## wp18120 — Selected chapters: Data; Forecast and Simulations

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---

### Data sources and sample
- Labor force participation rates (LFPR) by gender and age-group: Employment database of the OECD.
- LFPR definition: the fraction of the adult population (ages 15 and over) either working or looking for work.
- Availability:
  - Recent data: 33 advanced economies.
  - Sufficiently long historical series for cohort-based analysis: subset of 17 economies over 1985-2017 (cohort model uses 1985–2016 in estimation).
- Other series:
  - Output gap and unemployment rate: IMF World Economic Outlook Database.
  - Population projections used in forecasting participation rates: 2017 edition of the United Nations World Population Prospects database.

### Shift-share decomposition and cyclical effects (method)
- Objective: Decompose observed changes in aggregate LFPR by gender since 2008 into:
  - “Within changes”: changes in participation rates within each age group holding population shares fixed.
  - “Between changes” (aging effect): shift in relative sizes of age groups holding participation rates fixed (imputed change if age-group participation remained at 2008 levels).
  - Interaction term.
- Sample: 33 advanced economies; men and women separately.
- Formal decomposition notation: l_{a,i,t} = sum_{g=1}^n l_{a,g,i,t} (pop_{a,g,i,t} / pop_{i,t})
- Cyclical component estimation:
  - Detrended LFPR obtained using the Hodrick-Prescott (HP) filter: l_{a,∗,i,t}.
  - Regression: l_{a,∗,i,t} = sum_{k=0}^1 β_k OG_{i,t−k} + π_i + τ_t + ε_{i,t} (single lag specification; results robust to richer lag structures).
  - OG denotes the output gap.
  - Country fixed effects π_i and time fixed effects τ_t included.
  - Driscoll-Kraay correction applied to standard errors to account for cross-sectional dependence.
  - Estimated over annual data from 1980-2016, separately for men and women.
  - Cyclical effect at time t is the predicted value of the regression; change relative to 2008 captures the role of the cycle since 2008.
- Robustness checks (cyclical):
  - Results qualitatively similar when allowing varying sensitivity to the cycle across countries.
  - Results robust to using the Corbae-Ouliaris filter instead of the HP filter.
  - Results robust to calculating detrended LFPR as deviations from a three-year moving average to limit HP endpoint distortions.

### Cohort-based model (method)
- Purpose: Identify age effects and cohort effects in LFPR by country and gender; use these to forecast future participation trends and simulate policy scenarios.
- Sample and cohort coverage:
  - Annual LFPR for quinquennial age groups starting at 15 up to 64, aggregated for 65+, for 17 advanced economies over 1985–2016.
  - Cohorts born between 1925 and 1994 (each birth cohort must appear in at least two age-group equations).
- Model specification:
  - l_{a,g,t} = α_{a,g} + (1 / n_g) sum_{t−g}^{T} β_{a,g}^{C_{t−g}} + λ_{a,g} X_t + ε_{a,g,t}
    - α: gender- and age-specific constant.
    - C: birth cohort- and gender-specific dummy variables (value one if birth cohort t−g appears in age group g in year t).
    - β: gender- and birth-year-specific fixed effect, divided by number of birth cohorts in the age group n_g.
    - X: output gap; λ varies by gender and age group.
    - ε: error term.
- Estimation:
  - Seemingly unrelated regression (SUR) estimated simultaneously for 11 age groups, separately for men and women in each country.
  - Coefficients for each birth cohort β_{a,g} constrained to be the same across equations within each gender-country.
  - n_g set to 5 for quinquennial age groups and to 34 for the age group 65+.
- Conceptual interpretation:
  - Age effects: propensity to participate at a given age (life-cycle profile).
  - Cohort effects: shifts in the age participation profile associated with birth cohorts (reflect social norms, preferences, education, fertility, marriage, etc.).
  - Controlling for cohort-specific effects allows identification of upward or downward shifts of the age participation profile by birth year.

