This paper presents a simple methodology for decomposing changes in the aggregate labor force participation rate (LFPR) over time into demographic group changes in labor force participation behavior and in population share. The purpose is to identify the relative importance of behavioral changes and population changes as driving forces behind changes in the aggregate LFPR.Labor supply

Julie L. Hotchkiss

English

Research Papers in Economics

 
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Decomposing Changes in the Aggregate  
Labor Force Participation Rate 
 
Julie L. Hotchkiss 
 
Working Paper 2009-6 
March 2009  
 
 
The author thanks Alexander Ellis of the U.S. Census Bureau for his help in obtaining historical population projections. She also 
thanks Bruce Fallick for sharing his model’s forecasts of labor force participation rates. Helpful comments were received from 
Robert E. Moore and John Robertson. Additional assistance was received from Elaine Clokey, Kathryn Rees, and Amanda Kay 
Seals. The views expressed here are the author’s and not necessarily those of the Federal Reserve Bank of Atlanta or the 
Federal Reserve System. Any remaining errors are the author’s responsibility. 
 
Please address questions regarding content to Julie L. Hotchkiss, Research Department, Federal Reserve Bank of Atlanta, 1000 
Peachtree Street, N.E., Atlanta, GA 30309-4470, 404-498-8198, julie.l.hotchkiss@atl.frb.org. 
 
Federal Reserve Bank of Atlanta working papers, including revised versions, are available on the Atlanta Fed’s Web site at 
www.frbatlanta.org. Click “Publications” and then “Working Papers.” Use the WebScriber Service (at www.frbatlanta.org) to 
receive e-mail notifications about new papers. 
FEDERAL RESERVE BANK of ATLANTA       WORKING PAPER SERIES 
Decomposing Changes in the Aggregate  
Labor Force Participation Rate 
 
Julie L. Hotchkiss 
 
Working Paper 2009-6 
March 2009 
 
Abstract: This paper presents a simple methodology for decomposing changes in the aggregate labor force 
participation rate (LFPR) over time into demographic group changes in labor force participation behavior 
and in population share. The purpose is to identify the relative importance of behavioral changes and 
population changes as driving forces behind changes in the aggregate LFPR.  
 
JEL classification: J11, J21, E24 
 
Key words: labor force participation, decomposition, forecasting 
 
  
- 1 - 
Decomposing Changes in the Aggregate Labor Force Participation Rate 
 
I. Introduction 
  The percent of the population willing to supply their labor to the market can have a 
profound impact on the potential growth of the economy.  Human capital is an important 
component of the production process and an ever growing supply of labor allows an ever 
growing level of production without putting too much pressure on costs and, thus, prices of final 
products.  The percent of the population willing to supply their labor is measured by the labor 
force participation rate (LFPR) which experienced significant growth beginning in the mid-
1960s, driven largely by the rise in the LFPR among women (see Figure 1).  Since 1997, the 
aggregate LFPR began a decline that has continued (with fits and starts) through 2008. 
  There have been many attempts to identify the source of the relatively recent decline in 
the aggregate LFPR in the U.S.  Some have linked the decline to cyclical factors, yet the decline 
started before and continued past the 2001 economic downturn, suggesting an additional 
structural component to the change (see Aaronson et al. 2006).  Among different demographic 
groups, the most significant declines in labor force participation have been observed among the 
young and among working age women (see Cohany and Sok 2007, Lerman 2007, Mosisa and 
Hipple 2006, Hotchkiss 2006, Bradbury and Katz 2005, and Kirkland 2002). 
  These efforts to explain changes in the aggregate LFPR by focusing on behavioral 
changes among certain demographic groups neglects the simple algebraic contribution that 
population changes can make to the determination of the aggregate LFPR.  This paper illustrates 
how changes in the aggregate LFPR can be decomposed into changes in the labor force 
participation behavior of different demographic groups and changes in each group's population 
share.  This exercise demonstrates that the decline in population share of working age men and  
- 2 - 
women actually dominated the change in participation rates among working women and among 
youth that have received so much recent attention.  In addition, this paper illustrates how this 
decomposition, population projections, and simplistic assumptions about labor force 
participation can be used to construct a reduce-form, back-of-the envelope time path of future 
changes in the aggregate LFPR that matches fairly closely estimates from structural forecasting 
models. 
 
