Econometric Model and Data

The objective of the study was to estimate a simple probit model for the decision to enter retirement as it relates to individuals’ health, wealth, and the accrual of wealth associated with employer-provided pensions. The model is most comparable to those estimated by Coile and Gruber (Reference Coile and Gruber2000) and Baker et al. (Reference Baker, Gruber and Milligan2003). Specifically, I wanted to estimate the reduced form model

(1)

where individual i enters retirement at time t (R_it = 1) if the latent variable R_it* > 0, indicating that the expected present value of entering retirement (in utility terms) is greater than the expected present value of continuing to work. R_it = 0 if the individual continues to work. This retirement decision depends on the individual’s health status (H_it), pension wealth (W_it), and the accrual in pension wealth (ACC_it) that could be achieved if retirement were delayed, as well as other characteristics (X_it) we might consider important in the retirement decision.

Data, Measurement, and Identification Issues

To estimate the model, I used data from the SLID, a longitudinal survey following individuals for six years. From each year for the period 1996–2001, I took a sample of individuals who spent at least part of that year in the labour force, were aged 50 to 68, and flagged as paid workers during the year.Footnote ³ I excluded individuals whose labour force status or health information was missing. Further, I needed to observe an individual’s labour force status for two consecutive years in order to observe their transition into retirement. The panel aspect of this survey was heavily relied on to define and identify the effects of the key covariates.

Limitations of the survey data often guide the definition and measurement of variables. In this study, a person is defined as entering retirement during the observation year if they were in the labour force for at least part of the observation year and then not in the labour force at all the following year. The resulting probabilities of entering retirement at each age exhibit the expected spikes at age 55 (when many employer-provided pension plans allow early retirement), at age 60 (when individuals are first eligible for some public pension benefits), and at age 65 (when other public pension benefits are available and many individuals are subject to mandatory retirement). Few individuals who retired at the ages indicated in the samples are likely to exit retirement. We can see that only 5 per cent of individuals aged 60 to 64 exit retirement within two years (see Table 1), and 9 per cent exit retirement within four years of retirement. The rate of exit is shown to be much higher among younger individuals in my sample. Among those aged 50 to 54, 45 per cent will spend at least some time in the labour force (employed or unemployed) in the following four years.Footnote ⁴

Table 1: Rate of exit from retirement

Notes:

An individual enters retirement if they leave the labour force and do not participate in it at all the following year. Exit then refers to any re-entry to the labour force. This sample from the Canadian Survey of Labour and Income Dynamics (SLID) represents individuals who entered retirement in 1994 and 1997.

The measurement of health relies on individuals’ self-reported health status, categorized as poor, fair, good, very good, or excellent, as well as individual reports of disability. When estimating the model, I explored a variety of health measures in order to address several problems associated with measuring and identifying the effects of health on retirement. As a baseline, I began by using an indicator for poor health. The first identification problem is that measurement error is likely when health is self-reported, placing a downward (attenuation) bias on any estimated effect of poor health.Footnote ⁵ Measurement error also arises because this is not an objective measure of health (see Baker, Stabile, & Deri, Reference Baker, Stabile and Deri2004). I was unable to correct for this type of error given the limited health information in the SLID.

The second identification problem can be referred to as justification bias – a situation where people rationalize their retirement by reporting poor health. This can be expected to place an upward bias on the estimated effect of poor health. Whether this bias is significant is not clear. Au et al. (Reference Au, Crossley and Schellhorn2005) presented evidence suggesting that self-assessed health measures suffer from attenuation bias rather than justification bias. Other studies, such as that by Dwyer and Mitchell (Reference Dwyer and Mitchell1999), found no evidence of justification bias. Finally, there exists some evidence that health improves after retirement, particularly among blue collar workers (Marshall & Clarke, Reference Marshall and Clarke1998), giving rise to a third source of bias working in the opposite direction.

