What Happens to the Husband's Retirement Decision When the Wife's Retirement Incentives Change?

Several studies have documented a strong correlation in the timing of spouses’ retirement decisions. However, considerably less is known about the causal impact of one spouse’s retirement incentives on the retirement decision of the other spouse. Before, but not after, 2001 broad categories of Swedish local government workers in female dominated occupations were entitled to retire with full pension benefits already at the age of 63. In this paper, I utilize this reform – together with a micro data set covering the total Swedish population – to estimate the effect of a change in the wife’s incentive on the husband’s retirement behavior. I document a sharp decrease in pension benefit withdrawals among 63 year old wives in the local government sector in the years following the reform. However, I do not find any evidence of a response among husbands. This finding is at odds with most earlier results in the literature.


Introduction
Several studies (e.g. Hurd 1990and Schirle 2008 have documented a strong correlation in the timing of spouses' retirement decisions. However, considerably less is known about the causal impact of one spouse's retirement incentives on the other spouse's retirement decision. Suppose that the wife's pension benefit accrual increases.
If the substitution effect dominates, the wife works longer. But how is the husband's labor supply affected? While theories of family decision-making in general yield ambiguous predictions, it is an empirical issue of substantial policy relevance to find out in which direction the net effect goes, if there is any effect at all. If, for instance, complementarity in leisure is an important phenomenon, a delayed retirement age among female workers can potentially lead to an aggregate increase in labor force participation rates among elderly males.
There are at least two fundamental problems involved in estimating the causal impact of one spouse's retirement incentives on the retirement decision of the other spouse. Suppose that we would like to regress the husband's probability of retiring on the wife's benefit accrual rate. A first problem arises since individuals with correlated unobserved tastes for leisure are likely to marry each other. It is likely, in turn, that individuals with strong unobserved preferences for leisure sort into pension schemes with certain characteristics (e.g. pension schemes offering generous early pension benefits). 1 Thus, we can expect a spurious correlation between the error term and the regressor capturing the pension incentives of the wife.
A second identification problem occurs since pension incentives are typically functions of a set of observed personal characteristics that are plausibly also having direct effects on the husband's retirement decision. Suppose, for simplicity, that the wife's benefit accrual rate is a function of her age in a non-linear way. It would then be challenging to control for the direct impact of the wife's age on the husband's retirement decision in a flexible way without also destroying the identification.
The purpose of this paper is to estimate the effect of a change in pension incentives by exploiting a plausibly exogenous variation in the wife's retirement incentives. This procedure potentially overcomes these two methodological problems.
In Sweden, the workforce of local government employees is dominated by women. The old collectively agreed pension plan for this sector, which was in place prior to the turn of the millennium, provided ample incentives for broad occupational categories dominated by females to retire already at the age of 63. In contrast, the new DC plan provided incentives for the same categories of employees to work until they reached the age when they were obliged to retire. The first cohort of 63 year old workers to be exposed to the new pension plan was those born in 1938 -they turned 63 in 2001. In contrast, the collectively agreed pension plans in the private sector were not subject to any major changes during this time period. This allows us to compare retirement decisions over time of otherwise similar men who were married to women in the local government sector and in the private sector, respectively.
The main empirical analysis will be conducted on couples where the wife was 63 years old and where both spouses participated in the labor force the preceding year, 2000-2005. Since the data contain the whole universe of Swedish taxpayers, the sample size is larger than what has often been the case in earlier studies on this topic. An individual is considered to be retired if he/she receives a positive amount of pension income. A register data source containing the total Swedish population is used in the analysis.
This study documents a sharp decrease in retirement rates among married female 63 year old local government employees in the years following the occupational pension reform. Indeed, seen over the whole post-reform period 2001-2005, the relative decrease amounts to around 20 percentage points as compared to the pre-reform year 2000. However, it is striking that there was no significant response in retirement rates among men married to women in the local government sector. In the most preferred model, which includes a full set of control variables, the point estimate of the average treatment effect on the treated is 0.007. The 99 percent confidence interval ranges from 0.039 to 0.052. This result is clearly at odds with some earlier findings in the literature. In fact, earlier papers examining the interdependence between spouses' retirement decisions (e.g. Zweimüller et al 1996 andCoile 2004) have found an asymmetry in the way spouses react to each other's incentives: these papers find that husbands are sensitive to changes in their wives' incentives but that the opposite does not hold true. In one way or another, these studies suffer from the problems pointed out above (which, however, does not necessarily imply that such a causal effect does not exist in the demographic groups and countries studied). To my knowledge, this is the first quasi-experimental paper on the subject that exploits a reform affecting the retirement incentives of wives but keeps the husbands' own incentive variables at a constant level. 2 Therefore, it is interesting that I obtain a different result as compared to earlier studies. The main lesson is that an increase in the wife's benefit accrual rate does not necessarily translate into a change in the husband's propensity to retire.
The structure of this paper is as follows. Section 2 discusses the previous literature and Section 3 contains a brief theoretical discussion. The Swedish occupational pension system, which provides the source of exogenous variation exploited in the paper, is described in Section 4. In Section 5 we discuss the empirical specification. Section 6 provides a description of the data source and a descriptive analysis. Section 7 reports the regression results, and Section 8 concludes the paper.

