Appendix A
A new perspective on retirement processes: trajectories of transitions from work to retirement

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by Leroy O. Stone, Hasheem Nouroz, Alexandre Genest and Nathalie Deschênes

Introduction
Key concepts
Identifying the start of the retirement process using a scale named "TRANSCOR"
Mapping trajectories of work-to-retirement transitions
Classifying trajectories
Key limitations and issues
Bibliography

Introduction

This chapter introduces features of what we believe is a useful policy-relevant innovation in connection with the retirement processes followed by workers. We refer to these processes as "work-to-retirement transitions".²

What is this innovation? It is a new mapping and classification of long sequences of positions occupied by persons over periods that may cover many months, and which comprise steps in their work-to-retirement transitions (or their retirement processes). Other mappings and classifications exist (Blau 1994, Gustman and Steinmeier 1986, Gustman and Steinmeier 2000, Han and Moen 1999, Quinn, Burkhauser and Myers 1990); but ours is unprecedented in the detailed time intervals and activities that it includes (as shown below). These details are useful in making it easier to link the analysis of work-to-retirement transitions to a wide range of policy concerns. They also permit much improved understanding of the pathways by which people carry out one of life's major transitions, at least in socio-cultural contexts where the institution of retirement exists.

A central concern here is the sensitivity of the probabilities of specific types of retirement processes to aspects of the prevailing policy environment. Information about this sensitivity is vital when it is necessary to simulate the impacts of policies upon retirement processes. Ample evidence of this point can be found in the literature coming out of Europe, mostly, on the subject of pathways to retirement (see Dahl, Nilsen and Vaage 2000, Flippen and Tienda 1999, Guillemard 1995, OECD 2001, Riphahn 1997).

A key feature of our concept of trajectory of transition to retirement is its attention to the duration of stay in specified positions (possible states occupied as parts of a trajectory - such as spells of unemployment). This is achieved by using a relatively fine time interval such as a quarter of a year (some of the positions in our trajectories involve measuring changes from one month to another within a single quarter).³

Another important innovation in our work is that it presents the first display of several different properties of the said trajectories, which become bases for classifying large numbers of trajectories into small and meaningful categories. Eight properties of work-to-retirement trajectories are defined, and the text below presents indicators for measuring several of them.

We illustrate applications of the innovations cited above by presenting, in chapters 15 and 16, descriptive analyses focused on two areas of current interest: the distinctive retirement patterns of the self-employed, and differences in these patterns between public-sector and private-sector employees.

The purpose of this chapter is to exposit the innovations mentioned above. The focus will be on the concept, mapping and classification of trajectories of transition to retirement. In connection with the proposed indicators for use in measuring properties of trajectories, the chapter also presents some basic information about how the trajectories are distributed over categories of selected properties.

Key concepts

"Retired"

An almost bewildering variety of definitions of "retirement" exists in the literature (Burtless and Moffitt 1985, Gustman and Steinmeier 1984, Gustman and Steinmeier 2000, Honig and Hanoch 1985, Ruhm 1990a, Ruhm 1990b, Smeeding and Quinn 1997, Stein 2000, Stone 2003).⁴ A key issue is whether it is best to regard retirement as a state of being (thus a "position" that one may occupy at a moment of time) or whether it is a process (for related discussion see Han and Moen 1999). It is both, depending on the context in which the word is used.

When you see the word "retirement" used within the context of the phrase "transition to retirement", think of the state of being retired - a person "transits" toward the state of being retired. We identify the state of being retired in terms of a prolonged departure from the labour market, combined with the reception of some form of retirement-related income. (See Smeeding and Quinn 1997.) The people who return to the labour market after such a prolonged departure, are said to have "un-retired".⁵

Transition to retirement

Before formally defining "transition to retirement", a few words about the process that the term is designed to represent seem to be in order. Imagine a person who spends a major part of her (henceforth "her" will mean a woman or a man) waking hours selling her services in the job market or seeking to do so. Often that effort also involves preoccupation with plans and activities designed to enhance her competitiveness or increase her degree of success in the job market (training, seeking promotions or experience-enhancing opportunities, professional networking, etc.). Let us use the phrase "high commitment to employment" to refer to this combination of (a) activity in the labor market and (b) preoccupation with things to do to increase the chances of success in that activity.

After carrying on in this manner for many years, suppose the person begins to think about a different pattern of daily life, one that would involve no activity of selling one's services (or seeking to do so) and no preoccupation with things to do so as to enhance one's competitiveness or marketability in the labor market. This different way of life, a new stage in the person's life course, is what we have in mind when using the term "retired" above. But to reach this new stage of the life course, if the passage to that stage is voluntary, the person needs to undertake a series of decisions, plans and activities at the end of which she will find herself in the new stage of life.

Thus our formal definition of "transition to retirement" is that the phrase means a combination of decisions, steps and activities that leads a person from the stage of life in which she has high commitment to employment to a new one where one is in the state of being retired. This is a conceptual definition, as distinct from an operational one.⁶ (For related discussion see Han and Moen 1999, Moen et al. 2000.)

Figure A.1 illustrates our concept of transition to retirement. It is a schematic diagram that represents four transitional patterns, running from time t to time t + n, and the period n may be many months covering a number of years. The decisions, steps and activities which comprise the transition often cause the person engaged in the transition (whom we will often call "the transiter") to occupy a sequence of identifiable positions. These positions are represented as semi-circles in Figure A.1, and they stand for components of her transitional pattern. The leftmost pattern illustrated in Figure 1 indicates three positions, with the second one being occupied for a much longer period of time than the other two positions. The degree of elongation of the semi-circle indicates the length of time the position is occupied.

In almost all of the literature the usage of "transition" causes the reader to think of just two states, and a transition is the passage between those two states. The first arrow you see in Figure 1 illustrates this kind of transition. In contrast, here the term "transition" refers to the whole sequence of positions from the first one to the last one occupied.