### Forecast methodology (trend LFPR and aggregation)
- Trend age group- and gender-specific LFPR, la,g,∗t, calculated consistent with a closed output gap:
  - la,g,∗t = ˆαa,g + 1/ng T ∑t−g ˆβa,g Ca t−g
- Aggregate baseline trend LFPR through 2050:
  - l∗t = ∑g ∑a la,g,∗t / ∑g ∑a popa,g t
- Smoothing: abrupt changes in the trend LFPR smoothed via a three-year moving average.
- Population projections: United Nations World Population Prospects (medium fertility, migration flows and policies in line with historical trends); OECD population shares spliced with UN projections.
- Assumptions:
  - Output gap is closed for the trend forecast.
  - No effects from new cohorts entering the labor force are assumed given long projection horizon.
  - Illustrative policy scenarios use estimated elasticities from Grigoli et al. (2018) and IMF (2018), assuming policy settings converge to the “best possible” levels—defined as the 90th (or 10th) percentile of levels observed among the larger sample of advanced economies.

### Baseline historical facts and projections (key statistics)
- Historical trend:
  - Median trend LFPR across 17 advanced economies increased by 5.5 percentage points starting in the second half of the 1980s, reaching 62 percent in 2012.
  - Since 2012 the median trend LFPR started to decline to about 60 percent in 2016.
- Baseline projection (no policy changes that affect participation):
  - In the median country, trend LFPR could fall to 54.5 percent in 2050.
  - A decline in aggregate participation of 5.5 percentage points would translate into a 3 percentage point reduction in potential output by 2050 for the typical advanced economy.
  - Labor share assumption used in calculation: 56 percent (average labor share of income in 2017 for a subset of advanced economies: Australia, Canada, Germany, Italy, Japan, Spain, and the United States).
  - If this loss were to occur at the same rate every year, it would correspond to a loss in potential output of 0.09 percentage point a year over 33 years.

### Illustrative alternative scenarios and impacts (median country impacts by 2050)
- Closing Gender Gaps scenario:
  - Assumption: LFPR of women converges to that of men (la,m,∗t = la,f,∗t) over a 20-year horizon, then remains constant.
  - Impact: By 2050 the median trend LFPR would be 2.6 percentage points higher than in the baseline scenario.
- Extending Working Lives scenario:
  - Assumptions:
    - Trend LFPR of age 55–59 converges to that of age 50–54 over 20 years.
    - Trend LFPR of age 60–64 converges to that of age 50–54 over 40 years.
  - Impact: In 2050 the median trend LFPR would be 2.7 percentage points higher than in the baseline scenario.
- Implementation of Policies scenario:
  - Assumption: Broad-based adoption over 20 years of policy settings that are the “best possible” (90th/10th percentile) in the sample, based on policies shown to support participation.
  - Policy changes considered include: increasing spending on active labor market programs; raising public spending on child care and early childhood education; extending job-protected maternity leave; lifting constraints on part-time work; increasing the statutory retirement age; reducing the tax wedge and the generosity of unemployment benefits; implementing migration-friendly policies; and reducing spending on incapacity and old-age pensions.
  - Impact: By 2050 the median trend LFPR would be 1.2 percentage points higher than in the baseline scenario.
  - Caveat: The scenario is illustrative; changing all policies simultaneously may be difficult given fiscal costs and potential non-linear interactions.