Previous literature
Most papers on retirement behavior abstract from the interaction between spouses. 3 A plausible reason for the historical neglect of the joint nature of retirement decisions is that female labor force participation has been low in most industrialized countries in the past. As discussed by Hurd (1990), the modest female participation rates have also narrowed the range of feasible studies on small survey data sets.
To my knowledge, the only quasi-experimental study that examines cross-effects between spouses is Baker (2002). He studies the introduction of the Spouse's Allowance (SPA) to the Canadian Income Security system in 1975. SPA made age related benefits available to individuals aged 60 to 64 who were married to someone aged above 65. However, the benefits were means-tested on the basis of family income, creating an interaction between the two spouses' retirement incentives. Baker compares the retirement behavior of males (65 to 75) and females (60 to 64) to the retirement behavior among those who were not eligible due to the age of their spouse. He finds that there was a reduction in labor force participation rates among eligible males (aged 65 to 75), and he also detects a relative decrease in labor force participation among eligible females. It should be noted that Baker's (2002) paper has a different focus: Here, I study a reform affecting the retirement incentives of wives while keeping the husbands' own retirement incentive variables at a constant level. Thus, I can isolate the effects of the wife's incentives on the husband's decision.
Also in a reduced form, albeit not quasi-experimental, framework, Coile (2004) regresses the probability of retiring for each spouse on forward looking incentive measures for both spouses separately. Coile, who uses U.S. survey and register data from the 1992-2000 waves of the Health and Retirement Study, finds that the woman's retirement incentives have significant cross effects on her husband's retirement decision. Her estimation sample includes 6,204 observations that contain information on 1,152 unique couples 1980-1999. More specifically, when the wife's social security wealth accrual increases, the husband's probability of retiring decreases. However, she did not find the converse to be true: she did not detect any effects of the husband's incentive variables on the wife's retirement decision.
Coile's study potentially suffers from both methodological problems that were discussed in the introduction. As the independent variables, she includes incentive measures that are functions of e.g. the age of both spouses, life time earnings, current earnings and the social security benefit formula. Since these factors are most likely to have an independent impact on the retirement decision, she controls for these variables in a flexible way. Therefore, it appears as if the identification of the model rests upon the non-linear functional form of the social security benefit formula. 4 In contrast, the present study relies on identifying assumptions that are arguably more transparent.
With a special emphasis on retirement age, Zweimüller et al (1996) also study the interdependence between the two spouses' retirement decisions on an Austrian cross sectional data set of 1,886 individuals from a single year -1983. The authors estimate a bivariate probit model for joint retirement, where the key left-hand side variables are eligibility dummies for early and regular retirement and the (imputed) earnings replacement ratios for both spouses. Even though the institutional context and the analyzed incentive measures are different, Zweimüller et al obtain results that are similar to those reported by Coile (2004): Husbands react to the wives' incentives, but not vice versa.
While the above mentioned works are agnostic on the exact mechanism generating the observed behavior, a related, structural, strand of literature explicitly estimates parameters of a family model. Gustman and Steinmeier (2000) adopt a noncooperative dynamic model of family decision making and estimate a structural model where the retirement decision of one spouse depends on the retirement decision of the other spouse. On a sample of 564 U.S. couples from the time period 1969-1989, they find that the husband's retirement does not affect the retirement decision of the wife, but that the wife's retirement has a notable effect on the retirement decision of the husband. Gustman and Steinmeier (2004) exploit more recent survey data and use additional information on stated preferences on whether the interviewed spouse values leisure time together with his/her spouse or not. They find that the husband's retirement status influences the wife's retirement decision only if she values spending time in retirement with her husband. For husbands, the effect of the wife's retirement on his own retirement is roughly doubled if the husband enjoys spending time in retirement with his wife, but there is some effect even if he does not. On Norwegian data, Harnaes et al (2006) have estimated non-cooperative models of different types.
Another approach, which was proposed by Blau (1998) and further used by Mastrogiacomo (2002), is to estimate discrete choice, discrete-time retirement models.
In these papers, family behavior is viewed as an outcome of a utility maximization process where the family maximizes a weighted sum of individual utility functions. In addition to taking financial incentives into account, the model also allows for past labor force behavior to affect current decisions while controlling for permanent unobserved differences across couples. The couple-specific permanent error component is treated as a random effect to be integrated out of the likelihood function. 5 On longitudinal data from the U.S., Blau (1998) finds strong associations between the labor force transition probabilities of one spouse and the labor force status of the other spouse. Interestingly, this pattern cannot be explained by financial incentives. It actually appears as if these associations are due to preferences for shared leisure.