Trajectory of transition to retirement

Figure A.1 and the last paragraph highlight the notion of a sequence of positions occupied in the course of making the transition to the state of being retired. That is exactly what we intend to reference when using the phrase "trajectory of transition to retirement".

The third sequence, going from left to right, in Figure A.1 has letters of the alphabet within the semi-circles to suggest four labeled positions. The first one (with the label "a") could be a full-time bridge job, the second a spell of unemployment, the third a part-time job and the fourth a longer spell of unemployment. It is followed by the prolonged departure from the labor force discussed above. This is a schematic diagram of a trajectory.

Thus, by "trajectory of transition to retirement" we mean a sequence of designated "positions" that are occupied in the process of making this transition, including the duration of stay in each position. There may be a large number of positions occupied over several time points (t, t + 1, t + 2, ., t + n).

This means that you would not normally try to analyze variations among individual trajectories. Instead, trajectories should be grouped into a few broad classes, depending on their designated properties, as we will illustrate below.

Identifying the start of the retirement process using a scale named "TRANSCOR"

To present data about the kind of multi-state transition process discussed above, the researcher first needs to decide who, among a sample of potential retirees, has entered the process during a given time period.

Making this decision requires the use of a variety of indicators. Any indicator will be constrained by limitations of the available data. Our work uses the Canadian Longitudinal Survey of Labour and Income Dynamics (SLID), which suffers from a major defect relative to the requirements of a good indicator.

Unlike Wave 1 of the University of Michigan's Health and Retirement Survey (HRS), SLID provides no direct questions about retirement plans or intentions.⁷ Thus it is necessary to devise an indirect procedure to make inferences concerning who was in transition to retirement during a designated time period.

Other researchers that have faced this problem have used one or two variables to identify who has begun the retirement process (see Gustman and Steinmeier 1984, Honig and Hanoch 1985, Ruhm 1990a, Ruhm 1990b, Quinn and Kozy 1996). However, an attempt to define "transition to retirement" operationally brings one to the conclusion that a larger set of dimensions needs to be taken into account, as done in this appendix.

Using a set of partial indicators suggested in the literature and keeping in mind limitations of the SLID data such as the key one cited above, we developed a multi-dimensional "retirement transition scale" to measure the degree of a person's involvement in a transition to retirement. We hypothesize that the higher a person's scale score, the greater is the probability that the person is engaged in transition to retirement.

Components of the scale

A detailed definition of this multi-dimensional scale, which we have named "TRANSCOR", follows. We begin with a list the factors that the scale takes into account.

1. Receipt of retirement-related income, e.g. work-related pension income (see Han and Moen 1999:199, Smeeding and Quinn 1997).
2. Departure from the labor market - in North American terminology, the person moves from either employment or unemployment to being outside the labor force market (see, e.g., Gendell 2001, Gunderson 1980, Habtu 2003, Knuth 2002, Meghir and Whitehouse 1997, Oswald 1999, Taylor and Urwin 1999, Vanderhart 2003).
3. Change in the job of the person from her career job to another kind of job, including self employment (see Quinn and Kozy 1996:363, Quinn, Burkhauser and Myers 1990, Ruhm 1990a:100).
4. Reduction in hours of paid work, including reduction of hours in the same job (see Blau 1994, Gustman and Steinmeier 1984:403-415, Honig and Reimers 1987).
5. Reduction in earnings beyond that caused by job change or fewer hours of work (Honig and Hanoch 1985:24).
6. Onset of long-term unemployment after job loss among older workers (see Blau 1994, Guillemard 1995, Knuth 2002, Manning and Burdett 1996, Meghir and Whitehouse 1997, Oswald 1999, Pedersen and Westergaard-Nielsen 1993, Rowe and Nguyen 2003, VandenHeuvel 1999).
7. Encounter with a major health or other life event, if associated with a nearby (in time) change in a relevant aspect of employment status (see Crossley, Schelhorn and Au 2003, Honig and Hanoch 1985, Marshall 2003, Marshall and Clarke 1997).
8. Change in the place of residence, if associated with a nearby change in a relevant aspect of employment status.
   

The design of TRANSCOR

As stated above, the design of TRANSCOR has had to respect the limitations of the SLID data. Thus TRANSCOR relies entirely upon objective behavior of respondents, recognizing that often the meaning of a behavior is accurately ascertained only by asking questions about it.

Some TRANSCOR components (called "scale items" in psychometrics, where scaling methodology is most highly developed) measure change between two consecutive years because SLID provides only annual observations for the variable in question. In what follows, the first year is called, "Base Year", and the second, "Year Two". Our aim is to identify those who started their transitions to retirement between the beginning of Base Year and the end of Year Two.

A person's retirement transition scale score (her TRANSCOR value) will be the sum of the scores accorded to that person in the eight tests named below. The tests are labelled from S1 to S8. The value assigned to a test will be called its "weight".

The weights assigned initially to scale components. At first, the weights were assigned to the components based solely on judgment (informed by literature review) concerning their order of importance. The weights were later on adjusted, so that they would better reflect the relative statistical importance of the components in predicting who would have retired by the end of the six years of observation. Also, the sensitivity of the main findings to moderate changes in the weights was examined. Below is the list of the tests (the scale components) and the final weights assigned.

where

S₁ = (a) or (b) or (c)

(a) 4.0 if the person began receiving income from a stream normally associated with retirement from paid work between the beginning of the first year of observation (Base Year) and the end of the second year (Year Two); or
(b) 3.0 if the person received in Base Year any of the kinds of income identified above and had a job in the first quarter of Base Year, or
(c) 0 if neither (a) nor (b) is true.

