future. We propose a novel method to estimate preferences and the intra-household bargaining process, which relies on stated preferences data collected in the Health and Retirement Study. Respondents were asked to choose between hypothetical retirement trajectories describing the retirement ages and replacement rates of both spouses from three perspectives: considering their own preferences only, the preferences of their spouse only, or the most likely decision for the household. With these data, all model parameters are identified and potential sources of joint retirement can be disentangled. Our results suggest that males misperceive their wives’ preferences, overestimating their disutility of work. Our estimates correct for this. We find strong positive correlations between preferences for joint leisure (leisure complementarity) of the two partners. Counterfactual simulations with stylized retirement paths suggest that the leisure complementarities explain a substantial part of joint retirement, much more than correlation in unobserved heterogeneity or potential wage rates.

Introduction

Population aging has led to a debate on the labor force participation of older workers, increasing the need for understanding retirement decisions and their sensitivity for policy measures. Earlier studies often only focus on the retirement behavior of males, due to the fact that women often left the labor market long before reaching retirement age. Since the labor force participation rate of women has grown substantially over the last decades, understanding their retirement decisions has gained importance. Moreover, there is clear evidence that the retirement decisions within couples are interdependent, with a significant proportion of spouses retiring at approximately the same time, irrespective of their age difference (“joint retirement”). Hurd (1989) already pointed out that between 20 and 30 percent of all couples retire within one year of each other. Since then, a new line of research has emerged aimed at analyzing and understanding the retirement behavior of couples. Empirical evidence of joint retirement decisions has been documented for several cohorts and countries, including Blau (1998) (Retirement History Study), Gustman and Steinmeier (2000) (National Longitudinal Survey of Mature Women), Gustman and Steinmeier (2004) and Casanova Rivas (2010) (Health and Retirement Study), Banks et al. (2007) (English Longitudinal Study of Ageing), and Hospido and Zamarro (2014) (Survey of Health Ageing and Retirement in Europe).

There are several potential links between spouses’ retirement decisions that may explain joint retirement. The first one operates through the household budget constraint (see Blau, 1998, Casanova Rivas). Casanova Rivas (2010) shows that under certain conditions, the fact that resources are shared can increase the probability of joint retirement. In addition, the spouse allowance in the US old age social security benefit system creates financial incentives that explain coordination in retirement dates (see McCarty, 1990). The second channel originates from preferences: It is plausible that spouses enjoy spending leisure time together so that the marginal utility of retirement increases when the partner is also retired (complementarities in leisure, leading to a causal effect of the retirement of one spouse on retirement of the other spouse; see Gustman, Steinmeier, 2000, Gustman, Steinmeier, 2004, Gustman, Steinmeier, Stancanelli and van Soest (2016) or Michaud and Vermeulen, 2011). The third channel is the correlation in spouses’ (unobserved) tastes for leisure (See Gustman, Steinmeier, 2000, Gustman, Steinmeier, 2004) that can be due to assortative matching. The literature has not come to a clear conclusion on the relative importance of these three channels, but does conclude that ignoring joint retirement may severely underestimate the overall impact of reforms in retirement policy. For example, Coile (2004) finds that neglecting the spill-over effect on the behavior of the spouse leads to underestimating the overall impact of a typical policy by 13% to 20%.

To model joint behavior, the collective model empirically outperforms the neoclassical unitary model assuming that each household behaves as a single decision maker, both for consumption and labor supply behavior (Fortin and Lacroix (1997), Bourguignon et al. (1993), Cherchye et al., 2009). The collective model (Chiappori, 1988) starts from the basic assumption that in a multi-person household, household members have their own utility functions but cooperate in some bargaining process that results in a Pareto-efficient allocation. The assumption of cooperation seems quite natural, given that spouses interact very often.¹ Several studies found support for the collective model in the sense that its theoretical implications cannot be rejected when tested on multi-person household data (Chiappori et al. (2002), Cherchye et al., 2009). Yet, some assumptions of that model remain untested. In particular, it is assumed that each spouse knows the preferences of the other spouse and therefore can correctly pick a Pareto optimal outcome. To the best of our knowledge, no study has tested this assumption.