The retirement decision
I first briefly discuss the individual's retirement decision in isolation. The total worker's compensation, ŵ , includes both remuneration in the form of cash wages, but also 'fringe benefits' such as pension wealth accruals (Lazear 1985  If the model is formulated in continuous time, the slope of the lifetime budget constraint is given by ŵ w b m    . 6 In a defined benefit (DB) system, where the individual becomes eligible for full pension withdrawals at a certain age, the life time budget constraint is typically piecewise linear for a given w with kink points at ages where the benefit accrual rate changes. As in the standard static labor supply model, the optimal choice of h is given by the tangency condition that the marginal rate of substitution between C and h equals ŵ . In general, changes in ŵ bring about a positive substitution effect and a negative wealth effect (if leisure is a normal good).
In the present paper, I analyze a reform that increased the benefit accrual rate for local government sector employees without affecting the pension wealth earned up to December 31, 1997. Since the benefit accruals from inframarginal working years are to a large extent unaffected, the income effect from the reform is likely to be small.
Another issue is that the reform was unexpected for local government employees, at least in the sense that it was unknown prior to 1998. Thus, the first cohort that was treated by the reform (the 1938 cohort) knew of the reform as 60 year old workers. As discussed by Burtless (1986), unanticipated changes to retirement incentives pose special challenges in the structural modelling of retirement behavior. Since time cannot be made to run in reverse, the individual cannot retire at an earlier date even though this would have been optimal if the unanticipated change had been known at the beginning of the life cycle. 7

The interaction between spouses
To get an idea of the basic mechanisms involved, I first consider a fairly unrealistic sequential model where the wife first maximizes life time utility without considering the optimal choices of the husband. Moreover, I assume that the husband treats the wife's lifetime earnings and pension benefits as unearned income in his own optimization 6 Formally, in continuous time, the budget constraint can be written as ( , ) . 9 While still using the notation introduced in the previous section, I now let subscript f refer to the wife and subscript m to the husband. In this setting, an increase in the benefit accrual rate will have a positive substitution effect and a negative income effect on the wife's retirement decision.
As the second mover, the husband optimizes while taking the optimal choices of his spouse as given. Suppose now that the husband solves the following problem , max ( , , ) where the two latter terms on the right-hand side of the budget constraint are exogenous.
Similarly to his wife, the husband knows with certainty that he will live for T years.
Under these assumptions, the life cycle labor supply choice of the wife influences the husband's retirement decision through two channels. First, since the wife's retirement years enter the husband's utility function, the wife's labor supply decision has an externality. It is most often reasonable to believe that the husband's marginal utility from retirement years increases in the wife's retirement years (i.e. the husband enjoys spending time with his wife). Second, the wife's choice of life time income has an income effect on the husband's retirement decision.
In this paper, I analyze a situation where the wife's benefit accrual increases.
Suppose that the substitution effect dominates so that the wife delays her retirement.
Then, we can expect two effects going in opposite directions. The shared leisure effect, which arises since the wife's leisure time enters the husband's utility function, will induce the husband to work longer. The income effect will lead to a reduction in working years for the husband, given that leisure is a normal good.
These two mechanisms are present also in more general models of family labor supply behavior. A general class of models, which only assumes the outcome of the household decision making to be pareto-efficient, but nothing about the particular bargaining rule, is cooperative models of family decision making (or 'the collective household model'). 10 In this framework, spouses simultaneously solve the following constrained optimization problem , max ( , , ) (1) and ( , , ) The second constraint guarantees that the outcome is pareto-efficient. In other words, there is no way of making I better off without making J worse off. In this framework, an increase in the benefit accrual rate for the wife would not only affect the husband through the shared leisure effect and the income effect. It would also change the relative bargaining power between spouses. When the second constraint is dropped, we arrive at non-cooperative bargaining models where once more an exogenous change in the benefit accrual rate will have consequences for the relative bargaining power in the household.
It should be emphasized that the reduced form empirical analysis of this paper will be insufficient to discriminate between different models of family decision making.
Instead, I will be able to recover the net effect of a change in the wife's incentives on the husband's retirement decision by pursuing a transparent identification strategy.

