A Cohort-Based Model of Labor Force Participation, Schemes and Mind Maps of Statistics

Download A Cohort-Based Model of Labor Force Participation and more Schemes and Mind Maps Statistics in PDF only on Docsity! Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. A Cohort-Based Model of Labor Force Participation Bruce Fallick and Jonathan Pingle 2007-09 NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers. A Cohort-Based Model of Labor Force Participation by Bruce Fallick and Jonathan Pingle1 December 2006 Abstract The probability that an individual participates in the labor force declines precipitously beyond age 50. This feature of labor supply suggests that ongoing shifts in the age distribution of the population will put substantial downward pressure on the aggregate labor force participation rate. However, the aggregate rate is also influenced by trends within age groups. Neglecting to model both within-group influences and shifting population shares will doom any estimate of aggregate labor supply. We develop a model that identifies birth cohorts’ propensities to participate, uses these propensities to derive age-specific trends in participation rates, and explicitly incorporates the influence of shifting population shares in estimating aggregate labor force participation. 1The views expressed in this paper are those of the authors and do not represent the view of the Federal Reserve System or its staff. The authors wish to thank Stephanie Aaronson, Andrew Figura and William Wascher who co-authored a related paper on this topic. In addition, we received useful input from Daniel Aaronson, Julie Hotchkiss, Joseph Lupton, Mark Schweitzer, Daniel Sullivan, Joyce Zickler and seminar participants at the Bureau of Labor Statistics. Leslie Carroll and Andrew Strauss provided expert assistance. Author contact information: Bruce Fallick, Senior Economist, Board of Governors of the Federal Reserve System, 20th and C Streets, Washington, D.C., 20551-0001, 202-452-3722, bruce.fallick@frb.gov; Jonathan Pingle, Economist, Board of Governors of the Federal Reserve System, 20th and C Streets, Washington, D.C., 20551-0001, 202-452-3816, jonathan.f.pingle@frb.gov. 4 market, and discuss the results. The ninth section focuses on the past several years, and the tenth section concludes. II. The influence of population shifts In any period, the low-frequency changes in the aggregate participation rate can be decomposed into the influence of changes in the demographic distribution of the population and the influence of changes in labor supply behavior within the various demographic groups. One useful decomposition of the aggregate labor force participation rate into the contributions of the participation rates and population shares of the several groups follows the identity, , , , ,[( ) * ( )* ( ) *( )]t j j t j t j j j t j j t j j R R R R S R R S R R S S− = − + − + − −∑ (1) where R denotes a participation rate, S denotes a population share, t indexes years, j indexes demographic groups, and overbars denote means over time. Thus, Rt is the aggregate participation rate in year t, Rj,t is the participation rate of group j in year t , and R-bar and Rj–bar are, respectively, the mean of the aggregate participation rate and the group j participation rate over the sample period. In this way, the deviation of the aggregate participation rate in any year from its sample mean can be decomposed into the contributions of a) the typical difference between each demographic group’s participation rate and the overall rate, weighted by the group’s population share, b) the deviation of each group’s participation rate from its own mean, weighted by the group’s average population share, and c) an interaction term, which, it turns out, is negligible. Changes over time in the first term can be interpreted as the contribution of changes in a group’s population share to the evolution of the overall participation rate, and changes over time in the second term can be interpreted as the contributions of changes in the group’s participation rate to that evolution.3 3 A more common decomposition would be: , ,[ *( ) ( )* interaction]t j j t j j t j j j R R S S R R S= − + − +∑ 5 Figures 4 and 5 illustrate this decomposition for twelve age-sex groups. Looking back over history, the evolution of participation rates for particular groups has been the more important factor, although demographic shifts have played a role as well. Over the period roughly from 1948 to 1965, the aggregate participation rate was fairly flat, as an increase in the share of the population (especially women) over age 64 and declines in the participation rates of men in several age groups were offset by an increase in the participation rates of prime-aged (25-64) women. Over the period roughly from 1965 to 1990, the big story was a large increase in the participation rates of young and prime- aged women, which overwhelmed decreases in the participation rates of prime-aged and older men, and a further increase in the share of the population (again especially women) over age 64. From roughly 1990 to 2000, further, smaller, increases in the participation rates of prime-aged women were offset by small declines in the participation rates of young and prime-aged men. Since then, beginning at about the same time as the 2001 recession, the aggregate participation rate has fallen. How much of this is best described in terms of these sorts of low-frequency movements, and how much in terms of the business cycle and other temporary phenomena, is a question we will return to below. III. The influence of birth-year cohort The increases in the participation rate of women, and the concomitant decline in the participation rate of men, likely reflected numerous factors such as evolving tastes, reproductive technology, wealth, education, social attitudes, and the development of the retirement, welfare, and financial