### Empirical findings from historical decomposition and the cohort model
- Role of aging and cyclical effects since 2008 (sample averages across advanced economies):
  - Men: observed changes in participation broadly consistent with population age-profile shifts and the drag from the global financial and European debt crises; a very small unexplained residual remains.
  - Women: participation increased significantly despite aging and weak economic conditions; a very sizable unexplained component exists in observed changes in female participation rates across advanced economies.
  - Regional differences:
    - United States: participation of both men and women declined significantly more than aging and economic conditions would predict.
    - Europe and other advanced economies (Australia, Canada, Japan): gains in participation within demographic groups partially offset or exceeded the drag from aging.
  - Cyclical effects: High unemployment and poor job prospects after the crisis depressed participation (especially in Europe and the United States); the cyclical drag diminished as recoveries took hold.
- Age effects (cohort-based model, 17 AEs):
  - Men: hump-shaped profile; participation close to 90 percent during prime-age years (25–54); sharp rise early in life and dramatic decline after 55.
  - Women: less marked increase in late 20s/early 30s; participation substantially below men during prime age; many women leave labor force in late 20s/early 30s to start families and rejoin in 40s/50s.
  - Dispersion across countries is significantly wider for women than for men; standard deviation of age effects for prime-age women is 3 to 6 percentage points higher than for men.
  - Regional patterns: U.S. men participate less than in Europe and other AEs during prime-age years; European men join later and drop out earlier; other AEs enter later and participate at higher prime-age rates and remain in labor force later in life.
- Cohort effects:
  - Men: cohort effects fluctuate within a tight range around zero; becoming somewhat negative only for those born after 1975.
  - Women: successive cohorts born from 1940–44 up to 1975–79 contributed to increases in average LFPR in virtually all countries; cohort effects plateaued since 1980 and started to edge down more recently (especially in the United States).
  - Example magnitude: in the median country, LFPR of women born in the 1970s is up to 4 percentage points higher than LFPR of women born in the early 1930s.
  - Implication: Further gains from entries of new cohorts of women into the labor force may be limited for the median advanced economy.

### Robustness checks
- Cyclical effects:
  - Alternative specifications tested: added more lags; replaced output gap with unemployment gap; added crisis dummy and interaction with unemployment gap; allowed sensitivity to cycle to vary across countries; added squared terms; estimated in first differences; used Corbae-Ouliaris filter instead of HP filter; used deviations from a three-year moving average.
  - Result: qualitatively similar results across alternative specifications.
- Cohort analysis:
  - Transformations tested: logistic transformation, log transformation.
  - Alternatives: replace output gap with unemployment rate or unemployment gap; drop cohorts at end of sample to ensure each birth cohort observed in at least three or four age groups (dropping those born 1985–89 and 1980–84).
  - Result: results remain largely unchanged.
- Appendix A — Cyclical regression summary (detrended LFPR on lagged output gap):
  - Lag of output gap coefficients:
    - All: 0.055*** (0.011)
    - Men: 0.067*** (0.011)
    - Women: 0.043*** (0.015)
  - Observations: 1,010 (for each specification)
  - Countries: 33
  - R-squared:
    - All: 0.155
    - Men: 0.151
    - Women: 0.120
  - Notes: All specifications include country and year fixed effects; Driscoll-Kraay standard errors reported.

### Policy implications and conclusions
- Demographic aging and declining population growth pose risks to labor supply, potential growth, and sustainability of social insurance systems because older workers participate at much lower rates.
- Historical offsetting: many advanced economies have partially offset aging’s downward pressure on participation; about half of advanced economies saw aggregate LFPR increase after the global financial crisis.
- Gender and cohort dynamics:
  - Male aggregate participation declines largely explained by aging (almost entire change in male participation since 2008 in advanced Europe; around 70 percent of the decline in the United States).
  - Female participation increased in most countries despite aging and crisis drag; positive female cohort effects have plateaued since the cohort born in 1980 and edged down more recently.
- Projections and policy choices:
  - By 2050, LFPR could fall by over 5 percentage points for the median advanced economy absent policies to boost participation.
  - Even convergence to best-observed policy settings may not fully offset demographic pressures.
  - Policy options: immigration policy to boost domestic labor supply; policies to encourage older workers to postpone retirement; measures that raise participation (e.g., child care, active labor market programs, retirement age adjustments), recognizing fiscal constraints and potential non-linear interactions.

*Source: wp18120 — IMF staff calculations and analysis (chapters "2.1 Data" and "2.4 Forecast and Simulations").*

### 2.1    Data  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 

### 2.1    Data

### Data sources and sample
- Labor force participation rates (LFPR) by gender and age-group come from the Employment database of the OECD.
- LFPR definition: the fraction of the adult population (ages 15 and over) either working or looking for work.
- Recent data are available for 33 advanced economies; sufficiently long historical series for the cohort-based analysis exist for a subset of 17 economies over the period 1985-2017.
- Other series:
  - Output gap and unemployment rate: IMF World Economic Outlook Database.
  - Population projections used in forecasting participation rates: 2017 edition of the United Nations World Population Prospects database.

