Income Security Programs and Retirement in Canada
                           Michael Baker, University of Toronto and NBER
                                 Jonathan Gruber, MIT and NBER
                                Kevin Milligan, University of Toronto

                                              May 2000




We are grateful to Human Resources Development Canada, Statistics Canada and SSHRC
(Baker) for research support, Sue Biscope, Richard Dupuy, Leonard Landry and Garnett Picot
for assistance accessing the data, Terence Yuen for excellent research assistance and to Paul Finn
and participants in seminars at HRDC and the NBER for helpful comments. All views expressed
in this paper are the authors’ and do not necessarily reflect the views of HRDC or Statistics
Canada.
                                          Part 1: Introduction

        Government transfers to older persons in Canada are one of the largest and fastest

growing components of the government budget. Total expenditures on the three primary transfer

programs for older Canadians amounted to $22.7 billion in 1998/99 (current dollars), which

represented 20 percent of program spending in the federal budget of that fiscal year. In 1974/75,

total expenditures were only $3.4 billion (current dollars), amounting to just 10 percent of

program spending. The contributory public pension faces fiscal similar pressures. In 1975

contributions per capita exceeded benefits per capita by roughly $200 (1998 dollars). By 1998, it

was benefits per capita that exceeded contributions per capita by roughly $200 (Baker and

Benjamin 1999c). Moreover, without changes to the system, these trends will likely continue in

the foreseeable future. The ratio of persons aged 65 and over to persons aged 20-64 is projected

to grow from its current level of 19 percent to over 40 percent by the year 2075. As a result, the

payroll tax necessary to finance the public pension for older persons, the Canada/Quebec Pension

plan, will grow from 7.0 percent in of wages in 2000 to 9.9 percent by the year 2003. Similar

cost increases are in store for the transfer programs for older Canadians, which are financed from

general revenues: the Old Age Security demogrant, and the income tested Guaranteed Income

Supplement and the Spouse Allowance programs.

        In this context, a notable trend in labour force behavior in Canada is the steady decline in

work among many groups of older workers, as documented in Figure 1. It is particularly striking

for older males. Note that the participation rate for 45-to 64 year olds masks a large decline

among the older individuals in this group. For example, in 1960, 87 percent of men aged 55-64

were participating in the labour force; by 1999, this proportion had fallen to 61 percent. For




1
females, any trend towards earlier retirement appears to be swamped by the century long secular

increase in the participation of women.

        These time series span a period in which there were a variety of changes in the structure

of Income Support programs for older persons that has made retirement more attractive and work

less attractive. In 1960, for example, workers under the age of 70 were not entitled to any

income support upon retirement. By the mid-1990s, however, married low-income workers

could receive public retirement benefits that actually exceeded their pre-retirement incomes

(Gruber, 1999). Of course, it is difficult to causally relate these time trends; there were many

other developments over this time period, such as growing private pension coverage and rising

incomes, which may have also contributed to the decline in work among older Canadians.

        In the U.S., where there are similar trends, there is an extensive literature that examines

the relationship across individuals between Social Security entitlements and retirement

decisions.1 This research mostly suggests that Social Security incentives play an important role

in retirement decisions, but a modest one relative to the time trends. In contrast, there is little

complementary work in the Canadian context.2 Recent studies have examined the impacts of

changes in some of these programs in isolation. Baker and Benjamin (1999a) analyze the effects

of the removal of the earnings tests from the CPP and QPP in the 1970s. They also examine the

impact of the introduction of an early retirement option to the QPP in 1984 and to the CPP in

1987 (Baker and Benjamin 1999b, 1999d). Finally, Baker (1999) investigates the effects of the

introduction of the Spouse’s Allowance in 1975 on the labour market behaviour of eligible

couples. To our knowledge, however, there is no previous empirical study that provides a



1
 For a review of the literature and some empirical evidence see Coile and Gruber (1999).
2
 Papers by Burbidge (1987) and Pesando and Rea (1977) provide a careful outline of the
potential effects of the various IS programs, but no estimate of their empirical magnitude.


2
comprehensive analysis of the combined impacts of the web of Canadian Income Security

programs.

        The purpose of our study is to remedy this deficiency. This is done by drawing on a

comprehensive data set (based on the Statistics Canada Longitudinal Worker File) that has

information for a very large sample of older Canadians on their earnings histories, work

decisions, marital status and spousal characteristics, and the characteristics of their jobs. These

data are employed to construct a simulation model that incorporates the incentives for retirement

under the three pillars of the Canadian public Income Security (IS) system: the Canada Pension

Plan/Quebec Pension Plan; the Old Age Security (OAS) system comprising the basic OAS

benefit; the Guaranteed Income Supplement (GIS) and the Spouse Allowance (SPA).

        For each person in our data set, the financial incentives for retirement are computed along

two dimensions. First, the present discounted value of all future entitlements to benefits from the

different programs of the public IS system is calculated. This measure of Income Security

Wealth (ISW) is recalculated for each year the person appears in our data set to reflect the

changes to their benefit entitlements. The second dimension is a measure of how ISW evolves

through time. By comparing the ISW of the person if he/she retired in the present year to the

ISW of the person if he/she worked an extra year, an ISW accrual measure can be calculated.

Several different measures of accrual are contemplated, which alternatively assume that

individuals look only one year forward in making their retirement decision, and that individuals

look forward to some “optimal” retirement date in making their decision. An empirical model of

the retirement decision as a function of these incentive variables, as well as a rich set of control

variables designed to capture other impacts on retirement, is then estimated.




3
There are two findings of importance. First, for the typical worker, the public IS system

provides increasingly strong disincentives to work after age 60. Workers actually see the present

discounted value of their IS entitlement fall from additional work after age 61, and by age 69 the

reduction in IS entitlement amounts to 43 percent of what they would earn in that year. Second,

there is a significant impact of these disincentives on work decisions. Using both one year

forward measures and measures which account for the entire future path of incentives, we

estimate that workers with larger returns to additional work are less likely to leave the labor

force.

                                          Part II: Background

         The decision to retire in Canada is made in the context of a complicated web of program

incentives.

The Old Age Security System

         The oldest component of the Income Security system for older Canadians is the OAS

System, which was put into place in 1952, replacing a provincially run income tested benefits

system that had existed since 1927. This program is available to anyone aged 65 or over who

meets certain residence requirements.3 The program originally provided benefits to those of age

70 or over, and the age of eligibility was dropped to 65 over a five-year period beginning in

1966.

         The OAS pension itself is a uniform demogrant that was equal to $419.92 in March 2000.

Individuals who do not fully meet residence requirements may be entitled to a partial OAS



3
  Individuals must have been a Canadian citizen or legal resident of Canada at some point before
application, and have resided in Canada for at least 10 years (if currently in Canada) or 20 years
(if currently outside Canada). The benefit is prorated for pensioners with less than 40 years of
Canadian residence, unless they are “grandfathered” under rules that apply to the persons who
were over age 25 and had established attachment to Canada prior to July 1977.


4
benefit. OAS benefits have been indexed to the Consumer Price Index (CPI) since 1972. OAS

benefits are fully taxable. In addition, there is a clawback of OAS benefits from very high-

income individuals; the OAS for an individual is reduced by 15 cents per dollar of personal net

income exceeding $53,215. The OAS basic benefit is financed from general taxation revenues.

The Canada/Quebec Pension Plan

        The largest component of the income security system is the Canada Pension Plan (CPP)

and Quebec Pension Plan (QPP). These programs began on January 1, 1966, and are

administered separately by Quebec for the QPP, and the federal government for the CPP.

        The plan is financed by a payroll tax of 3.5 percent (2000) each, on both employers and

employees. This payroll tax is levied on earnings between the Year's Basic Exemption ($3,500)

up to the Year's Maximum Pensionable Earnings (YMPE), $37,600 in 2000 (which approximates

median annual earnings). The YMPE is indexed to the growth in average wages in Canada.

        Eligibility for this plan is conditioned on contributions in at least one calendar year

during the contributory period, which is the period from attainment of age 18, or January 1, 1966

if later and normally extended to age 70 or commencement of the retirement pension, whichever

is earlier. Benefits are then computed in several steps.

        First, the number of months used to compute the retirement pension is determined by

subtracting from the number of months in the contributory period, months (a) receiving a

disability pension, (b) spent rearing small children,4 (c) between age 65 and the commencement

of the pension5 , and (d) 15 percent of the remaining months. The last three of these conditions is

subject to the provision that it not reduce the contributory period below 120 months after taking


4
  This is defined as months where there was a child less than 7 years of age and the worker had
zero or below average annual earnings.




5
into account the allowable offset for months of disability pension receipt. In addition, excess

earnings in one month above 1/12 of the YMPE may be applied to months in the same year

where earnings are below 1/12 of the YMPE.

        Second, the remaining months of earnings history are converted to current dollars, using

the following adjustment factor – up to 1998, the ratio of the YMPE in each year to the average

of the YMPE over the three years prior to (and including) the year of pension receipt. This

average was raised to four years for benefits claimed in 1998 and five years for benefits

beginning in 1999. Finally, the benefit is computed as 25 percent of the average of this real

earnings history. This 25 percent ratio has been in place since 1976; from 1967-1976, the

program was phased in, with the share of average earnings paid out in benefits rising from 2.5

percent in 1967 to 25 percent in 1976. The maximum retirement benefit is $762.92 in 2000.

        Until 1984 for the QPP and 1987 for the CPP, benefits could not be claimed before the

65th birthday, and there was no actuarial adjustment for delayed claiming. Beginning at these

times, individuals were allowed to claim benefits as early as age 60, with an actuarial reduction

of 0.5 percent for each month of early claiming (before age 65), and an actuarial increase of 0.5

percent for each month of delayed claiming (after age 65, and up to the age of 70).

        Since this early retirement provision has been in place, about half the new CPP recipients

each year have claimed a retirement benefit before the age of 65. The Office of the

Superintendent of Financial Institutions (OSFI) estimated that after 1991, a CPP pension for

someone retiring before the age of 65 was, on average, 82 percent of what it would have been

had they not opted for early retirement.6



5
  Periods after age 65 to age 70 can be substituted for periods prior to age 65 if this will increase
their future retirement pension.
6
  Special calculations for the 1992 Old Age Security Program Evaluation performed by OSFI.


6
        Initially, receipt of benefits between ages 65 and 70 under the CPP and QPP was

conditioned on low earnings levels, with earnings above these ceilings taxed away at high rates.

In 1975 and 1977, these earnings tests were eliminated from the CPP and QPP, respectively.

With the introduction of early retirement in the 1980s, workers can only claim early benefits if

their annual rate of earnings at that point does not exceed the maximum retirement pension

payable at age 65, for the year in which the pension is claimed. This earnings test is only applied

at the point of application, however; after that point, there is no additional check on the

individual's earnings.7 Moreover, the earnings test does not apply once the individual reaches age

65.

        CPP/QPP benefits are based on an individual's earnings history, and the retirement

benefits of one spouse are not linked to that of the other spouse.8 But there is interdependence

through survivor benefits (as well as the interdependencies through the income-tested programs

described below).    Spouses are eligible for survivor pensions if the deceased contributor made

contributions for the lesser of 10 years or one third of the number of years in the contributory

period, and if the spouse is over age 45 or is disabled or has dependent children. For non-

disabled spouses with children, the CPP benefit is pro-rated downward by age between 45 and

35.9 For spouses under age 65, the survivor pension is a combination of a flat rate portion plus

37.5 percent of the earnings-related pension of the deceased spouse. For spouses age 65 and

above, the survivor's pension is equal to 60 percent of the earnings-related pension. The pension

used to calculate the survivor's benefit is not subject to actuarial adjustment. If the surviving


7
  There are no restrictions on returning to work after the benefit is being paid.
8
  Couples do have the option of sharing their benefits for income tax purposes, since taxation is
at the individual level. Each spouse can claim up to half of the couple’s total CPP/QPP pension
credits. The exact calculation depends on the ratio of their cohabitation period to their joint
contributory period.



7
spouse is receiving his or her own CPP disability or retirement pension then the combination of

the earnings-related portion of the two pensions cannot exceed the maximum retirement pension

available in the year. Under changes made effective in 1998, the two benefits do not stack up to

this ceiling; rather the contributor receives the larger of the two earnings-related portions plus 60

percent of the smaller. As well, if under the age o 65, the survivor receives the flat rate portion
                                                   f

of the survivor benefit or, if a disability pensioner, the (larger) disability flat rate benefit only.

        Children of deceased contributors are also entitled to a CPP survivor's benefit if under 18

or a full time student between 18 and 25; this benefit is a flat amount. The corresponding QPP

benefit ends at age of 18. There is also a lump sum death benefit, which is generally equal to

one-half of the annual CPP/QPP pension amount up to a maximum ($3,500 in 1997)10 .

        Since 1973 benefits have been legislated to increase annually with the CPI: this annual

indexation factor is the ratio of the CPI average over the 12 month period ending with October of

the preceding year to the average of the prior 12 month period. Benefits are fully taxable by the

federal and provincial governments.

        Another dimension of the CPP/QPP that is potentially important here is the disability

benefit program. This program provides benefits to those workers unable to work due to

disability. The basic benefits structure consists of two portions: a flat-rate portion, which is a

lump sum paid to all disabled workers; and an earnings-related portion, which is 75 percent of

the applicable CPP/QPP retirement pension, calculated with the contributory period ending at the

date of disability. This program is fairly stringently screened, and fewer than 5 percent of older

Canadian men are on CPP/ QPP disability.



9
  QPP rules for younger surviving spouses differ from those of the CPP.
10
   Under the 1997 legislation, this maximum is fixed at $2,500 for all years after 1997, and in the
case of the QPP all death benefits are set at this level.


8
        The maximum CPP disability benefit was increased by 30 percent per month in 1987.

Earlier disability coverage was also extended to new entrants. As well, persons receiving

survivor benefits no longer had their benefits discontinued on remarriage.

The Guaranteed Income Supplement and Spouse’s Allowance

        GIS is an income-tested supplement available to recipients of OAS that was introduced in

1967. Individuals must re-apply for the GIS each year, and the income test for eligibility is

repeated. The definition of income for the purpose of income testing is the same as for income

tax purposes, with the important exclusion of OAS pension income. Unlike the OAS clawback or

CPP/QPP, GIS benefits are based on family income levels.

        There are separate single and married guarantee levels for the GIS; in 2000 (January to

March), these were $499.05 for singles and $325.06 (per person) monthly for married. Benefits

are then reduced at a rate of 50 percent as other income rises, although a couple with one

member over age 65 and one under age 60 is taxed at only 25 percent with an initial amount of

income exempted.

        The SPA, which was introduced in 1975, is an income-tested monthly benefit available to

60-64 year old spouses of OAS recipients and to 60-64 year old widows/widowers. For the

spouse of an OAS recipient, the benefit is equal to the OAS benefit plus GIS at the married age;

the OAS portion is reduced by 75 percent of other income until it is reduced to zero, and then the

combined GIS benefits of both spouses are reduced at 50 percent, as other income rises. For a

widowed spouse, the benefit is equal to the OAS plus GIS at the widowed rate, and is "taxed-

back" equivalently. Both the GIS and SPA guarantees are also indexed to inflation, and neither

source of income is taxable by either the federal or provincial governments.




9
Other Public Programs

        In addition to the federal retirement programs, there are a variety of provincial programs

that provide supplements to low-income retirees. For example, the GAINS-A program in Ontario

provides $80/month to Ontario residents who are recipients of the GIS; these benefits are taxed

back at 50 percent as other (non-OAS or GIS) income rises.

Private Pension Coverage

        Another important feature of the retirement landscape is private pensions. Defined

benefit pension plans share many of the same incentive features as public insurance plans. In

fact, many Canadian workers are covered by occupational pensions, or RPP’s. In 1997, 41.2

percent of paid workers were covered by occupational pensions, with coverage slightly higher

for males than for females (Statistics Canada 1999). Eighty-six percent of plan members were in

defined benefit plans, although the share in defined contribution plans has been growing

recently. Defined contribution plans may also affect retirement through income effects, but there

should not be tax/subsidy effects on the work decision since the payout is not dependent on work

patterns.

        One weakness of the data that are employed in this study is a lack of information about

private pension plan coverage. As a result, it is only possible to include an indicator for whether

the individual is likely to have a pension (based on industry of employment), but not for the

retirement incentives inherent in that particular pension plan (as is done, for example, in Gruber

and Madrian, 1995). The methods and data sources for this imputation are described below.

The Different Paths to Retirement

        Given the differences in the age of initial eligibility across the different IS programs, and

the availability of other income support programs before the age of 65, there are a variety of




10
paths that individuals may follow into retirement. Perhaps the most straightforward is from

employment onto IS benefits at age 65 or later. At these ages an individual is eligible for all the

IS programs so the full potential retirement income from public sources will be available.