systems. Some of these changes arguably were to be internalized into the behavior of new generations more easily than into the behavior of mature cohorts who had already made “sticky” choices. And, indeed, among women in particular, much of the change in the aggregate participation rate appears to have resulted from progressively higher average participation rates of successive cohorts, as opposed to increases in age-adjusted participation within cohort; that is, entering cohorts of women had higher participation rates for their ages than did the cohorts who proceeded them. However, such a formula attributes a positive contribution to aggregate participation to any group whose population share rises, and a negative contribution to any group whose population share falls, regardless of whether the group’s participation rate is above or below the average. In contrast, formula (1) takes into account that when the population share of one group rises, that necessarily means that the share of the other groups falls. 6 The model we propose in the next section estimates observed attachment of cohorts in the labor force as a basis for considering their future attachment, building on a rich literature. John D. Durand (1948) recognized policymakers’ need for labor force and participation rate projections for the post-war period. Not surprisingly, his work modeled demographic shifts and trends toward early retirement. However, he explicitly recognized an intrinsic propensity to supply labor that was birth-year specific: “As they grew older, each successive generation of women seems to have retained the greater propensity to be in the labor force which it developed in early adulthood, and so the higher percentages of labor force members have gradually been transmitted throughout the age groups from the late 20’s to the early 60’s,” he wrote, relying on decennial censuses from 1890 to 1940 for his analysis.4 Durand’s observation was prescient. Figure 6 shows the labor force participation rates for three age groups of women: age 35 to 44, age 45 to 54 and age 55 to 64. Each line shows the participation rate of an age group over time. However, instead of the year of observation, the x-axis shows the birth year for the middle age of the group. In this way, the lines are shifted so that each birth cohort is vertically aligned with itself at different ages. The participation rate of the 45-54 year old group (the dashed line) appears to exhibit three rough inflections, in the vicinity of years 1960, 1975, and 1997, corresponding to the cohorts born around 1910, 1925, and 1947. The first two of these inflections line up well with the 55 to 64 year old group (the dotted line), meaning that the inflection points in the two age groups seem to be related to when the cohorts born in 1910 and 1925 passed through. The cohort associated with the third inflection (those born around 1947) are not quite old enough to exhibit that inflection in the older group. But that third inflection point can be seen when that cohort was 35-44 years old (the solid line). Similarly (not shown), beginning in the mid-1960s and ending in the late 1970s, successive cohorts of 16-24 year old women had higher participation rates than their predecessors. Participation rates of successive cohorts 25-34 year olds stopped rising about ten years later, in the late 1980s, suggesting that the participation rate in each of these age groups at a given time is at least partly related to which birth cohort is passing through that age at that time. 4 Durand (1948), page 123. See also Goldin (2006). 9 fixed effect; b is birth year; ε* is an error term, and we have suppressed the gender subscripts. This specification assumes that each birth-year cohort has a general propensity to participate in the labor force that is determined by various unmeasured factors. This propensity is quantified by β, the log of which can be viewed as a cohort-specific intercept. However, the members of different cohorts share a common baseline pattern of participation over the life cycle, being, for example, low when at school or retirement ages and higher during prime earning years. This common baseline age profile is represented by the age-specific intercepts, α* , which are assumed to be constant over the sample period. For practical reasons, we wish to aggregate this up to the fourteen age groups for which participation rates are published by the Bureau of Labor Statistics. Equation (3) does not aggregate easily, but we can approximate it by a set of fourteen estimating equations (one for each age group in the data) for each gender of the form: 1989 , , , , 1907 1log log log logg t g g t g b t b g t bg LFPR X C n α λ β ε = = + + +∑ g = 1 to 14 (4) where g indexes the age groups, t indexes the calendar year, and b indexes birth years. The Cg,b,t are indicator variables that equal one if the corresponding cohort b appears in that age group g at time t , and ng is the number of ages in age group g. Xt is a vector of cyclical (and, later, other variables), the α are age group fixed effects, and the β are birth year or cohort fixed effects. The degree of cyclical sensitivity (λ) varies by age group, while the cohort effects do not -- that is, the cohort effects are constrained to be the same across all equations in which the cohort appears. The age effects (α) are constant. For each gender, the 14 equations are estimated simultaneously using a least squares algorithm. Counting both the men and the women, we estimate about 260 parameters in 28 equations. The age effects (α) and the cohort effects (ß) can be combined to calculate a trend participation rate for each age-sex group. 