I have tackled these last two endogeneity problems by taking advantage of the longitudinal aspect of the SLID. A key problem with this health measure is that respondents are interviewed in January following the survey year about their current (and potentially post-retirement) health. To address this, I have included several specifications that rely on past reports of health, effectively representing the individual’s health at the beginning of the observation year in which the retirement decision was made.

Making use of past health reports, however, misses events that happen during the year to worsen a person’s health and push them into retirement. With this in mind, I also have provided specifications in this article that use health measures reflecting a change in health status. I have created a measure reflecting whether a person reports not having a disability at the beginning of the year, but reports having a disability at the end of the year (new disability) and measures for small shocks and large shocks to an individual’s health.Footnote ⁶

The measurement of the financial incentives variables, wealth, and the accrual of wealth associated with pensions, has been done in several steps. I used information available in the SLID to obtain estimates of the components of the accrual equation

(2)

and the wealth equation

(3)

where y represents non-labour income, w represents wages, B(r) represents pension benefits that depend on the timing of retirement, and r * is the age of retirement at which pension wealth is maximized. The wealth measure (W) represents the expected present discounted value of lifetime income if a person retired. The measurement of accrual then represents the amount to be gained by delaying retirement to an optimal future age. This is similar in spirit to that measured by Stock and Wise (Reference Stock and Wise1990) in their option value framework, except that I have effectively placed a linear utility function over income. Here, I have allowed individuals to live up to age 102 (T) and retire up to age 69 (r). A discount rate of 3 per cent is used (β = 0.97) and the survival probabilities (π) have been based on Statistics Canada’s sex-specific life tables (Statistics Canada, 2002).Footnote ⁷

There are two components to the future pension benefits included in Equations (2) and (3), public pensions and employer-provided pensions, neither of which is directly observable. For public pensions, I have determined the initial benefit an individual would be eligible for from three sources: (a) Canada Pension Plan/Quebec Pension Plan (CPP/QPP) (an earnings-related public pension available to individuals over aged 60), (b) Old Age Security (OAS) (a universal transfer payment available after over aged 65), and (c) Guaranteed Income Supplement (GIS) and Spouses Allowance (SPA) (income-tested benefits generally available after age 65) given a specific retirement age, observable individual characteristics and earnings, and the policy rules in place in the observation year. For CPP/QPP benefit eligibility, a wage history has been imputed for each individual based on sex-specific annual wage regression estimates from the Survey of Consumer Finances and the SLID, with covariates including experience, education, province, and marital status. The reported years of full-time full-year experience in the SLID was used to define the length of the wage history.Footnote ⁸ The initial public pension benefit was then indexed to expected inflation.Footnote ⁹

For employer-provided pensions, I developed an average potential pension formula to impute the future pensions of individuals who reported having access to employer-provided pension benefits. Here, I estimated the pension amount a person would initially receive upon retirement based on the individual’s age, job tenure, union status, public- or private-sector status, occupation, wage, and size of employer. The estimates were obtained using a standard Heckman selection model, accounting for the fact that I could not observe the potential pension amounts for individuals who chose not to retire. The selection equation is a retirement probit, with explanatory variables including indicators for health status, marital status, whether a spouse was in the labour force, the number of children in the census family, and non-linear functions of tenure and wages.Footnote ¹⁰ As with the public pension amount, the initial imputed pension amount was then assumed to increase with expected rates of inflation.Footnote ¹¹ The projections of future incomes that I describe here approximate the actual distributions of each source of income fairly well.

The resulting distribution of pension wealth (by age) is presented in Table 2.Footnote ¹² In Table 2, the estimates of wealth based only on the public pension amounts are also presented, demonstrating the importance of employer-provided pensions. Among the individuals with the least pension wealth (at the 10th percentile), pension wealth was heavily dominated by public pensions. For the typical individual, represented by the median, pension wealth was generally split between public pension wealth and employer-provided pension wealth. As we might expect, those with the highest levels of pension wealth (the 90th percentile) received much larger employer-provided pensions so that employer-provided pensions made up the majority of their pension wealth.