        Early entitlement for CPP/QPP benefits is available starting at age 60. Receipt is

conditioned a one-time retirement test, although beneficiaries are free to work once the test is

met. Since other sources of support such as OAS and GIS are not available until age 65, benefit

income may be augmented by earnings from full or part time employment. Income is also

potentially available from other social insurance programs such as Employment Insurance,

although there are conditions (e.g., unemployment) and pension income is deducted from any

benefits from this source.

        Even if early CPP/QPP benefits are not claimed, Employment Insurance benefits and/or

Social Assistance benefits are another potential source of support for older workers and thus a

path into IS receipt. Also, disabled individuals are eligible for a CPP/QPP pension prior to age

60 that gets automatically converted to a “retirement pension’’ at age 65. Finally individuals

who participate in RPP’s with attractive early retirement packages may start claiming these

benefits as a prelude to IS benefit receipt at later ages.

        As explained below, our measure of retirement is based on earnings (or the lack thereof),

and therefore employment. We have no direct measure of IS benefit receipt, so alternative

definitions of retirement on this basis are not possible. Our data do record Employment

Insurance benefit receipt, however, so there is some possibility of tracking individuals who use

this path to retirement. Data on other forms of income such as an RPP pension or Social

Assistance are not available, however, so these paths are also not visible.




11
        In table 1 we provide a view of the employment and program participation of older

Canadians using data from the 1998 Individual Files of the Survey of Consumer Finances. Full-

time work declines dramatically for both males and females between the ages of 50 and 64.

Between the ages of 60 and 64, 34 percent of men and just 13 percent of women are in this

category. A constant fraction of males work part-time in each age group, but for females the

proportion displays a moderate decline before age 65 and dramatic falloff in the oldest age

group. The proportions not working, and therefore by some measures retired, rise steadily for

either sex with age. Interestingly in the age group 60-64, when early CPP/QPP benefit receipt is

available, 60 percent of males and 77 percent of females are not working. In the older age group

just 10 percent of males and virtually no females are still employed.

        The table also reveals that benefits from a variety of programs may support those in the

younger age groups that are not working. The proportion drawing a private pension or RRSP

benefits rises steadily to almost 1 in 3 males and 1 in 5 females by ages 60-64. Income from

Employment Insurance and Social Assistance flows to a relatively constant proportion (17

percent of males and 13 percent of females) between the ages of 50 and 64. The popularity of

the early retirement option of the CPP/QPP program for both sexes is apparent: over 40 percent

of both males and females between the ages of 60 and 64 receive this sort of income. The

statistics also show that females are far more likely to take advantage of the SPA program, and

thus receive OAS/GIS/SPA income between the ages of 60 and 64, than males.

        This message here, therefore, is that in the late 1990s a majority of older Canadians are

not working by ages 60 to 64. In fact a significant minority are not working by ages 55 to 59.

Income support at these younger ages may be coming from private pensions and other social




12
insurance programs. In their early 60s, a significant number of Canadians also avail themselves

of the early retirement option in the public pension program.



                                             Part III: Data

        There are few Canadian data sets that provide both large sample sizes of older individuals

and the information necessary to calculate their incentives to retire. This has hindered research

on retirement in Canada. To overcome this obstacle, the analysis here makes use of data from a

number of sources. These data provide the most comprehensive setting available in which to

study the incentives of the Canadian IS system on retirement.

        The primary data source is the Longitudinal Worker File (LWF) developed by the

Business and Labour Market Analysis (BLMA) Division of Statistics Canada.11 It is a 10

percent random sample of Canadian workers for the period 1978-1996. These data are the

product of information from three administrative data files: the T-4 file of Revenue Canada, the

Record of Employment (ROE) file of Human Resources Development Canada and the

Longitudinal Employment Analysis Program (LEAP) file of BLMA.

        T-4 tax forms are issued annually by employers for any employment earnings that (1)

exceed a certain annual threshold and/or (2) trigger income tax, contributions to Canada’s public

pension plans, or Employment Insurance (EI) premiums.1213 The earnings information from this



11
  The construction of the database is described in Picot and Lin, (1997) and Statistics Canada
(1998). Our description draws heavily on these sources.
12
  The data include incorporated self-employed individuals who pay themselves a salary, but
not other self-employed workers.
13
  The federal program that provides insurance against unemployment changed names from
Unemployment Insurance to Employment Insurance in 1996. In this paper we use Employment
Insurance throughout when referring to this program.


13
source has several advantages over its counterparts in survey data and other administrative files.

Most importantly, it is based on employers’ reports under the provisions of the income tax laws.

Therefore, the earnings variable should be free of the measurement error often observed in

survey data.

         Employers issue ROE forms to employees in insurable employment14 whenever an

earnings interruption occurs. Earnings interruptions result from events such as strikes, layoffs,

quits, dismissals, retirement and maternity or parental leave. The reason for the interruption is

recorded on the ROE form.

        Finally the LEAP is a longitudinal data file on Canadian businesses at the company level.

It is the source of information on the company size and industry of the jobs in which employees

work.

        The LWF data provide information on the (T-4) wages and salaries and 3-digit industry

for each job an individual holds in a given year, their age and sex,15 the province and size

(employees) of the establishment for which they work,16 and their job tenure starting in 1978.



14
   Over the sample period, insurable employment covers most employer-employee
relationships. Exclusion includes self-employed workers, full time students, employees who
work less than 15 hours per week and earn less than 20 percent of maximum weekly
insurable earnings (20 percent*$750=$150 in 1999). Individuals working in insurable
employment pay Employment Insurance (EI) contributions on their earnings and are eligible
for EI benefits subject to the other parameters of the EI program.
15
    Information on the age and sex of individuals is taken from the T-1 tax returns which
individuals file each year. To obtain this information, therefore, it is necessary that he or she
filed a tax return at least once in the sample period.
16
   The records of the LWF data are at the person/year/job level. For some calculations it is
necessary to aggregate the data to the person/year level. In years in which an individual has
more than one job, there will be multiple measures of tenure, industry, firm size and in some
cases province. In these cases the characteristics of the job with the highest earnings for the year
are used.



14
Because T-4’s are also issued for EI income we also observe any insured unemployment

/maternity/sickness spells.

          For current purposes the prime advantage of the LWF data are the earnings histories

stretching back to 1978. These were extended further to 1975 for each individual using the T-4

earnings files for these years. For the purposes of calculating CPP/QPP entitlement these

histories are still nine years short, however, as these programs started operating in 1966. Our

methods of backcasting the missing years are described below.

          The focus of the analysis is the period 1985-1996. Separate samples of males and

females aged 55 through 69 in 1985 are drawn, and then younger cohorts of individuals are

added as they turn 55 in the years 1986-1991.17 Agricultural workers and individuals in other

primary industries are excluded.18 The sample is selected conditional on working so that the

incentives for retirement conditional on being in the labour force are examined. Work is defined

as positive T-4 earnings in two consecutive years. If an individual has positive earnings in one

year and zero earnings in the next, the year of positive earnings is considered the retirement year.

Since T-4’s are not issued to the unincorporated self-employed, this definition of retirement will

also capture any persons moving from paid employment into this sector.19 Only the first


17
     Individuals with missing age, sex or province variables are excluded from the sample
18
   We make this exclusion because our definitions of retirement are based on earnings, and the
earnings streams for these workers, given high rates of self employment and special provisions in
the Employment Insurance system for fishers and other seasonal workers, are difficult to
interpret. For example, individuals in these industries are observed with years of very small
earnings (in the hundreds of dollars) and no (or sporadic) evidence of EI benefits, who were too
young to collect IS benefits. One possibility is that they are primarily unincorporated self-
employed and therefore the majority of their earnings are unobserved.
19
   While older individuals do work in unincorporated self-employment, the proportion doing so
remains fairly constant over our sample period. For males, Canadian Census data (Individual
Files for 1981, 1986, 1991, 1996) reveal that the proportion of the population of 60-64 year olds
(65+ year olds) working in this sector is 0.08-0.09 (0.04) in Quebec and 0.13-0.16 (0.06-0.8) in


15
observed “retirement” for each individual is considered. If a person re-enters the labour market

after a year of zero earnings, the later observations are not used. Finally, individuals are only

followed until age 69. The retirement of an individual who has positive earnings in every year

up to this age is not observed since it presumably occurs after the age of 69. The working

sample, therefore, is a panel data set for the years 1985 through 1996 of individuals between the

ages of 55 and 69, who worked in 1985 or in the year they turned 55, whichever is later.20

        The marital status and any spouses of individuals in our sample are identified using

information from the T-1 family file maintained by Statistics Canada. T-4 earnings histories for

the period 1975-1996 are then constructed for the spouses, again through reference to the T-4

earnings files for these years.

        An important piece of information for calculating retirement incentives that is not

available in the LWF data is participation in a RPP. We estimate the probability of RPP

coverage by 3-digit industry21 using cross section samples of males or females from the 1986-

1990 Labour Market Activity Survey (LMAS) and the 1993-1996 Survey of Labour and Income

Dynamics (SLID). In these surveys individuals are asked if they participate in any RPP. These

probabilities are then imputed to individuals in the LWF, matching on industry codes.




the rest of Canada between 1980 and 1995. For females the statistics are 0.01 (0.00-0.01) in
Quebec and 0.2-0.4 (0.01) in the rest of Canada.
20
   ROE’s were considered as an alternative source of information on when individuals retired. It
was found, however, that generally less than one-third of individuals who retired in the earnings
sense (e.g., had zero T-4 earnings), also had “retirement” coded on their last ROE. “Still
working” or “unknown” were the most common codes for those in the complementary group.
The ROE’s, therefore, would appear to impose a restrictive definition of retirement that has an
unknown basis.
21
    Some industries are aggregated to obtain sufficient sample sizes. Unfortunately, the sample
sizes of these data sets would not permit us to calculate these probabilities exclusively for older
individuals.


16
Probabilities for the years 1991 and 1992 are simple linear interpolations. The sample

definitions for these additional data sources are described in the Appendix.



                        Part IV: Earnings and Non-Labor Income Projections

         The following analysis involves constructing each sample individual’s entitlement to IS

benefits at any given age, as well as estimates of future entitlements. To calculate the CPP/QPP

component, we require a full earnings history from 1966, the year in which the program started.

As noted above, our earnings information only extends back until 1975. In estimating future

entitlement, we must project future earnings to construct the relevant earnings history.

Therefore, both earnings backcasts and forecasts are needed for these calculations.

         After experimenting with a number of projection methods, earnings are forecasted by

applying a real growth rate of zero percent per year to the average of an individual’s observed

earnings in the three years preceding the retirement year. Within sample evaluation revealed this

method a better predictor (in a mean-squared error sense) of future earnings than methods

involving a projection equation that included demographic variables, lagged earnings and

individual fixed effects.

         To backcast the missing earnings data, cohort specific earnings growth rates calculated

from the 1972, 1974 and 1976 Census Family files of the Survey of Consumer Finance22 were

applied to a three year average of an individual’s last valid earnings observations in the LWF

sample. This allows us to construct earnings histories back to 1971. For the remaining five

years, earnings growth rates implied by the cross section profile from the 1972 SCF were used,




22
     We use samples of paid workers with positive earnings in the relevant birth cohorts.



17
appropriately discounted for inflation and productivity gains using the Industrial Composite

wage for the period 1966-1970.23

         The GIS/SPA and OAS components of IS benefits are fully or partly means tested. Our

data set contains no information on non-labour income although these are clearly a crucial input

to calculating entitlement to these benefits. To project non-labour income, we construct age

profiles of family level income by sex/region/industry and sex/region/marital status cells for

individuals in and out of the labour market respectively.24 The data for these profiles are from

the 1986 and 1991 census family files of the Canadian Census. While the formal definition of

the measure of non-labour income is provided in the Appendix, it includes investment income

and income from private pensions.

         When entitlement is projected in future retirement years, it is necessary to impute the

level of non-labour income an individual will receive at different ages when he/she is retired. To

do this, we use the age profile for this income for individuals out of the labour market in the

relevant sex, region and marital status cell. Likewise, for individuals who continue to work past

age 65 (60 for the SPA), it is necessary to impute their level of non-labour income to calculate

the benefits they might draw from OAS/GIS/SPA. To do this, the age profile for employed

individuals in the relevant sex, region and industry cell is used. The sample and cell definitions

that are employed are also described in the Appendix.

         Both projected earnings and non-labour income are net of federal and provincial income

taxes. Also deducted are the employee’s portion of the CPP/QPP payroll tax that they would pay


23
   The data on the Industrial Composite wage are from Statistics Canada (1983). The obvious
limitation of this backcasting approach is that we will not predict absences from the labour
market, which may be important at younger ages.
24
     The age profiles are appropriately inflated by the CPI for use in future years.



18
if they worked. In either case the parameters of the tax system are held constant in real terms for

all future years.



                           Part V: Construction of the Incentive Measures

Benefit Entitlements

          The retirement incentives inherent in the three pillars of the Canadian Income Security

system for seniors are calculated: the OAS, the GIS/SPA and the CPP/QPP. The first step is to

calculate an individual’s entitlement in any given year. This will involve both his/her

entitlements to each of the programs and the entitlements of any spouse.

          The OAS benefit is the most straightforward as it is a uniform benefit available to anyone

who is 65 years or order. Two possible complications are the residency requirements and the

clawback of benefits from high-income recipients. The residency requirement for this benefit is

not implemented, as there is no information on the place of birth or year of arrival in Canada of

individuals in the sample. The clawback provisions (starting in 1989) are fully implemented,

however, based on projections of labour and non-labour income.

          The GIS/SPA entitlement is a function of the age requirements described above and

family income. The ages of individuals and any spouses are directly observable in the data. The

income test on benefits is again fully incorporated based on projections of labour and non-labour

income.

          As discussed above, non-labour income is projected using census data and matched to our

data. For each individual, the OAS and GIS/SPA benefit, entitlement with and without the

imputed level of non-labour income is calculated. The two results are then averaged using the

cell specific probability that non-labour income is positive as weights.




19
        The calculation of CPP/QPP entitlement involves constructing an individual’s and their

spouse’s earnings history over the contributory period. Given the age range in the sample this is

the period starting in 1966. The direct observations on T-4 earnings back to 1975 and predicted

earnings in the period 1966-1974 are used. The drop out provisions for years between the 65th

birthday and the commencement of retirement and for low earnings months up to 15 percent of

the contributory period are fully implemented. Disabilities or time spent in childcare are not

observed, however, and therefore deletions for these reasons are not captured.25 This

information in tandem with earnings projections for future years permits the construction of

Average Pensionable Earnings (APE) at all future retirement dates for any given individual. The

reforms of the CPP/QPP system over the period are also accounted for, including the

introduction of early retirement to the CPP, the retirement test on benefit receipt at ages 60-64

and the actuarial adjustment to benefits for initiating benefit receipt at ages other than 65, all in

1987.

Spousal Behaviour

        A complete model of family labour supply is beyond the scope of this paper. The

simplifying assumption that the spouse starts collecting any entitlement at the earliest age

possible under the current rules of IS programs is made: for most of the sample period this is age

65 for OAS and GIS, age 60 for the SPA and age 60 for the CPP/QPP. For CPP/QPP benefits

prior to age 65 and any income-tested benefit, the assumption implies a cessation of the spouse’s

employment (i.e., retirement). Gruber (1999) and Baker and Benjamin (1999c) provide

estimates of age/employment profiles and employment hazards (the conditional probability of



25
   Note that the dropout provisions for child care came in to effect in 1977 under the QPP and
1978 under the CPP. The childbearing years of many females in our sample will have been prior
to these dates.


20
labour market exit) for older men and women over the sample period. This evidence provides

some justification for this assumption about labour market exit rates in our analysis of the male

sample, in which spouses are females. On the other hand, this assumption may prematurely

remove the male spouses of individuals in our sample of females from the labour market. This is

unlikely to have a large effect on our estimates, as the independence across spouses in

determination of most of the benefits means that spousal retirement is only a minor contributor to

IS incentive calculations.

The Present Discounted Value of ISW

        Once these calculations of entitlement for each of the programs are made, the expected

net present value of the family’s Income Security Wealth (ISW) associated with each retirement

date is constructed. For single workers this is the sum of future benefits discounted by time

preference and survival probabilities. For married workers we account for the likelihood of the

joint survival of worker and the spouse, and the survivor provisions of the CPP/QPP and SPA, as

described in more detail in Gruber (1999). We use a real discount rate of 3 percent and survival

probabilities from the age/sex specific Canadian life tables from Statistics Canada (Statistics

Canada 1984).