10 , , 11989 , , , , 1907 ( )g b t gC n gender g t gender g gender b b TrendLFPR α β = = ∏ (5) In other words, we compute the trend participation rate for each age group and gender for each year from the estimates of the age effect and the cohort effects for the cohorts that appear in that age group in that year. These group-specific trends can be weighted by the relevant population shares at each point in time and summed to produce an aggregate trend: , , 114 1989 , , , , 1 1907 ( )g b t gC n t gender g t gender g gender b gender g b TrendLFPR popshare α β = = = ∑ ∑ ∏ (6) Through the population weights, the model explicitly incorporates the more traditionally modeled demographic shifts in the age and gender distribution. V. Estimation Issues There are a few technical issues worth noting before we move on to discuss the estimates from this model. A. Adjustments to the data on the labor force In order to make the data on the labor force participation rates consistent over time, we have adjusted the published data for discontinuities caused by the introduction at various times of updated population weights, the redesign of the CPS in 1994, and the change to compositing procedures in 1998. B. Cyclical controls The business cycle is represented in the model by the contemporaneous and two lagged deviations of employment in the nonfarm business sector from an estimate of its trend. The trend is derived from an HP filter, with the smoothness parameter for the quarterly data set to 2800. This has the virtue of setting the trend so that it tends to coincide with the actual level of employment when the unemployment rate was at the Congressional Budget Office’s estimate of the NAIRU. In order to prevent endpoint 11 bias in the HP filter from unduly affecting the estimate of trend employment in recent years, we assumed that trend employment increased at an annual rate of ½ percent after the fourth quarter of 2001, the last quarter in which the HP filter was equal to the actual level of employment.5 C. Identification and normalization The cross-equation constraints (i.e., that the cohort effects are the same at all ages) identify the cohort effects up to a scale factor. As a cohort moves from one age category to the next, observed changes in the age group’s participation rate identify the relative level of the cohort’s effect. However, a normalization is needed because the allocation of the overall level of the aggregate participation rate, so to speak, between the cohort effects and the age effects is arbitrary. We could allow the cohort effects to be in the units of the dependent variable, or allow the age effects to be in the units of the dependent variable. We chose the latter. In particular, we set the cohort effect for the cohort born in 1969 equal to one. Thus, for that cohort only, the estimated age profile directly represents that cohort’s trend participation rate at each age. D. Cohorts with few observations Although each birth year’s cohort effect is constrained to be equal across all age categories, we do not constrain the cohort effects to evolve in a particular way from birth year to birth year. Rather, each cohort effect is freely estimated (relative to the “numeraire” cohort born in 1969). However, we estimated the cohort effects for the cohorts that entered the labor market after 1996 were in a different fashion. We treated these eight cohorts differently because there are too few observations with which to reliably estimate their cohort effects. In particular, we are concerned about the possible 5 We chose the post-2001 growth rate to match the average change in employment from 2001:Q3 to 2005:Q4 because the unemployment rate in both quarters was 5 percent. Because of concerns about the endogeneity of the unemployment rate to changes in labor force participation and the potential for correlated measurement errors in the two series (which are derived from the same survey), we did not use the unemployment rate gap directly. 14 ways not correlated with their birth years. In other words, the female age profile was evolving with time while the basic model assumes it was fixed.9 VII. Evolution of the age and cohort profiles: The enhanced model The baseline age profile represented by the αg parameters in equation (4) is assumed to be constant across time. It is intended to capture a basic pattern of life-cycle behavior, and the level of the age effect for any age group is identified by the labor force behavior of the cohorts that appear in that age equation during the sample period. Similarly, the cohort effects represented by the β parameters in (4) are assumed to be constant across time. They are intended to capture the basic propensity of a birth cohort to participate. As the estimates from the basic model demonstrated, the life-cycle pattern of participation does not appear to have been close enough to constant across cohorts (or time) for that model to be an adequate approximation of reality. Or, equivalently, the relative propensity to participate of a cohort has not been sufficiently constant across ages (or time).10 As various economic and social factors evolved, the age profile of participation evolved as well. The failure of the basic model to capture the curvature in the participation rates of women, in particular, can be attributed to the model’s failure to allow cohort profiles or age profiles to evolve. In this section we put forward an “enhanced” model that allows these profiles to change. In doing so, we necessarily blur the analytically convenient distinction between the influence of age and the influence of “era” on participation. One approach to modeling these changes would be to allow the age effects or the cohort effects to evolve slowly over time according to some predetermined process. However, this method puts a great deal of the weight of identification upon the choice of process, and does not contribute to economic interpretation of the evolution. Instead, we estimate changes in the shape of the age profiles by including on the right-hand side of the model variables that represent the economic and social changes that 9 In addition, although the model fits the aggregate trend for men fairly well, the estimated trends for men in their 60s exhibit too little bend in the opposite direction. 