### Shift-share analysis and cyclical effects (method summary)
- Purpose: Decompose observed changes in aggregate LFPR by gender since 2008 into:
  - “Within changes”: changes in participation rates within each age group while holding population shares fixed.
  - “Between changes” (aging effect): shift in the relative sizes of age groups while holding participation rates fixed — imputed change if participation rates for each age group remained at their 2008 levels.
  - Interaction term.
- Sample for shift-share: 33 advanced economies, men and women separately.
- Formal decomposition notation:
  - l_{a,i,t} = sum_{g=1}^n l_{a,g,i,t} (pop_{a,g,i,t} / pop_{i,t})
- Cyclical component estimation:
  - Detrended LFPR, l_{a,∗,i,t}, obtained using the Hodrick-Prescott (HP) filter.
  - Regression: l_{a,∗,i,t} = sum_{k=0}^1 β_k OG_{i,t−k} + π_i + τ_t + ε_{i,t} (single lag specification; results robust to richer lag structures)
  - OG denotes the output gap.
  - Country fixed effects π_i and time fixed effects τ_t included.
  - Driscoll-Kraay correction applied to standard errors to account for cross-sectional dependence.
  - Estimated over annual data from 1980-2016, separately for men and women.
  - Cyclical effect at time t is the predicted value of the regression; change relative to 2008 captures the role of the cycle since 2008.
- Robustness checks:
  - Results are qualitatively similar when allowing varying sensitivity to the cycle across countries.
  - Results robust to using the Corbae-Ouliaris filter instead of the HP filter.
  - Results robust to calculating detrended LFPR as deviations from a three-year moving average to limit HP endpoint distortions.

### Cohort-based model (method summary)
- Purpose: Identify age effects and cohort effects in LFPR by country and gender, and use these to forecast future participation trends and simulate policy scenarios.
- Sample: Annual LFPR for quinquennial age groups starting at 15 years up to 64 years, aggregated for 65+, for 17 advanced economies over 1985–2016.
- Cohort coverage: cohorts born between 1925 and 1994 (each birth cohort must appear in at least two age-group equations).
- Model structure:
  - l_{a,g,t} = α_{a,g} + (1 / n_g) sum_{t−g}^{T} β_{a,g}^{C_{t−g}} + λ_{a,g} X_t + ε_{a,g,t}
  - α is gender- and age-specific constant.
  - C is a set of birth cohort- and gender-specific dummy variables (take value one if birth cohort t−g appears in age group g in year t).
  - β is gender- and birth-year-specific fixed effect, divided by number of birth cohorts in the age group n_g.
  - X is the output gap; λ is the coefficient on the output gap varying by gender and age group.
  - ε is the error term.
- Estimation approach:
  - Seemingly unrelated regression (SUR) estimated simultaneously for 11 age groups, separately for men and women in each country.
  - Coefficients for each birth cohort β_{a,g} constrained to be the same across equations within each gender-country.
  - n_g set to 5 for quinquennial age groups and to 34 for the age group 65+.
- Conceptual interpretation:
  - Age effects: propensity to participate at a given age (life-cycle profile).
  - Cohort effects: shifts in the age participation profile associated with birth cohorts (reflecting social norms, preferences, education, fertility, marriage, etc.).
  - Controlling for cohort-specific effects allows identification of upward or downward shifts of the age participation profile by birth year.