The One-Year Accrual Calculation

        We compute a number of different incentive variables using these estimates of the

present discounted value (PDV) of ISW at all future retirement dates. The first is the one-year

accrual of ISW resulting from an additional year of work. In the Canadian system an additional




21
year of work can raise ISW through the drop out provisions of the CPP/QPP, and it can either

raise or lower ISW through the actuarial adjustment of benefits.26

        The first of these factors is fairly small. In the Canadian system, the contributory period

is a fixed age interval, so that other things equal the marginal year replaces only 15 percent of a

low earnings year.27 Furthermore, this benefit is attenuated in the period examined here, by the

real decline in the Year’s Maximum Pensionable Earnings (YMPE) in the early 1970s. Initially

set to match average wages, the YMPE declined dramatically in the initial years of the program,

falling to 67 percent of the Industrial Composite wage in 1973.28 In 1975 both the CPP and QPP

were amended to allow the YMPE to rise at a rate of 12 ½percent per annum until equality with

average wages was re-attained, but this did not occur until 1987. The upshot is that even

individuals with low wages would have made the maximum contribution to the system in the

1970s. Therefore, a marginal year in the late 1980s and early 1990s would not necessarily

dominate earlier years when the relative YMPE was much lower.

        Starting at age 60 (in years 1987+ for the CPP) an additional year of work also implies a

delay in claiming, and thus both an (upward) actuarial adjustment in benefits and reduction in the

years of potential receipt. The actuarial adjustment between ages 60 and 70 is a linear 6 percent

per annum.29 Whether this provides a net increment or decrement to ISW depends on the size of

the adjustment relative to the expected number of years of remaining life-time over which


26
   We use here the value of the accrual, rather than normalizing the accrual by earnings to form
an implicit tax/subsidy, as is done in Gruber (1999). We do this because we are controlling for
earnings itself in the regression model, so that we in essence capture both pieces of the incentive
to work (earnings and ISW accrual) separately.
27
   This contrasts, for example, with the U.S. Social Security system where the substitution is one
for one: for those with less than 35 years of work the marginal year replaces a zero in the SS
calculation; for those with 35 years or more of work it replaces a full low earnings year.
28
    The YMPE equaled 99.8 percent of the Industrial Composite wage in 1966.
29
   CCH Canadian Limited (1996).



22
benefits will be collected. Given the linear nature of the adjustment, it will clearly become more

and more unfair with age. This adjustment also interacts with the income testing of the GIS/SPA

program. Low-income individuals may get some of the actuarial reduction in CPP/QPP benefits

for early retirement back starting at age 65 through qualification for a higher GIS benefit. This

further increases the disincentives for additional work after age 60 for those who are likely to be

on the GIS program. Another way of looking at this is that the actuarial increase in benefits for

delaying retirement may reduce entitlement to means tested benefits starting at age 65. For these

individuals, therefore, the effective actuarial adjustment is less than 6 percent per year and

therefore, much more likely to be unfair.

The Peak Value Calculation

        Forward looking measures of retirement incentives that involve the future path of ISW

are also considered. The simple measure of one-year accrual only accounts for the immediate

benefit to working an additional year. But an additional year of work also sustains the option of

retiring at an even later date. The value of this choice can be important if there are large non-

linearities in the accrual profile. For example, if there is a small negative accrual at age 59, but a

large positive accrual at age 60, it would be misleading to say that the system induces retirement

at age 59; the disincentive to work at that age is dominated by incentives to work at age 60.

        One way of capturing this possibility is to use the “peak value” calculation suggested by

Coile and Gruber (1999). Rather than taking the difference between ISW today and next year,

peak value takes the difference between ISW today and in the year in which the expected value

of ISW is maximized. This measure therefore captures the tradeoff between retiring today and

working until a year with a much higher ISW: the option dollar value of continued work. In




23
years beyond the year of peak expected value ISW, this calculation collapses to the simple one-

year accrual variable.

The Option Value Calculation

          If a utility function that captures work preferences can be appropriately defined then an

approach that compares the utility of retirement at future dates is preferable. To explore this

approach, the option value calculation of Stock and Wise (1988) is used. Here the utility of

retiring today is compared to its value at the optimal retirement year in the future. The

calculation uses a specification of the individual’s indirect utility function

                              R −1                       T
(1)               Vt ( R) = ∑ p s |t d s − t ( y s ) g + ∑ p s |t d s −t [k ⋅ Bs ( R)] g
                              s= t                      s= R



where

      Ø R is the retirement date,

      Ø d is the discount rate,

      Ø p is the probability of being alive at some future date conditional on being alive today,

      Ø y is income while working,

      Ø B is retirement benefits,

      Ø g is the parameter of risk aversion,

      Ø k is a parameter to account for disutility of labour ( k ≥ 1)

      Ø T is maximum life length.

In this model additional years of work have three effects. First they raise total wage earnings,

increasing utility. Second, they reduce the number of years over which benefits are received,

lowering utility. Third, they may raise or lower the benefit amount depending on the shape of

the benefit function B(R). The last two effects receive greater weight than the first due to the

disutility of labour. The optimal year for retirement is the year in which the utility gained from


24
additional earnings is outweighed by the utility lost from the reduction in retirement income.

The option value is the difference in utility from retirement at the optimal date and retirement

today.

         Relative to peak value, option value has one major advantage, and several disadvantages.

The advantage is that the reference year in the peak value calculation (the year in which ISW is

maximized) is arbitrary; there is no particular reason why this should be the year to which a

given worker compares this year’s ISW in making their retirement decision. The option value

approach more carefully specifies the optimal retirement date, and as such provides an economic

basis for the reference year.

         Offsetting this advantage, however, are a number of disadvantages. The option value

approach requires a particular specification of the indirect utility function, and evaluation of its

structural parameters. Also, earnings enter directly into the utility calculation and thus will drive

some part of the variation of the option value across individuals. If earnings are in turn

correlated with some unobserved component of tastes for retirement, the identification of the

option value effects can be undermined.

         To implement this approach, values of k, the parameter for the disutility of labour, d, the

discount rate, and g, the parameter of risk aversion, are taken from the literature. Following

Stock and Wise (1988), k=1.5 and g=0.75, while d=0.03 following Coile and Gruber (1999).

Sensitivity analysis suggests that the results are not dramatically different for sensible variations

in these parameter values.

Sample Estimates of the Different Incentive Measures

         In table 2 we provide information on the distribution of the one-year accrual measure, by

age, for the male sample. The median ISW rises to a peak at age 61, then starts on a smooth




25
descent. The median one-year accrual is positive to age 60, but becomes increasingly negative

thereafter. The initial positive accrual is due to the dropout provisions, which work in favour of

the worker with the median PDV of ISW. This effect is attenuated with age, however, as the

implied larger CPP/QPP entitlement reduces GIS/SPA entitlement through the income test. The

negative accruals start at age 61 as the early retirement provisions of the CPP/QPP come into

play. Important here is that the linear CPP/QPP actuarial adjustment becomes increasingly

unfair as the person delays retirement. There is an additional consideration for individuals who

will eventually claim on GIS benefits (45 percent of OAS pensioners received GIS benefits in

1990). The higher CPP/QPP benefits gained by delaying retirement, either through improving

the earnings history or the actuarial adjustment are offset by reduced income tested GIS benefits

at older ages. The net effect of these factors is increasingly negative, as the median accrual falls

from -$249 to -$1397 between ages 61 and 64. The median accrual rises in absolute value at age

65 as OAS and GIS benefits come on line (there are SPA benefits in this range as well, given that

the spouses of these male workers are typically several years younger). This jump reflects the

fact that additional earnings after 65 will decrease the OAS, GIS, and SPA benefits through the

income test for many workers. From age 66 to age 69, the accrual becomes more negative

quickly, reflecting the increasingly unfair actuarial adjustment of CPP/QPP benefits, and that

continued work sacrifices GIS benefits through the income test, and OAS benefits, if earnings

are high enough, through the clawback. Overall, the loss in ISW wealth in table 2 is substantial

between ages 61 and 69: the sum of the median accrual over these ages is -$21709.

        In the second last column the Median Tax/Subsidy Rates are reported. This is calculated

as the median ratio of the one-year accrual to current after tax earnings. After the initial period

of subsidy the tax rate becomes positive at age 61. By age 69, the median tax rate is about 43




26
percent. These figures are somewhat lower than the estimates from Gruber (1999), presumably

reflecting the fact that the dropout provisions have greater value here because we use real rather

than simulated earnings histories. That is, if the real earnings history is more variable than a

simulated earnings history, there will be more value to replacing lower earnings years that will in

turn increase the incentive to continue working.

        The median accrual masks considerable variation in the one-year accrual across

individuals. For example, the standard deviation averages $1122 across age groups. The accrual

at the 90th percentile does not turn negative until age 65. Presumably few of these individuals

would qualify for GIS due to private pensions and savings. Many should also be in the clawback

range for the OAS. As a consequence, we might not expect age 65 to be so pivotal for these

individuals. That said, average non-labour income is imputed to individuals, and this will be

more inappropriate for people in the tails of the income distribution.

        Corresponding information for the peak value accrual is provided in table 3. Not

surprisingly, the main difference from the one-year accrual is at ages 55 to 59. The median

accrual is larger at these ages, but the change is fairly modest. For example, the median one-year

accrual at age 57 is $534, while the median peak value accrual is $1164. Correspondingly,

adding together the median one-year accruals in table 3 between ages 55 and 60, the distance to

the “peak” is not that large. The primary inducement to continued work at older ages is the drop

out provisions of the CPP/QPP, which, as explained above, are modest, and attenuated in the

period we examine due to the real decline in YMPE over the 1970s. That is, continued work

may not qualify the individual for a larger CPP/QPP entitlement. Furthermore, the CPP/QPP is

only one of three components of ISW. Therefore we might expect the financial option value of




27
continued work to be modest at older ages. 30 Note that once age 60 is reached the peak value

calculation is the same as the one-year calculation for most individuals, since they have already

reached their peak.

         Table 3 also contains information on the option value accrual. Here the accrual is

positive throughout the age range reflecting the fact that the median optimal age of retirement by

this measure is at age 70 or 71. The magnitudes of these numbers are difficult to interpret as

they are in units of utility.

         In Table 4 we present corresponding information on the one-year accrual in the female

sample. The age profile of the one-year accrual largely reflects the same factors as the profile for

males (e.g., drop out provisions of the CPP/QPP, the straight line actuarial adjustment of

CPP/QPP benefits). One might reason that females’ lower earnings entitle them to smaller

CPP/QPP benefits and therefore their ISW entitlement should be smaller. This effect is

attenuated by the large relative decline in the YMPE over the 1970s and that CPP/QPP is only

one of three components of the IS package. Another consideration is that the longer lifespan of

females means that the actuarial adjustment for delayed receipt of CPP/QPP benefits will be

fairer for this group. We can see this in the smaller proportionate changes in the accrual over the

age profile. For males, the median accrual increases (in absolute value) by $1427 between ages

60 and 64 and by $1409 between ages 65 and 69. For females the corresponding changes are

$938 and $931 respectively. Also it is important to remember that the sample individuals are

selected conditioning on positive earnings in the first year the individual enters the sample.




30
  In contrast, Coile and Gruber (1999) report large differences between one-year and peak value
accrual for the US. This is not surprising, for as explained above the drop out provisions of the
US Social Security can lead to large changes in Social Security wealth with work at older ages.


28
These, therefore, are a select sample of females who worked at older ages, yet belong to birth

cohorts that historically have not had high participation rates.31

         The peak value and option statistics presented in table 5 are also very similar to their

counterparts for males. Again the early peak in ISW, and the lack of any strong variation in

accrual mean there are only modest differences between the one-year and peak value

calculations.

         In figures 2 and 3 we graph the age profiles of the median of the various measures of

accrual. The relative levels are meaningless, as the option value is measured in utility units. A

comparison of the age profiles of the different measures of accrual, however, is meaningful,

highlighting the differences among the measures. For both sexes the one-year and peak value

have very similar age profiles. The median accruals decline over the full age range, with

increases in the rate of decline noticeable at ages 60 and 65. The difference in the peak value

measure is all in the age range 55-59. The option value calculation provides a very different

profile, as accrual declines continuously at a decreasing rate over the age range.



                       Part VI: Empirical Framework and Estimation Results

The Empirical Framework

         The regression equation relates the retirement decisions of individuals to their

demographic and economic characteristics as well as their ISW. ISW plays a dual role in the

decision. First, higher levels of ISW have wealth effects which cause individuals to retire

earlier; more wealth through IS programs will lead to increased consumption of all goods,

including leisure. Second, however, higher accruals of ISW from additional work should have a


31
     The participation rate of 45-64 year old females was 41 percent in 1976, 48 percent in 1986,



29
substitution effect which leads to later retirement; if there is a large financial incentive to

additional years of work, then individuals will retire later.

          Therefore equations are estimated of the form:

                  Rit = δ0 + δ1 ISWit + δ2 ACCit + δ3 AGEit + δ4 EARN it +
(2)
                  δ5 APEit + δ6 SPEARN it + δ7 SPAPE + δ8 RPPit + δ9 X it + υit .

where

      Ø Rit is a variable which equals one in the year of retirement and 0 otherwise,

      Ø ISW it ` is the expected PDV of ISW in year t,

      Ø ACCit is one of the measures of accrual outlined above: the simple one-year accrual, the

          peak value accrual, or the utility based option value accrual,

      Ø AGEit represents a set of dummy variables for each age in our sample, and a measure of

          the difference in ages across spouses,

      Ø EARN it and APEit represent cubics in measures of the individual’s projected earnings in

          year t and his/her Average Pensionable Earnings (for CPP/QPP calculations),

      Ø SPEARN it and SPAPEit are the corresponding variables of any spouse,

      Ø RPPit is the measure of the probability of RPP coverage at the 3-digit industry level,32

      Ø X it are a set of additional control variables, including a dummy variable for marital

          status, a quadratic in tenure on the job and a dummy variable which equals one if tenure

          is censored at 1978, a quadratic in the individual’s and his/her spouse’s labour market



and 58 percent in 1996 (source CANSIM).
32
    The standard errors here are potentially biased due to a correlation of the error term across
individuals within 3-digit industry (the “grouped data problem”). Correcting for this bias would
lead to larger estimated standard errors on the parameter on RPP.



30
        experience measured as the number of years of positive T-4 earnings between 1975 and

        year t, 11 industry dummies, dummies for 6 categories of establishment size and province

        and year effects.

To capture potential non-linear relationships between earnings and retirement decisions, we

include a full set of interactions between the cubics in EARN it and APEit , and SPEARN it and

SPAPEit . The equations are estimated separately for males and females as a probit.

        As mentioned at various points of this discussion, the Canadian IS system went through a

number of reforms in our period of analysis. This is a distinct advantage of evaluating the

retirement incentives of the Canadian IS system relative to other countries. These policy

interventions potentially provide more credible identifying variation for the parameters of the

ISW incentive variables than the variation across individuals due to differences in earnings

histories, family circumstances and tastes. This advantage is highlighted in the reforms of the

CPP system that do not have a counterpart in the QPP system in the period 1985-1996. In this

case, the residents of Quebec provide a control group for the effects of the reform. Of particular

importance here is the introduction of early retirement to the CPP system in 1987. A similar

reform of the QPP was accomplished in 1984.33


Sample Characteristics

        In tables 6 and 7 some average demographic and job characteristics for the male and

female samples are presented, calculated over all the observations.34 The average age in our

male sample is almost 60 years old. Fifty six percent of the sample observations are for married


33
   Another reform during our sample period is the introduction of the clawback of OAS benefits
in 1989. This applied to individuals in all parts of the country.
34
   An alternative would be to calculate the means over individuals.



31
men. Average projected earnings for the males are $19503, while the average APE is $19847.

The corresponding averages for the spouses’ are $3033 and $5393 respectively. 35 Finally, the

average probability of RPP coverage across observations is 58 percent.

        The average age in our female sample is 59½years. Both the married and RPP

proportions are lower than in the male sample, at 0.40 and 0.43 respectively. Average projected

earnings are $11458, while the average APE is $13871. It is interesting to note that these female

workers have similar tenure (length of time with the current employer) and experience (number

of years in the labour market) as their male counterparts, but this is likely because our measures

are only since 1978 (tenure) and 1975 (experience); over the full working life, presumably these

means are much lower for women. The reason that the means of spousal earnings are lower than

own earnings for women is because average spousal earnings is calculated using zeros for non-

married working women.

        In figures 4 and 5 we present estimates of the retirement hazard for males and females in

our sample, calculated across all birth cohorts in the sample and all years. The hazard for each

sex displays a distinct jump at age 59/60, which is the point of first eligibility for CPP/QPP

benefits. This is also the age at which individuals are first eligible for the SPA. They then

increase modestly at ages 61 through 64. Finally, there is a spike at age 65. Relative to the

profile for males, the hazard for females is slightly higher at ages younger than 60, rises more

quickly and higher at 59/60, remains above its male counterpart until age 64, and has a smaller

spike at age 65.




35
  Note that the averages for the spouses are much less than the averages for the males. This is
part because we calculate these averages over all males, including those who have no spouse or
whose spouse doesn’t work. In these cases, spousal earnings will be 0, thus lowering the
average.