10 Because age, birth year, and time are linearly dependent, allowing the age effects to change over time is equivalent to allowing them to change across cohorts, and allowing the cohort effects change over time is equivalent to allowing them to change across ages. 15 we suspect have been, or are likely to be, of greatest significance. That is, we amend the basic model to include more than just the cyclical controls in the X vector. Thus, equation (4) is replaced by 1989 , , , , , 1907 1log log log logg t g g g t g b t b g t bg LFPR X C n α λ β ε = = + + +∑ g = 1 to 14 (7) again suppressing the sex subscripts, where now the variables in the vector X can vary by age group (g) as well as time. Altogether, we estimate 322 parameters in 28 equations. We continue to assume that conditional on the variables in X , the age and cohort effects are constant over time. However, these effects now have a different character: The additional variables mean that the age and cohort effects by themselves will no longer fully describe how participation rates evolve as a person ages or across cohorts. Put differently, the age or cohort effects will no longer fully describe the age or cohort profiles of participation; these profiles will now also depend upon the variables in X. The age effects themselves may be viewed as defining a baseline or average age profile from which particular cohorts deviate in accordance with the X variables, or as residuals that pick up the life-cycle pattern that we have failed to capture through the included variables. Similarly, the cohort effects may be viewed as defining the fundamental propensity of a cohort to participate, from which that cohort may deviate at particular ages in accordance with the X variables, or as residuals that pick up the influences on the cohort that we have failed to measure with the included variables, i.e., a persistent residual that is constant across time and age. In either case, full age or cohort profiles, of the sort shown in figure 7 and figure 8 for the basic model, will need to include both the age or cohort effects and the relevant variables, and it will no longer be possible to decompose the trend in participation into disjoint age and cohort components. The condition that the variables in X may vary by both age and time is quite general. In the cases of some of the variables we will discuss momentarily, such as educational attainment, the variable is constant across time within a cohort – it “ages” with the cohort, so to speak – but varies across cohorts. While in others, such as marriage 16 rates, the variable varies over time or age within a cohort, as well as varying across cohorts. Note that the coefficients on each variable in X vary freely by age/sex group, except where we have imposed our prior that the coefficient be zero. Because the coefficients differ across age groups, movements in the variables over time change the shapes of the age profiles even in those cases where the variable itself does not vary by age group. The included variables fall into three broad categories: human capital, retirement financing, and family structure. We will discuss each in turn, as well as one category – immigration – that we did not include. There is a good a priori case to be made for each of the variables we discuss (and others that we do not) to have a significant and independent effect on labor force participation, that is, a good case for including each of them in the model. However, many of these variables have shared broad patterns of movement over our sample period. Indeed, several are largely monotonic: Life expectancies, dependency ratios, and educational attainment have mostly risen over time; fertility and the frequency of defined-benefit pensions have mostly fallen. The series do exhibit variation that will facilitate identification. Even life expectancies are not completely smooth and exhibit non-linear variation, and educational attainment accelerated for the cohorts eligible for the Vietnam era draft, then flattened out and more recently, for women in particular, attainment has picked up again. However, because many important economic influences have trended similarly over the last three decades, choosing which variables to include and in just what fashion is largely a matter of judgment, and the coefficients on the relatively few included variables must be interpreted cautiously. The estimated coefficients from our preferred specification of the enhanced model appear in table 1. A. Human capital a. Return to education. The first human capital variable we include in the model is an estimate of the return to a college education relative to a high school education. This variable is constructed from a regression of wages on a standard set of variables that 19 Aside from education, which we treated above, several factors would appear to be among the most likely to affect the ability to finance retirement.15 a. Parameters of the Social Security program. The four most important changes to the Social Security retirement system in our sample period have been to the earnings test, the early retirement rules, the retirement age, and the delayed retirement credit. We summarize the latter three developments by including two variables for the average fraction of the Primary Insurance Amount (PIA) a man would receive if he were to retire at a particular age. One variable is used for the 62-64 age group, and a higher value is equivalent to a smaller penalty for retiring early. The other is used for the 65-69 age group, and a higher value of the variable implies a greater reward for delaying retirement. The coefficients on these two variables have the expected signs, with a smaller penalty for retiring early lowering participation among 62-64 year old men, and a