### Key empirical findings and projections (summary from paper)
- Across advanced economies, on average:
  - Changes in male LFPR since 2008 are broadly consistent with shifts in age profile and the drag from the global financial crisis.
  - Women became significantly more likely to work or seek employment despite aging; positive female cohort effects provided a sizable boost to aggregate female LFPR, counteracting drags from aging and adverse cyclical conditions in many advanced economies.
  - Cohort effects plateaued recently and even edged down, especially pronounced in the United States.
- Projections and simulation highlights:
  - In the absence of policies to boost participation and assuming no further cohort effects, the trend participation rate would fall by about 5.5 percentage points on average over the next 30 years due to projected population aging.
  - This decline in participation could wipe out as much as 3 percent of potential economic output in the median advanced economy.
  - Policies aimed at raising participation of women and older workers are necessary to limit the fall in participation rates.

*Source: wp18120 - 2.1    Data*

### 2.4    Forecast and Simulations

### 2.4 Forecast and Simulations

### Methodology for Forecasting Trend LFPR
- Trend age group- and gender-specific LFPR, la,g,∗t, is calculated consistent with a closed output gap as:
  - la,g,∗t = ˆαa,g + 1/ng T ∑t−g ˆβa,g Ca t−g
- Aggregate baseline trend LFPR through 2050 is constructed as:
  - l∗t = ∑g ∑a la,g,∗t / ∑g ∑a popa,g t
- Abrupt changes in the trend LFPR are smoothed by taking a three-year moving average.
- Population projections used are from the United Nations World Population Prospects (medium fertility, migration flows and policies in line with historical trends); OECD population shares (consistent with LFPR data) are spliced with UN projections.
- Assumptions:
  - Output gap is closed for the trend forecast.
  - No effects from new cohorts entering the labor force are assumed given the long projection horizon.
  - Illustrative policy scenarios use estimated elasticities from Grigoli et al. (2018) and IMF (2018), assuming policy settings converge to the “best possible” levels—defined as the 90th (or 10th) percentile of levels observed among the larger sample of advanced economies.

### Baseline Projection and Key Statistics
- Historical trend:
  - Median trend LFPR across 17 advanced economies increased by 5.5 percentage points starting in the second half of the 1980s, reaching 62 percent in 2012.
  - Since 2012 the median trend LFPR started to decline to about 60 percent in 2016.
- Baseline projection (no policy changes that affect participation):
  - In the median country, trend LFPR could fall to 54.5 percent in 2050.
  - A decline in aggregate participation of 5.5 percentage points would translate into a 3 percentage point reduction in potential output by 2050 for the typical advanced economy.
  - For this calculation, the labor share of income is assumed to be 56 percent (the average labor share of income in 2017 for a subset of advanced economies: Australia, Canada, Germany, Italy, Japan, Spain, and the United States).
  - If this loss were to occur at the same rate every year, it would correspond to a loss in potential output of 0.09 percentage point a year over 33 years.

### Illustrative Alternative Scenarios and Quantified Impacts
- Closing Gender Gaps scenario:
  - Assumption: LFPR of women converges to that of men (la,m,∗t = la,f,∗t) over a 20-year horizon, then remains constant.
  - Impact: By 2050 the median trend LFPR would be 2.6 percentage points higher than in the baseline scenario.
- Extending Working Lives scenario:
  - Assumptions:
    - Trend LFPR of age 55–59 converges to that of age 50–54 over 20 years.
    - Trend LFPR of age 60–64 converges to that of age 50–54 over 40 years.
  - Impact: In 2050 the median trend LFPR would be 2.7 percentage points higher than in the baseline scenario.
- Implementation of Policies scenario:
  - Assumption: Broad-based adoption over 20 years of policy settings that are the “best possible” (90th/10th percentile) in the sample, based on policies shown to support participation (per Grigoli et al. (2018) and IMF (2018)).
  - Policy changes considered include: increasing spending on active labor market programs; raising public spending on child care and early childhood education; extending job-protected maternity leave; lifting constraints on part-time work; increasing the statutory retirement age; reducing the tax wedge and the generosity of unemployment benefits; implementing migration-friendly policies; and reducing spending on incapacity and old-age pensions.
  - Impact: By 2050 the median trend LFPR would be 1.2 percentage points higher than in the baseline scenario.
  - Note: The scenario is illustrative; changing all policies simultaneously may be difficult given fiscal costs and potential non-linear interactions.