S₂ = (a) or (b) or (c)

(a) 0.8 if the person was outside the labor market at the end of Year Two but was in the labor market at the beginning of Base Year, and was either disabled during Base Year or Year Two, or had encountered a major health or other life event during Base Year or Year Two, and was outside the labor market throughout another month during Base Year and Year Two; or
(b) 0.1 if the person was outside of the labor market at the end of Year Two but was in the labor market at the beginning of Base Year, and was either disabled during Base Year or Year Two or had encountered a major health or other life event during Base Year or Year Two, and was in the labor market in all other months during Base Year and Year Two; or
(c) 0 if neither (a) nor (b) is true

S₃ = (a) or (b) or (c)

(a) 2.5 if the person was outside of the labor market at the end of Year Two but was in the labor market at the beginning of Base Year, and was neither disabled during Base Year or Year Two nor had encountered a major health or other life event during Base Year or Year Two and was outside the labor market throughout another month during Base Year and Year Two; or
(b) 0.3 if the person was outside the labor market at the end of Year Two but was in the labor market at the beginning of Base Year, and was neither disabled during Base Year or Year Two nor had encountered a major health or other life event during Base Year or Year Two and was in the labor market in all other months during Base Year and Year Two; or
(c) 0 if neither (a) nor (b) is true.

S₄ = (a) or (b)

(a) 0.3 if the person ended her job of longest duration during either Base Year or Year Two and moved to another job, or changed jobs (moved from one employer to another, or from employment to self-employment or vice-versa) during the same period, and if the job of longest duration had been held continuously for at least 10 years in the case of a man or five years in the case of a woman. (Women are assigned this weight with only five years because of their greater tendency to have work histories marked by job interruptions); or
(b) 0 if (a) is not true.

S₅ = (a) or (b)

(a) 0.1 if the person reduced hours of paid work from full-time levels to part-time levels, or by at least 40% while still working full time, at some time during Base Year and Year Two (job change is not required for eligibility to get this score); or
(b) 0 if (a) is not true.

S₆ = (a) or (b) or (c)

(a) 1.0 if the person had an earnings reduction of 50% between Base Year annual earnings and Year Two annual earnings and had no positive score on any of items S2, S3, S4 or S5 above; or
(b) 0.8 if the person had earnings reduction of 50% between Base Year annual earnings and Year Two annual earnings and had a positive score on any of the items S2, S3, S4 or S5 above.
(c) 0 if (a) is not true.

S₇ = (a) or (b)

(a) 0.3, if the person was employed in the first month of Base Year, and at the end of Year Two she had been unemployed for six consecutive months; or
(b) 0 if (a) is not true.

S₈ = (a) or (b)

(a) 0.3 if the person changed residence during Base Year or Year Two (although the principles stated in Appendix A imply that residence change needs to be associated with some other condition more directly indicative of transition to retirement, the scale weight given to this variable is so low that it was decided to program the rule as if only residence change matters); or
(b) if (a) is not true.

One of these tests merits further comment here. Test S1 refers to the receipt of income from a stream normally associated with retirement from paid work. Drawing upon the SLID database, the income streams in question are private pension income, Canada or Quebec Pension income, and RRSP withdrawals. However, some CPP/QPP payments may be received for reasons other than retirement. Also, RRSP withdrawal need not be for retirement purposes.

Condition (b) of test S1 violates our basic principle of focusing on identifying those that began their transitions after the start of Base Year. However, it is reasonable to the extent that it allows us to assign a non-zero score to those who actually began receiving such income during that year. We increase the chances of identifying that subset by requiring that the person had a job in the first quarter of Base Year. There is no SLID variable that identifies the month when the person began receiving the kinds of income just cited.

Distribution of the scale levels

Table A.1 presents unweighted distributions of TRANSCOR (the TRANSCOR value of zero is a lower bound; but the maximum of 7.7 is simply the highest score observed in the two samples). We hypothesize that the distribution of TRANSCOR is a proxy for an underlying distribution of the probability of being engaged in transition to retirement in 1993-1994 and 1996-1997, for the two cohorts respectively. Given this hypothesis, the higher the value of TRANSCOR, the more likely it was that the person had initiated her transition to retirement.

Thus, in order to judge who, among the SLID respondents in Panel Two (1996 cohort), had begun their transitions to retirement during the 1996 to 1997 period, it seemed reasonable to chose a threshold within the range of TRANSCOR values. Persons with TRANSCOR values above that threshold were judged to have begun their transitions to retirement during the 1996 to 1997 period. We initially set the TRANSCOR threshold at 3.3; but, under pressure from unduly small sample sizes for some key population subgroups, the threshold was lowered to 3.0, provided that persons be in the labor force in the first quarter of the two-year period with respect to which their TRANSCOR ratings are computed.

Since those with ages close to 45 in 1996 were very unlikely to have begun their work-to-retirement transitions during 1996 to 1997, it is important to show the percentages of persons above the TRANSCOR threshold by age. Chart A.1 does so, and identifies men and women separately. For both sexes, the percentage found to be in transition to retirement ranges from under 10% at age 45 to over 65% at age 64.

A crude check on the reasonableness of our classification of the sample of those that began their transitions during 1996 to 1997 and those that had not done so, is available by way of roughly comparable data from two other surveys. Charts A.2 and A.3 present data from the Health and Retirement Survey (HRS) of the USA and the General Social Survey (GSS) of Canada.

Based on Wave One (1992) of the HRS, Chart A.2 shows percentages by age and sex of those who reported either that they were partially retired or that they expected to retire within the next year. These two groups would include most or all of those who were in transition to final withdrawal from the labor force (the definition of "retirement" used in this paper) at the time they were asked the questions in Wave One of the HRS.