Table 2: Distribution of pension wealth, by age

Notes:

Amounts represent the 10th, 50th, and 90th percentiles of wealth within each one-year age group. See text for a description of the wealth measures and the sample used.

Problems arose in estimating the effects of pension incentives on the decision to retire because the variation in pensions was partly based on individual variation in work histories. The variation we see in work histories may capture individual heterogeneity in preferences for leisure and work. For example, we would expect that individuals with a higher preference for work would also have longer and more complete work histories, and potentially higher wealth and accrual measures. If this heterogeneity were not controlled for, the estimated effects of wealth and accruals might be biased downward.

I took two approaches to controlling for this type of heterogeneity. First, I provided specifications of the retirement probit that included control variables for lifetime earnings, experience, and current wages, as these variables should proxy for the heterogeneity in leisure preferences.Footnote ¹³ Second, I used a fixed-effects probit estimator to deal directly with the individual unobserved heterogeneity. The individual-specific fixed-effects model presented here allowed each individual in the sample to have a different intercept in Equation (1) representing their greater or lesser probability of entering retirement relative to other individuals in the sample. This individual-specific intercept will capture the heterogeneity in leisure preferences as well as heterogeneity in any individual characteristics that do not change over time.

In all the specifications presented next, I have included a set of indicators for age, province, sex, marital status, whether a spouse continued to work or entered retirement, whether a spouse had poor health, and the number of children in the census family under the age of 18 as a basic set of covariates.Footnote ¹⁴

Discussion of Results

The results of the various retirement probits are presented in Tables 3 and 4. In each table, the marginal effects of each variable (representing the effect of a one-unit increase in that variable on the probability of entering retirement) are presented rather than the probit coefficients.

Table 3: Retirement probit results I (marginal effects)

Notes:

***, **, and * indicate the marginal effects are significantly different from zero at the 1%, 5%, and 10% levels of significance, respectively. Sample is described in the text. The retirement probits used 25,810 observations. For the fixed-effects estimator, only 3,195 observations (representing 1,131 individuals) are available. See text for definitions of variables. Specifications include the basic set of covariates. Marginal effects were evaluated for a 60-year-old single male in Ontario. Standard errors are in parentheses.

Table 4: Retirement probit results II (marginal effects)

Notes:

***, **, and * indicate the marginal effects are significantly different from zero at the 1%, 5%, and 10% levels of significance, respectively. Sample is described in the text. The probit in column 1 uses 25,810 observations, and the retirement probits in columns 2–6 use 17,618 observations. See text for definitions of variables. Specifications include the basic set of covariates and controls for experience and wages. Marginal effects were evaluated for a 60-year-old single male in Ontario. Standard errors are in parentheses.

As expected, pension wealth has a positive and significant effect on an individual’s probability of entering retirement. The results in the first column of Table 3 indicate that a $10,000 increase in pension wealth increases the probability of entering retirement by 1.8 percentage points. Given that the sample retirement rate is 7 per cent, this implies a substantial increase in the retirement rate by 25 per cent. When the individual fixed-effects estimator is used to control any bias associated with individual preferences for leisure, the estimated marginal effect of pension wealth is actually the same. Although the marginal effect appears much larger, the data restrictions required here to use the fixed-effects estimator result in a sample retirement rate of 33 per cent so that a $10,000 increase in pension wealth implies an increase in the retirement rate of 25 per cent. This would suggest that the use of lifetime earnings and experience measures are adequate to control for this type of bias.

The accrual of wealth also has a significant and substantial impact on the probability of retirement, with estimates indicating that the retirement rate would decrease by 25 per cent if individuals were given an additional $10,000 to delay retirement for at least one year. This estimate is fairly consistent across specifications. It is interesting to note that the results presented here have been largely driven by the variation in employer-provided pensions rather than public pensions. As presented in Table 5, specifications using only public pensions in the measures of wealth and accrual result in insignificant estimates of the effect of wealth while the specifications using only employer-provided pensions result in estimates similar to those presented in Table 3.Footnote ¹⁵

Table 5: Additional retirement probit results (marginal effects)

Notes:

***, **, and * indicate the marginal effects are significantly different from zero at the 1%, 5%, and 10% levels of significance, respectively. Marginal effects were evaluated for a 60-year-old single male in Ontario. The results in column (3) represent the full specification of the results presented in column (1) of Table 3.