II. The Decomposition 
  The aggregate LFPR can be expressed as a population weighted average of the LFPR for 
different demographic groups: 
        ∑   
      
 
   (1) 
where  t LFPR  is the aggregate labor force participation rate at time t, 
i
t LFPR  is the labor force 
participation rate of demographic group i, and 
i
t p  is the population share of demographic group i.  
The change in the labor force participation rate from t-1 to t is given by: 
                     ∑        
              
     
        
        
          
       (2) 
which allows the change in the aggregate LFPR to be represented by the change in the 
participation rate of each demographic group (weighted by the group's current period population 
share) and by the change in the population share of each demographic group (weighted by the 
group's previous period LFPR). 
  Others have presented similar decompositions of the aggregate LFPR.  Juhn and Potter 
(2006) decompose changes in the aggregate LFPR as described in equation (2) but fix the 
population weights to their 1979 levels to conclude that changes in population weights accounted 
for very little of the change in the aggregate LFPR between 1969 and 2004.  The decomposition  
- 3 - 
results in this paper show that, except for the period between 1970 and 1980, population changes 
have contributed significantly to changes in aggregate LFPR, and have even dominated most of 
the time since 1950. 
  Aaronson et al. (2006) and Fallick and Pingle (2007) decompose deviations of the 
aggregate LFPR from its mean over time as a function of deviations of the population shares and 
demographic group participation rates from their respective historical averages.  This 
decomposition identifies the contribution of each group's evolution in participation rates and 
population shares to the evolution of the aggregate LFPR.  Fallick and Pingle point out that the 
evolution in population shares accounts for most of the evolution in the aggregate LFPR. 
  The focus of these earlier analyses was on how to better understand the evolution of labor 
force participation rates within different demographic groups.  The goal of this paper is 
simplicity; to demonstrate how little information can be used in the exploitation of the algebraic 
relationship in equation (2) to understand the driving force behind the historical evolution of the 
aggregate LFPR and to predict the future path of the aggregate LFPR. 
 
III. Changes in the Aggregate LFPR from 1950 to 2008 
  Table 1 presents each of the contributions of changes in labor force participation behavior 
and changes in population shares to five-year changes in the aggregate LFPR.  The exercise can 
be expanded to many more demographic groups and be repeated on any frequency desired.  The 
groups in Table 1 include everyone 16-24 years of age, women between 25 and 54 years, men 
between 25 and 54 years, and everyone 55 years and older.  The last two rows of Table 1 show 
the percent of the total absolute value contributions attributable to absolute value changes in 
behavior (sum of absolute value changes in LFPRs across groups) and to absolute value changes  
- 4 - 
in population shares. 
  Except during the period of time when women's labor force behavior was changing 
dramatically (1970-1980), changes in population shares contributed significantly to changes in 
the aggregate LFPR.  Turning to the period between 2000 and 2005, the decline in population 
shares of men and women between 25 and 54 years of age overwhelm the downward 
contribution imposed by behavioral changes of 16-24 year olds and working aged women.  The 
largest off-setting factor of those declines was an increase in labor supply behavior among the 
elderly. 
 
IV. Projecting Changes in Population Shares Forward 
  This simple accounting for changes in population shares follows a similar path projected 
by structural behavioral models of long-term labor force participation trends.  The structural 
models will necessarily be more accurate in pin-pointing aggregate levels of labor force 
participation in the short-term, but population changes appear to be a driving force in these 
models when making longer-term predictions.   
  Figure 2 plots LFPR projections from various sources, along with the projection derived 
from equation (2) that accounts for U.S. Census Bureau population projections and two simple 
behavioral assumptions: no behavioral change from 2008 and repeated 2007-2008 behavioral 
change.  The assumption of no behavioral change is more consistent with the projections from 
the structural models. 
 
