A cohort model of labor force participation.

Kudlyak, Marianna

The aggregate labor force participation (LFP) rate measures the share of the civilian noninstitutionalized population who are either employed or unemployed (i.e., actively searching for work). Prom 1963 to 2000, the LFP rate was rising, reaching its peak at 67.1 percent. The LFP rate has been declining ever since, with the decline accelerating after 2007. Between December 2007 and December 2012, the LFP rate declined from 66 percent to 63.6 percent. Prior to 2012, the last year when the LFP rate was below 65 percent was 1986.

The decline in the LFP rate, which coincided with the Great Recession, raises the question: Is the LFP rate at the end of 2012 close to or below its long-run trend? The question is important to policymakers and economists. If a large portion of the workers who are currently out of the labor force represents workers who are temporarily out of the labor force, then the unemployment rate by itself might not be a good measure of the slack in the economy.

In this article, we discuss the change in the aggregate LFP rate from 2000 to 2012, with an emphasis on the changes in the age-gender composition of the population and changes in the LFP rates of different demographic groups. We then estimate a cohort-based model of the LFP rates of different age-gender groups and construct the aggregate LFP rate using the model estimates. The model is a parsimonious version of the model studied in Aaronson et al. (2006). It contains age-gender effects, birth-year cohort effects, and the estimated deviations of employment from its long-run trend as the cyclical indicator. We Content not available due to copyright restrictions.

1. WHAT COMPONENTS DRIVE THE CHANGES IN THE AGGREGATE LFP RATE DURING 2000-12?

After reaching its peak of 67.3 percent in the first half of 2000, the aggregate LFP rate declined from 2000 to Q2:2004, stabilized for a few years, and then started falling again in 2008. (1) Figure 1 shows the aggregate LFP rate and the aggregate unemployment rate.

[FIGURE 1 OMITTED]

The aggregate LFP rate can be decomposed into the weighted sum of the LFP rates of different demographic groups, i.e.,

[LFP.sub.t] = [summation over (i)] [s.sub.t.sup.i][LFP.sub.t.sup.i], (1)

where [LFP.sub.t.sup.i] is the labor force participation rate of group i, [s.sub.t.sup.i] is the population share of group i, i.e., [s.sub.t.sup.i] [equivalent to] [Pop.sub.t.sup.i]/[Pop.sub.t], and [Pop.sub.t.sup.i] is the population of group i.

Content not available due to copyright restrictions. Figure 3 shows the LFP rates of different age-gender groups. As can be seen from the figures, the developments that took place between Q4:2007 and Q4:2012 are a continuation of the developments that have

[FIGURE 3 OMITTED]

As can be seen from the figure, the experiment with holding the LFP rates of 55-64 and 65+ year-old workers fixed (the dashed blue line) delivers the largest discrepancy between the actual aggregate LFP (the solid black line) and the counterfactual one. Since the LFP rate of older workers has increased, the counterfactual rate lies below the actual LFP rate, and in Q4:2012 stands at 61.7 percent.

The second largest discrepancy (in absolute value) between the actual aggregate LFP and the counterfactual one is obtained from holding the population shares fixed at their 2007 levels (the dashed red line). In this case, the counterfactual LFP rate exceeds the actual one and stands at almost 65 percent in Q4:2012. We see that between 2007 and 2012 the population composition has shifted toward a composition with lower labor force attachment.

The results also show that the counterfactual based on the fixed LFP of 16- to 24-year-old workers (the dashed green line) Content not available due to copyright restrictions. Content not available due to copyright restrictions. and the counterfactual based on the fixed LFP of men (the yellow dashed line)

[FIGURE 4 OMITTED]

The observations above show that the demographic composition of the population and the changes in the LFP rates of different groups have played an important role in the change of the aggregate LFP rate. We now proceed to examine the age-gender and cohort effects in the LFP rates of different demographic groups on the aggregate LFP rate.