greater reward for retiring later raising participation among 65-69 year old men. Changes to the earnings test during this period coincided with the changes in the delayed retirement credit, so the estimates may reflect some influence of this change although we did not include a separate variable for them. We tried these variables in the equations for older women. However, the coefficients were never statistically significant and their signs and magnitudes made little sense. This may be because the participation rates of women over most of our sample period are already so low by the ages at which these parameters would be most relevant, leaving little room for the changes in the Social Security program to make an estimable difference. If so, then these program parameters may play more of a role in the years ahead as more women may be nearer to the line between participation and nonparticipation at these older ages. b. Private pension plans. Large changes have taken place in the coverage and character of private pension plans as well. As is well known, the percentage of workers covered by defined benefit pension plans has been declining for some time, while the incidence of defined contribution plans has been rising.16 DB pension plans tend to 15 For an overview of the economic influences on the labor force attachment of older individuals, see Burtless (1999). For an analysis of recent changes to social security programs and rules, see Loughran and Haider (2005). For details on the Delayed Retirement Credit see Pingle (2006). 16 See Poterba, Rauh, Venti and Wise (2006). 20 provide strong incentive for covered workers to remain at work until a particular date or age, and then incentive for them to retire, while DC pensions tend to be more neutral towards the date of retirement. As a result, we might expect the changing composition of private pensions to affect labor force participation rates at various ages. We tried variables for both the level and the proportion of DB coverage, but found no significance for these variables in our model. We left them out of our preferred specification. c. Life expectancy. In any forward looking model of labor supply in which workers do not rely entirely upon Social Security or private defined-benefit pensions to finance their retirement, or where the values of those benefits are fixed in nominal terms, we would expect a longer expected lifespan to increase the number of years a person chooses to work, in order to save more for the longer expected retirement and to reduce the number of years of retirement that need to be financed. We expect these extra years to primarily take the form of later retirement. We do not expect persons in prime working years to be near this margin; and it is our considered opinion that young people, who may, in principle, choose to begin working sooner or increase their schooling in anticipation of a longer life, do not, in fact, give much thought to the far future. In addition, to the extent that life expectancy is correlated with better health more generally, longer life expectancies should imply that older individuals would be physically able to work longer into their lives. We include a variable for gender-specific life expectancy as of age 65, calculated from life tables published by the Census Bureau,17 in the equations for ages 62 and above. Greater life expectancy is associated with higher rates of labor force participation for men and women in the three oldest age groups (although not statistically significantly so for the 65-69 age group of women). d. The age distribution of the population. The prospects for the generosity of the Social Security system and of private pensions plans depends in large part on the ratio of potential retirees to likely workers, and it is the current and impending increases in this 17 These are not true forecasts of the longevity of an individual or cohort, in that they do not take into account how age-specific mortality rates may change as a cohort ages. Rather, in each year they are based on the current mortality rates for individuals of various ages. Thus, the life expectancy of a person aged 65 in any given year reflects the state of medical knowledge and technology, environment, wealth, and other factors as of that year. Nevertheless, in broad terms this variable does reflect the advances in health over history. 21 ratio that drive the current concerns about the future of Social Security and Medicare. Accordingly, we used Census Bureau estimates and projections to construct a “potential dependency ratio”, defined as the ratio of the population over age 64 to the population age 25-64 that a cohort saw or can expect to see at age 65. However, we found that this variable did not add to the power of the model once the variable for life expectancy was included, and so we did not include it in the specification presented here. e. Private wealth. For many persons, private wealth, including both financial assets and housing wealth, play an important role in financing retirement. Therefore, one might expect the level of a private wealth to influence the timing of retirement. Indeed, a popular explanation offered for the increase in the labor force participation of older persons following 2000, while the participation rates of other age groups were falling, was that the decline in stock prices, especially to expectations formed during the long bull market, had induced many to delay their retirements. Several researchers have explored the role of wealth in retirement decisions, and suggested that it may be an important element.18 We experimented with several measures of household wealth as explanatory variables in our model, including total household net wealth, stock market wealth, and housing wealth, but found no measures with reasonable explanatory power, even for the age groups near retirement age. f. Disability benefits. Numerous studies have reported a relationship between SSDI and the long-run downward trend in participation among men. We tried a variable for the disability award rate—the fraction of applications for benefits that were approved in each year—to represent the generosity of the Federal disability insurance program, and, in particular, the changes over time in the stringency of the criteria for being awarded disability benefits. Although this variable is not completely independent of other factors that influence participation—the composition of the applicant pool surely varies with the state of the labor market, for example—it is an improvement in this regard relative to using a measure of disability benefits recipiency. The disability variable did not add significantly to the explanatory power of the model, so we left it out of our preferred specification. 