32
Retirement Regression Results

        In table 8 are the regression results (estimates of equation (2)), for males using the one-

year accrual incentive variable. In the first panel of the column are the results for a parsimonious

specification in which ISW and one-year accrual are the only explanatory variables. Here the

ISW incentives are allowed to have the maximum impact. The first thing to note is that one-year

accrual has an expected negative sign, while the level of ISW has an unexpected negative sign.

This latter result suggests that higher levels of ISW lower the probability of retirement, although

in this specification ISW could be capturing the effects of excluded individual level

characteristics that are correlated with both ISW and retirement. For example, individuals with

high earnings over their lifetime will have higher ISW and may also have higher propensities for

work. Each $1000 in accrual lowers the probability of retirement by 3.88 percentage points

which is 26.2 percent of the baseline retirement rate of 14.8 (table 6).

        In the second panel of this column we add some simple controls for age. The first is a

dummy variable for age 65. This should help control for any institutional bases for retirement at

this age, such as mandatory retirement rules or RPP provisions. The second is the interaction of

a dummy variable for being between ages 60 and 64 and a dummy variable which equals 1 if

CPP or QPP pension receipt is currently available as early as age 60. As noted above early

pension receipt was available from the QPP in all years of the sample, and from the CPP starting

in 1987.

        The addition of these controls lowers the estimated effect of the accrual variable and

almost doubles the estimated effect of ISW. Also, the added age controls hold some interest in

their own right. First, the estimate of the age 65 dummy (not reported) is positive and

significant, capturing the large increase in the probability of retirement at this age (see figure 4).




33
Second, the estimate of the “early retirement” at ages 60 to 64 interaction is positive, indicating

an increase in retirement at this age in jurisdictions where early CPP/QPP benefit receipt was

available. This coefficient is partly identified by Quebec/rest of Canada differences in retirement

rates at this age in 1986, when early receipt was available under the QPP but not the CPP.

        In the succeeding columns we control for additional individual and employment

characteristics that may also be important determinants of retirement. A potential problem with

the results in column 1 is if these variables are also correlated with our ISW variables. The

expectation, therefore, is that the ISW effects will be smaller as we add the additional controls.

        This is indeed the case in column 2 we add controls for marital status, own tenure, own

and spouse’s labour market experience, a linear control for age, a variable which measures the

age difference between spouses, single year effects, province effects, industry effects and

dummies for five categories of establishment size. We again compare the results with (second

panel) and without (first panel) the dummies for age 65, and the age 60 to 64 in early retirement

jurisdictions interaction. Now a $1000 in accrual decreases the probability of retirement by 2.65

percentage points (2.12 points with the extra age controls) which is 17.9 (14.3) percent of the

baseline retirement rate. The estimated coefficient on the level of ISW is now positive without

the age controls, but becomes negative again with the age controls included. The message here,

therefore, is that the added variables are important correlates with both the probability of

retirement and with the ISW incentive variables.

        The parameters on most of the added explanatory variables are as expected. Of particular

interest is that the effect of our measure of the probability of RPP coverage is positive and

statistically significant. This is consistent with a wealth effect as result of the additional savings

represented by the RPP entitlement. Marriage and larger age differences (Agediff) between




34
spouses have a negative relationship with the probability of retirement. Conditional on age, both

experience and tenure reduce the probability of retirement, although in each case at a decreasing

rate.

        The estimates of the year effects (not reported) reveal that most of the time effects are

cyclical. Also, the probability of retirement displays a vague U shape with establishment size:

larger in the smallest and largest establishments. The higher probability of retirement in the

largest establishments may be partly an (unobserved) RPP effect.

        In column 3 we add earnings controls: cubics in own and spouse’s projected earnings and

APE as well as a full set of interactions between the cubics in projected earnings and APE. This

is potentially an important innovation because ISW is mechanically a function of past earnings,

and accrual depends on projected earnings, but either earnings may have independent effects on

retirement. The cubics and the interactions provide a very flexible way of accounting for these

independent effects. The result is two important changes in inference. First, the coefficient on

the level of ISW is now consistently positive as expected, and quite large. Each $10,000

increase in ISW increases the probability of retirement by 1.97 percentage points (0.92 with the

age controls). In previous specifications ISW may have been picking up the independent effects

of earnings on retirement. Conditional on the earnings controls, however, ISW has the expected

wealth effect. Second, the estimate on one-year accrual is again smaller. For the specification

without the extra age controls a $1000 increase in accrual now reduces the probability of

retirement by 2.21 percentage points (1.49 with age controls).

        In the final column we replace the linear variable in the worker’s age with age dummies

for ages 56 through 69. Here we absorb any age specific tastes for retirement in a very flexible

way. The estimated effects of ISW and accrual are now fairly similar across the specifications




35
with and without the additional age controls. This suggests that differences between these

specifications in previous columns were driven by the inclusion of the age 65 dummy which is

now present in both panels of column 4. A $10,000 increase in ISW increases the probability of

retirement by 0.51 percentage points (first panel), which is 3.4 percent of the baseline retirement

rate. A $1000 increase in accrual reduces the probability of retirement by 1.52 percentage points

which is 10.3 percent of the baseline rate. The IS system, thus, has two countervailing impacts

on retirement decisions: larger IS entitlements raise retirement, but larger accruals for additional

work lower retirement.

        Table 9 contains corresponding results using the peak value measure of accrual. Again,

moving across columns we gradually add control variables moving from a parsimonious to very

rich specification, while the second panel contains results conditional on the extra age controls.

There are strong similarities with the results in table 8. As an example, the estimated effects of

the IS incentive variables grow smaller as we add more control variables. The estimated effect

of the level of ISW is generally similar to the previous estimates, but the effects of the accrual

are more modest. In column 4, a $10,000 increase in ISW increases the probability of retirement

by 0.51 (0.54 percentage points with extra age controls). A $1000 increase in peak value reduces

the probability of retirement by 0.73 (0.68 percentage points), roughly half of the corresponding

estimates from Table 8. As is clear in figure 2, at the median there is little difference in the one-

year and peak value accrual after age 60. What distinguishes the two measures is their profile

between age 50 and 59. Peak value would predict a greater slope in the run up in retirement rates

leading to age 60.

        Table 10 contains the results using the option value incentive measure. Here there are

some substantial differences from previous results. First, the profile of the age dummies in




36
column 4 are unintuitive: largely negative to as late as age 64 (the excluded age is 55).

Importantly, the estimated effect of the level of ISW switches from positive to negative as more

controls are included, although the estimates in column 4 are not statistically significant. Finally,

one point of agreement with the previous results is the negative effect of accrual, although in this

case the effect is not easily quantified because the variable is measured in units of utility.

        Comparing figure 2 to figure 4, the age profile of the option value accrual has no visibly

obvious relationship with the age profile of the retirement hazard, at least at the median. It

would predict a monotonically increasing hazard with age, with gradually decreasing slope. In

this case, then, the other variables must compensate. For example, the profile of the age

dummies is flatter in the age intervals 55 through 59 and 60 through 64 to compensate for the

fact that the change in option value would predict the probability of retirement increasing at a

faster clip than the other two measures of accrual.

        Tables 11, 12 and 13 contain corresponding results for females. The one-year accrual

results in table 11 are broadly consistent with the one-year accrual results for males. One

distinguishing feature is that the presence of an RPP has a greater effect. In column 4 it raises

the probability of retirement by 3.3 percentage points or 22 percent of the baseline hazard of 15.1

(table 7). The corresponding estimate for males (column 4 of table 8) implies the presence of an

RPP increases the probability of retirement 2.4 percentage points 16 percent of the male baseline

rate. Note also that the effect of the age difference between spouses is now positive.

        The estimated effect of the level of ISW and one-year accrual are very similar to the male

results. In the richest specifications (column 4), $10,000 in ISW raises the probability of

retirement by about 0.45 to 0.47 percentage points while $1000 in accrual lowers it by 1.28 to

1.22 percentage points.




37
        Table 12 contains the peak value results. Relative to the one-year results the changes are

again similar to those observed for males. The effect of the level of ISW is little changed, while

the accrual effect is much weaker. Here $10,000 in ISW raises the probability of retirement 0.60

percentage points while $1000 in accrual lowers the probability 0.17 percentage points (top panel

column 4).

        Finally, the option value results for females are in table 10. As was the case for males

there are some unintuitive estimates, particularly in the richer specifications. While the effect of

the level of ISW is positive in each column, the effect of accrual is also positive in columns 3

through 4. Again, it is difficult to provide context for the magnitude of the latter coefficient as

the variable is measured in units of utility.



                                        Part VII: Policy Simulations

        The results presented above are difficult to interpret in a vacuum. Thus, we have applied

our model to the consideration of two significant reforms to the Canadian system. The first is an

increase of three years in the age of both early and normal entitlement for income security

programs. The second is a shift to a system with a 60% replacement rate at age 65 for all, and an

actuarial adjustment both before and after age 60 of 6% per year (the “common” reform for all

countries).

        The results of these simulations are presented in Tables XX-YY. For the purposes of this

discussion, we focus on the results from Table 8, our richest specification; we will return below

to discussing the differences that emerge from other specifications. We show the results from

each of our models: accrual, peak value, and option value. Since the option value model




38
performs fairly badly, as documented above, we focus on the results from accrual and peak value

models.

          For the first reform, we estimate that there would be a significant reduction in retirement

rates at all ages. The effects rise with age in absolute value, but are similar in percentage terms.

At age 55, there is a 0.5 to 1.2 percentage point effect; this represents a 7 to 16 percent effect (the

smaller estimate is from the accrual model; the larger from the peak value model). The effects

grow with age, and become fairly large between ages 60 and 65, peaking at a 5 (peak) to 8

(accrual) percentage point effect (or 10 to 16 percent). The effects then fall, although they

remain non-trivial even at age 69. Thus, we estimate that this reform would lower retirement by

10 to 16 percent.

          The second reform serves to lower retirement rates at younger ages, and then raise them

at older ages. The key to understanding the impacts of this reform is to recognize that this

common reform would in essence replace the complicated set of IS incentives with an expanded

CPP-like program. This amplifies the impact of actuarial adjustments, since the benefit under

this common plan is so much larger than under the CPP. Thus, the lower retirement rates before

age 60 are due to the fact that the actuarial adjustment under the common reform is fairer than

under the CPP plan, which is further magnified by the fact that these adjustments apply to a 60%

replacement rate. From age 60 to 64, there is little effect of the common reform. This appears to

reflect the canceling of two opposing forces: on the one hand, the actuarial adjustment is

increasingly unfair, and it applies to a larger base of benefits; on the other hand, this reform gets

rid of the excess taxes through the GIS and SPA programs. Then, after age 65, we predict much

larger retirement rates under the common reform, due to the increasing unfairness of the actuarial

adjustment; once again, this has large effects because it applies to such a large benefit. By age




39
69, these effects are enormous; we estimate that retirement rates at that age will be 6.3 to 10

percentage points higher (22 to 42%). Of course, since these effects apply to the small base of

workers still in the labor force at those older ages, there may be only a small cumulative effect

on the size of the labor force.

        The results from the other models, shown in the earlier tables for males, are fairly similar

to those discussed above in age pattern, although the magnitudes differ somewhat. But, overall,

the conclusion is clear: delaying the age of retirement benefit eligibility by three years lowers

retirement rates at all ages; the common reform first lowers, then raises, retirement rates.

        For women, the direction of the results are similar. The three year delay simulation

shows smaller effects in percentage point terms, but similar impacts in percentage terms. The

common reform shows much smaller effects, however, in particular after age 65. This is because

the 6% actuarial adjustment is more actuarially fair for the longer lived females.



                                             PART VIII: Conclusions

        The aging of the Canadian population, coupled with a trend towards earlier retirement,

places financial stress on the Canadian IS system. It is important, therefore, to understand how

this complicated system effects retirement decisions. Other papers have suggested some role for

IS programs, but no previous paper has taken a comprehensive look at how this panoply of

programs impacts retirement in Canada. This paper accomplishes this task, using an excellent

data source matched to a rich simulation model that allows us to assign IS entitlements to our

sample workers. Also, a variety of parameterizations of the incentives for retirement are

considered.




40
         We have two findings of importance. First, for the typical worker, the IS system provides

increasingly strong disincentives to work after age 60. Workers actually see the present

discounted value of their IS entitlement fall from additional work after age 61, and by age 69 the

reduction in IS entitlement amounts to 43 percent of what they would earn in that year. Second,

there is a significant impact of these disincentives on work decisions. Using both one year

forward measures and measures which account for the entire future path of incentives, we

estimate that workers with larger returns to additional work are less likely to leave the labor

force.

         This finding in turn has implications for policy evaluation. Evaluations of changes to the

Canadian IS system cannot be done assuming static retirement decisions; these evaluations must

build in the type of dynamic retirement behavior that we observe. We illlustrate these effects

through two reforms, and show that these changes can have important effects on the retirement

decisions of older Canadian workers.




41
Appendix: Data Descriptions and Sample Definitions



LWF Data

List of Variables from LWF data

Agediff: A variable recording the difference in age between an individual and his/her spouse (in
       years).

AGE55-AGE69: A dummy variable that equals 1 if an individual is the indicated age and 0
     otherwise. Age55 is the excluded variable.

APE: a variable recording an in estimate of an individual’s current Average Pensionable
       Earnings.

Experience: A variable recording the number years since 1975 that an individual has had positive
       T-4 earnings.

Married: A dummy variable that equals 1 if the individual is married and 0 otherwise.

RPP: A variable that ranges between 0 and 1 recording the proportion of workers in an
      individual’s 3-digit industry that is a member of an RPP.

Tenure: A variable recording the number of years since 1978 that an individual has been with the
       current firm.

Tenure Censored: A dummy variable that equals 1 if an individual has been with his/her current
       firm continuously since 1978.

Y85-Y96: a dummy variable that equals 1 in the indicated year and 0 otherwise. Y90 is the
      excluded variable.

S04-S500p: a dummy variable that equals 1 for the indicated size of the workforce at the place of
      work and 0 otherwise. Categories are 0-4,5-19,20-49,50-99,100-199,200-499,500+.
      S5099 is the excluded variable.

IND1-IND10: A dummy variable that equals 1 for the indicated industry of employment and 0
      otherwise. IND1 is the excluded variable. The ten are:
             IND1 – manufacturing (SIC 100 to 399)
             IND2 – construction (SIC 400 to 449)
             IND3 – storage and transportation (SIC 450 to 499)
             IND4 – wholesale trade (SIC 500 to 599)
             IND5 – retail trade (SIC 600 to 699)
             IND6 – finance, insurance, real estate (SIC 700 to 769)



42
               IND7 – business services (SIC 770 to 809)
               IND8 – government services (SIC 810 to 849)
               IND9 – education, health and social services (SIC 850 to 909)
               IND10 – accommodation, food, and other services (SIC 910 to 999)

NF:    A dummy variable that equals 1 if resident of Newfoundland and 0 otherwise.

PEI:   A dummy variable that equals 1 if resident of PEI and 0 otherwise.

NS:    A dummy variable that equals 1 if resident of Nova Scotia and 0 otherwise.

NB:    A dummy variable that equals 1 if resident of New Brunswick and 0 otherwise.

QU:    A dummy variable that equals 1 if resident of Quebec and 0 otherwise.

ON:    A dummy variable that equals 1 if resident of Ontario and 0 otherwise
       (excluded variable).

MB:    A dummy variable that equals 1 if resident of Manitoba and 0 otherwise.

SA:    A dummy variable that equals 1 if resident of Saskatchewan and 0 otherwise.

AB:    A dummy variable that equals 1 if resident of Alberta and 0 otherwise.

BC:    A dummy variable that equals 1 if resident of British Columbia and 0
       otherwise.

TERR: A dummy variable that equals 1 if resident of Yukon or Northwest Territories
      and 0 otherwise.




43
Reconciliation of Sample Sizes from LWF Data



                                   Observations                                Individuals


                           Males                Females               Males                  Females


Base Sample               770989                523322               141182                  103726
from LWF
Missing Earnings           20306                  10165                2563                   1378
Data
Primary                    44158                  23146                6444                   4387
Industries
Already Retired            99196                100203                14244                  20579
at Age 55
Final Sample              607329                389808               117931                  77382




Notes: LWF is the Longitudinal Worker File. The base sample is all individuals aged 55
through 69 in 1985, plus the cohorts of individuals who turn age 55 in years 1986 through 1991.
The deletions for missing earnings data are due to nonsensical earnings records for some
individuals in Quebec in 1992 (e.g., some individuals with earnings of $46 billion). An attempt
was made to replace these records with information from an alternative T4 data set for this year.
This was not successful in all cases, however, which led to the deletion of all observations for
these individuals. The deletions for employment in primary industries are explained in the text.
The sample is conditioned on employment at age 55, so individuals with 0 earnings at this age
are deemed to have already retired and are thus deleted from the data set.