V. Conclusion 
    This paper has shown that in spite of the attention the changing behavior of youth and  
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working age women have received in trying to explain the decline in the aggregate LFPR since 
2000, changing population shares accounted for an even greater portion of that decline.   
  Going forward, simply accounting for changes in population shares (and assuming no 
behavioral change) yields a projection of aggregate LFPR that is consistent with structural 
models produced from a variety of sources.  The implication of identifying most of the 
anticipated declines in aggregate LFPR being rooted simply in changes in population shares is 
that there are predictable underlying changes that may constrain economic growth, at least 
through 2020 (see Aaronson et al. 2006).   
  However, changes in labor productivity will be important in determining how any level 
of labor force participation translates into economic growth.  Indeed, many are convinced that 
immigration, gains in productivity, and normal price fluctuations in the labor market will resolve 
any labor shortage issues that might be expect to arise from projected declines in labor force 
participation (for example, see Freeman 2006 and Grossman 2005). 
- 6 - 
References 
Aaronson, Stephanie; Bruce Fallick; Andrew Figura; Jonathan Pingle; and William Wascher.  
"The Recent Decline in the Labor Force Participation Rate and Its Implications for 
Potential Labor Supply."  Brookings Papers on Economic Activity 1 (2006): 69-134. 
 
Bradbury, Katharine and Jane Katz.  "Women's Rise: A Work in Progress."  The Federal Reserve 
Bank of Boston Regional Review 14(3) (Q1 2005): 58-67. 
 
Cohany, Sharon R. and Emy Sok.  "Trends in Labor Force Participation of Married Mothers of 
Infants."  Monthly Labor Review (February 2007): 9-27. 
 
Fallick, Bruce and Jonathan Pingle.  "A Cohort-Based Model of Labor Force Participation."  
Finance and Economics Discussion Series #2007-09 (April 2007). 
 
Freeman, Richard B.  "Is a Great Labor Shortage Coming? Replacement Demand in the Global 
Economy."  NBER Working Paper #12541 (September 2006). 
 
Grossman, Robert J.  "The Truth about the Coming Labor Shortage."  HRMagazine 50(3) 
(March 2005). 
 
Hotchkiss, Julie L.  "Changes in Behavioral and Characteristic Determination of Female Labor 
Force Participation, 1975-2005."  Federal Reserve Bank of Atlanta Economic Review 
(2006, Quarter 2): 1-20. 
 
Juhn, Chinhui and Simon Potter.  "Changes in Labor Force Participation in the United States."  
Journal of Economic Perspectives 20(3) (Summer 2006): 27-46. 
 
Kirkland, Katie, "Declining Teen Labor Force Participation."  Issues in Labor Statistics, 
Summary 02-06 (September 2002). 
 
Lerman, Robert I.  "Career-Focuesd Education and Training for Youth."  In Harry J. Holzer, 
Demetra Smith Nightingale, eds.  Reshaping the American Workforce in a Changing 
Economy, pp. 41-90.  Washington, D.C.: Urban Institute Press, 2007. 
 
Mosisa, Abraham and Steven Hipple.  "Trends in Labor Force Participation in the United 
States."  Monthly Labor Review (October 2006): 35-57. 
 
   
- 7 - 
  Figure 1. Labor Force Participation Rate, 1948-2008. 
 
Source: Bureau of Labor Statistics. 
 
 
Figure 2. Projected Aggregate LFPRs, 2004-2020. 
 
 
Sources (not otherwise referenced): BLS, "Labor Force and Demographic Data" 
<http://www.bls.gov/emp/emplab1.htm>; CBO, "The Budget and Economic Outlook: Fiscal Years 2009 to 2019 
(Key Assumptions in CBO's Projection of Potential Output), January 2009 
<http://www.cbo.gov/doc.cfm?index=9957>; SSA, "The 2008 Annual Report of the Board of Trustees of the 
Federal Old-age and Survivors Insurance and Federal Disability Insurance," 10 April 2008 
<http://www.ssa.gov/OACT/TR/TR08/tr08.pdf>. 
 
