## Section 3, 3.3, 5.2, 6.1, and Appendices (CPS description, empirical transitions, FOM failure, FOM with observable heterogeneity, HMM specification and estimates, separation from stable employment, robustness) ## Source details **Canonical URL:** [Section 3, 3.3, 5.2, 6.1, and Appendices (CPS description, empirical transitions, FOM failure, FOM with observable heterogeneity, HMM specification and estimates, separation from stable employment, robustness)](https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019282-print-pdf.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2019/wpiea2019282-print-pdf.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2019/wpiea2019282-print-pdf.pdf.json) --- ### CPS description, sample construction, and matching - CPS conducts monthly interviews of approximately 60,000 households and 100,000 to 150,000 individuals since January 1976. - Rotation and match structure: - Households interviewed 4 consecutive months, rotated out 8 months, then 4 more months — track labor force status up to 8 months in a 16-month period. - Each monthly file contains 8 rotation groups; in month t, rotation group 1 is eligible to be matched for 8 months spanning the next 15 months. - Matching algorithm follows Madrian and Lefgren (2000) as in Shimer (2012); τ ∈ {0,1,2,3,12,13,14,15} for complete eight-month history. - Matching keys: household identifier, household replacement number, personal identifier, sex, age (allowed to differ by increment of one between consecutive months), and race. - Matching outcomes and sample restrictions: - Average monthly file contains around 18,000 individuals in rotation group 1. - >80 percent matched within next four months; ~65 percent matched for months 12 to 15. - Sample restricted to individuals 16–64 with complete eight-month labor force status history. - Final sample: 2,420,463 observations for the entire period and 6,320 average monthly observations. - Weighting correction and bias checks: - Reassign sample weights by multiplying original weights by inverse of matching probability conditional on gender, age, race, education, and labor force status; predicted probabilities from a logit model. - Rotation group bias (Bailar, 1975) mitigated by limiting to respondents who responded in all eight months; unemployment rates in matched data verified against official BLS series. - Classification errors: - Paper does not mechanically adjust CPS for classification errors; the HMM observation matrix accounts for measurement errors and allows more than three unobserved states interpreted as labor market attachments. ### Empirical transition probabilities (January 1976–July 2014; monthly averages) - Monthly sample size in Table 1: 6,320. - Distribution in month t=0 (counts in parentheses): - Employment (4,434) - Unemployment (312) - Out of the Labor Force (1,574) - Transitions from Employment (4,434): - One month later: Employment 4,248 (95.8%), Unemployment 57 (1.3%), Out of the Labor Force 129 (2.9%) - Three months later: Employment 4,159 (93.8%), Unemployment 93 (2.1%), Out of the Labor Force 182 (4.1%) - 12 months later: Employment 4,030 (90.9%), Unemployment 124 (2.8%), Out of the Labor Force 280 (6.3%) - Transitions from Unemployment (312): - One month later: Employment 71 (22.9%), Unemployment 167 (53.5%), Out of the Labor Force 73 (23.5%) - Three months later: Employment 112 (35.9%), Unemployment 119 (38.2%), Out of the Labor Force 80 (25.9%) - 12 months later: Employment 153 (49.3%), Unemployment 75 (24.0%), Out of the Labor Force 83 (26.7%) - Transitions from Out of the Labor Force (1,574): - One month later: Employment 98 (6.2%), Unemployment 63 (4.0%), Out of the Labor Force 1,413 (89.8%) - Three months later: Employment 162 (10.3%), Unemployment 69 (4.4%), Out of the Labor Force 1,343 (85.3%) - 12 months later: Employment 271 (17.2%), Unemployment 69 (4.4%), Out of the Labor Force 1,234 (78.4%) - Illustrative summaries: - Initially employed: 4,248 (96 percent) remain employed one month later; 4,030 (91 