Chart A.3 is based on a battery of retirement planning questions that were asked of persons who said they were not retired in the 2002 round of the Canadian General Social Survey. It shows percentages for those who reported either that they had changed the nature of their work as part of their plans for retirement or that they planned to retire within the next year. These two groups would include most or all of those who were in transition to final withdrawal from the labor force at the time they were asked the questions in the 2002 GSS.

Clearly, no direct comparisons of numbers should be pursued among Charts A.1 to A.3 for several reasons. These charts come from quite different policy and cultural environments; they involve different survey questions asked in different years. Unlike Chart A.1, Charts A.2 and A.3 show results of subjective responses about retirement plans or intentions in a context where each respondent was left free to define what "retirement" meant to her.

Thus we should only ask whether the "broad drift" of the curves in Charts A.2 and A.3 suggest that the estimates in Chart A.1 are reasonable. All three figures show a prominent upward "spike" at age 64, and a generally flat trend up to the mid-50s in age. The HRS agrees with the estimates in Chart A.1 in showing a distinct upward turn in the curve below but near age 60, while that is seen in the GSS curves only in the 60s.

Despite the major differences among the data sources, the orders of magnitudes of the percentages are broadly similar across all three figures at ages 62 to 64. This is in sharp contrast to the younger ages where the percentages for the GSS and HRS are very much higher than those of the estimates in Chart A.1. This divergence at the younger ages could be a result of the fact that the HRS and GSS respondents often defined "retirement" as leaving their perceived career jobs (often to go to other kinds of jobs); whereas the SLID-based estimates focus on departure from the paid labor market and receiving retirement-related income.

In summary, our concept of the work-to-retirement transition requires, for its application in statistical analyses, an identification of who has entered the transitional process within a given time period. This is done most easily when survey respondents are asked about their retirement-related expectations, plans and activities; although this subjective information needs to be combined with observations of their behavior. However, SLID has no such questions, and consequently a multi-dimensional index that relies entirely upon observations of behavior is unavoidable.

Mapping trajectories of work-to-retirement transitions

Since a trajectory of transition to retirement is a sequence comprising a number of changes among the members of a defined class of "positions", an initial task in identifying trajectories is to define the list of positions. For this study the positions are defined in terms of (a) labor force states occupied throughout a quarter (three consecutive months) and (b) changes in labor force states from one month to another within a quarter.⁸ The adopted definitions are such that in any quarter a person may be in one and only one of the following positions.

1. Employed full time and with no job change throughout the quarter⁹.
2. Employed part-time and with no job change throughout the quarter.
3. Employed in the first and last month of a quarter, and had a voluntary job change during the quarter.
4. Employed in the first and last month of a quarter and had an involuntary job change during the quarter.
5. Unemployed throughout the quarter.
6. Unemployed or outside of the labor force in the first month of the quarter but employed in the last month.
7. Employed in the first month of the quarter but unemployed in the last month.
8. In the labor force in the first month of the quarter but outside the labor force in the last month.
9. Not in the labor force in all three months of the quarter, and receiving some kind of pension or old-age security income during the current year (the income conditions are added here to increase the chances that a person in this position is on the way to retirement).
10. Unclassified.

Thus our study defines positions in terms of different aspects of the respondent's orientation to the labor market. It is herewith acknowledged that in certain studies, key life events and changes in family responsibilities should be considered in mapping trajectories. The list of positions shown here was developed for a study where it was desired to include key life events and changes in family responsibilities among the explanatory variables that help to explain the changes of positions defined solely in terms of labor-market-related behavior.

It is also important to note that although trajectories of transition to retirement are defined relative to the last four of the six-year observation period (thus a total of 16 quarters) for SLID Panel Two, there is no necessary restriction of trajectory measurement and mapping to 16 quarters. We have already computed 24-quarter trajectories that cover all six years. These are useful when one needs to know who actually began closing their trajectories - concept defined below - during the 1996 to 1997 period, as was the case in Chapter 13. However, all text below refers to the 16-quarter trajectories.

In each of the 16 quarters that comprise the last four years of observation, a respondent who remained in the survey throughout the four years is assigned to one of the ten positions listed above, based on her attributes.¹⁰ This sequence of 16 positions is the operationally defined trajectory of transition to retirement for that respondent during those four years. In their study of persons' career trajectories. Han and Moen (1999) also used a sequence of code numbers to map a trajectory. Charts A.4 and A.5 illustrate two of the trajectories found among the respondents judged to be in transition to retirement as of 1996-1997.

The trajectory in Chart A.4 comprises the following sequence of 16 code numbers: [1111222299999999]. Each code number refers to the respondent's position in a single quarter, and the number is interpreted by referring to the list of positions provided above. This remark will now be clarified by reference to the more complex trajectory in Chart A.5.

This trajectory comprises the following sequence of codes [9656145155675555]. During the first quarter of 1998, the person was out of the labor force throughout the quarter, and received some kind of retirement-related income during 1998 (position #9). During the first month of the second quarter, she was unemployed but, in the last month of this quarter, was employed (position #6). The person then became unemployed during all months of the third quarter (position #5). During the first month of the fourth quarter, she was unemployed but, in the last month of this quarter, was employed (position #6). In the fifth quarter she was employed full time throughout the quarter (position #1). In the sixth quarter the person was employed in the first and last months and had an involuntary job change in the quarter (position #4). The person then became unemployed throughout the seventh quarter (position #5). However, throughout the eighth quarter the person had the same full-time job (position #1). In the ninth and the tenth quarters the person was again unemployed throughout the quarters (position #5). In the eleventh quarter the person was unemployed or was outside the labor force in the first month but was employed in the last month (position #6). In the twelfth quarter the person was employed in the first month but became unemployed in the last month (position #7). From the thirteenth to the sixteenth quarters the person was unemployed in all the months (position #5).