A major challenge of the collective model is the identification of parameters in a realistic context with externalities and public goods. Additional identifying assumptions are usually needed in order to estimate the model and test its validity. Chiappori, 1988, Chiappori, 1992 shows that if preferences are egoistic, the usual data on actual household choices are enough to identify the sharing rule up to a constant. The assumption of egoistic preference, however, is quite restrictive in the context of retirement, since it means that the marginal rate of substitution (MRS) between own leisure and consumption remains the same regardless of the spouse’s labor supply and therefore does not allow for complementarities (externalities) of leisure activities - one of the possible explanations for joint retirement. Many activities such as taking meals or traveling on holidays will usually be more enjoyable when they can be done together with the spouse. A natural assumption for older couples is therefore that the marginal utility of own leisure depends on leisure of the spouse, that is, preferences are interdependent (See Gustman, Steinmeier, 2000, Gustman, Steinmeier, 2004, Gustman, Steinmeier; Michaud and Vermeulen, 2011). Michaud and Vermeulen (2011) allow for complementarities in leisure, identifying the model by making use of panel data with couples and individuals who became a widow(er) in the observation period, along with the assumption that an individual’s preferences can only change after the death of the spouse.

Models of joint retirement behavior also typically assume that expectations regarding the future are rational (Blau, 1998, Gustman, Steinmeier, 2000). A large literature has studied how expectations regarding mortality, health and other risks deviate from rational expectations in the general population and these deviations are predictive of behavior (Hurd, 2009). Manski (2004) argues that direct measurement of expectations and their inclusion in behavioral models is desirable in order to make inferences about preferences. Yet, we know of no application of collective models which uses subjective expectations on risks (longevity, disability, etc).

The main contribution of the current paper is to provide a novel approach to obtain identification of a general version of the collective model for labor supply and retirement in a context that allows for subjective (and not necessarily rational) expectations and imperfect knowledge of preferences of the spouse. Specific to this model is that it avoids imposing restrictions on individual preferences such as egoistic preferences: externalities and public goods are both allowed to enter the individual utility functions. The paper solves the identification problem by using stated preferences (SP) data, aimed at directly identifying the main components of the model. Survey respondents were offered several pairs of simplified retirement trajectories. They were asked to choose between two trajectories three times: first only accounting for their own preferences, then using only their spouse’s preferences, and finally they were asked what would be the most likely choice of their household, accounting for both individuals’ preferences as well as the decision-making process in their household. As in Kapteyn and Kooreman (1992), the rich SP data directly helps to estimate the individual utility functions and demand for leisure equations that can be used to identify all preference parameters. The answers to the question on the most likely choice in the household then identify the household decision process and, in particular, the weights of both partner’s utility functions for the household choice.

The method of Stated Preferences (SP) has been commonly used in marketing and transportation sciences for many years (see, e.g., Louviere et al., 2000), and is gaining ground in economics since Barsky et al. (1997) and Revelt and Train (1998). Elsayed et al. (2018) and Van Soest and Vonkova (2014) apply stated preferences to labor supply and retirement decisions of individuals. The latter motivate the use of SP data from the fact that they want to analyze preferences for plans that do not yet exist (e.g., retirement after the mandatory retirement age). Moreover, it is often not clear which alternative retirement scenarios workers can choose in real life, when not only the rules of their pension plan but also limited flexibility of their employer may restrict their actual choice set in ways that remain unobserved in the data. Moreover, the actual choice set depends on labor market history and is therefore potentially endogenous to the individual’s labor supply preferences. SP data allow for a design where choice opportunities are exactly known, and variation in choices is substantial and by construction exogenous to preferences. In the current study, an important additional argument for using SP data is that, as discussed above, not all the parameters of interest can be identified with revealed preference data only.

The SP data are collected for a subsample of respondents in the Health and Retirement Study (HRS). They are used to estimate a stylized structural model of labor supply and retirement of both partners. Our main findings are the following. Our results suggest that males misperceive their wives’ preferences, overestimating their disutility of work. Our estimates correct for this. We find strong positive correlations between preferences for joint leisure (complementarities in leisure) of the two partners. Counterfactual simulations with stylized retirement paths suggest that the leisure complementarities explain a substantial part of joint retirement, while correlation in unobserved heterogeneity or potential wage rates explain a smaller part.

The remainder of this paper is organized as follows. Section 2 uses a simple example to illustrate the idea of identification in a stylized collective model. Section 3 describes the sample and our SP data. The empirical specification of the structural collective model is discussed in Section 4. The estimation results are discussed in Section 5. Section 6 presents the results of some simulation exercises, validating the SP data by comparing simulated retirement ages with data on expected retirement ages of the same individuals, and then using counterfactual simulations to indicate how complementarities in leisure and correlation between preferences of the two partners contribute to joint retirement outcomes. Section 7 concludes.