LMAS and SLID Data


        Cross section samples from the 1986-1990 LMAS and the 1993-1996 SLID. In each

year, males or females, 23-69, who are paid workers in jobs in the month of September of the

indicated year. The RPP coverage probabilities are calculated by 3-digit industry. Probabilities

for 1991-1992 are simple linear interpolations of the 1990 and 1993 data.



44
Census Family Files of the Canadian Census


        The data are from the 1986 and 1991 public use microdata files. In each year, males or

females who are 54 and older are selected. Non-labour income is defined as the sum of

“Investment Income of census family or non-family person” plus “Retirement pensions and other

money income of census family or non-family person” (recorded separately as “Retirement

Pensions, Superannuations and Annuities of census family or non-family person” and “Other

Money Income of census family or non-family person” in the 1991 sample). Separating

individuals who work (weeks and earnings greater than 0) and don’t work (weeks and hours

equal to 0), the probability non-labour income is positive and its conditional mean are calculated

for the following cells:

Males who are Employed: region (East; Ontario; West) by industry (Manufacturing;

Construction; Transportation and Communications; Wholesale and Retail Trade; FIRE and

Business Services; Government, Health and Education Services; Accommodation, Food,

Beverage and Other Services) by age(54-55, 56-57, …,60-61, 62-64 65+),

Males Who are Not Employed: region (East; Ontario; West) by marital status (married, spouse’s

age < age-1; married, spouses age = age1+/- 1; married, spouse’s age > age+1; not married) by

age(54-60, 61-63, 64-66, …,73-75, 76+),

Females who are Employed: region (East; Ontario; West) by industry (Manufacturing,

Construction, Transportation and Communications; Wholesale and Retail Trade; FIRE and

Business Services; Government, Health and Education Services; Accommodation, Food,

Beverage and Other Services) by age(54-55, 56-57, …,60-61, 62-64 65+),




45
Females Who are Not Employed: region (East; Ontario; West) by marital status (married,

spouse’s age < age-1; married, spouses age = age1+/- 1; married, spouse’s age > age+1; not

married) by age(54-60, 61-63, 64-66, …,73-75, 76-80, 81+).




46
References



Baker M., (1999), “The Retirement Behavior of Married Couples: Evidence From the Spouse's
      Allowance”, NBER Working Paper No. W7138, May 1999.

Baker M. and D. Benjamin, (1999a), “How do Retirement Tests Affect the Labour Supply of
       Older Men?”, Journal of Public Economics, 71, January, 27-51.

Baker M. and D. Benjamin, (1999b), “Early Retirement Provisions and the Labour Force
       Behavior of Older Men: Some Evidence from Canada”, Journal of Labour Economics,
       17, October, 724-756.

Baker M. and D. Benjamin, (1999c), “Public Pension Programs and Attachment to the Labour
       Force”, in F. St-Hilaire and W.C. Riddell (eds.), Adapting Public Policy to a Labour
       Market in Transition, IRPP, forthcoming.

Baker M. and D. Benjamin, (1999d), “Working Time Over the Life-Cycle: Do Public Pensions
       Matter?”, in S. Houseman and A. Nakamura (eds.), Changes in Working Time in Canada
       and the US, W.E. Upjohn, forthcoming.

Burbidge, J., (1987), Social Security in Canada. Canadian Tax Paper No. 79, Canadian Tax
       Foundation.

CCH Canadian Limited, Canadian Employment Benefits and Pension Guide Reports, North
     York, ON: CCH Canadian Limited, v.1, 1996.

Coile, Courtney, and Jonathan Gruber (1999). “Social Security and Retirement,” mimeo, MIT.

Gruber, Jonathan (1999). “Social Security and Retirement in Canada,” in Social Security and
       Retirement Around the World, J. Gruber and D. Wise, eds. Chicago: University of
       Chicago Press, 1999, 73-100.

Gruber, Jonathan, and Brigitte Madrian (1995). “Health Insurance Availability and the
       Retirement Decision,” American Economic Review, 85, 938-948.

Pesando, J.E. and S.A. Rea, (1977), Public and Private Pensions in Canada: An Economic
      Analysis. Toronto: University of Toronto Press.

Picot, Garnett and Zhengxi Lin, (1997). “Are Canadians More Likely to Lose Their Jobs in the
        1990s?”. Analytical Studies Branch Research Paper No. 96. Ottawa: Statistics Canada.

Statistics Canada, (1983), Historical Statistics of Canada, 2nd edition. Catalogue No. E86-103,
         Ottawa.




47
Statistics Canada, (1984), Life tables, Canada and provinces' 1980-1982. Catalogue No. 84-532,
         Ottawa.

Statistics Canada. (1998). Permanent Layoffs, Quits and Hirings in the Canadian Economy.
         Catalogue No. 71-539-XIB. Ottawa.

Statistics Canada, (1999), Pension Plans in Canada, Catalogue No. 74-401-XPB. Ottawa.




48
Table 1: Labour Market Participation and Program Participation in 1997/98


                                                                       Age
                                          50-54              55-59              60-64              65+
                                                 Males
                                 Labour Market Participation In April 1998
Working Full Time                        0.76               0.60                0.34               0.07
Working Part-Time                        0.04               0.05                0.05               0.04
Not Working                              0.21               0.35                0.60               0.89
                                      Program Participation in 1997
Received OAS/GIS/SPA                     0.00               0.00                0.03               0.97
Benefits
Received CPP/QPP Benefits                  0.05               0.07              0.44               0.92
Received Private Pension/RRSP              0.05               0.15              0.30               0.58
Benefits
Received Employment Insurance              0.10               0.09              0.06               0.01
Benefits
Received Social Assistance                 0.06               0.08              0.12               0.08
Benefits
                                                Females
                                 Labour Market Participation In April 1998
Working Full Time                        0.50               0.33                0.13               0.01
Working Part-Time                        0.14               0.13                0.10               0.02
Not Working                              0.36               0.54                0.77               0.97
                                      Program Participation in 1997
Received OAS/GIS/SPA                     0.00               0.00                0.15               0.97
Benefits
Received CPP/QPP Benefits                  0.06               0.09              0.40               0.74
Received Private Pension/RRSP              0.03               0.10              0.20               0.35
Benefits
Received Employment Insurance              0.07               0.07              0.04               0.00
Benefits
Received Social Assistance                 0.05               0.06              0.09               0.11
Benefits

Notes: Source ~ Individual Files of the 1998 Survey of Consumer Finances (1997 Income Year). The statistics on
labour market participation are for the reference week (April 1998). The statistics for program participation are for
the reference year (1997).




50
                                   Table 2: The Distribution of the One -Year Accrual, Male Sample

                         Median        Median       10th Percentile   90th Percentile   Standard    Median Tax    Median
Age           N
                         ISW ($)          ($)              ($)               ($)        Deviation     Rate 1     Tax Rate 2
     55     57387         107533         1169             547               1736           467        -0.049       -0.042
     56     61167         108702          829               0               1775           655        -0.038        0.005
     57     63818         109531          534               0               1821           729        -0.027        0.036
     58     65091         110065          320               0               1873           775        -0.018        0.037
     59     65541         110385          218               0               1933           807        -0.012        0.038
     60     60051         110603           30            -1259              1620          1103        -0.002        0.077
     61     52539         110633         -249            -1491              1270          1068         0.014        0.085
     62     45898         110384         -648            -1987               853          1108         0.037        0.085
     63     39711         109737        -1053            -2479               505          1217         0.063        0.096
     64     33776         108684        -1397            -2903               209          1335         0.086        0.186
     65     27118         107287        -2931            -4694              -838          1518         0.188        0.367
     66     13932         104356        -3334            -5095             -1252          1514         0.237        0.413
     67      9008         101022        -3718            -5403             -1532          1497         0.298        0.396
     68      6812          97304        -4040            -5749             -1826          1513         0.366        0.327
     69      5480          93265        -4340            -6026             -2131          1523         0.425        0.340



Notes: N=number of observations, ISW=Income Security Wealth. All dollar values in 1998 US dollars. Definitions of the different
measures of Income Security Wealth accrual are provided in the text. The numbers reported are the result of the Income Security
wealth calculation described in the text. Median Tax Rate 1 is calculated from the analysis sample. Median Tax Rate 2 is from Gruber
(1999).




51
                        Table 3: The Distribution of the Peak Value and Option Value Accrual, Male Sample

                                   Peak Value                                                  Option Value
                         th                90th                                              10th
            Median     10 Percentile                    Standard            Median                     90th Percentile   Standard
Age                                     Percentile                                        Percentile
             ($)           ($)                          Deviation            ($)                             ($)         Deviation
                                            ($)                                               ($)
     55       2997             1012        9363            3423              16804           7814           26397         10764
     56       1998              120        8283            3399              14839           7040           23719          9983
     57       1164               0         7061            3082              12965           5980           21106          9484
     58        807               0         5592            2642              11131           4686           18657          8771
     59        577               0         4188            2183               9396           3555           16296          8011
     60         47            -1258        2929            2100               8151           2755           14319          6903
     61       -247            -1491        1766            1798               6993           2108           12324          6790
     62       -647            -1987        1149            1621               5878           1424           10471          6333
     63      -1053            -2479         654            1503               4820            835            8707          5841
     64      -1397            -2902         278            1374               3808            381            6996          5141
     65      -2931            -4694        -838            1563               2698             97            5556          4675
     66      -3334            -5095       -1252            1549               1695          -2186            4538          5142
     67      -3718            -5403       -1532            1520                977          -4177            3400          4886
     68      -4040            -5749       -1826            1529                516          -4865            2270          4427
     69      -4340            -6026       -2131            1523                210          -5257            1128          3151



Notes: N=number of observations. All dollar values in 1998 US dollars. Definitions of the different measures of Income Security
Wealth accrual are provided in the text. The numbers reported are the result of the Income Security wealth calculation described in
the text.




52
                                   Table 4: The Distribution of the One -Year Accrual, Female Sample


                                        Median       Median       10th Percentile   90th Percentile   Standard    Median Tax
               Age           N
                                        ISW ($)         ($)              ($)               ($)        Deviation     Rate 1
                 55        43062         102235         673              116              1426           475        -0.049
                 56        43889         102908         563               79              1408           492        -0.045
                 57        44160         103471         526               20              1445           531        -0.045
                 58        43528         103997         484                0              1483           568        -0.045
                 59        42611         104481         448                0              1510           597        -0.046
                 60        37306         104929         107             -980              1455           933        -0.011
                 61        31320         105036         -30            -1130              1115           895         0.003
                 62        26480         105007        -307            -1460               777           915         0.030
                 63        22364         104700        -614            -1815               560           996         0.061
                 64        18646         104086        -831            -2198               403          1090         0.087
                 65        15072         103255       -2391            -3962              -642          1278         0.241
                 66         8298         100865       -2631            -4364              -797          1365         0.301
                 67         5564          98234       -2825            -4748              -899          1467         0.357
                 68         4196          95409       -3038            -5130             -1157          1533         0.423
                 69         3312          92371       -3321            -5389             -1406          1585         0.481



Notes: N=number of observations, ISW=Income Security Wealth. All dollar values in 1998 US dollars. Definitions of the different
measures of Income Security Wealth accrual are provided in the text. The numbers reported are the result of the Income Security
wealth calculation described in the text. Median Tax Rate 1 is calculated from the analysis sample.




53
                       Table 5: The Distribution of the Peak Value and Option Value Accrual, Female Sample


                                     Peak Value                                                Option Value
                                             90th                                            10th
            Median     10th Percentile                  Standard            Median                     90th Percentile   Standard
Age                                       Percentile                                      Percentile
             ($)             ($)                        Deviation            ($)                             ($)         Deviation
                                              ($)                                             ($)
     55       2684           708             7407          2683              10589           2994           19840          7051
     56       2205           399             6639          2576               9431           3153           17416          6254
     57       1736           182             5771          2345               8253           2859           15323          5484
     58       1235            44             4671          2041               7135           2377           13323          4786
     59        741             0             3562          1785               6038           1836           11498          4257
     60        194          -979             2769          1821               5230           1421           10193          3859
     61        -14         -1130             2019          1586               4531           1149            8910          3613
     62       -303         -1460             1382          1399               3795            828            7624          3262
     63       -612         -1815              944          1284               3118            517            6322          2787
     64       -831         -2198              506          1164               2427            242            5203          2543
     65      -2391         -3962             -642          1363               1626          -1691            3991          2491
     66      -2631         -4364             -795          1451                960          -2309            3057          2248
     67      -2825         -4748             -899          1519                576          -3560            2245          2351
     68      -3038         -5130            -1157          1557                283          -4343            1521          2404
     69      -3321         -5389            -1406          1585                114          -4867             747          2278



Notes: N=number of observations. All dollar values in 1998 US dollars. Definitions of the different measures of Income Security
Wealth accrual are provided in the text. The numbers reported are the result of the Income Security wealth calculation described in
the text.




54
Table 6: Summary Statistics for the Male Sample


                                      Mean               Standard Deviation
Retired                               0.148                    0.355
Probability of RPP                    0.582                    0.256
Married                               0.558                    0.497
Tenure                                8.763                    4.500
Tenure Censored                       0.441                    0.496
Experience                           15.235                    5.162
Spouse’s Experience                   5.144                    6.848
Age                                  59.779                    3.375
Age Difference                        2.067                    3.820
Projected Earnings                   $19503                    29088
Projected Spousal                     $3033                     7732
Earnings
APE                                  $19847                     4525
Spouse’s APE                          $5393                     7996
Observations                         607329
Individuals                          121204


Table 7: Summary Statistics for the Female Sample

                                      Mean               Standard Deviation
Retired                               0.151                    0.358
Probability of RPP                    0.428                    0.262
Married                               0.404                    0.491
Tenure                                8.660                    4.423
Tenure Censored                       0.374                    0.484
Experience                           14.450                    5.551
Spouse’s Experience                   5.279                    7.187
Age                                  59.488                    3.365
Age Difference                       -0.684                    2.718
Projected Earnings                   $11458                     8433
Projected Spousal                     $4050                    12897
Earnings
APE                                  $13871                     6924
Spouse’s APE                          $7500                    10189
Observations                         389808
Individuals                           77845

Notes: The reported statistics are means (averages) calculated over all observations in the male
and female data sets, respectively (rather than over all individuals). All dollar values are in 1998
US dollars. APE is Average Pensionable earnings. Definitions of all variables are provided in
Appendix A.


55
Table 8: Retirement Probits using the One -Year Accrual Incentive Variable- Males Sample

                        1                   2               3                 4
ISW                  -0.008              0.012           0.093            0.025
                     (0.001)           (0.002)         (0.003)          (0.004)
$10000 change         -0.18               0.27            1.97              0.51
ACCRUAL              -1.988             -1.343          -1.183           -0.798
                     (0.012)           (0.022)         (0.023)          (0.028)
$1000 change          -3.88              -2.65           -2.21             -1.52
RPP                                       0.100           0.125           -0.031
                                        (0.012)         (0.013)          (0.002)
MARRIED                                  -0.103          -0.539            0.002
                                        (0.012)         (0.018)         (0.0001)
TENURE                                   -0.053          -0.029            0.026
                                        (0.002)         (0.002)          (0.007)
TENURESQ                                  0.003           0.002           -0.020
                                       (0.0001)        (0.0001)          (0.002)
TENURE CENS                               0.027           0.026            0.000
                                        (0.006)         (0.006)         (0.0001)
EXP                                      -0.029          -0.022           -0.028
                                        (0.002)         (0.002)          (0.003)
EXP SQ                                    0.001           0.000            0.001
                                      (0.00004)        (0.0001)         (0.0001)
SPOUSE EXP                               -0.028          -0.027           -0.031
                                        (0.001)         (0.003)          (0.002)
SPOUSE EXPSQ                              0.001           0.001
                                       (0.0001)        (0.0001)
AGE                                       0.045           0.013
                                        (0.001)         (0.001)
AGEDIFF                                  -0.002           0.003           -0.003
                                        (0.001)         (0.001)          (0.001)
AGE56                                                                     -0.036
                                                                         (0.011)
AGE57                                                                     -0.053
                                                                         (0.011)
AGE58                                                                      0.002
                                                                         (0.012)
AGE59                                                                      0.050
                                                                         (0.012)
AGE60                                                                      0.199
                                                                         (0.012)
AGE61                                                                      0.162
                                                                         (0.014)
AGE62                                                                      0.162
                                                                         (0.015)
AGE63                                                                      0.171
                                                                         (0.016)
AGE64                                                                      0.309
                                                                         (0.017)
AGE65                                                                     -0.036
                                                                         (0.011)
AGE66                                                                     -0.053
                                                                         (0.011)
AGE67                                                                      0.002
                                                                         (0.012)



56
AGE68                                                                                            0.050
                                                                                                (0.012)
AGE69                                                                                            0.199
                                                                                                (0.012)
Pseudo R-squared              0.058             0.076                 0.103                      0.116
                    Estimates Adding Dummy Variables for Early Retirement and Age 65

ISW                         -0.014                 -0.005                 0.045                 0.025
                            (0.001)                (0.002)               (0.004)               (0.004)
$10000 change                -0.30                  -0.11                  0.92                  0.51
ACCRUAL                     -1.487                 -1.061                -0.781                -0.781
                            (0.013)                (0.023)               (0.024)               (0.030)
$1000 change                 -2.96                  -2.12                 -1.49                 -1.49
EARLY*AGE6064                0.168                  0.105                 0.065                 0.019
                            (0.005)                (0.009)               (0.006)               (0.012)
Pseudo R-squared             0.072                  0.087                 0.113                 0.116
INDUSTRY
                              NO                    YES                    YES                   YES
CONTROLS
FIRM SIZE
                              NO                    YES                    YES                   YES
CONTROLS
PROVINCE
                              NO                    YES                    YES                   YES
CONTROLS
EARNINGS
                              NO                     NO                    YES                   YES
CONTROLS
YEAR CONTROLS                 NO                    YES                    YES                   YES

Notes: ISW=Income Security Wealth. Agediff is the difference in ages between the individual and his spouse
(coded 0 for singles). * ~ reported statistic is the percentage point change in the probability of retirement for the
indicated change in ISW or accrual. Other control variables are 11 industry dummies, dummies for 6 categories of
establishment size, province and year effects, a cubic in both own and spouse’s predicted earnings and APE, and a
full set of interactions between these cubics. The estimated parameters on these additional variables are not
reported.