Charts A.4 and A.5 are presented here as concrete examples of the notion of trajectory of transitions to retirement, which was defined as an abstract concept earlier. Table A.2 illustrates in detail many trajectories from the 1996 cohort. All the trajectories have a certain feature in common. They represent the classic retirement transition pattern - a direct move (between two consecutive quarters) from the same full-time job held during three consecutive months into a position where the person was outside the labor market in the next three consecutive months and was also in receipt of some kind of retirement-related income. Furthermore, she did not return to the labor market up to the end of the observation period (December 2001).

Chart A.6 shows the age pattern of the prevalence of this class of trajectories among the members of the SLID cohort of 1996. Chart A.6 shows that the classic pattern of transition from work to retirement was most likely to be found in the 55 to 59 age group, and that the magnitude of concentration in this age group was notably higher for women than for men. The second highest probability of using this pattern is found in the 60 to 64 age group.

All the trajectories listed in Table A.2 are said to be "closed" because for six consecutive months at the end of the six years of observation, the persons were outside the labor market and in receipt of some kind of retirement-related income. However, some of these persons may have returned to the labor market after those six months (i.e., after December 2001); with the probability of doing so varying inversely with age (Quinn, Burkhauser and Myers 1990:ch. 5).

Due to the wide age range covered in the data, a substantial percentage of trajectories are unclosed at the end of the six years. Chart A.7 shows the proportion of closed trajectories according to age at the beginning of the observation period.

As one might expect, Chart A.7 shows a strong upward trend in the percentage with closed trajectories as age in 1996 increases from 45 to 49 to 60 to 64. Chart A.7 shows that a very small percentage (5.4% for both sexes) of individuals in 45 to 49 age group had closed trajectories by the end of the last year of observation in 2001. This is in sharp contrast to a figure close to 70% for the 60 to 64 age group. The figure for the 45 to 49 age group illustrates the fact that a great majority either had not left the labor market up to the end of 2001 or had come back to the labor force after having left it.

In introducing the concept of closure of a trajectory, we have begun to move toward procedures whereby trajectories could be classified into a small set of meaningful classes for analysis. Chapter 13 has used a stricter definition of closure in developing its classification of trajectories into six broad groups. How to classify trajectories is the topic to which we now turn.

Classifying trajectories

In his 1995 review of the state of the art of classifying trajectories in various fields of research, notably that of personal life histories, Abbot (1995) cited two approaches. Within each approach a variety of specific methods is in use (see also Abbot and Tsay 2000). The first approach is based upon specifying an overall measure of distance or similarity between two trajectories. Using pair-wise comparisons, groups are then generated so as to maximize the within group similarity and between-group differences. The term "optimal matching" is now used to refer to the techniques that use this approach.

The second approach relies upon sets of rules for grouping that are specified by experts, and it is often called "judgment-based grouping" or "rules-based grouping". A notable feature of rules-based grouping is that the same set of trajectories will be grouped in different ways, depending upon the rules that are adopted. Blau (1994), Quinn, Burkhauser and Myers (1990), and Gustman and Steinmeier (2000) use rules-based rules to generate their groupings of trajectories of work-to-retirement transitions. In dealing with career trajectories, Han and Moen (1999) used a combination of optimal matching and rules-based grouping.

Our opinion is that the results of the grouping trajectories of transitions to retirement should facilitate research focused on major matters of public-policy concern that involve later-life transitions involving the labor market, changes in health and functional capacity, shifting family responsibilities and standard of living. A focus upon such concerns tends to lead to considerable priority for rules based grouping.

Concerns expressed in the scientific and policy literature about retirement include the following:

• The progressive abandonment of the classic pattern of going straight from a career job into retirement
• The influence and relative importance of government policies in stimulating decisions to seek early retirement
• Gradual retirement, where people leave their career jobs and then move to part-time or full-time bridge jobs before finally exiting the labor market
• Patterns of retirement by older workers who are forced out of their jobs
• Patterns of re-entry to the labor market by persons who left it in order to "retire"
• Patterns of transition to retirement by those looking for a job and not finding it (especially the long-term unemployed among older workers)
• Gender differences in patterns of transition to retirement followed by men and women
• Patterns of transition to retirement among persons that never had a career job as this is usually defined (a job held for at least ten years and departed in connection with making the transition to retirement).

Such a list of concerns suggests that work-to-retirement trajectories have a variety of properties that can be defined conceptually and operationally so as to form bases for classifying them. A list of eight possible properties of trajectories follows. They are called:

• Speed of closure of trajectory
• Presence of indications of enhanced market-based vulnerability
• Presence of indications of enhanced total vulnerability
• Instability of market-related status
• Presence of flexibility among options for transition to retirement
• Propensity for bridging
• Propensity for returning to the labor market after departure
• Propensity to un-retire.

Speed of closure of trajectory

A person is said to have closed her trajectory when (a) she has left the labor market and has been in receipt of some form of retirement-related income for at least six-consecutive months, and (b) following those six months she did not return to the labor market up to the end of the period of observation. As already suggested in an earlier comment about Table A.2 (which presents many closed trajectories that involve the classic pattern of retirement), in terms of the sequence of code numbers used to define a trajectory, a closed trajectory has a string of uninterrupted code 9s including "99" in the last two of the 16 quarters over which trajectories are measured. See Figure A.2 for an illustration.

Figure A.2 is a schematic diagram designed to illustrate the concept of speed of closure of a closed trajectory. Trajectory One began closing in the ninth quarter, whereas closure began in fourteenth quarter for Trajectory Two. Trajectory One closed faster than Trajectory Two. Generally, the sooner the person begins the period of uninterrupted departure from the labor force the faster is her speed of closure.

However, those classified as having the fastest speed may in some cases represent persons that had left the labor market before the first quarter of 1996 - in the case of our data their period of uninterrupted departure from the labor market began before the start of 1996.