percent) remain employed after a year. - Initially unemployed: 267 (54 percent) still unemployed one month later; after a year, 153 (24 percent) remain unemployed. - Initially nonparticipants: 98 (6.2 percent) move to employment and 1,413 (90 percent) remain out of the labor force one month later; after a year, 1,234 (78 percent) remain out of the labor force. ### First-Order Markov model (FOM): setup and empirical failure - FOM setup: - Observed statuses y_t ∈ {E, U, O}; one-month transition probabilities π_{y_t,y_{t+1}}; transition matrix C (3×3); implied τ-step transition matrix C^τ. - Empirical mismatch: - Homogeneous-worker FOM significantly misses empirical transition probabilities over horizons up to 15 months (Figure 1). - Example discrepancy: FOM implies probability an unemployed worker is unemployed two months later = 30 percent and after a year <5 percent; data show 24 percent unemployed a year later. - Causes of failure: - History dependence: transition probabilities depend on prior labor market history beyond current state; job-finding probability declines with unemployment duration; job-separation probability declines with tenure. - Unobserved and observable heterogeneity: transitions vary by sex, race, age, education and by exit reason (e.g., “laid off” >45 percent chance of finding a job next month; “job losers” <20 percent). - Two mechanisms for declining hazards among unemployed: - Composition (heterogeneity): high-exit workers leave unemployment pool. - Genuine duration dependence: individual exit rates decline over spells (human capital depreciation, statistical discrimination, discouragement). - Motivation: - FOM’s homogeneous-worker, first-order transition assumption is insufficient; motivates Hidden Markov Model (HMM) allowing multiple unobserved attachment states, duration dependence, and measurement-error accounting via observation matrix. ### FOM extended for observable heterogeneity (29 types) and its limits - CPS finer classification produces 29 observed types (6 × 4 = 24 unemployed types plus marginally attached and other nonparticipants). - Transition-matrix size and parameter count: - 29×29 = 841 entries by construction; structural zeros and row-sum constraints reduce effective parameters to 212. - Fit: - Extended 29-state FOM misses empirical transition probabilities by 9 percentage points on average (mean absolute deviation). - Conclusion: extended 29-state FOM incorporating duration and observable heterogeneity still fails to generate persistent dynamics over 15 months. - Motivation for unobserved heterogeneity: observed within-status behavioral differences remain insufficient to match 15-month transitions; propose unobserved attachment states. ### Hidden Markov Model (HMM) specification and estimation - Model structure: - L workers, observed statuses Y (M = 3: E, U, O), S unobserved attachment states X_t ∈ {1,...,S}. - Initial distribution p_s = Pr(X_0 = s); hidden-state transitions q_ss' = Pr(X_{t+1}=s' | X_t=s) forming Q (S×S); observation/emission σ_s(y) = Pr(Y_t = y | X_t = s) forming S×M matrix. - Choice of S: - Selected S = 9 (AIC/BIC suggest S = 10 but Monte Carlo shows instability at 10; S = 9 yields stable, meaningful states). - HMM nests homogeneous FOM when S = M and observation matrix = I_M (then Q = C). - Estimation: - MLE via EM algorithm; likelihood formed using diagonal emission matrices and Q; parameters {P, Q, σ} estimated. - Identification: - Uses Allman, Matias, and Rhodes (2009) Theorem 6: with M = 3 and T = 7 (seven months), up to S = 10 states generically identifiable given combinatorial condition. - Practical issues: label-swapping; tradeoff between longer T (permits larger S) and complexity of observable histories. ### Fit comparison: HMM versus FOM variants (MAD metric) - MAD definition: - Average percentage point difference between model-implied and empirical transition probabilities for τ ∈ T = {0,1,2,3,12,13,14,15} across statuses y,y' ∈ {E,U,O}; 9 transitions × 7 months = 63 data points. - MAD