General description
In general, Swedish retirees obtain most of their pension income from the public pension system that is financed via payroll taxes. However, the occupational pension system is a crucial complement. 12 In contrast to the U.S., where the characteristics of employer-sponsored 401 (k)-plans differ between firms, the rules governing the Swedish occupational pension system are quite uniform within a small number of large sectors of the labor market. The pension plans are determined by collective agreements that have been signed by the unions and the employers' associations. An overwhelming majority of Swedish employees (around 90 percent) are covered by collective agreements. There are four main occupational pension schemes: one for blue-collar private sector workers, one for white-collar private sector workers, one for local government employees and one for state-level government employees. Here, the focus will be on the reforms in the scheme for local government workers that occurred around the turn of the millennium. During the period of study, i.e. 1999 to 2005, there were no major changes in the private sector collective agreements.

The occupational pension reform for local government workers
The old agreement, PA-KL, which came into place in 1985, was a defined benefit (DB) plan that interacted with the old Swedish public pension system in an interesting way.
As described in Appendix B, the old pension plan was a so-called gross pension system.
Thus, the occupational pension plan stipulated that the sum of the annual occupational pension benefit and the annual pension benefit from the public pension system should amount to a certain fraction of the individual's qualifying income.
For a 63 year old local government female full time employee with an average wage rate, the gross replacement rate was around 73 % in 2000. 13 If this employee was eligible for annual benefits from the public pension system of 60 % of her qualifying income the annual occupational pension benefit amounted to 13 % of her qualifying income; the occupational benefit was the residual amount. Hence, the early withdrawal penalties in the public pension system were irrelevant for those covered by the old collective agreement for local government workers. Rather, from the employee's perspective it was sufficient to know about the gross replacement rate.
Under the old DB plan, different occupational categories in the local public sector faced different retirement ages. The 'retirement age' could either be defined as a specific point in time (the month the employee turned 65) or an interval, 63-65. At the lower end of the age interval, the employee was entitled to full retirement benefits given that he/she fulfilled the other criteria for eligibility. At the upper end of the time interval, the employee was obliged to retire unless the employer offered a prolongation.
Early withdrawals before the retirement age could be made from the age of 60 under the PA-KL agreement. Early retirement was subject to a penalty, i.e. a reduction in the gross replacement rate (see Appendix B). Likewise, a small adjustment was made for every month the employee postponed retirement after his/her 65 th birthday. Under simplified assumptions, column (1) of Table 1 shows the benefit accrual rates at different ages under the old PA-KL plan for an individual who was subject to the 63-65 rule. It is interesting that the benefit accrual became negative already when the individual turned 62. Thus, even though the individual could increase her annual pension benefit by postponing retirement one year, the early withdrawal penalty did not fully offset the gain from receiving pension benefits the year she was 62. In other words, the system was not actuarially neutral at this age. 14 Most striking is the sharp fall in the benefit accrual rate at the age of 63. At this point, the individual did not earn any incremental pension rights. At this age the individual loses SEK 175,000 in pension wealth from continuing working an additional year. The benefit accrual of age s is the difference in pension wealth from claiming retirement benefits directly after turning s years old and directly after turning s+1 years old. The stock of pension wealth has been discounted back to age s-1. The discount rate is set to 3%. Benefit accruals are expressed in SEK in the price level of 2012. 1 EUR = 9 SEK. I assume that the individual lives until she is 86. I also assume that the individual has earned a yearly income of 5.6 price base amounts (SEK 246,400 in 2012) since the age of 25.
In 1998  increased price base amounts. 16 Accordingly, under the new system, the individual could always increase her pension wealth by postponing retirement until the age when she was obliged to retire. 17 Crucially, owing to the abolishment of the gross pension system the local government worker became subject to the incentives created by the public pension system. Local government workers born in 1938 and onwards were 15 A search in the virtual press archive 'Presstext', which covers the biggest daily newspapers in Sweden, reveals that the first article mentioning 'PFA98' is written in the fall of year 2000. 16 For wages above the cap of 7.5 increased price base amounts, a DB system was retained. This cap roughly coincided with the ceiling of the public pension system. Above the ceiling, the employer still made a small DC contribution (1.0 %). 17 The DC component of the new system was a fully funded system. The first fund choice was held late 2000/early 2001. Approximately 60 % of local government employees made an active fund choice.
exposed to the early withdrawal penalties in the public pension system. The second column of Table 1 shows the benefit accrual rates for local government workers born in 1942. In contrast to the accrual rates of column (1), one needs to the take the public pension system into account when computing the figures of column (2). We see that post-reform accrual rates are positive at all ages. In particular, there is an enormous change in retirement incentives at the age of 63, even though accrual rates also increases for 61 and 62 year olds. It should be noted that those born in 1938 were also the first cohort to be exposed to the new Swedish public pension system, which has been described by e.g. Sundén (2006). 18 This nation-wide reform affected all individuals born after 1937 included in the empirical analysis. The new public pension system was phased in gradually. Those who were born in 1938 received 4/5 of their benefits from the old system and 1/5 from the new one. Each cohort then increased its share of benefits from the new system by 1/20. Benefits from the new system were distributed for the first time in 2001.
As a general rule, both the Swedish occupational pension system and the public pension system were individual-based. Thus, the stream of pension benefits received upon retirement was independent of the earnings-history of the spouse. The exception was the survivor's pension, which under some conditions could be claimed both from the public pension system and the occupational pension system. In fact, the rules for the survivor's pension were similar in the old PA-KL plan and in the new PFA98 plan.
Therefore, the survivor's pension does not pose any threat to identification in this paper.
Finally, occupational pension recipients were subject to an earnings test. The main rule in the old PA-KL plan was that benefits decreased at a rate of 100% in the benefit recipient's earnings. In the post-reform PFA98 plan, the reduction rate was 73.5 %.
However, the benefit recipient could get special provisions to work under both plans.