Information presented in Chapter 13 indicates that the size of this bias may be negligible, however. For that chapter, the definition of TRANSCOR was modified so that points could be earned due to receiving retirement-related income in year T only if that kind of income was zero in year T - 1. Despite this restriction, the distribution of speed of closure still had a strong local mode in the first few quarters after respondents were judged to have begun making the transition to retirement.

Using the concepts just presented, we can classify trajectories according to the speed of closure, as Chart A.8 illustrates. The sample for this chart is limited to those who began their transitions during the 1996 to 1997 period, and who were wage and salary earners in both 1996 and 1997.¹¹ In this chart scores of distinct trajectories are grouped into sixteen classes of speed of closure. The vast majority of trajectories were either closed in or before the first quarter of 1998 or were unclosed at the end of 2001. Three small local modes in the distribution are located at the first quarter of each year from 1999, 2000 and 2001 (quarters 5, 9 and 13, respectively).

Presence of indications of enhanced market-based vulnerability

In this text "vulnerability" means risk of loss, or setback or damage in or to a desired state of affairs or a plan; where the risk arises from an event or an experience. Here we are referring to risk of setback or damage to whatever plans or arrangements the person has made concerning standard of living in retirement. For example, an event such as a job loss can be said to heighten or enhance vulnerability when it is deemed to have increased the risk of setback or damage to plans or arrangements of the kinds just cited.

Our index of vulnerability (called "VULSCORE") focuses on the presence within a trajectory of indications of enhanced market-based vulnerability. The following trajectory positions are pertinent:

Position 4: Employed in the first and last month of a quarter and had an involuntary job change during the quarter. Position 5: Unemployed throughout the quarter. Position 6: Unemployed or outside of the labor force in the first month of the quarter but employed in the last month. Position 7: Employed in the first month of the quarter but unemployed in the last month. Position 0: Unclassified, and there is an experience of unemployment within the quarter.

Although we have emphasized reliance upon the properties of trajectories (aspects of specific positions such as those listed above), it is important to take into account at least one "auxiliary variable", in defining levels of our vulnerability scale. This variable involves the business climate within which a person experienced a setback such as unemployment, since the consequences of the unemployment will be worse in a business cycle downturn than in a business cycle upturn. This factor was taken into account by special weighting of the VULSCORE value obtained by someone that experienced unemployment. Details of this idea are presented in Appendix A.3.

Chart A.9 shows how those who began making the transition during the 1996 to 1997 period, and who were employed throughout the last quarter of 1997, were distributed according to multiple levels of the index of vulnerability. The distribution of the sample among scale scores forms a steeply sloped "inverted J" curve. Just over 85% of the sample had a zero score on the scale, and this is called the "Low" level in the main text. The vast majority of the remaining persons were focused at scores of 1 or 2 (accounting for about 10% of the sample), on a scale whose maximum is 7.

Presence of indications of enhanced total vulnerability

The expression "total vulnerability" is meant to extend the vulnerability index just discussed so as to take into account certain damaging events that do not involve the labor market. Trajectories with enhanced total vulnerability are trajectories in which there was (a) some enhanced market-based vulnerability (the concept discussed above) and (b) the coincidence of a major life event such as onset of disability or loss of a key family member. No statistical work has yet been done with this property of trajectories.

Instability of market-related status

The greater the number of quarter-to-quarter changes of position within a trajectory, the greater is its index of market-related instability. The measure for this concept simply counts the number of such changes within a trajectory. Much higher than average instability may have negative consequences for certain aspects of quality of life in retirement (see Marshall 2003 and chapter 17).

Chart A.10 shows how those who began making the transition during the 1996 to 1997 period were distributed according to multiple levels of the index of instability. The distribution of the sample among scale scores forms a gently sloped "inverted J" curve. Just over 40% of the sample had a zero score on the scale, and this is called the "Low" level in the main text. Just over one-third of the sample were concentrated at scores 1 and 2 of the scale, which has a few scores at the maximum value of 14.

Presence of flexibility among options for transition to retirement

Although the notion of flexibility of retirement options has subjective and institutional components that cannot be gleaned from the study of the movements that comprise a trajectory, the presence (and their frequency) of certain kinds of movements could be used as an indirect indicator of the said flexibility. An example would be the presence of voluntary job changes. The absence of disruptions such as involuntary job change or unemployment could also be regarded as enhancing flexibility.

The score on our flexibility scale, named "FLEXSCORE", arises from a complex set of criteria involving several trajectory positions (see Appendix B for the details). In essence, a person's FLEXSCORE is increased each time there is either:

• A voluntary job change, or
• A reduction in hours of work within the same job, or
• A move from a fulltime job throughout one quarter to a part-time job throughout the next quarter, or
• Certain reductions of hours of work found along with Positions 0 or 8. (See Appendix B for the details.)

However, the FLEXSCORE value is then reduced by one-half if the trajectory has a non-zero value on VULSCORE (the vulnerability scale). This is because of our notion that job-loss or involuntary job change detract from flexibility.

There is a further weighting of FLEXSCORE that takes speed of closure into account. The longer the person delays closure of her trajectory, the greater is the indication of flexibility. Thus delayed closure gives a slight boost to FLEXSCORE, (see Appendix B for the details).

Chart A.11 shows how those who began their transitions during the 1996 to 1997 period were distributed according to multiple levels of the index of flexibility. The distribution of the sample among scale scores forms a steeply sloped "inverted J" curve, though not quite as steep as that found for the index of vulnerability above. Roughly 80% of the sample had a zero score on the scale. This is called the "Low" level in the main text. The first range of non-zero scores (from 0.5 to 1.0) contains nearly 15% of the sample.

Propensity for bridging

Among those who are identified as leaving career jobs, the frequency and duration of employment in other jobs would measure their propensity for resorting to bridge jobs over the course of the transition to retirement. Quinn, Burkhauser and Myers (1990), seem to be the innovators of this concept.