2. A COHORT-BASED MODEL OF LABOR FORCE PARTICIPATION

The results in Section 1 show that the time-variation in the LFP rates of different demographic groups are important for the variation in the aggregate LFP rate. In this section, we propose a model for the trend in the LFP rates of different demographic groups. We then estimate the trend in the aggregate LFP rate using the estimated trends in the Content not available due to copyright restrictions.

[FIGURE 5 OMITTED]

As this cohort ages and moves through the age distribution, its stronger labor force attachment carries over to the respective age group.

We think of the demographic and the cohort effects in the LFP rates of different demographic groups as the determinants of the long-run labor force participation trend. To estimate this trend, we specify the following model:

In [LFP.sub.t.sup.i] = [alpha] + in [[alpha].sub.n] [1996.summation over (b=1917)] [C.sub.b,i,t.sup.f] In [[bata].sub.b.sup.f] + 1/n [1996.summation over (b=1917)] [C.sub.b,i,t.sup.m] In [[beta].sub.b.sup.m] + [[epsilon].sub.i,t], (2)

where [LFP.sub.t.sup.t] is the labor force participation rate of age-gender group i, [[alpha].sub.i] is the fixed effect of age-gender group i, [C.sub.b,i,t.sup.m] is the dummy variable that takes value 1 if age-gender group i in period t includes women born in year b, [C.sub.b,i,t.sup.f] is the dummy variable that takes value 1 if age-gender group i in period t includes men born in year b, and n denotes the number of ages in group i. We specify separate cohort effects for men and women, i.e., [[beta].sub.b.sup.f] ([[beta].sub.b.sup.m]) is the cohort-specific fixed effect of a cohort of women (men) born in year b. We assume that each cohort has equal importance in the corresponding age group conditional on the number of cohorts in the group. For the oldest group, 65+, we set n = 20 (setting n = 30 does not have a substantial effect on the results). To identify age-gender and cohort effects, we normalize in ai = 0 and ln [[beta].sub.1969.sup.f] = 0. The model is estimated using pooled quarterly data on the LFP rates of 14 age-gender groups.

The model in equation (2) is a simplified version of a model in Aaronson et al. (2006). Using the estimates from equation (2), we obtain the time series of in [LFP.sub.t.sup.i] for the 14 age-gender groups, [^.[ln [LFP.sub.t.sup.i]]] and calculate [^.[LFP.sub.t.sup.i]] = exp ([^.[ln [LFP.sub.t.sup.i].sub.t.sup.i]] + [[sigma].sub.e.sup.2/2]), where [[sigma].sub.e.sup.2/2] is the variance of [^.[[epsilon].sub.i,t]]. We then construct the estimated aggregate LFP rate as

[^[LFP.sub.t]] = [summation over (i)] [s.sub.t.sup.t] [^.[LFP.sub.t.sup.i]], (3)

where [s.sub.t.sup.i] denotes the actual population share of group i in quarter t. Thus, the population shares capture the effect of the change in the demographic composition of the labor force, while [^.[LFP.sub.t.sup.i]] reflects the age-gender and cohort effects of the different demographic groups. We refer to [^.[LFP.sub.t]] from model (2) as the estimated trend in the aggregate LFP rate.

Life-Cycle, Cohort, and Cyclical Effects

To further understand the behavior of the aggregate LFP rate, we also estimate a model similar to the one in equation (2) with a cyclical indi- Content not available due to copyright restrictions.

Empirical Results

One way to obtain the predictions from the models described in equations (2) and (4) is to estimate the models using the 1976-2012 data, obtain the trend in the aggregate LFP rate (from equation [3]) and the model-predicted aggregate LFP rate from the model with a cyclical indicator, and compare the estimates with the actual LFP rate during 2008-12. Another way is to estimate the model on the 1976-2007 data and then use the estimates together with the assumptions on cohort effects and predict the aggregate LFP rate for 2008-12. The cohort model is sensitive to which approach is used.