The private sector occupational pension plans
There are two large occupational pension systems in the private sector: one for bluecollar workers and one for white-collar workers. None of these were reformed during the period of study, even though both agreements have changed after this period (primarily for younger cohorts not included in the present analysis). The pension scheme for blue-collar workers ('the SAF-LO plan') was a pure DC scheme, where the employer paid contributions amounted to 3.5% of the employee's wage. The scheme for white-collar workers ('the ITP scheme'), on the other hand, was mainly a DB system with a smaller DC component ('ITPK').
As will be discussed below in Section 6.2, I will define the retirement variable based on pension income receipt. To what extent is it possible to work and at the same time withdraw occupational pension benefits? As pointed out above, in the local government sector there was an earnings test preventing workers from doing this.
White-collar private workers aged below 65 are not allowed to withdraw pension benefits if they work more than 8 hours per week. There are no such restrictions for blue-collar private workers. However, once a blue-collar worker starts to receive DC benefits, he cannot accumulate any new DC wealth. Under both these schemes individuals are allowed to withdraw benefits from the age of 55.

Empirical model
The idea of this paper is to estimate the effect of the pension reform on the husbands' behavior. The empirical model will allow us to recover the average treatment effect on the treated (ATET). All husbands and wives included in the analysis belonged to the labor force the preceding year, i.e. they received no pension income and reported positive earnings. The 'treatment group' consists of husbands married to female local government sector workers who were 63 years of age and who were exposed to the new DC plan. The 'control group' consists of men married to 63 year old female private sector workers who were not exposed to the occupational pension reform in the local government sector. In the next section, I will further discuss the definitions of these concepts. The 1938 cohort of female local government workers -the first cohort to be  Therefore, I also report estimates of the treatment effect for each specific year.
The crucial identifying assumption is that the outcome variable evolved in the same way in the treated group (husbands married to wives in the local government sector) as in the non-treated group (husbands married to wives in the private sector) in the absence of a pension plan reform. Below, in Section 7.3, I will further discuss the identifying assumption.