No statistical work has yet been done for this trajectory property, despite the substantial block of literature concerning bridge jobs. This is because we have wished to avoid a heavy focus on people who are seen as departing a career job in later life, in order to give due weight to groups among whom a relatively low percentage have had career jobs, according to the usual definition (a job held for at least 10 years, from which they left in order to begin making the transition to retirement). For related literature see Quinn, Cahill and Giandrea (2005).

Propensity for returning to the labor market after departure

Among those who are identified as leaving the labor market while receiving some form of retirement-related income, we can measure the proportion who subsequently returned to the labor market. Our measure for this concept (called "RETMARKET") begins by identifying whether a trajectory has a quarter in Position 9. Then, in such a trajectory, it finds later quarters with any of positions 1, 2, 3 or 4 - since all of these involve having a job for at least one month.

Also, among those who return to the labor market, the longer the time spent in the market before making the final exit, the greater is the value of RETMARKET. See Quinn, Burkhauser and Myers (1990), for an application of this concept.

This dimension also includes those who were outside of the labor force in the first month of the quarter but employed in the last month (Position 6), as well as those with the sequences of the type (,,,8,,,(1,2,3,4,)). This symbol means that following any quarter where the respondent was in Position 8, she subsequently occupied any of positions 1, 2, 3 or 4 - since all of these involve having a job for at least one month.

Appendix B has related details concerning the design of the measure for this concept. Essentially, each separate return to the labor market (from being outside of it) increases RETMARKET by one, and there is a multiplier of certain of these returns according to the number of quarters in which the person held the same job for three consecutive months.

Chart A.12 shows how those who began making the transition during the 1996 to 1997 period, and who left the labor market during that same period, were distributed according to multiple levels of the index of propensity to return to the labor market. The distribution of the sample among scale scores forms a very steeply sloped "inverted J" curve. Roughly 85% of the sample had a zero score on the scale, and this is called the "Low" level in the main text. The other scale positions tend to have similar very small percentages of respondents.

Propensity to un-retire

This feature is embedded in the one just defined - propensity for returning to the labor market after departure - but it pre-supposes an operational definition of being retired.

Chapter 13 illustrates the use of such a definition. It defines as "retired" a person who was outside the labor market for a whole year, and during that time was receiving some kind of retirement-related income. In terms of our trajectory, that would be a string of four consecutive code 9s, and no return to the labor market following that string.

To find those that un-retired, we would modify this definition so as to consider a person who had such a string, but who subsequently returned to the labor market. Having identified the trajectories that show un-retirement and we could ask several questions about labor market activity following un-retirement - e.g. duration of stay before retiring again, number of job changes, number of spells of unemployment, etc. However, no statistical work has yet been done with this property of trajectories.

Summary regarding the classification of trajectories

Thus a wide array of classifications of trajectories can be developed. Eight different classifications can be supported by the concepts presented above. Each one would be designed to facilitate research on an important question, including those that are related to policy issues being debated.

In the retirement literature, describing and classifying trajectories of transitions to retirement is a neglected subject, despite its importance. We have found only four articles that focus on classifying trajectories of transition to retirement, where the trajectories are defined as sequences of movements among multiple positions defined in terms of aspects of labor market participation. (See Blau 1994, Gustman and Steinmeier 1986, Gustman and Steinmeier 2000, Quinn, Burkhauser and Myers 1990.) Han and Moen (1999) have published a related article that deals with classification of lifetime career trajectories.

Gustman and Steinmeier (1986:560 to 566) used the term "retirement sequence" to represent what we call "trajectory of transition", and their sequences involved movements among three possible positions: working full-time, partially retired, fully retired. Their time interval was one year. In a sample of 494 Retirement History Survey respondents, they identified 22 distinct trajectories.

Quinn, Burkhauser and Myers (1990:ch. 5) implicitly indicate an attention to sequences in using the term "exit pattern" to refer to movements toward the state of being retired made by RHS respondents after leaving their defined career jobs. They identify four classes of patterns (or "types of trajectory" in our terminology) in terms of whether the movements involve: doing part-time work in the career job, doing part-time work in a new job, taking a new full-time job and fully exiting the labor force upon leaving the career job. The authors do not, however, display the detailed trajectories (as defined above) underlying the first three patterns.

Blau (1994) studied quarterly movements from 1969 to 1979 of older men among "labor force states defined by full-time employment (F), part-time employment (P), and out of the labor force (O)." (Apparently, the database he used did not permit identification of unemployment as a separate labor force state.) He identified 18 types of sequences of movements (or trajectories) where, at the last observation, the person was outside the labor force. However, he did not formulate any criteria for judging which of those 18 sequences should be considered to have ended in retirement. Also, his trajectories contain no information on the duration of time spent in a particular state.

Gustman and Steinmeier (2000) studied movements of Health and Retirement Survey (HRS) respondents, all born between 1931 and 1941 and between pairs of four waves of the survey. The movements are among the following positions: "retired" (R), "partially retired" (P), "not retired" (F), and "question not relevant" (X). (Table A.3) The authors used the respondents' subjective assessments of their retirement status. As regards duration of time spent in any of the states defined above, Gustman and Steinmeier's article provides little information.

The duration of time spent in a given state (such as months of continuous unemployed), the return to a key state after departing it (such as going back to paid employment after leaving the labor market for a while), the number of times a particular kind of move takes place (e.g., the number of involuntary job changes) are all policy-relevant aspects of trajectories. Yet, among the four papers just cited, only Quinn, Burkhauser and Myers (1990) pay systematic attention to these aspects of trajectories of transitions to retirement.

Quinn, Burkhauser and Myers (1990) seem to have paid explicit attention to durations of stay in different states. However, they do not identify specific trajectories or "retirement sequences" in the terminology of Gustman and Steinmeier.