18 For example, Coronado and Perozek (2003). 24 Immigration also has the potential to influence the population shares. For example, unmeasured immigration may have shifted the population distribution toward age groups with high participation rate without being captured in the government’s population estimates. However, the influence of such missing persons is likely small in the aggregate. For example, if one holds within-group participation rates constant and adds a hypothetical 100,000 persons per year in unmeasured immigration since 2002 to the population estimates for 25-29 year old men (who participate with more than 90 percent likelihood), this would raise the level of the participation rate by less than one- tenth percentage point.21 VIII. Results from the enhanced model As described in section V, we use a measure of the deviation of employment from trend, and two lags, to control for the business cycle. The elasticity of the participation rate with respect to this employment gap for each demographic group (summarized by summing the coefficients) are shown in table 2. For both sexes, the youngest group (those 16 and 17 years old) is by far the most sensitive to the business cycle. Beyond that, among men participation rates are most cyclically sensitive for the youngest and oldest age groups, while the middle age groups (35-59) display relatively little sensitivity. For women, the estimated cyclical sensitivity remains fairly high through their mid forties, but the estimates suggest that women’s participation is countercyclical in their late 50s and early 60s. The relative importance for the historical evolution of the aggregate labor force participation rate of the various other explanatory variables described in section VII depends not only on their estimated coefficients, but also on the extent of variation in each of the variables during our sample period. In order to provide a sense of this, table 3 presents the estimated effect of a one standard deviation increase in each variable on the aggregate trend participation rate. For this illustration, we used 2005 population weights to aggregate the estimates from the 28 separate equations. 21 If this seems small compared to the influence of retiring baby-boomers, bear in mind that an immigrant raises the population as well as the labor force, while a retiree lowers the labor force without affecting the population. 25 Of the included variables, variation in the marriage rate is estimated to have had by far the largest influence on the historical trend, as the increases in participation have coincided in recent decades with the tendency of more couples to postpone marriage or forgo marriage altogether. Indeed, the decline in marriage rates slowed in the years around 1990, at about the same times that female participation rates stopped their rapid ascent. Aside from marriage and its interaction with young children, life expectancy and college attainment are estimated to have had the largest impact on the aggregate rate. Note, however, that although the model estimates that longer life expectancies have raised participation by raising within-group participation rates, that estimate does not incorporate the effect of the corresponding increase in the relative number of elderly individuals, which would put downward pressure on the trend. Note also that although changes in the social security program are estimated to have had, on net, relatively little influence, they are more important within the narrow age groups where these variables are relevant. As we emphasized above, in the enhanced model the age and cohort effects do not fully represent the age and cohort profiles, that is, how average participation rates evolve over the life-cycle or across cohorts. Instead, age or cohort profiles must include both the age or cohort effects and the influence of the time-varying variables, except those that capture cyclical changes in participation. To construct cohort profiles, we calculate the trend participation rate for each age group in each year as 1989 , , , , 1919 1log log log logg t g g g t g b t b bg TrendLFPR Z C n α λ β = = + + ∑ , (8) where Z excludes the cyclical variables from the X vector in equation (4). Then for each age group, we trace out a cohort profile by plotting this trend over time, averaging across the birth cohorts that appear in that age group in each year, and indexing by birth year rather than calendar year.22 The age profiles are computed in a similar fashion, except that the contributions of the cohort effects are omitted from the calculation to remove the direct effects of the changing mix of cohorts in an age group over time. In principle, for each birth cohort we 22 Thus, the cohort profiles shown are a centered moving average of the true cohort profiles. 