### Empirical Findings from Historical Decomposition and Cohort Model
- Role of aging and cyclical effects since 2008 (sample averages across advanced economies):
  - For men: observed changes in participation are broadly consistent with population age-profile shifts and the drag from the global financial and European debt crises; a very small unexplained residual remains.
  - For women: participation increased significantly despite aging and weak economic conditions; there is a very sizable unexplained component in observed changes in female participation rates across advanced economies.
  - Regional differences:
    - United States: participation of both men and women declined significantly more than aging and economic conditions would predict.
    - Europe and other advanced economies (Australia, Canada, Japan): gains in participation within demographic groups partially offset or exceeded the drag from aging.
  - Cyclical effects: High unemployment and poor job prospects after the crisis depressed participation (especially in Europe and the United States); the cyclical drag diminished as recoveries took hold.
- Age effects (cohort-based model, 17 AEs):
  - Men: hump-shaped profile; participation close to 90 percent during prime-age years (25–54); sharp rise early in life and dramatic decline after 55.
  - Women: less marked increase in late 20s/early 30s; participation substantially below men during prime age; many women leave labor force in late 20s/early 30s to start families and rejoin in 40s/50s.
  - Dispersion across countries is significantly wider for women than for men; standard deviation of age effects for prime-age women is 3 to 6 percentage points higher than for men.
  - Regional patterns: U.S. men participate less than in Europe and other AEs during prime-age years; European men join later and drop out earlier; other AEs enter later and participate at higher prime-age rates and remain in labor force later in life.
- Cohort effects:
  - Men: cohort effects fluctuate within a tight range around zero; becoming somewhat negative only for those born after 1975.
  - Women: successive cohorts born from 1940–44 up to 1975–79 contributed to increases in average LFPR in virtually all countries; cohort effects plateaued since 1980 and started to edge down more recently (especially in the United States).
  - Example magnitude: in the median country, LFPR of women born in the 1970s is up to 4 percentage points higher than LFPR of women born in the early 1930s.
  - Implication: Further gains from entries of new cohorts of women into the labor force may be limited for the median advanced economy.

### Robustness Checks
- Cyclical effects:
  - Modified specifications: added more lags; replaced output gap with unemployment gap (gap between current unemployment and NAIRU); added crisis dummy (currency crisis, sudden stop, debt crisis, banking crisis) and interaction with unemployment gap; allowed sensitivity to cycle to vary across countries; added squared terms of output or unemployment gap; estimated in first differences; used Corbae-Ouliaris filter instead of HP filter; constructed deviation from a three-year moving average.
  - Result: qualitatively similar results across alternative specifications.
- Cohort analysis:
  - Transformations tested: logistic transformation, log transformation.
  - Alternatives: replace output gap with unemployment rate or unemployment gap; drop cohorts at end of sample to ensure each birth cohort observed in at least three or four age groups (dropping those born 1985–89 and 1980–84).
  - Result: results remain largely unchanged.

### Policy Implications and Conclusions
- Demographic aging, coupled with declining population growth, poses risks to labor supply, potential growth, and sustainability of social insurance systems because older workers participate at much lower rates.
- Historical success: many advanced economies have partially offset aging’s downward pressure on participation; about half of advanced economies saw aggregate LFPR increase after the global financial crisis.
- Gender and cohort dynamics:
  - Male aggregate participation declines largely explained by aging (almost entire change in male participation since 2008 in advanced Europe; around 70 percent of the decline in the United States).
  - Female participation increased in most countries despite aging and crisis drag; positive female cohort effects have plateaued since the cohort born in 1980 and edged down more recently.
- Projections and policy choices:
  - By 2050, LFPR could fall by over 5 percentage points for the median advanced economy absent policies to boost participation.
  - Even convergence to best-observed policy settings may not fully offset demographic pressures.
  - Policy options to consider include immigration policy to boost domestic labor supply and policies to encourage older workers to postpone retirement, alongside measures that raise participation (e.g., childcare, ALMPs, retirement age adjustments), recognizing fiscal constraints and potential non-linear interactions.