57
Table 9: Retirement Probits using the Peak Value Incentive Variable- Males Sample

                        1                   2               3                4
ISW                  -0.010             -0.008           0.088            0.025
                     (0.001)           (0.002)         (0.004)          (0.004)
$10000 change         -0.21              -0.17            1.86             0.51
ACCRUAL              -1.207             -0.777          -0.626           -0.373
                     (0.008)           (0.014)         (0.017)          (0.018)
$1000 change          -2.41              -1.57           -1.21            -0.73
RPP                                       0.099           0.122            0.122
                                        (0.012)         (0.013)          (0.013)
MARRIED                                   0.007          -0.525           -0191
                                        (0.013)         (0.021)          (0.022)
TENURE                                   -0.055          -0.033           -0.033
                                        (0.002)         (0.002)          (0.002)
TENURESQ                                  0.003           0.002            0.002
                                       (0.0001)        (0.0001)         (0.0001)
TENURE CENS                               0.018           0.027            0.027
                                        (0.006)         (0.006)          (0.007)
EXP                                      -0.029           -0.20           -0.018
                                        (0.002)         (0.002)          (0.002)
EXP SQ                                    0.001           0.000            0.000
                                      (0.00004)        (0.0001)         (0.0001)
SPOUSE EXP                               -0.020          -0.030           -0.029
                                        (0.002)         (0.003)          (0.003)
SPOUSE EXPSQ                              0.001           0.001            0.001
                                       (0.0001)        (0.0001)         (0.0001)
AGE                                       0.059           0.033
                                        (0.001)         (0.001)
Agediff                                  -0.004           0.002          -0.003
                                        (0.001)         (0.001)         (0.001)
AGE56                                                                    -0.033
                                                                        (0.011)
AGE57                                                                    -0.050
                                                                        (0.012)
AGE58                                                                    -0.003
                                                                        (0.012)
AGE59                                                                     0.036
                                                                        (0.012)
AGE60                                                                     0.202
                                                                        (0.013)
AGE61                                                                     0.174
                                                                        (0.014)
AGE62                                                                     0.191
                                                                        (0.015)
AGE63                                                                     0.214
                                                                        (0.016)
AGE64                                                                     0.362
                                                                        (0.017)
AGE65                                                                     1.033
                                                                        (0.019)
AGE66                                                                     0.661
                                                                        (0.021)
AGE67                                                                     0.339
                                                                        (0.023)



58
AGE68                                                                                            0.262
                                                                                                (0.024)
AGE69                                                                                            0.238
                                                                                                (0.026)
Pseudo R-squared             0.055              0.076                 0.101                      0.115
                    Estimates Adding Dummy Variables for Early Retirement and Age 65

ISW                          -0.015                -0.024                 0.038                  0.027
                             (0.001)               (0.002)               (0.004)                (0.004)
$10000 change                 -0.32                 -0.50                  0.78                   0.54
ACCRUAL                      -0.908                -0.692                -0.415                 -0.349
                             (0.009)               (0.013)               (0.018)                (0.018)
$1000 change                  -1.84                 -1.40                 -0.81                  -0.68
EARLY*AGE6064                 0.120                 0.086                 0.055                  0.103
                             (0.006)               (0.005)               (0.006)                (0.011)
Pseudo R-squared              0.073                 0.088                 0.113                  0.115
INDUSTRY
                               NO                    YES                   YES                    YES
CONTROLS
FIRM SIZE
                               NO                    YES                   YES                    YES
CONTROLS
PROVINCE
                               NO                    YES                   YES                    YES
CONTROLS
EARNINGS
                               NO                    NO                    YES                    YES
CONTROLS
YEAR CONTROLS                  NO                    YES                   YES                    YES


Notes: ISW=Income Security Wealth. Agediff is the difference in ages between the individual and his spouse
(coded 0 for singles). * ~ reported statistic is the percentage point change in the probability of retirement for the
indicated change in ISW or accrual. Other control variables are 11 industry dummies, dummies for 6 categories of
establishment size, province and year effects, a cubic in both own and spouse’s predicted earnings and APE, and a
full set of interactions between these cubics. The estimated parameters on these additional variables are not
reported.




59
Table 10: Retirement Probits using the Option Value Incentive Variable- Males Sample

                         1                 2                3                4
ISW                   0.000             0.044            0.052           -0.005
                     (0.001)          (0.002)          (0.004)          (0.004)
$10000 change          0.00              0.91             1.08             -0.10
ACCRUAL              -0.598            -0.483           -0.831           -1.021
                     (0.003)          (0.005)          (0.023)          (0.025)
$1000 change           n.a.               n.a.             n.a.             n.a.
RPP                                      0.130            0.121            0.123
                                       (0.013)          (0.013)          (0.013)
MARRIED                                 -0.268           -0.330           -0.013
                                       (0.012)          (0.021)          (0.023)
TENURE                                  -0.036           -0.029           -0.027
                                       (0.002)          (0.002)          (0.002)
TENURESQ                                 0.002            0.002            0.001
                                      (0.0001)         (0.0001)         (0.0001)
TENURE CENS                              0.042            0.034            0.031
                                       (0.006)          (0.006)          (0.007)
EXP                                     -0.010           -0.015           -0.015
                                       (0.002)          (0.002)          (0.002)
EXP SQ                                   0.000            0.000            0.000
                                      (0.0001)         (0.0001)         (0.0001)
SPOUSE EXP                              -0.025           -0.027           -0.028
                                       (0.002)          (0.003)          (0.003)
SPOUSE EXPSQ                             0.001            0.001            0.001
                                      (0.0001)         (0.0001)         (0.0001)
AGE                                      0.029            0.028
                                       (0.001)          (0.002)
AGEDIFF                                 -0.001            0.001           -0.002
                                       (0.001)          (0.001)          (0.001)
AGE56                                                                     -0.073
                                                                         (0.011)
AGE57                                                                     -0.141
                                                                         (0.013)
AGE58                                                                     -0.149
                                                                         (0.013)
AGE59                                                                      -0165
                                                                         (0.013)
AGE60                                                                     -0.017
                                                                         (0.014)
AGE61                                                                     -0.062
                                                                         (0.015)
AGE62                                                                     -0.063
                                                                         (0.016)
AGE63                                                                     -0.058
                                                                         (0.018)
AGE64                                                                      0.074
                                                                         (0.019)
AGE65                                                                      0.765
                                                                         (0.020)
AGE66                                                                      0.389
                                                                         (0.022)
AGE67                                                                      0.042
                                                                         (0.024)



60
AGE68                                                                                            -0.064
                                                                                                (0.026)
AGE69                                                                                            -0.109
                                                                                                (0.027)
Pseudo R-squared             0.075             0.092                  0.100                       0.118
                    Estimates Adding Dummy Variables for Early Retirement and Age 65

ISW                         -0.007                   0.029                0.005                 -0.004
                            (0.001)                (0.002)               (0.004)                (0.004)
$10000 change                -0.15                   0.59                 0.10                   -0.09
ACCRUAL                     -0.512                  -0.479               -0.903                 -1.014
                            (0.004)                (0.005)               (0.023)                (0.024)
$1000 change                  n.a.                    n.a.                 n.a.                   n.a.
EARLY*AGE6064                0.079                   0.030                0.023                  0.126
                            (0.005)                 (0.005)              (0.006)                (0.011)
Pseudo R-squared             0.094                   0.105                0.114                  0.118
INDUSTRY
                              NO                     NO                    YES                   YES
CONTROLS
FIRM SIZE
                              NO                     NO                    YES                   YES
CONTROLS
PROVINCE
                              NO                     NO                    YES                   YES
CONTROLS
EARNINGS
                              NO                     NO                    NO                     NO
CONTROLS
YEAR CONTROLS                 NO                     NO                    YES                   YES

Notes: ISW=Income Security Wealth. Agediff is the difference in ages between the individual and his spouse
(coded 0 for singles). * ~ reported statistic is the percentage point change in the probability of retirement for the
indicated change in ISW or accrual. Other control variables are 11 industry dummies, dummies for 6 categories of
establishment size, province and year effects, a cubic in both own and spouse’s predicted earnings and APE, and a
full set of interactions between these cubics. The estimated parameters on these additional variables are not
reported.




61
Table 11: Retirement Probits using the One -Year Accrual Incentive Variable- Female
Sample

                         1                  2                3                4
ISW                   -0.004             0.002            0.091            0.022
                      (0.001)          (0.002)          (0.005)          (0.005)
$10000 change          -0.10              0.05             1.96             0.45
ACCRUAL               -2.301            -2.076           -1.074           -0.653
                      (0.018)          (0.030)          (0.033)          (0.040)
$1000 change           -4.52             -4.07            -2.06            -1.28
RPP                                       0.150            0.164            0.161
                                        (0.016)          (0.016)          (0.017)
MARRIED                                  -0.016           -0.254           -0.079
                                        (0.016)          (0.020)          (0.021)
TENURE                                   -0.057           -0.009           -0.008
                                        (0.002)          (0.002)          (0.002)
TENURESQ                                  0.003            0.001            0.001
                                       (0.0001)         (0.0001)         (0.0001)
TENURE CENS                              -0.015           -0.038           -0.037
                                        (0.008)          (0.008)          (0.008)
EXP                                      -0.023           -0.038           -0.038
                                        (0.002)          (0.002)          (0.002)
EXP SQ                                    0.001            0.001            0.001
                                      (0.00004)        (0.00004)        (0.00004)
SPOUSE EXP                               -0.007           -0.010           -0.010
                                        (0.003)          (0.007)          (0.007)
SPOUSE EXPSQ                              0.000            0.000            0.000
                                       (0.0001)         (0.0002)         (0.0002)
AGE                                       0.021            0.010
                                        (0.001)          (0.002)
AGEDIFF                                   0.004            0.015           0.004
                                        (0.001)          (0.001)         (0.001)
AGE56                                                                     -0.010
                                                                         (0.013)
AGE57                                                                     -0.010
                                                                         (0.013)
AGE58                                                                      0.007
                                                                         (0.013)
AGE59                                                                      0.063
                                                                         (0.014)
AGE60                                                                      0.227
                                                                         (0.015)
AGE61                                                                      0.146
                                                                         (0.016)
AGE62                                                                      0.159
                                                                         (0.018)
AGE63                                                                      0.169
                                                                         (0.019)
AGE64                                                                      0.250
                                                                         (0.020)
AGE65                                                                      0.844
                                                                         (0.023)
AGE66                                                                      0.456
                                                                         (0.025)
AGE67                                                                      0.169



62
                                                                                                (0.028)
AGE68                                                                                            0.053
                                                                                                (0.030)
AGE69                                                                                            0.046
                                                                                                (0.032)
Pseudo R-squared             0.050             0.060                  0.107                      0.117
                    Estimates Adding Dummy Variables for Early Retirement and Age 65

ISW                         -0.006                 -0.009                 0.041                  0.023
                            (0.001)                (0.002)               (0.005)                (0.004)
$10000 change                -0.14                  -0.20                  0.85                   0.47
ACCRUAL                     -1.862                 -1.887                -0.649                 -0.626
                            (0.020)                (0.031)               (0.035)                (0.042)
$1000 change                 -3.74                  -3.73                 -1.27                  -1.22
EARLY*AGE6064                0.125                  0.126                 0.078                  0.029
                            (0.006)                (0.007)               (0.007)                (0.015)
Pseudo R-squared             0.057                  0.066                 0.115                  0.117
INDUSTRY
                              NO                     NO                    YES                   YES
CONTROLS
FIRM SIZE
                              NO                     NO                    YES                   YES
CONTROLS
PROVINCE
                              NO                     NO                    YES                   YES
CONTROLS
EARNINGS
                              NO                     NO                    NO                     NO
CONTROLS
YEAR CONTROLS                 NO                     NO                    YES                   YES

Notes: ISW=Income Security Wealth. Agediff is the difference in ages between the individual and his spouse
(coded 0 for singles). * ~ reported statistic is the percentage point change in the probability of retirement for the
indicated change in ISW or accrual. Other control variables are 11 industry dummies, dummies for 6 categories of
establishment size, province and year effects, a cubic in both own and spouse’s predicted earnings and APE, and a
full set of interactions between these cubics. The estimated parameters on these additional variables are not
reported.




63
Table 12: Retirement Probits using the Peak Value Incentive Variable- Female Sample

                        1                   2                3               4
ISW                  -0.004             -0.013            0.090           0.029
                     (0.001)           (0.002)          (0.005)         (0.005)
$10000 change         -0.09              -0.28             1.94            0.60
ACCRUAL              -1.349             -1.262           -0.345          -0.083
                     (0.011)           (0.018)          (0.022)         (0.023)
$1000 change          -2.74              -2.55            -0.69           -0.17
RPP                                       0.161            0.159           0.158
                                        (0.016)          (0.016)         (0.017)
MARRIED                                   0.040           -0.271          -0.112
                                        (0.016)          (0.020)         (0.021)
TENURE                                   -0.059           -0.012          -0.008
                                        (0.002)          (0.002)         (0.002)
TENURESQ                                  0.003            0.001           0.001
                                       (0.0001)         (0.0001)        (0.0001)
TENURE CENS                              -0.021           -0.032          -0.032
                                        (0.008)          (0.008)         (0.008)
EXP                                      -0.027           -0.039          -0.038
                                        (0.002)          (0.002)         (0.002)
EXP SQ                                    0.001            0.001           0.001
                                      (0.00004)        (0.00004)       (0.00004)
SPOUSE EXP                                0.005           -0.008          -0.009
                                        (0.003)          (0.007)         (0.007)
SPOUSE EXPSQ                              0.000            0.000           0.000
                                       (0.0001)         (0.0002)        (0.0002)
AGE                                       0.027            0.030
                                        (0.001)          (0.002)
AGEDIFF                                   0.003            0.010          0.003
                                        (0.001)          (0.001)        (0.001)
AGE56                                                                    -0.010
                                                                        (0.013)
AGE57                                                                    -0.013
                                                                        (0.013)
AGE58                                                                    -0.002
                                                                        (0.014)
AGE59                                                                     0.047
                                                                        (0.014)
AGE60                                                                     0.232
                                                                        (0.015)
AGE61                                                                     0.155
                                                                        (0.017)
AGE62                                                                     0.182
                                                                        (0.018)
AGE63                                                                     0.203
                                                                        (0.019)
AGE64                                                                     0.293
                                                                        (0.021)
AGE65                                                                     0.971
                                                                        (0.022)
AGE66                                                                     0.599
                                                                        (0.024)
AGE67                                                                     0.325
                                                                        (0.027)



64
AGE68                                                                                            0.223
                                                                                                (0.029)
AGE69                                                                                            0.233
                                                                                                (0.031)
  Pseudo R-squared         0.050             0.061                  0.104                        0.116
                  Estimates Adding Dummy Variables for Early Retirement and Age 65

ISW                         -0.006                 -0.022                  0.037                 0.030
                            (0.001)                (0.002)               (0.005)                (0.005)
$10000 change                -0.13                  -0.48                   0.78                  0.62
ACCRUAL                     -1.117                 -1.167                 -0.140                -0.058
                            (0.012)                (0.018)               (0.023)                (0.023)
$1000 change                 -2.31                  -2.37                  -0.28                 -0.12
EARLY*AGE6064                0.050                  0.077                  0.064                 0.101
                            (0.006)                (0.006)                (0.007)               (0.014)
Pseudo R-squared             0.059                  0.068                  0.114                 0.116
INDUSTRY
                              NO                     NO                    YES                   YES
CONTROLS
FIRM SIZE
                              NO                     NO                    YES                   YES
CONTROLS
PROVINCE
                              NO                     NO                    YES                   YES
CONTROLS
EARNINGS
                              NO                     NO                    NO                     NO
CONTROLS
YEAR CONTROLS                 NO                     NO                    YES                   YES

Notes: ISW=Income Security Wealth. Agediff is the difference in ages between the individual and his spouse
(coded 0 for singles). * ~ reported statistic is the percentage point change in the probability of retirement for the
indicated change in ISW or accrual. Other control variables are 11 industry dummies, dummies for 6 categories of
establishment size, province and year effects, a cubic in both own and spouse’s predicted earnings and APE, and a
full set of interactions between these cubics. The estimated parameters on these additional variables are not
reported.