26 could trace out the trend as we move from age group to age group. For purposes of presentation, however, we aggregated into five-year groups of cohorts. Figure 11 shows the cohort profiles for selected age groups. For men, the cohort profiles are generally declining, as successive cohorts have lower propensities to participate in the labor force than their predecessors in each age group, with the notable exception of the oldest age group. Individuals in this oldest group (which begins with the cohort born 1907) exhibit an increasing propensity to participate that no doubt reflects greater expected longevity and better health rather than a latent increasingly favorable attitude towards work at retirement age. Women share this feature at ages 65 and over. In addition, teenage women, like teenage men, have been, by and large, increasingly less likely to participate in the labor force. In the middle age groups, however, successive cohorts of women display higher participation rates to a point, then peak and in the turn down. The age profiles in figure 12 are shown for selected groups of birth cohorts that are well represented in those age groups in order to highlight how those profiles have evolved over time. The profiles for men have been remarkably stable. As can be seen in the upper panel, the age profile segments for the various groups of birth cohorts lie on top of each other for those ages for which they overlap, suggesting that a single age profile applies to all cohorts in the sample. In contrast, the age profiles for women (in the lower panel) are disjoint, suggesting that they have evolved significantly over time. Most notably, more recent cohorts appear to have reached their peak rates of participation earlier in life: Participation rates of the oldest cohorts shown – those born in the 1930s – apparently peak in their late 40s, while rates for those born in the late 1940s peak in their early 40s, and the rates for those born in the late 1960s seem likely to be peaking in their early 30s. Figure 13 shows the enhanced model’s estimated trend for the aggregate labor force participation rate. The model appears to fit the aggregate participation rate rather well. The aggregate trend follows the familiar pattern of rising then flattening, and the enhanced model captures the bend that the basic model missed. The trends for men and women are shown separately in figure 14. 29 especially that the participation of teens failed to recover even after employment growth resumed in earnest in 2003. The decline is puzzling in part because little of it is explained by shifts from market work to school enrollment.25 Even examining the available BLS time use surveys from 2003 to 2005, a period of cyclical recovery in employment, shows that over the two years 16-to-24-year olds reduced both the average hours per day working and the average hours per day in school or school-related activities. In contrast, time spent in personal care and other activities rose noticeably. Minimum wages are also an unlikely culprit. The model already incorporates the real value of the minimum wage, and no discrete change in minimum wages occurred in 2001-2002 to link to the precipitous fall in teenage labor market attachment at that time. More generally, the earnings of younger workers relative to older workers showed no deterioration in the past few years. The low levels of participation among teens remains a puzzle. X. Conclusion In this paper we presented a model of the aggregate labor force participation rate that makes several contributions to the literature on labor supply. First, the model provides a trend-cycle decomposition that is an appealing alternative to aggregate time series models and other smoothing algorithms. For example, the Kalman Filter necessarily relies on history to decide how much recent innovation to pass through to trend. Such a filter risks falsely extrapolating historical experience, and in addition, could misidentify cyclical influences at the end of any estimation period. In contrast, the model we proposal abstracts from the cyclical influence of the most recent data, and allows the observed behavior of cohorts identified over full business cycles to project forward future labor force attachment. In addition, the trends estimated in the paper are more directly interpretable in an economic context, as the influence of demographics and cohorts can be deciphered. Thus, although our model also risks falsely extrapolating historical experience, we can point to the assumptions that lead us astray, or test the 25 As noted by Aaronson, Fallick, Figura, Pingle, and Wascher (2006), much of the decline in participation among teens is due to a decline in the participation rate of teens enrolled in school. Kirkland (2002) suggests that an increased emphasis on school work (instead of working while attending school) has contributed significantly to the decline in teen labor force participation. 30 sensitivity of our model to the underlying assumptions. Arguably, the model we propose thus offers a useful tool for projecting future estimates of labor supply. Second, the model uncovers several interesting features of aggregate labor supply. In particular, in identifying the patterns among female birth cohorts, the model estimates that female labor force participation rates have leveled off not solely because of contemporaneous developments in the labor market opportunities for women, but also because the increases in the generation-specific attachment of successive cohorts of women in the labor force began leveling off with the cohorts born in the early 1950s. This conclusion is based not on simple extrapolations of recent trends, but on observing these cohorts for 40 years, and their successors through several business cycles. The model thus suggests that, barring major changes in policy or environment, women’s labor supply will likely show little further gain in the coming years. Indeed among some age groups, female labor supply has changed direction and is trending down. Entering cohorts of women no longer exhibit substantially more attachment than exiting cohorts, suggesting that this social phenomenon is no longer