*Source: IMF staff calculations and analysis in "Forecast and Simulations" (wp18120).*

### References

### wp18120 - References

### Key references cited
- Aaronson, Stephanie et al. (2014). “Labor Force Participation: Recent Developments and Future Prospects”. In: Brookings Papers on Economic Activity 2014.2, pp. 197–275.
- Aaronson, Stephanie et al. (2006). “The Recent Decline in the Labor Force Participation Rate and its Implications for Potential Labor Supply”. In: Brookings Papers on Economic Activity 2006.1, pp. 69–154.
- Balleer, Almut, Ramon Gomez-Salvador, and Jarkko Turunen (2014). “Labour Force Participation Across Europe: A Cohort-Based Analysis”. In: Empirical Economics 46.4, pp. 1385–1415.
- Blagrave, Patrick and Marika Santoro (2017). “Labor Force Participation in Chile: Recent Trends, Drivers, and Prospects”. In: International Monetary Fund Working Paper 17/54.
- Bloom, David E et al. (2015). “Macroeconomic Implications of Population Ageing and Selected Policy Responses”. In: The Lancet 385.9968, pp. 649–657.
- Burniaux Jean-Marc, Romain Duval and Florence Jaumotte (2004). “Coping with Ageing: A Dynamic Approach to Quantify the Impact of Alternative Policy Options on Future Labour Supply in OECD Countries”. In: OECD Working Paper ECO/WKP(2003)5.
- CEA (2014). “The Labor Force Participation Rate Since 2007: Causes and Policy Implications”. In: Council of Economic Advisers, Executive Office of the President of the United States.
- Clements, Benedict J et al. (2015). “The Fiscal Consequences of Shrinking Populations”. In: Staff Discussion Note, 15/21, International Monetary Fund.
- Corbae, Dean and Sam Ouliaris (2006). “Extracting Cycles from Nonstationary Data”. In: Econometric Theory and Practice: Frontiers of Analysis and Applied Research, pp. 167–77.
- Elsby, Michael WL, Bart Hobijn, and Ayşegül Şahin (2015). “On the Importance of the Participation Margin for Labor Market Fluctuations”. In: Journal of Monetary Economics 72, pp. 64–82.
- Fallick, Bruce and Jonathan F Pingle (2007). “A Cohort-Based Model of Labor Force Participation”. In: FEDS Working Paper No. 2007-09.
- Fern ández, Raquel (2013). “Cultural Change as Learning: The Evolution of Female Labor Force Participation over a Century”. In: American Economic Review 103.1, pp. 472–500.
- Goldin, Claudia (2006). “The Quiet Revolution that Transformed Women’s Employment, Education, and Family”. In: American Economic Review 96.2, pp. 1–21.
- Gourinchas, Pierre-Olivier and Maurice Obstfeld (2012). “Stories of the Twentieth Century for the Twenty-First”. In: American Economic Journal: Macroeconomics 4.1, pp. 226–65.
- Grigoli, Francesco, Zsoka Koczan, and Petia Topalova (2018). “Drivers of Labor Force Participation in Advanced Economies”. In: International Monetary Fund Working Paper, forthcoming.
- IMF (2013). “The Dog That Didn’t Bark: Has Inflation Been Muzzled or Was It Just Sleeping?” In: World Economic Outlook, Chapter 3, International Monetary Fund.
- IMF (2015). “Uneven Growth: Short and Long-term Factors”. In: World Economic Outlook, Chapter 3, International Monetary Fund.
- IMF (2017). “Seeking Sustainable Growth: Short-Term Recovery, Long-Term Challenges”. In: World Economic Outlook, Chapter 1, October, International Monetary Fund.
- IMF (2018). “Labor Force Participation in Advanced Economies: Drivers and Prospects”. In: World Economic Outlook, Chapter 2, International Monetary Fund.