Data source, sample selection and variables
This study exploits a register data source that covers the total Swedish population for the years 1998 to 2005. 19 Crucially, since there is an identifier for the household, I observe married couples. Furthermore, a number of demographic characteristics are included in the data. Importantly, there is information on sector affiliation for all years.
From the sector affiliation code, it is possible to observe whether the individual is employed in the local government sector, the central government sector or in the private sector.
As already mentioned, the population of interest in this study is men married to It should be noticed that even though it is possible to identify individuals as local government employees, it is not feasible to observe eligibility for the 63-65 rule. Thus, the treatment group also includes wives who faced a retirement age of 65 in the prereform system. However, all wives in the local government sector went from a DB to a DC plan regardless of retirement age. Note also that the individual's stock of social security wealth cannot be calculated as the data set both lacks information on earnings histories and information on specific retirement age rules.
The main advantage of register based data -as compared to smaller self-reported survey data sets -is that some types of measurement errors are, in principle, absent and that the entire population can be studied. On the other hand, as discussed by Hallberg (2008) for instance, a disadvantage in the context of studying retirement decisions is that the tax registers provide data on a yearly, rather than monthly, basis. Hence, we typically observe pension income and earnings, but it is not possible to tell whether the individual has been retired on a part time basis or on a full time basis for a shorter period of time. In our data, the age variable is defined based on the age of the individual as of December 31. Accordingly, some of the '63 year olds' have been aged 62 and have faced the marginal pension incentives applying to 62 year olds during 11 months of the year.
In this paper, I define the indicator for retirement in the following way: Individuals who receive a positive amount of pension income will be classified as retired. Naturally, this is quite a generous definition, which also includes those who only withdrew a smaller amount of pension income. However, as described in Section 4.3, the different collective agreements contained rules that prevented workers and/or made it unattractive for workers to work and receive pension benefits at the same time.
Moreover, individuals who received a disability pension can also be subsumed under this retirement concept prior to 2003. 22 As a robustness check an earnings based retirement definition will also be used ( Table 7).
The dummy variable for being a local government employee is defined based on information from the preceding year. I also divide the studied population into six educational categories and define dummies for the educational level based on these.
Finally, I also construct 21 dummy variables for the county of residence. Descriptive statistics for all variables used in the empirical analysis are reported in Appendix A. Figure 1 depicts the distribution of husbands' ages. Figure 1A shows this distribution in the estimation sample. Remember that the estimation sample has been selected based on the criterion that both spouses were part of the labor force in the preceding year.

Graphical analysis
Since there is a dramatic increase in pension benefit withdrawals among 65 year olds, there is a huge hole in the distribution starting at age 66. Therefore, it can be interesting to look at a sample where the restriction that the husband must be in the labor force in year t-1 is dropped, but all other selection criteria are the same. In this sample (shown in Figure 1B), the mean age difference between husbands and wives is 2.9 years. This is in line with the well-known empirical regularity that husbands typically are older than their wives. In the estimation sample, on the other hand, the mean age difference is -0.89. This should be kept in mind when interpreting the estimated model parameters.    respectively. From ocular inspection, we note that the two lines track each other surprisingly well. In 2002 there is a tiny relative decrease for men married to women employed in the private sector, but otherwise it is striking how close the lines are. One may notice that the level of the conditional retirement probability on average is higher for husbands than for wives. This can be explained by the fact that around 17 percent of the husbands are 65 years of age -65 year olds have a retirement probability that is close to 1 (see Table A  For the difference-in-difference approach to be valid, the group-specific fixed effect should be the same across years  LGW  of equation (2) should be time invariant.
Thus, we want the composition of the treatment and control groups to be unchanged by the reform. If there were a large response among 62 year old women to the occupational reform, a duration model would be called for. 24 Of particular interest is the fact that those who were aged 63 in 2001 were exposed to the new DC plan already in the year 2000 as 62 year olds. Indeed, Table 1 showed that benefit accrual rates increased also for 62 year olds, even though the magnitude of the increase was substantially larger for 63 year old local government workers.

The correlation between the two spouses' retirement decisions
Before turning to the regression analysis it can be fruitful to examine the prevalence of joint retirement in Sweden. More specifically, we look at the correlation between the two spouses' retirement probability, conditional on that the two spouses were in the labor force year t-1. Table 2 illustrates the correlation coefficient between the wife's retirement and the husband's retirement in the data 1999-2005 for the ages 60-65. In general, the retirement decision of spouses of age s are most strongly correlated with the other spouse's retirement decision if the other spouse is also aged s . 25 The grey shaded column of Table 2 is of special interest as it reflects a large subset of the estimation sample. In couples where both spouses are aged 63, the correlation coefficient is 0.19. 25 The only exception is that 62 year old women's retirement decisions are more correlated with 64 year old men's retirement decisions than 62 year old husbands' retirement decisions. The number of observations is in parenthesis. The sample is selected in the same way as the estimation sample, i.e. both spouses should be in the labor force year t-1, none of the spouses should be employed in the central government sector and the husband should not be employed in the local government sector. The grey shaded column reflects a subset of the estimation sample.