The results in Tables 3 and 4 also consistently demonstrate that health status has a significant effect on the probability of retirement. The effect is substantial, as estimates in the first column of Table 3 imply that having poor health raises the probability of entering retirement by 24 percentage points relative to an individual who is not in poor health. The results presented in Table 4 make use of the various measures of health to check the robustness of this result in light of the various identification issues involved in estimating the effect of health.Footnote ¹⁶ The specification presented in the first column makes use of all categories of current health. The results suggest that a person with poor health will be 27.3 percentage points more likely to enter retirement than a person with excellent health. Not surprisingly, having fair (relative to excellent) health also has a substantial effect on the probability of retirement, raising the probability by 9.1 percentage points. A person in good health is only 2.3 percentage points more likely than a person in excellent health to enter retirement.

The next two columns of Table 4 address the concern that justification bias creates an upward bias in the estimated effect of health. The resulting estimated effect of health is only slightly smaller when using the individual’s report of health at the beginning of the year (past health), lending support to the conclusions of Au et al. (Reference Au, Crossley and Schellhorn2005) that justification bias is fairly small. The smaller estimates, however, may reflect the importance of changes in health that may occur throughout the year.

The estimates in the remaining columns represent the effect of changes in health on the probability of retirement. The onset of a new disability raises the probability of entering retirement by more than nine percentage points. A large health shock has a comparable effect, raising the probability of entering retirement by eight percentage points. A small health shock also has a significant effect, raising the probability of entering retirement by two percentage points.

The models presented here do not enable us to address any measurement error in self-assessed health. The results, however, further support the conclusions of Au et al. (Reference Au, Crossley and Schellhorn2005) as they suggest that attenuation bias is a large problem. As Au et al. pointed out in their work, measurement error problems can be exacerbated by allowing for fixed effects, as I have in Table 3. The fixed-effects estimate of the effect of poor health is obviously much smaller than the probit estimates. The effect remains positive and significant, however, attesting to the robustness of this result.

The results presented in Tables 3, 4, and 5 suggest that there are not important interactions between health and pension incentives that would lead to omitted variables bias. In the first column of Table 5, I have provided estimates of the effect of pension wealth and accrual resulting from a retirement probit specification with only these two variables as covariates. Adding the poor-health variable, as in the second column of Table 5, does not change the estimated effect of pension wealth or accrual. Also, the estimated effects of pension wealth and accrual are not particularly sensitive to the choice of health measure used, as in Table 4. Furthermore, several specifications of the retirement probit that included interaction terms for poor health and pension wealth were estimated, and these coefficients were not at all significant.

The effects of other variables on the retirement decision (presented in Table 5) are worth noting. As expected, there is a clear increase in the probability of entering retirement as individuals age. At age 55, individuals are nearly five percentage points less likely to enter retirement than they are at age 60. At age 65, the average individual is 20 percentage points more likely than they are at age 60 to enter retirement. As expected, having a spouse that is employed will reduce the probability of entering retirement, although being married will itself increase the probability of entering retirement. Interestingly, being male, having more children under the age of 18, and having a spouse with poor health do not appear to be important components of the retirement decision.

Although not presented here, it is interesting to note that specifications of the probit model that included indicators for access to health, life, and disability insurance through an employer, as well as interaction terms for poor health and access to insurance were also estimated to check whether these factors might act as a constraint on retirement as they appear to in the United States. Not surprisingly, the effects of insurance on the probability of retirement were insignificant in the Canadian context. Furthermore, the effects of poor health did not differ between individuals with and without health or disability insurance.