65
Table 13: Retirement Probits using the Option Value Incentive Variable- Female Sample

                          1                 2                3                4
ISW                    0.012             0.060            0.082            0.021
                      (0.001)          (0.002)          (0.005)          (0.006)
$10000 change           0.25              1.28             1.75             0.43
ACCRUAL               -0.852            -0.886            0.106            0.019
                      (0.006)          (0.009)          (0.040)          (0.041)
$1000 change            n.a.               n.a.             n.a.             n.a.
RPP                                       0.202            0.157            0.159
                                        (0.016)          (0.016)          (0.017)
MARRIED                                  -0.118           -0.259           -0.085
                                        (0.016)          (0.021)          (0.022)
TENURE                                   -0.036           -0.011           -0.007
                                        (0.002)          (0.002)          (0.002)
TENURESQ                                  0.002            0.001            0.001
                                       (0.0001)         (0.0001)         (0.0001)
TENURE CENS                               0.018           -0.029           -0.031
                                        (0.008)          (0.008)          (0.008)
EXP                                      -0.013           -0.038           -0.037
                                        (0.002)          (0.002)          (0.002)
EXP SQ                                    0.000            0.001            0.001
                                      (0.00004)        (0.00004)        (0.00004)
SPOUSE EXP                               -0.015           -0.009           -0.009
                                        (0.003)          (0.007)          (0.007)
SPOUSE EXPSQ                              0.000            0.000            0.000
                                       (0.0001)         (0.0002)         (0.0002)
AGE                                      -0.005            0.039
                                        (0.001)          (0.002)
AGEDIFF                                   0.019            0.008           0.001
                                        (0.001)          (0.001)         (0.001)
AGE56                                                                     -0.013
                                                                         (0.013)
AGE57                                                                     -0.019
                                                                         (0.013)
AGE58                                                                     -0.011
                                                                         (0.014)
AGE59                                                                      0.037
                                                                         (0.015)
AGE60                                                                      0.226
                                                                         (0.016)
AGE61                                                                      0.148
                                                                         (0.017)
AGE62                                                                      0.173
                                                                         (0.018)
AGE63                                                                      0.193
                                                                         (0.020)
AGE64                                                                      0.280
                                                                         (0.021)
AGE65                                                                      0.962
                                                                         (0.022)
AGE66                                                                      0.587
                                                                         (0.024)
AGE67                                                                      0.310
                                                                         (0.027)



66
AGE68                                                                                            0.206
                                                                                                (0.029)
AGE69                                                                                            0.212
                                                                                                (0.031)
Pseudo R-squared              0.072            0.081                  0.104                      0.116
                    Estimates Adding Dummy Variables for Early Retirement and Age 65

ISW                           0.008                 0.049                 0.028                  0.022
                             (0.001)               (0.002)               (0.005)                (0.006)
$10000 change                  0.17                  1.06                  0.57                   0.45
ACCRUAL                      -0.769                -0.875                 0.059                  0.021
                             (0.006)               (0.009)               (0.040)                (0.041)
$1000 change                   n.a.                  n.a.                  n.a.                   n.a.
EARLY*AGE6064                 0.030                 0.035                 0.070                  0.117
                             (0.006)               (0.007)               (0.007)                (0.014)
Pseudo R-squared              0.083                 0.090                 0.114                  0.116
INDUSTRY
                               NO                    NO                    YES                   YES
CONTROLS
FIRM SIZE
                               NO                    NO                    YES                   YES
CONTROLS
PROVINCE
                               NO                    NO                    YES                   YES
CONTROLS
EARNINGS
                               NO                    NO                    NO                     NO
CONTROLS
YEAR CONTROLS                  NO                    NO                    YES                   YES

Notes: ISW=Income Security Wealth. Agediff is the difference in ages between the individual and his spouse
(coded 0 for singles). * ~ reported statistic is the percentage point change in the probability of retirement for the
indicated change in ISW or accrual. Other control variables are 11 industry dummies, dummies for 6 categories of
establishment size, province and year effects, a cubic in both own and spouse’s predicted earnings and APE, and a
full set of interactions between these cubics. The estimated parameters on these additional variables are not
reported.




67
Table S1: Model 1 Simulation Results – Male Sample

                  Accrual Model                Peak Value Model              Option Value Model
Age    Baseline      3 Year   Common    Baseline    3 Year   Common    Baseline    3 Year   Common
 55     0.092         0.103     0.046    0.080      0.061      0.041    0.072       0.058    0.076
 56     0.103         0.100     0.072    0.098      0.070      0.067    0.085       0.068    0.090
 57     0.108         0.097     0.087    0.110      0.081      0.084    0.099       0.079    0.107
 58     0.109         0.101     0.093    0.119      0.097      0.095    0.116       0.093    0.126
 59     0.109         0.110     0.096    0.128      0.112      0.100    0.135       0.109    0.147
 60     0.132         0.114     0.100    0.149      0.121      0.112    0.151       0.126    0.164
 61     0.144         0.114     0.119    0.160      0.129      0.131    0.168       0.145    0.181
 62     0.163         0.114     0.151    0.174      0.136      0.155    0.185       0.164    0.198
 63     0.182         0.142     0.186    0.186      0.158      0.178    0.201       0.182    0.214
 64     0.199         0.158     0.227    0.198      0.171      0.202    0.219       0.199    0.231
 65     0.297         0.179     0.273    0.256      0.187      0.232    0.238       0.219    0.254
 66     0.321         0.198     0.351    0.270      0.199      0.281    0.255       0.238    0.282
 67     0.345         0.217     0.446    0.284      0.211      0.342    0.278       0.260    0.325
 68     0.371         0.300     0.532    0.299      0.260      0.399    0.298       0.281    0.365
 69     0.392         0.330     0.585    0.312      0.278      0.438    0.311       0.295    0.393




Table S2: Model 2 Simulation Results – Male Sample

                  Accrual Model                Peak Value Model              Option Value Model
Age    Baseline      3 Year   Common    Baseline    3 Year   Common    Baseline    3 Year   Common
 55     0.088         0.098     0.051    0.079      0.067      0.044    0.069       0.059    0.072
 56     0.095         0.096     0.069    0.091      0.073      0.064    0.080       0.067    0.083
 57     0.098         0.093     0.080    0.100      0.082      0.077    0.091       0.077    0.096
 58     0.098         0.095     0.084    0.107      0.093      0.086    0.105       0.088    0.110
 59     0.098         0.102     0.085    0.113      0.104      0.089    0.119       0.101    0.126
 60     0.143         0.133     0.112    0.150      0.132      0.117    0.147       0.128    0.155
 61     0.153         0.132     0.127    0.158      0.138      0.131    0.160       0.145    0.168
 62     0.167         0.131     0.152    0.168      0.143      0.149    0.173       0.161    0.181
 63     0.179         0.153     0.177    0.176      0.160      0.165    0.186       0.175    0.193
 64     0.192         0.165     0.207    0.184      0.169      0.182    0.200       0.188    0.207
 65     0.494         0.389     0.444    0.494      0.431      0.450    0.495       0.479    0.505
 66     0.233         0.157     0.252    0.205      0.162      0.207    0.210       0.200    0.227
 67     0.250         0.169     0.322    0.215      0.170      0.248    0.229       0.217    0.261
 68     0.267         0.222     0.389    0.225      0.201      0.288    0.245       0.233    0.293
 69     0.282         0.243     0.433    0.234      0.214      0.316    0.256       0.245    0.316




68
Table S3: Model 3 Simulation Results – Male Sample

                  Accrual Model                Peak Value Model              Option Value Model
Age    Baseline      3 Year   Common    Baseline    3 Year   Common    Baseline    3 Year   Common
 55     0.066         0.067     0.042    0.058      0.049      0.034    0.054       0.038    0.062
 56     0.080         0.073     0.065    0.073      0.060      0.054    0.067       0.047    0.080
 57     0.092         0.080     0.083    0.088      0.073      0.071    0.083       0.058    0.100
 58     0.100         0.089     0.094    0.102      0.089      0.086    0.101       0.071    0.124
 59     0.109         0.102     0.104    0.118      0.107      0.097    0.122       0.087    0.151
 60     0.132         0.114     0.110    0.142      0.124      0.113    0.145       0.107    0.178
 61     0.153         0.125     0.135    0.163      0.142      0.138    0.171       0.130    0.205
 62     0.179         0.135     0.171    0.187      0.161      0.168    0.196       0.155    0.234
 63     0.204         0.165     0.209    0.211      0.191      0.199    0.223       0.180    0.261
 64     0.230         0.189     0.254    0.236      0.217      0.230    0.252       0.207    0.291
 65     0.316         0.218     0.300    0.294      0.244      0.267    0.283       0.236    0.325
 66     0.341         0.242     0.370    0.318      0.267      0.317    0.298       0.259    0.354
 67     0.371         0.269     0.454    0.346      0.294      0.379    0.320       0.286    0.394
 68     0.401         0.346     0.529    0.376      0.348      0.438    0.342       0.315    0.432
 69     0.430         0.383     0.583    0.407      0.383      0.486    0.358       0.335    0.461




Table S4: Model 4 Simulation Results – Male Sample

                  Accrual Model                Peak Value Model              Option Value Model
Age    Baseline      3 Year   Common    Baseline    3 Year   Common    Baseline    3 Year   Common
 55     0.069         0.074     0.047    0.063      0.058      0.037    0.060       0.045    0.066
 56     0.080         0.079     0.064    0.076      0.068      0.054    0.072       0.053    0.081
 57     0.089         0.085     0.077    0.087      0.079      0.067    0.084       0.063    0.098
 58     0.095         0.092     0.085    0.098      0.092      0.078    0.100       0.075    0.116
 59     0.101         0.102     0.092    0.109      0.106      0.086    0.117       0.088    0.137
 60     0.137         0.129     0.113    0.142      0.135      0.110    0.140       0.109    0.163
 61     0.153         0.138     0.132    0.159      0.149      0.130    0.159       0.128    0.184
 62     0.173         0.146     0.159    0.176      0.163      0.152    0.179       0.147    0.205
 63     0.192         0.170     0.187    0.193      0.186      0.174    0.197       0.166    0.224
 64     0.211         0.189     0.221    0.210      0.205      0.197    0.218       0.186    0.245
 65     0.494         0.415     0.458    0.494      0.456      0.449    0.495       0.450    0.528
 66     0.266         0.203     0.277    0.251      0.219      0.240    0.244       0.216    0.284
 67     0.290         0.223     0.342    0.273      0.237      0.287    0.260       0.235    0.318
 68     0.314         0.278     0.404    0.296      0.278      0.335    0.276       0.255    0.350
 69     0.339         0.307     0.451    0.321      0.306      0.376    0.287       0.269    0.373




69
Table S5: Model 5 Simulation Results – Male Sample

                  Accrual Model                Peak Value Model              Option Value Model
Age    Baseline      3 Year   Common    Baseline    3 Year   Common    Baseline    3 Year   Common
 55     0.064         0.048     0.056    0.059      0.037      0.052    0.052       0.031    0.066
 56     0.077         0.052     0.083    0.073      0.044      0.078    0.066       0.039    0.086
 57     0.089         0.057     0.107    0.086      0.052      0.099    0.082       0.048    0.109
 58     0.098         0.065     0.124    0.099      0.062      0.119    0.101       0.060    0.136
 59     0.109         0.076     0.139    0.114      0.075      0.136    0.123       0.075    0.165
 60     0.134         0.087     0.151    0.139      0.089      0.158    0.146       0.093    0.192
 61     0.159         0.100     0.185    0.166      0.107      0.195    0.173       0.117    0.223
 62     0.187         0.110     0.228    0.192      0.125      0.233    0.199       0.143    0.252
 63     0.213         0.137     0.270    0.219      0.152      0.269    0.225       0.167    0.278
 64     0.241         0.160     0.316    0.248      0.177      0.306    0.254       0.193    0.307
 65     0.319         0.187     0.361    0.302      0.205      0.346    0.284       0.222    0.341
 66     0.332         0.208     0.421    0.317      0.229      0.391    0.296       0.243    0.373
 67     0.352         0.237     0.490    0.337      0.260      0.441    0.317       0.269    0.423
 68     0.372         0.303     0.547    0.358      0.311      0.485    0.338       0.300    0.470
 69     0.377         0.320     0.575    0.366      0.327      0.507    0.347       0.314    0.499




Table S6: Model 6 Simulation Results – Male Sample

                  Accrual Model                Peak Value Model              Option Value Model
Age    Baseline      3 Year   Common    Baseline    3 Year   Common    Baseline    3 Year   Common
 55     0.066         0.058     0.057    0.063      0.050      0.052    0.058       0.040    0.065
 56     0.078         0.064     0.076    0.075      0.058      0.070    0.071       0.049    0.081
 57     0.087         0.070     0.092    0.086      0.067      0.085    0.084       0.058    0.098
 58     0.096         0.078     0.104    0.097      0.077      0.100    0.100       0.069    0.117
 59     0.105         0.088     0.115    0.109      0.089      0.113    0.118       0.083    0.138
 60     0.135         0.109     0.137    0.138      0.111      0.139    0.141       0.104    0.163
 61     0.156         0.122     0.162    0.159      0.128      0.165    0.161       0.126    0.184
 62     0.177         0.132     0.191    0.178      0.143      0.191    0.180       0.148    0.203
 63     0.196         0.154     0.219    0.197      0.164      0.214    0.197       0.166    0.219
 64     0.216         0.173     0.252    0.218      0.184      0.240    0.216       0.185    0.238
 65     0.496         0.400     0.502    0.496      0.431      0.506    0.495       0.453    0.522
 66     0.264         0.196     0.308    0.254      0.210      0.284    0.242       0.215    0.286
 67     0.283         0.218     0.360    0.273      0.233      0.322    0.262       0.233    0.336
 68     0.302         0.263     0.407    0.292      0.268      0.357    0.282       0.255    0.384
 69     0.310         0.278     0.432    0.301      0.281      0.376    0.291       0.267    0.414




70
Table S7: Model 7 Simulation Results – Male Sample

                  Accrual Model                Peak Value Model              Option Value Model
Age    Baseline      3 Year   Common    Baseline    3 Year   Common    Baseline    3 Year   Common
 55     0.073         0.068     0.060    0.073      0.061      0.059    0.073       0.052    0.081
 56     0.076         0.068     0.071    0.077      0.063      0.069    0.077       0.053    0.087
 57     0.080         0.068     0.079    0.080      0.065      0.076    0.080       0.054    0.092
 58     0.092         0.080     0.093    0.092      0.077      0.091    0.092       0.063    0.106
 59     0.104         0.094     0.106    0.104      0.089      0.104    0.103       0.072    0.121
 60     0.148         0.128     0.140    0.148      0.126      0.145    0.148       0.109    0.169
 61     0.154         0.129     0.151    0.155      0.131      0.155    0.154       0.121    0.174
 62     0.168         0.134     0.171    0.168      0.142      0.173    0.168       0.139    0.187
 63     0.182         0.151     0.193    0.182      0.158      0.191    0.181       0.154    0.200
 64     0.232         0.198     0.256    0.232      0.206      0.246    0.232       0.202    0.251
 65     0.496         0.415     0.489    0.496      0.445      0.498    0.495       0.457    0.518
 66     0.359         0.290     0.388    0.359      0.318      0.381    0.360       0.331    0.403
 67     0.260         0.205     0.322    0.260      0.229      0.296    0.261       0.232    0.337
 68     0.245         0.214     0.332    0.244      0.227      0.292    0.245       0.218    0.350
 69     0.236         0.211     0.338    0.236      0.222      0.291    0.236       0.213    0.364