results (preserve source values): - HMM (S = 9): MAD = 0.3 percentage points. - Extended 29-state FOM: MAD = 8.9 percentage points. - HMM with S = 3 and 14 parameters: MAD = 2.9 percentage points. - Baseline FOMs (as reported): FOMbase MAD = 10.086; FOMmle MAD = 9.536; FOMext MAD = 8.862. - Table fragments (preserved source entries): - HMM3 2.9 14 FOMbase 10.086 - HMM4 2.10 23 FOMmle 9.536 - HMM5 1.4534 FOMext 8.86212 - HMM6 1.3747 - HMM7 0.8962 - HMM8 0.5479 - HMM9 0.2998 - HMM10 0.26119 - Interpretation: - HMM reduces deviation by a factor of 30 relative to extended FOM; improvements not solely due to parameter count—HMM with S = 3 (14 parameters) outperforms FOM variants with many more parameters because it models unobserved attachment and time-varying type changes. ### HMM diagnostics, robustness, and alternatives - One-month transitions: - By construction, FOM one-month transitions equal empirical probabilities; HMM one-month transitions differ by <0.3 percentage points on average. - Conditional independence assumption (Y_t depends only on X_t) is not empirically restrictive. - Alternative models: - Finite mixture (Q = I_S) and fixed unobserved heterogeneity FOM produce higher MADs than HMM with comparable parameter sizes and do not allow type changes over time. - More observed states: - Incorporating additional observed detail (e.g., full-time/part-time) reduces MAD for E/U/O transitions by factor 1.5–2.8 with diminishing returns as S increases. ### Economic interpretation and mechanisms captured by HMM - HMM implications: - Two workers with identical observed status can have different future transition probabilities (unobserved heterogeneity). - Workers can change unobserved attachment type over time while observed status unchanged, allowing genuine duration dependence (e.g., moving to more persistent unemployment attachment while remaining unemployed). - Mechanisms reproduced: - Composition effects and genuine duration dependence emerge from changing distribution over attachment states via Q. ### HMM estimates: attachment states, observation and outcome matrices (S = 9) - Characterization of nine attachment states (first-dimension current-month association; second-dimension persistence/future outcomes): - E1: most persistent employment state; chance employed six months later = 99 percent. - E2: second-most persistent employment; chance employed six months later = 83 percent; 13 percent chance of becoming unemployed. - E3: E-prone with highest (42 percent) chance of moving out of labor force among E-prone. - U1: among U-prone, highest chance (70 percent) of being employed six months later. - U2: most persistent unemployment attachment (highest chance of being unemployed six months later). - U3: U-prone with higher (63 percent) chance of leaving labor force. - O1: nonparticipant most likely to become employed six months later (45 percent). - O2: O-prone more attached to labor force (21 percent chance of being unemployed six months later). - O3: most persistent out-of-labor-force (96 percent remain O; 2.6 percent chance of employment six months later). - Numerical monthly transition probabilities (preserve source values): - Job finding probabilities (in %): HMM U1 35.6; HMM U3 9.6; HMM U2 3.8; FOM U 23.0. - Job separation probabilities of E-prone (in %): HMM E2 6.4; HMM E3 2.0; HMM E1 .01; FOM E 1.3. - Interpretation: - FOM single job-finding probability = 23.0% for all unemployed; HMM unemployed vary 3.8%–35.6%. - FOM single separation probability = 1.3% masks HMM heterogeneity across E1,E2,E3. ### HMM dynamics: duration dependence and composition - Duration dependence captured by evolving X_t (first-order Markov over hidden states): - Observed job-finding probability declines with unemployment duration; HMM reproduces empirical decline. - Bayes rule used to compute Pr(X_t = s | employment history); conditional distribution evolves via estimated matrices, converging to steady state under first-order Markov, causing hazard flattening after sufficient