In short, the current gap in published information about trajectories of transition to retirement across the spectrum of OECD countries is quite major, and perhaps serious in terms of handicapping the policy-development processes concerning issues linked to pathways to retirement and gradualness of transition to retirement in preparation for managing the effects of the massive wave of transitions that the Baby Boom Generation will unleash during the second decade of this century.

Principles and procedures for mapping and classifying a large number of trajectories are presented and illustrated above. It is proposed that classification be primarily rules-based, where there is a focus on defined properties of trajectories. However, combinations of rules-based grouping and optimal matching would, in some research contexts, be desirable.

Key limitations and issues

Key limitations of this work arise in connection with concepts, data source, estimation and analysis method, at least. The following is a listing of some of the limitations.

Concepts

At the conceptual node of limitations there are key problems connected with the central concepts:

• Retirement - it is not a purely behavioral (objectively measurable) variable; it is intrinsically a social institution that includes norms and collectively supported values as well as behavior
• Transition to the state of being retired - the component events are highly subject to analysts' choices and whether that has a well defined commencement point is an issue for debate
• Closed trajectory - why choose exactly six months of absence from the labor market with reception of retirement-related income to identify closure, and what should we make of the person who seems to re-open her trajectory after the end of the observation period?

Data source

Our data source creates problems for analysis at both ends of the six-year observation period. At the start, there is insufficient information about respondents' reception of certain kinds of income and labour market behaviour in the preceding year. This has made difficult a precise identification of the start date of the transition for certain respondents. In this connection, knowing the month in which a person began receiving certain kinds of retirement-related income would be very useful - for example, it would allow is to use only one calendar year's data for determining who had begun the transition to retirement.

Although it would be prohibitively expensive to correct this defect, it is worthy of note that problems arise in the analysis because of trajectories that are unclosed in December 2001. Knowing what happened in these trajectories after that date would be very useful, especially for measuring the durations of transitions. Without this information an interval-level measurement is not possible.

As pointed out with emphasis earlier, the data source fails to include the crucial subjective dimension of retirement processes, and provides a sample that is too small for several key population subgroups.

Finally, it badly needs improved coverage of the work-history, health, social-participation and family-caring dimensions of respondents' lives.

Despite these limitations, SLID is an extremely valuable data resource for studying labor-market-related behaviour of people in the prime ages for making the transition to retirement. For explanatory models, it contains a wealth of auxiliary variables that no administrative data source has any chance of matching. We note particularly the data on life events and on cultural background - the latter being covered in a manner superior to any other Statistics Canada database in our opinion.

Estimation

Linked partly to the data source limitations are substantial shortcomings in measurement/estimation procedures:

• Issues exist regarding identifying who is making the transition to retirement and when they began the process, and who really has a very low probability of re-entering the labor market after being absent from it, while receiving retirement-related income, for six months right at the end of the observation period (our measure of closure).
• Although durations of stay are computable, we could greatly improve their accuracy by timing all events down to their month of occurrence, and if we had questions that allowed us to identify certain starting dates that occurred before the first reference date of the survey.
• There is a key duration-measurement issue regarding speed of closure - we should have timed departure from the labor market along with reception of retirement-related income down to the month, including months before the January 1996.
• There is an issue of inappropriate omission concerning people who have retired in all reasonable senses except they are not receiving any form of retirement-related income. An effort should be made to tease out an estimate of how many people of this kind are in our data set and what are certain features among their attributes.

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Notes

1. The authors thank the peer reviewers for their contributions to improving earlier drafts of this chapter. The comments of Stéphane Crespo, Hervé Gauthier and Georges Langis were especially helpful. Assistance from Harpreet Randhawa is gratefully acknowledged. All opinions and errors herein are our sole responsibility.
2. Many readers will insist that retirement is only a process. Current usage in the literature indicates that "retirement" has different meanings depending on the context created by the sentence in which it is being used.
3. While at least two other sudies (Blau 1994, Quinn 2003) contain information which states or implies that quarterly time intervals were used, neither of them provides descriptions of trajectories that allow anyone gaining access to their lists of trajectories to compute a variety of usful measures of durations of stay.
4. The definitions of "retirement" in the literature tend ot focus upon one or more of the following: either (a) individuals' attitudes and intentiosn known via their declarations, or (b) individuals' behavior relative to the labor market, or (c) individuals' commencement of reception of pension or other retirement-related income. One key feature of the widely used definitions is that they refer, at least implicitly, to a process in which a person departs either from a long-held "career job" or from the paid-labor market.
5. Addign subjective information (peoples' sense of their life stage, and their related plans and expectations) would greatly improve this definition. This dimension is omitted here because gaps in our data source prevent its application.
6. We acknowledge that such decisions, steps or activities are not always voluntary. In many persons' lives , they may be forced upon the persons by circumstances beyond their control.
7. In subsequent waves of the HRS, questions about retirement plans and intentions were not repeated. Thus researchers starting with any HRS wave other than Wave 1 have the same limitation we are now identifying in SLID.
8. Since the list that follows implies extensive manipulation of monthly data, it is worthwhile to comment on why there is so muchfocus on the time interval of one quarter. We felt that where one wishes to refer to a respondent holding down a new job, or to the person leaving the labor market, the duration of stay in either of these two states should be long enough to prompt an analyst to think that the respondent was on the way to settling into the state. One month seemed too short a period, and three months seemed more useful. It is recognized that these are only judgments.
9. The number that precedes each position described in this list is used below in describing trajectories.
10. Sixty-three of 709 respondents in the 1996 cohort who were judged to be in transition were lost from teh survey (due to death, for example) over the four years.
11. By restricting the sample to those that were paid employees in both years, we greatly reduce the potential bias from accidentally including persons that in fact began their transitions before 1996.