Table S8: Model 8 Simulation Results – Male Sample

                  Accrual Model                Peak Value Model              Option Value Model
Age    Baseline      3 Year   Common    Baseline    3 Year   Common    Baseline    3 Year   Common
 55     0.073         0.068     0.060    0.073      0.061      0.060    0.073       0.051    0.082
 56     0.076         0.068     0.071    0.077      0.063      0.070    0.077       0.053    0.088
 57     0.080         0.068     0.079    0.080      0.065      0.077    0.080       0.054    0.092
 58     0.092         0.080     0.093    0.092      0.077      0.092    0.092       0.063    0.107
 59     0.104         0.094     0.106    0.104      0.089      0.105    0.103       0.071    0.121
 60     0.148         0.128     0.140    0.148      0.126      0.146    0.148       0.110    0.169
 61     0.155         0.129     0.151    0.155      0.131      0.157    0.154       0.121    0.174
 62     0.168         0.134     0.171    0.168      0.142      0.175    0.168       0.139    0.188
 63     0.182         0.151     0.193    0.182      0.158      0.192    0.181       0.154    0.200
 64     0.232         0.198     0.256    0.232      0.206      0.247    0.232       0.202    0.252
 65     0.496         0.416     0.489    0.496      0.446      0.500    0.495       0.456    0.518
 66     0.359         0.291     0.388    0.359      0.318      0.381    0.360       0.330    0.403
 67     0.260         0.206     0.321    0.260      0.230      0.296    0.261       0.232    0.337
 68     0.245         0.215     0.331    0.244      0.227      0.291    0.245       0.218    0.349
 69     0.236         0.212     0.336    0.236      0.222      0.289    0.236       0.213    0.363




71
Table S9: Model 1 Simulation Results – Female Sample

                  Accrual Model                Peak Value Model              Option Value Model
Age    Baseline      3 Year   Common    Baseline    3 Year   Common    Baseline    3 Year   Common
 55     0.110         0.119     0.059    0.092      0.084      0.030    0.086       0.064    0.079
 56     0.113         0.116     0.068    0.101      0.087      0.036    0.095       0.069    0.088
 57     0.114         0.113     0.078    0.112      0.094      0.046    0.109       0.080    0.102
 58     0.115         0.113     0.083    0.123      0.104      0.057    0.124       0.092    0.119
 59     0.115         0.118     0.086    0.135      0.115      0.062    0.141       0.108    0.137
 60     0.138         0.119     0.074    0.155      0.124      0.069    0.156       0.123    0.152
 61     0.147         0.120     0.089    0.166      0.133      0.090    0.171       0.139    0.168
 62     0.164         0.120     0.111    0.179      0.142      0.113    0.186       0.158    0.184
 63     0.180         0.145     0.138    0.192      0.163      0.135    0.202       0.173    0.199
 64     0.196         0.159     0.170    0.204      0.177      0.155    0.218       0.190    0.216
 65     0.306         0.178     0.190    0.268      0.191      0.178    0.243       0.209    0.238
 66     0.330         0.196     0.263    0.281      0.204      0.228    0.260       0.230    0.273
 67     0.343         0.214     0.339    0.289      0.215      0.280    0.280       0.252    0.309
 68     0.367         0.311     0.429    0.303      0.272      0.344    0.303       0.282    0.359
 69     0.384         0.333     0.467    0.313      0.284      0.372    0.311       0.292    0.385




Table S10: Model 2 Simulation Results – Female Sample

                  Accrual Model                Peak Value Model              Option Value Model
Age    Baseline      3 Year   Common    Baseline    3 Year   Common    Baseline    3 Year   Common
 55     0.104         0.112     0.061    0.091      0.085      0.032    0.083       0.063    0.077
 56     0.106         0.109     0.069    0.099      0.088      0.038    0.091       0.068    0.085
 57     0.107         0.107     0.076    0.108      0.094      0.048    0.103       0.078    0.097
 58     0.107         0.107     0.080    0.117      0.102      0.057    0.117       0.089    0.112
 59     0.108         0.111     0.083    0.126      0.111      0.063    0.132       0.103    0.128
 60     0.149         0.134     0.088    0.153      0.127      0.074    0.151       0.122    0.146
 61     0.156         0.134     0.101    0.161      0.135      0.093    0.163       0.136    0.160
 62     0.169         0.134     0.121    0.172      0.143      0.113    0.177       0.153    0.174
 63     0.183         0.155     0.144    0.182      0.160      0.131    0.190       0.167    0.187
 64     0.196         0.166     0.170    0.192      0.171      0.148    0.205       0.181    0.202
 65     0.453         0.328     0.307    0.453      0.373      0.331    0.451       0.413    0.443
 66     0.266         0.169     0.217    0.240      0.181      0.196    0.234       0.209    0.244
 67     0.277         0.182     0.279    0.246      0.190      0.237    0.251       0.228    0.276
 68     0.296         0.254     0.357    0.257      0.233      0.290    0.271       0.253    0.320
 69     0.309         0.270     0.389    0.265      0.243      0.312    0.278       0.262    0.342




72
Table S11: Model 3 Simulation Results – Female Sample

                  Accrual Model                Peak Value Model              Option Value Model
Age    Baseline      3 Year   Common    Baseline    3 Year   Common    Baseline    3 Year   Common
 55     0.097         0.102     0.056    0.084      0.082      0.031    0.079       0.050    0.074
 56     0.102         0.102     0.065    0.093      0.084      0.034    0.087       0.053    0.086
 57     0.107         0.104     0.077    0.103      0.091      0.044    0.100       0.061    0.104
 58     0.111         0.108     0.084    0.115      0.102      0.054    0.117       0.072    0.126
 59     0.115         0.115     0.089    0.128      0.114      0.060    0.136       0.086    0.148
 60     0.138         0.120     0.076    0.151      0.126      0.067    0.155       0.102    0.167
 61     0.150         0.124     0.092    0.166      0.139      0.088    0.174       0.121    0.190
 62     0.170         0.128     0.116    0.184      0.153      0.113    0.195       0.142    0.213
 63     0.190         0.154     0.146    0.201      0.178      0.137    0.217       0.162    0.234
 64     0.210         0.172     0.180    0.219      0.197      0.161    0.239       0.182    0.257
 65     0.317         0.194     0.202    0.288      0.217      0.188    0.269       0.205    0.285
 66     0.345         0.217     0.277    0.309      0.236      0.244    0.279       0.226    0.318
 67     0.367         0.243     0.359    0.327      0.256      0.304    0.294       0.250    0.354
 68     0.392         0.339     0.450    0.347      0.318      0.374    0.307       0.278    0.397
 69     0.415         0.367     0.491    0.367      0.341      0.410    0.308       0.282    0.419




Table S12: Model 4 Simulation Results – Female Sample

                  Accrual Model                Peak Value Model              Option Value Model
Age    Baseline      3 Year   Common    Baseline    3 Year   Common    Baseline    3 Year   Common
 55     0.099         0.108     0.061    0.088      0.089      0.034    0.084       0.055    0.078
 56     0.102         0.106     0.067    0.094      0.090      0.036    0.090       0.057    0.088
 57     0.104         0.106     0.074    0.102      0.094      0.043    0.101       0.064    0.102
 58     0.105         0.107     0.078    0.111      0.102      0.052    0.115       0.073    0.120
 59     0.106         0.110     0.081    0.120      0.111      0.057    0.130       0.085    0.138
 60     0.147         0.135     0.085    0.153      0.134      0.070    0.152       0.103    0.160
 61     0.156         0.136     0.098    0.164      0.143      0.088    0.166       0.119    0.177
 62     0.171         0.137     0.118    0.176      0.153      0.109    0.181       0.135    0.194
 63     0.186         0.159     0.143    0.189      0.173      0.128    0.197       0.150    0.210
 64     0.201         0.173     0.171    0.201      0.187      0.147    0.213       0.165    0.226
 65     0.451         0.327     0.302    0.452      0.379      0.317    0.450       0.379    0.457
 66     0.280         0.179     0.223    0.255      0.197      0.197    0.234       0.190    0.267
 67     0.297         0.198     0.292    0.268      0.211      0.246    0.244       0.207    0.296
 68     0.317         0.274     0.374    0.283      0.260      0.304    0.252       0.227    0.335
 69     0.336         0.296     0.411    0.298      0.277      0.333    0.250       0.227    0.351




73
Table S13: Model 5 Simulation Results – Female Sample

                  Accrual Model                Peak Value Model              Option Value Model
Age    Baseline      3 Year   Common    Baseline    3 Year   Common    Baseline    3 Year   Common
 55     0.093         0.071     0.078    0.088      0.065      0.070    0.086       0.069    0.089
 56     0.094         0.069     0.088    0.090      0.064      0.078    0.088       0.069    0.098
 57     0.101         0.073     0.104    0.099      0.069      0.093    0.099       0.077    0.113
 58     0.112         0.081     0.121    0.113      0.080      0.112    0.114       0.090    0.133
 59     0.122         0.090     0.133    0.128      0.091      0.128    0.130       0.103    0.151
 60     0.144         0.100     0.128    0.148      0.105      0.143    0.148       0.118    0.169
 61     0.165         0.114     0.154    0.172      0.124      0.174    0.173       0.139    0.199
 62     0.187         0.126     0.183    0.194      0.142      0.203    0.196       0.159    0.224
 63     0.206         0.146     0.212    0.214      0.162      0.227    0.217       0.178    0.247
 64     0.231         0.167     0.244    0.240      0.186      0.255    0.244       0.203    0.273
 65     0.291         0.185     0.265    0.272      0.204      0.280    0.264       0.222    0.296
 66     0.310         0.213     0.324    0.292      0.234      0.321    0.286       0.254    0.324
 67     0.328         0.243     0.378    0.311      0.266      0.359    0.308       0.287    0.350
 68     0.351         0.310     0.440    0.335      0.312      0.401    0.332       0.321    0.377
 69     0.343         0.307     0.451    0.327      0.308      0.405    0.328       0.319    0.377




Table S14: Model 6 Simulation Results – Female Sample

                  Accrual Model                Peak Value Model             Option Value Model
Age    Baseline      3 Year   Common    Baseline    3 Year   Common    Baseline   3 Year   Common
 55     0.096         0.085     0.084    0.092      0.081      0.081    0.092      0.086    0.092
 56     0.094         0.082     0.087    0.092      0.080      0.083    0.091      0.085    0.093
 57     0.100         0.086     0.096    0.099      0.086      0.093    0.099      0.092    0.102
 58     0.109         0.094     0.107    0.110      0.096      0.107    0.111      0.103    0.115
 59     0.117         0.102     0.116    0.121      0.106      0.118    0.122      0.113    0.127
 60     0.146         0.124     0.130    0.147      0.128      0.142    0.147      0.137    0.153
 61     0.164         0.138     0.150    0.166      0.146      0.164    0.167      0.156    0.173
 62     0.180         0.148     0.170    0.182      0.161      0.183    0.183      0.171    0.190
 63     0.193         0.163     0.189    0.195      0.174      0.198    0.196      0.184    0.204
 64     0.211         0.181     0.212    0.214      0.192      0.218    0.215      0.203    0.223
 65     0.448         0.377     0.409    0.448      0.413      0.445    0.448      0.431    0.459
 66     0.248         0.199     0.248    0.236      0.214      0.245    0.232      0.223    0.243
 67     0.266         0.223     0.289    0.256      0.239      0.273    0.253      0.247    0.264
 68     0.290         0.269     0.338    0.280      0.271      0.305    0.278      0.275    0.289
 69     0.284         0.265     0.340    0.274      0.266      0.302    0.274      0.271    0.286




74
Table S15: Model 7 Simulation Results – Female Sample

                  Accrual Model                Peak Value Model              Option Value Model
Age    Baseline      3 Year   Common    Baseline    3 Year   Common    Baseline    3 Year   Common
 55     0.099         0.094     0.086    0.099      0.090      0.091    0.099       0.094    0.099
 56     0.093         0.086     0.084    0.093      0.084      0.088    0.093       0.087    0.094
 57     0.095         0.087     0.089    0.095      0.085      0.092    0.095       0.089    0.097
 58     0.103         0.095     0.098    0.103      0.093      0.102    0.103       0.097    0.106
 59     0.117         0.109     0.112    0.117      0.105      0.116    0.117       0.110    0.121
 60     0.163         0.148     0.141    0.163      0.148      0.161    0.163       0.154    0.168
 61     0.158         0.141     0.140    0.158      0.143      0.158    0.158       0.149    0.163
 62     0.172         0.150     0.157    0.173      0.157      0.174    0.173       0.163    0.178
 63     0.182         0.162     0.172    0.183      0.167      0.185    0.183       0.173    0.188
 64     0.216         0.194     0.210    0.216      0.200      0.220    0.216       0.206    0.222
 65     0.448         0.390     0.401    0.448      0.422      0.449    0.448       0.434    0.456
 66     0.329         0.281     0.316    0.329      0.311      0.337    0.329       0.320    0.338
 67     0.254         0.216     0.267    0.255      0.243      0.267    0.254       0.249    0.263
 68     0.240         0.223     0.277    0.240      0.235      0.257    0.240       0.237    0.249
 69     0.228         0.214     0.272    0.229      0.224      0.248    0.229       0.227    0.239




Table S16: Model 8 Simulation Results – Female Sample

                  Accrual Model                Peak Value Model              Option Value Model
Age    Baseline      3 Year   Common    Baseline    3 Year   Common    Baseline    3 Year   Common
 55     0.099         0.093     0.087    0.099      0.090      0.094    0.099       0.093     0.099
 56     0.093         0.086     0.084    0.093      0.083      0.090    0.093       0.087     0.094
 57     0.095         0.087     0.089    0.095      0.085      0.094    0.095       0.089     0.098
 58     0.103         0.095     0.099    0.103      0.093      0.104    0.103       0.097     0.107
 59     0.117         0.109     0.113    0.117      0.105      0.118    0.117       0.110     0.121
 60     0.163         0.147     0.142    0.163      0.148      0.164    0.163       0.154     0.168
 61     0.158         0.141     0.142    0.158      0.144      0.161    0.158       0.149     0.163
 62     0.172         0.150     0.158    0.173      0.157      0.176    0.173       0.163     0.178
 63     0.182         0.162     0.173    0.183      0.167      0.187    0.183       0.173     0.188
 64     0.216         0.194     0.211    0.216      0.200      0.221    0.216       0.206     0.222
 65     0.448         0.391     0.404    0.448      0.423      0.452    0.448       0.434     0.456
 66     0.329         0.282     0.317    0.329      0.312      0.339    0.329       0.320     0.339
 67     0.254         0.217     0.267    0.255      0.244      0.268    0.254       0.249     0.264
 68     0.240         0.224     0.276    0.240      0.235      0.256    0.239       0.237     0.249
 69     0.228         0.214     0.271    0.229      0.224      0.247    0.229       0.227     0.239




75
                                                                                            Figures

                         Figure 1: Historical Trends in the Labour Force Participation of Older Males and Females

     100


     90


     80


     70


     60
                                                                                                                                                              Males 45-64
                                                                                                                                                              Males 65+
     50
                                                                                                                                                              Females 45-64
                                                                                                                                                              Females 65+
     40


     30


     20


     10


      0
           1960


                  1962


                           1964


                                  1966


                                         1968


                                                1970


                                                       1972


                                                              1974


                                                                     1976


                                                                            1978


                                                                                     1980


                                                                                              1982


                                                                                                      1984


                                                                                                             1986


                                                                                                                    1988


                                                                                                                           1990


                                                                                                                                  1992


                                                                                                                                         1994


                                                                                                                                                1996


                                                                                                                                                       1998
                                                                                   Year


Source: Historical Statistics of Canada and CANSIM. These series span the change in the labour force questionaire in 1976.




76
                  Figure 2:The Age Profile of the Median One-Year, Peak Value and Option Value Accrual
                                                    in the Male Sample




                                                                                                          One-Year
                                                                                                          Peak Value
                                                                                                          Option Value




     55      56      57      58      59      60      61      62      63     64   65   66   67   68   69




                                                             Age



Notes: The profiles are graphs of the numbers reported in tables 2 and 3.




77
                  Figure 3: The Age Profile of the Median One-Year, Peak Value and Option Value Accrual
                                                   in the Female Sample




                                                                                                          One-Year
                                                                                                          Peak Value
                                                                                                          Option Value




     55      56       57     58      59      60      61      62      63     64   65   66   67   68   69




                                                             Age


Notes: The profiles are graphs of the numbers reported in tables 4 and 5.




78
                                          Figure 4: The Retirement Hazard for Males

              0.6




              0.5




              0.4
     Hazard




              0.3




              0.2




              0.1




               0
                    55   56   57     58      59      60      61      62      63      64   65   66   67   68   69
                                                                     Age




Source: Authors calculations from the analysis sample of males (see the Appendix).




79
                                       Figure 5: The Retirement Hazard for Females

               0.5


              0.45


               0.4


              0.35


               0.3
     Hazard




              0.25


               0.2


              0.15


               0.1


              0.05


                0
                     55   56   57     58      59      60      61      62      63       64   65   66   67   68   69
                                                                     Age


Source: Authors calculations from the analysis sample of females (see the Appendix).




80
81