The wives' own response
The main purpose of this study is to examine the husbands' response to the pension reform in the local government sector. However, as a first step we examine the wives' own response to the shift in the occupational pension plan. In the specification without covariates, reported in column 1 of Table 3, the estimate of the ATET is 0.202. The heteroskedasticity robust standard error is rather small  the 99 percent confidence interval ranges from 0.26 to 0.15. According to this estimate, the probability of withdrawing retirement benefits among 63 year old wives, who were in the labor force as 62 year olds, decreased by 20 percentage points in the local government sector relative to the private sector during the post-reform period.
The same qualitative pattern was noticed by Glans (2009), even though he did not focus on 63 year olds.
If the treatment dummy is orthogonal to the error term, we expect the estimate of the ATET to be unaffected by the inclusion of control variables. Intuitively, if the addition of control variables has a large impact on the estimate, there might be some concern that unobserved characteristics are also correlated with the regressor of interest.
Column (2)  In fact, recent studies that exploit policy discontinuities for identification (Liebman et al 2009 andManoli andWeber 2011) indicate that females are more responsive than males at the retirement margin.
The response in retirement entries should, of course, be viewed in relation to the magnitude of the incentive change. I have made back-of-the-envelope calculations of the elasticity of the retirement decision with respect to the one minus the implicit tax rate, where I use information from Table 3, column (4), and LGW WIFE

RETIRED
is the retirement probability of local government wives in year 2000 and  is the implicit tax caused by the pension system. The implicit tax rate at age 63 is defined as minus the benefit accrual divided by annual earnings, i.e.

 
63 63 LGW WIFE  is the implicit tax rate for a local government worker under the assumptions in Table 1. _

PS WIFE
 is the implicit tax rate for a blue-collar private sector worker, where all other assumptions are the same as in Table 1. The change in the implicit tax between 2000 and 2005 in the latter group is small. (1) (2) (3)  (2) in the main text. Robust standard errors are in parenthesis. * denotes significance at 10%, ** at 5% and *** at 1%. The number of observations is 15,518. All regressions include an intercept, a dummy for the local government sector and a full set of year dummies. The control variables are 17 dummies for the husband's age, 5 dummies for the wife's level of education, 5 dummies for the husband's level of education, 20 region dummies and interactions between year dummies and educational dummies.

The husbands' response
We now turn to the husbands' response, which is the main focus of the paper. The results for the husband's retirement status are displayed in Table 4.
Again, columns (1)-(2) report a treatment effect that is assumed to be with the results in e.g. Zweimüller et al (1996) and Coile (2004) who both find that husbands are sensitive to changes in their wives' incentives.

Placebo tests
Once more, the crucial identifying assumption is that the outcome variable would have evolved in the same way in the treated group (husbands married to wives in the local government sector) as in the non-treated group (husbands married to wives in the private sector) in the absence of a pension plan reform. To obtain a view on the validity of this identifying assumption, I will exploit the fact that our data set allows us to define the dependent variable also for 1999, an earlier pre-reform year. 27 Therefore, we can perform 'placebo-type' regressions where we assume that the pension plan reform instead affected the 1937 cohort (those who turned 63 in 2000), but not the 1936 cohort (those who turned 63 in 1999). In reality, both cohorts were unaffected by the reform.
The following regression will be performed on data for 1999 and 2000: The placebo tests for wives, with and without controls, are reported in columns (1)-(2) of Table 5. If the pre-reform trends were the same for the two groups, the coefficient for the interaction term in equation (3) should not be significantly distinct from 0. From Table 5 we can infer that it is indeed the case that the coefficients for the 27 The data set contains data for the years 1998-2005. But since we need to condition on labor force participation in the preceding year, we cannot include the retirement decision in 1998 in the analysis.
interaction term are close to zero (and very insignificant). Thus, consistent with the graphical evidence provided in Figure 2.A. the placebo estimates are close to zero both for wives and husbands.