putting discernable upward pressure on the aggregate rate. Third, the model can be used to ask many interesting questions that we have not yet explored. For example, with appropriate caution, the model could be used to simulate the changes in future labor supply due to changes in immigration policy or further increases in longevity. The model simulations could also be used to build trends for economic aggregates heavily influenced by labor force participation rates, such as aggregate labor income. In sum, we developed a model of the labor force participation rate that combines differences in labor force participation across birth cohorts, differences in participation across ages, and the evolution of the age distribution of the population into a unified structure. We introduced a basic model that captures the intuition of how labor force attachment has evolved over the past thirty years, and an enhanced model that captures more nuanced evolution associated with measurable developments in education, family structure, government programs, longevity, and other variables. While the model fits well over most of history for most age/sex groups, there remain anomalies in the past few years – among teenagers and older persons, in particular. Despite these puzzles, the 31 framework we propose for estimating broad trends in labor supply appears to have many potential uses and offer an interesting line of research. Figure 1 Aggregate Labor Force Participation Rate, 1948:Q1-2006:Q3 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 58 60 62 64 66 68 58 60 62 64 66 68 Percent Aggregate Labor Force Participation Rate Simulation holding within-age participation rates constant at 1996:Q4 levels Source. Bureau of Labor Statistics Note. Shaded area is NBER dated recessions. Figure 2 Population Shares by Age Group (as a percent of the male 16+ population) 16 to 19 20 to 24 25 to 29 30 to 34 35 to 39 40 to 44 45 to 49 50 to 54 55 to 59 60 to 64 65 to 69 70 plus 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 Percent Age Range (Years) 1985 1995 2005 2015 Source: Bureau of Labor Statistics. Note: Figures are adjusted to be methodically consistent. Figure 3 Population Shares by Age Group (as a percent of the female 16+ population) 16 to 19 20 to 24 25 to 29 30 to 34 35 to 39 40 to 44 45 to 49 50 to 54 55 to 59 60 to 64 65 to 69 70 plus 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 Percent Age Range (Years) 1985 1995 2005 2015 Source: Bureau of Labor Statistics. Note: Figures are adjusted to be methodically consistent. Figure 6 Female Labor Force Participation Rates 1890 1895 1900 1905 1910 1915 1920 1925 1930 1935 1940 1945 1950 1955 1960 1965 20 30 40 50 60 70 80 20 30 40 50 60 70 80 Percent Age 35 to 44 Age 45 to 54 Age 55 to 64 Birth year rather than calendar year is shown on X-axis Source: Bureau of Labor Statistics. Note: Figures are adjusted to be methodically consistent. Figure 7 Fixed Effect Value by Age 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 Fixed effect value Age 16 to 17 18 to 19 20 to 24 25 to 29 30 to 34 35 to 39 40 to 44 45 to 49 50 to 54 55 to 59 60 to 61 62 to 64 65 to 69 70 plus Male Female Figure 8 Fixed Effect Value by Birth Year 1910 1915 1920 1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 Fixed effect value Birth year Male Female Figure 11 Labor Force Participation Cohort Profiles 1920 1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 20 30 40 50 60 70 80 90 100 20 30 40 50 60 70 80 90 100 Percent Age 18 to 19 Age 25 to 29 Age 35 to 39 Age 45 to 49 Age 55 to 59 Age 65 to 69 Men 1920 1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 10 20 30 40 50 60 70 80 90 10 20 30 40 50 60 70 80 90 Percent Age 18 to 19 Age 25 to 29 Age 35 to 39 Age 45 to 49 Age 55 to 59 Age 65 to 69 Women Figure 12 Labor Force Participation Age Profiles 16-17 18-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-61 62-64 65-69 70+ 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 Percent Birth year 1935-39 Birth year 1945-49 Birth year 1955-59 Birth year 1965-69 Men 16-17 18-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-61 62-64 65-69 70+ 30 40 50 60 70 80 30 40 50 60 70 80 Percent Birth year 1935-39 Birth year 1945-49 Birth year 1955-59 Birth year 1965-69 Women Figure 13 Aggregate Participation Rate Enhanced Model Results 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 60 61 62 63 64 65 66 67 68 69 70 60 61 62 63 64 65 66 67 68 69 70 Percent Aggregate LFPR Aggregate Trend LFPR Aggregate Predicted LFPR Note: Model estimated from 1977 to 2005. Figure 16 Female Labor Force Participation Rates Enhanced Model Results 1980 1985 1990 1995 2000 2005 30 40 50 30 40 50 Percent Actual Trend Ages 16-17 1980 1985 1990 1995 2000 2005 50 60 70 50 60 70 Ages 18-19 1980 1985 1990 1995 2000 2005 60 65 70 75 60 65 70 75 Ages 20-24 1980 1985 1990 1995 2000 2005 50 60 70 80 50 60 70 80 Ages 25-29 1980 1985 1990 1995 2000 2005 50 60 70 80 50 60 70 80 Ages 30-34 1980 1985 1990 1995 2000 2005 50 60 70 80 50 60 70 80 Ages 35-39 1980 1985 1990 1995 2000 2005 50 100 50 100 Ages 40-44 1980 1985 1990 1995 2000 2005 50 60 70 80 50 60 70 80 Ages 45-49 1980 1985 1990 1995 2000 2005 50 60 70 80 50 60 70 80 Ages 50-54 1980 1985 1990 1995 2000 2005 40 50 60 70 40 50 60 70 Ages 55-59 1980 1985 1990 1995 2000 2005 30 40 50 60 30 40 50 60 Ages 60-61 1980 1985 1990 1995 2000 2005 20 30 40 50 20 30 40 50 Ages 62-64 1980 1985 1990 1995 2000 2005 10 15 20 25 10 15 20 25 Ages 65-69 1980 1985 1990 1995 2000 2005 4 6 8 4 6 8 Ages 70P Figure 17 Contributions to the De-Meaned Aggregate Labor Force Participation Rate 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 Actual LFPR Within-group LFPRs Population shares Figure 18 Labor Force Participation Rate, Ages 16 to 19 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 42 44 46 48 50 52 54 56 58 60 42 44 46 48 50 52 54 56 58 60 Percent of civilians, ages 16 to 19 Actual Trend Simulation