### Appendix A — Calculation of the Cyclical Effects (estimation results)
- Table A.1: Regressions of Detrended LFPR (dependent variable: detrended LFPR)
  - Lag of output gap coefficients:
    - All: 0.055*** (standard error reported in parentheses: (0.011))
    - Men: 0.067*** (0.011)
    - Women: 0.043*** (0.015)
  - Observations: 1,010 (for each specification)
  - Countries: 33
  - R-squared:
    - All: 0.155
    - Men: 0.151
    - Women: 0.120
  - Notes:
    - All specifications include country and year fixed effects.
    - Driscoll-Kraay standard errors are reported in parentheses.
    - ***, **, and * indicate statistical significance at 1, 5, and 10 percent, respectively.

### Appendix B — Country-specific estimates and visual findings
- Figure B.1: Age Effects by Country
  - Age groups displayed: 15to19, 25to29, 35to39, 45to49, 55to59, 65to99.
  - Countries shown: AUS, BEL, CAN, DEU, DNK, ESP, FRA, GBR, GRC, ISR, ITA, JPN, LUX, NOR, PRT, SWE, USA.
  - Notes: The red and blue lines denote the men and women age effects, respectively.

- Figure B.2: Cohort Effects by Country
  - Cohorts shown: 1925to1929, 1945to1949, 1965to1969, 1985to1989.
  - Vertical scales vary by country (examples visible):
    - AUS, BEL, DEU, ESP, GRC, ISR, JPN, LUX, NOR, PRT, SWE, USA: scales include -6 to 2 or similar.
    - CAN: -4 to 1.
    - DNK: -1.5 to 1.
    - FRA, GBR, ITA: -3 to 2 ranges in various panels.
  - Notes: The red and blue lines denote the men and women age effects, respectively.

- Figure B.3: Actual and Trend LFPR by Country (Percent)
  - Time span displayed on x-axis: 1985, 1990, 1995, 2000, 2005, 2010, 2015.
  - Vertical ranges vary by country—for example:
    - AUS: 61 to 66 (approximate tick marks shown: 61, 62, 63, 64, 65, 66)
    - BEL: 48 to 56 (48, 50, 52, 54, 56)
    - CAN: 64 to 68
    - DEU: 54 to 62
    - DNK: 62 to 68
    - ESP: 50 to 65 (50, 55, 60, 65)
    - FRA: 54.5 to 57 (54.5, 55, 55.5, 56, 56.5, 57)
    - GBR: 61 to 64
    - GRC: 48 to 54
    - ISR: 56 to 64
    - ITA: 47 to 51
    - JPN: 59 to 64
    - LUX: 50 to 60
    - NOR: 68 to 74
    - PRT: 57 to 62
    - SWE: 70 to 74
    - USA: 62 to 67
  - Notes: The black lines denote actual participation rates. The red line denotes the trend participation rates.

- Figure B.4: Trend Projections of LFPR by Country (Percent)
  - Projection horizon on x-axis: 2015, 2020, 2025, 2030, 2035, 2040, 2045, 2050.
  - Vertical ranges vary by country; examples:
    - AUS: 60 to 66
    - BEL: 46 to 54
    - CAN: 58 to 66
    - DEU: 52 to 62
    - DNK: 56 to 62
    - ESP: 45 to 60
    - FRA: 52 to 57
    - GBR: 56 to 64
    - GRC: 40 to 55
    - ISR: 62 to 72
    - ITA: 40 to 50
    - JPN: 54 to 62
    - LUX: 46 to 56
    - NOR: 66 to 72
    - PRT: 50 to 60
    - SWE: 67 to 72
    - USA: 58 to 63
  - Scenario lines and interpretation:
    - Black lines denote the actual participation rates.
    - Black, red, yellow, and blue lines denote:
      - baseline scenario,
      - scenario in which the participation rates of prime-age women increase,
      - scenario in which the participation rate of the 55 and older increase,
      - scenario featuring the implementation of policies, respectively.
  - Notes: Source: Authors' calculations.

*Source: Authors’ calculations (as presented in wp18120 - References).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp18120.pdf_