Further robustness checks
One potential concern of the analysis is related to the dynamics of the retirement response. There are, indeed, two problems at hand. First, in Section 4.2 we noted that retirement incentives for local government workers born in 1938 changed already when they were 62 years old. Thus, even though the graphical analysis did not indicate any substantial response of the 1938 cohort at the age of 62, it is desirable to examine this further in a regression analysis.
Second, we cannot a priori rule out that husbands reacted to the change in the wives' incentives by retiring before the wife retires. In order to examine this hypothesis I construct a new regression sample that includes all couples where both partners were in the labor force in period t-2. I then define a binary outcome variable that takes the value of 1 if the individual either retires in period t or in t-1 (assuming that retirement is an absorbing state). With these modifications I run the same regressions defined by equation (2) above. I now allow for a response, both of husbands and wives, the year before the wife turns 63. The number of observations increases from 15,518 to 21,793.
It is now impossible to perform placebo tests as 1998 is the first year of data and the sample is selected based on labor force status in year t-2.  (3) is estimated to be 0.013 instead of 0.007 in the baseline model (column 2, Table 4).
Note that this exercise also serves as a robustness check of the way in which I select the regression sample. Until now I have defined the sample based on labor force status in year t-1. When running regressions with the standard binary outcome variable (which is 1 if the individual retires in period t) on the larger sample defined based on information in t-2 I obtain results that are similar (not reported). Table 6. The probability to retire in year t or in year t-1 Wives Finally, one might wonder what happens if one instead uses an earnings based outcome variable. In the analysis above we defined an individual as being retired if he/she received a positive amount of pension income in year t. Since earnings will be positive the year an individual retires an earnings based definition necessarily needs to be based on earnings information as of year t+1. One candidate is to impose an arbitrary earnings limit for t+1. In what follows, I let the outcome variable take on the value of 1 in period t if the individual had earnings below 1.75 price base amount in t+1. 28 The average male retirement rate in the sample now slightly falls from 0.29 to 0.25.
To achieve comparability with the baseline results I will define the regression sample in the same way as before: those who had positive earnings and received zero pension income in year t-1 are considered as being in the labor force in year t-1 and are, hence, included in sample. However, since the dependent variable now builds on information from period t+1 I will not be able to use data for 2005, the most recent year in the data set. As can be seen from Table 7 the results are roughly similar to those in the main analysis.
If one instead sets the earnings cut-off limit to 0, which is considerably less arbitrary, there is a dramatic drop in retirement rates in the sample. The average male retirement then falls from 0.29 to 0.12. Accordingly, this retirement definition is very restrictive; it assigns some of those who we would consider as being genuine retirees to the working population. The regression results, which can be provided upon request, are now qualitatively similar to those in the main analysis. The female response is, however, approximately half as large as in the main analysis.  (2) in the main text. In columns 3 and 6 the regression equation follows equation (3) in the main text. Robust standard errors are in parenthesis. * denotes significance at 10%, ** at 5% and *** at 1%. The number of observations is 12,068 (3,923) in columns 1,2,4 and 5 (columns 3 and 6). All regressions include an intercept, a dummy for the local government sector and a full set of year dummies. The control variables are 17 dummies for the husband's age, 5 dummies for the wife's level of education, 5 dummies for the husband's level of education, 20 region dummies and interactions between year dummies and educational dummies.

Concluding discussion
In Sweden, the workforce of local government employees is dominated by women. The old collectively agreed pension plan for this sector, which was in place prior to the turn of the millennium, provided ample incentives for broad occupational categories dominated by females to retire already at the age of 63. In contrast, the new DC plan provides incentives for the same categories of employees to work until they reach the age when they are obliged to retire. In this paper, I have exploited this reform to study how a change in the wife's retirement incentive affects the retirement decision of the husband.
I make two major findings. First, there was a clear reduction in retirement rates among 63 year old female local government workers after the reform. Seen over the whole post-reform period 2001-2005, the decrease was 20 percentage points relative to private sector workers. Second, it was not the case that husbands married to local sector employees changed their retirement behavior in comparison to those who were married to wives who were private sector employees. The point estimate in the main specification is 0.007; the 99 percent confidence interval ranges from -0.039 to 0.052.
Both key findings are robust to alternative specifications.
The main lesson from this paper is that an increase in the wife's benefit accrual rate does not necessarily translate into a change in the husband's propensity to retire.
The results are broadly consistent with the analysis of Blau (1998)

Appendix B
The total benefit level in the gross pension system As described in Section 4.2, the pension plan for local government workers that was in place prior to 2000, PA-KL, stipulated that the sum of the public pension benefit (PB) and the occupational pension benefit (OB) should be equal to a certain fraction,  , of the individual's qualifying income (QI). Thus, the OB was determined as a residual amount: where TB denotes the total annual pension benefit. The local government worker was eligible for full pension benefits given that he/she had reached the retirement age and had worked at least 30 years since the age of 28 in the sector. The QI was defined as an average of the five best earnings years out of the of the seven most recent earnings years.  where APP is the average pension points earned during the 15 best earnings years. At maximum, the individual could earn 6.5 pension points each year. 1 pension point amounted to 1 price base amount, BA. PP N is the number of years that the individual has earned pension points.  is a parameter that determines the level of basic pension.  was 96 % for singles and 78.5 % for married individuals. 29

Early and late withdrawals in the gross pension system
Early withdrawals before the retirement age could be made from the age of 60 under the PA-KL agreement. Early retirement was subject to a penalty. Table B2 shows the monthly adjustment of the gross pension benefit (TB) in percent. Suppose that the employee, under the old agreement, was subject to the 63-65 rule, i.e. she was eligible for full pension benefits by the month she turned 63. If she withdrew pension benefits already from the month she turned 60, the gross pension benefit was reduced by 12 0.5% 12 0.45% 12 0.35% 15.6%       .
Note, however, that the individual is unaffected by the early withdrawal penalty in the public pension system.