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Projected Total LFPRs
Assuming 2007-2008  repeated behavior Assuming no behavioral change from 2008
Fallick and Pingle (2007-09), updated Aaronson et al. (2006)
CBO (Projections January 2009) BLS (LFPRs, 2006-2016, to 2050)
SSA (email correspondance) 
- 8 - 
 
 
Table 1. Contributions of changes in labor force behavior and changes in population share to changes in the aggregate LFPR. 
 
1950-
1955 
1955-
1960 
1960-
1965 
1965-
1970 
1970-
1975 
1975-
1980 
1980-
1985 
1985-
1990 
1990-
1995 
1995-
2000 
2000-
2005 
2005-
2008 
5 Year Change in Aggregate LFPR  0.02 0.10 -0.54 1.54 0.93 2.43 1.05 1.77 0.05 0.49 -1.04 -0.07 
 
Change in LFP of 16-24 year olds  -0.60 0.05 -0.12 0.87 1.10  0.75 0.06 -0.18 -0.16 -0.08 -0.81 -0.32 
Change in population share,  
16-24 year olds  -1.48 0.90 1.47 0.95 0.67  -0.46 -1.88 -1.18 -0.93 -0.12 0.07 -0.12 
 
Change in LFP of women, 25-54 year olds  0.91 0.91 0.63 1.30 1.30  2.29 1.55 1.25 0.47 0.32 -0.42 0.16 
Change in population share of women,  
25-54 year olds  0.10 -0.40 -0.72 -0.47 -0.29 0.04 0.77 0.89 0.54 -0.21 -0.82 -0.51 
 
Change in LFP of men, 25-54 year olds  0.25 -0.11 -0.08 -0.22 -0.34  -0.05 -0.08 -0.14 -0.51 0.00 -0.30 0.00 
Change in population share of men,  
25-54 year olds  0.22 -1.20 -1.63 -0.83 -0.28 0.25 1.23 1.54 0.69 -0.31 -0.71 -0.47 
 
Change in LFP of 55+ year olds  -0.23 -0.31 -0.40 -0.14 -1.13  -0.52 -0.69 -0.05 -0.03 0.65 1.38 0.67 
Change in population share, 
 55+ year olds  0.84 0.27 0.31 0.08 -0.10 0.13 0.08 -0.36 -0.03 0.24 0.56 0.52 
          
% of total contribution of (absolute 
value) changes in LFP  43.00 33.29 22.98 51.94 74.26 80.37 37.43 29.02 34.62 54.36 57.32 41.56 
% of total contribution of (absolute 
value) changes in Pop  57.00 66.71 77.02 48.06 25.74 19.63 62.57 70.98 65.38 45.64 42.68 58.44 
 
 
 

A Cohort-Based Model of Labor Force Participation.&quot;

Career-Focuesd Education and Training for Youth.&quot;

Changes in Behavioral and Characteristic Determination of Female Labor Force Participation, 1975-2005.&quot; Federal Reserve Bank of Atlanta Economic Review

Changes in Labor Force Participation in the United States.&quot;

Declining Teen Labor Force Participation.&quot;

Is a Great Labor Shortage Coming? Replacement Demand in the Global Economy.&quot;

The Recent Decline in the Labor Force Participation Rate and Its Implications for Potential Labor Supply.&quot;

The Truth about the Coming Labor Shortage.&quot; HRMagazine 50(3)

Trends in Labor Force Participation in the United States.&quot; Monthly Labor Review

Trends in Labor Force Participation of Married Mothers of Infants.&quot; Monthly Labor Review

Women's Rise: A Work in Progress.&quot; The Federal Reserve Bank of

Decomposing changes in the aggregate labor force participation rate

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Decomposing changes in the aggregate labor force participation rate

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