One of the concerns associated with cohort models is the end-of-the-sample effect. In particular, the young cohorts observed in the 1976-2012 sample (i.e., those born in 1985-1996) are observed only during the period of the declining aggregate LFP rate. Thus, the model identifies these cohorts' propensity to participate from the period of overall low participation, attributing low LFP to these young cohorts rather than to the model's residual. Given the severity and the length of the Great Recession, the effects of the cohorts born prior to 1985 are also, to a large extent, identified from their labor force participation rates during 2008-2012, the period of the overall low LFP. This is the case for cohorts for which, for example, at least half of the observations come from the 2008-12 period.

To avoid the end-of-sample effect on the estimates, we estimate the models in equations (2) and (4) using the data from 1976-2007. To construct the prediction of the aggregate LFP rate for 2008-12, we assign, for cohorts born after 1991, the average cohort effect of the last 20 cohorts. Figure 7 shows the following series: (1) the actual aggregate LFP rate, (2) the LFP rate constructed from the model with only age-gender effects, (3) the LFP rate constructed from the model with age-gender and cohort effects estimated on 1976-2007 data, and (4) the LFP rate constructed from the model with age-gender, cohort, and cyclical effects estimated on 1976-2007 data. (4)

As can be seen from the figure, the aggregate LFP rate estimated from the model with only age-gender and cohort effects on the 19762007 sample exceeds the actual aggregate LFP rate after 2008, and the two lines coincide at the end of 2012. This measure constitutes our preferred measure of the trend in the LFP rate. The aggregate LFP rate estimated from the model with age-gender, cohort, and cyclical Content not available due to copyright restrictions.

Content not available due to copyright restrictions. cohort and the next is the same as for a set of cohorts observed over the last full business cycle. The aggregate LFP rate based on the models with restricted and unrestricted cohorts are similar, so the figure shows only the results without restrictions. (5)

Discussion

In the model, the cohort effect stands for an average effect of all non-modeled factors (beyond life-cycle, gender, and cyclical effects) that affect the labor force participation of a cohort (i.e., the workers born in a particular year) throughout the period the cohort is observed in the sample. These factors can include both structural and cyclical variables. For example, the availability of and the rules that govern Social Security benefits and disability insurance might influence the decision to look for work versus drop out of the labor force. The wage premium from higher educational attainment might influence the decision of younger workers to go to school rather than participate in the labor force. The availability and cost of child care can influence the decision of mothers to join the labor force.

Consequently, the cohort effects constitute a black box that aggregates these influences and serve as a useful device for accounting exercises. The cohort model, however, might not be the best laboratory for long-term forecasts. In our estimation, we recognize explicitly that the effect of young cohorts is to a large degree identified from the few years during which we observe these cohorts in the data. In particular, for the youngest cohorts, a low cohort effect can be due to the true low propensity of these cohorts to participate or due to the model attributing low cyclical LFP to the cohort effect. In our exercise, we control for these effects. A forecasting exercise would inevitably involve assumptions about the cohort effects going forward. It is possible that, for example, the youngest cohorts who are not participating currently due to schooling will, in fact, increase their LFP as they grow older. The cohort model does not provide information to support or reject such scenarios.

Content not available due to copyright restrictions. influence the labor force participation decision of different demographic groups.

The author is grateful, without implicating them in any way, to Bob Hetzel, Andreas Hornstein. Marios Karabarbounis, Steven Sabol, and Alex Wolman for their comments. The author thanks Peter Debbaut and Samuel Marshall for excellent research assistance. The views expressed here are those of the author and do not necessarily reflect those of the Federal Reserve Bank of R ichmond or the Federal Reserve System. E-mail: marianna.kudlyak@rich.frb.org.

REFERENCES

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(1.) The data reported in the article are from HAVER (SA), unless stated otherwise. The last data point at the time of the analysis: December 2012.

(4.) The estimates are available from the author.

(5.) The result with restrictions is available from the author. This result motivates estimation of the benchmark model (i.e., using the 197&2007 data) without restrictions on cohorts.