duration. - Distributional shifts with spell length: - Employment durations: 90 percent of workers employed in month 0 remain employed for five consecutive months; as duration increases, composition shifts to E1 from E2 and E3. - Unemployment durations: ~20 percent of unemployed in month 0 remain unemployed after five months; composition shifts toward U2 with duration. - Out-of-labor-force durations: ~70 percent of O in month 0 are in O3; at month 6, 80 percent remain O and fraction in O3 increases to ~90 percent. - Summary: longer spells entail growing shares of the most persistent attachment state for that status. ### Mapping attachment states to observables and earnings (selected exact figures) - Average monthly earnings (2005 US$) by E-prone: - E1: 3,994 - E2: 3,118 - E3: 2,129 - Employment-type distributions across E-prone (selected figures): - Full Time distribution: E1 82.2, E2 13.2, E3 4.6 - Part-Time for Economic Reasons: E1 63.0, E2 26.4, E3 10.6 - Part-Time for Non Economic Reasons: E1 66.0, E2 16.8, E3 17.3 - Share in E-prone (in Percent): E1 78.9, E2 14.3, E3 6.8 - Unemployment reasons and shares (U-prone): - Temporary Layoff: U1 73.3, U2 18.4, U3 8.3 - Job Loser: U1 49.5, U2 39.6, U3 10.9 - Re-Entrant/New-Entrant: U1 31.5, U2 26.1, U3 33.9 - Share in U-prone (in Percent): U1 48.8, U2 31.7, U3 19.5 - Out-of-labor-force characteristics and shares (O-prone): - Marginally Attached: O1 29.1, O2 39.7, O3 31.2 - Others: O1 17.9, O2 8.9, O3 73.2 - Share in O-Prone (in Percent): O1 18.4, O2 9.4, O3 72.2 - Industry and demographic patterns (selected): - Construction (E-prone): E1 7.3, E2 19.8, E3 6.3 - Government (E-prone): E1 84.9, E2 10.9, E3 6.9 - Demographic example (E1 U2 O3 columns in Table 6): - Men: 61.0, 1.8, 10.1 - College +: 68.9, 0.8, 9.1 - Married: 59.6, 1.0, 16.3 - Share in Population (in Percent): 54.1, 1.5, 16.6 - Behavioral interpretations: - Full-time concentrated in E1; part-time for economic reasons concentrated in E2; part-time non-economic concentrated in E3. - Temporary layoffs concentrated in U1; job losers concentrated in U2. - Marginally attached more likely in O1 or O2; other non-participants concentrated in O3. ### HMM numerical estimates: P and Q (preserve presented values) - Initial distribution P (in Percent): - E1: 53.8 - E2: 10.8 - E3: 5.6 - U1: 2.5 - U2: 1.4 - U3: 1.3 - O1: 4.5 - O2: 2.7 - O3: 17.4 - Transition matrix Q (rows → columns E1 E2 E3 U1 U2 U3 O1 O2 O3) preserved as presented: - Row E1: 99.5, 0.1, 0.4, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 - Row E2: 10.8, 21.2, 91.9, 0.8, 6.1, 0.0, 0.0, 0.0, 0.0 - Row E3: 5.6, 34.5, 1.4, 66.5, 0.2, 0.0, 0.0, 27.3, 0.0 - Row U1: U1 2.5, U2 10.0, E3 32.1, U1 0.7, U2 60.3, U3 4.6, O1 0.0, O2 1.2, O3 1.1 (table formatting preserved) - Row U2: U21.4 U20.0 0.0 0.0 5.3 90.5 0.0 0.0 4.2 0.0 (preserved as presented) - Row U3: U31.3 U30.0 0.0 6.4 0.0 0.0 36.6 5.6 51.5 0.0 (preserved) - Row O1: O14.5 O10.0 0.0 26.6 1.8 0.0 1.1 65.2 0.2 5.1 (preserved) - Row O2: O22.7 O20.0 0.1 0.0 1.9 1.2 20.0 1.7 72.6 2.5 (preserved) - Row O3: O317.4 O30.0 0.0 0.0 0.0 0.0 0.0 1.1 0.5 98.4 (preserved) - Note: Q table preserved as presented in source, including original ordering and numeric formatting. ### Bootstrap, Monte Carlo, and robustness summaries (selected outcomes) - HMM performance and alternatives (Table 9 summary preserved values): - Hidden Markov Model: - HMM3: MAD = 2.04, #ofPara = 14 - HMM4: MAD = 0.96, #ofPara = 23 - HMM5: MAD = 0.72, #ofPara = 34 - HMM6: MAD = 0.37, #ofPara = 47 - HMM7: MAD = 0.25, #ofPara = 62 - HMM8: MAD = 0.24, #ofPara = 79 - HMM9: MAD = 0.21, #ofPara = 98 - HMM10: MAD = 0.19, #ofPara = 119 - First Order Markov Model: - FOMbase: MAD = 9.48, #ofPara = 6 - FOMmle: MAD = 8.40, #ofPara = 6 - FOMext: MAD = 7.90, #ofPara = 12 - One-month transition probabilities (Table 10; preserve values in percent): - Data month1→month2: - From Employment: Employment 96.07, Unemployment 1.25, Out-of-the-Labor-Force 2.68 - From Unemployment: Employment 23.35, Unemployment 53.93, Out-of-the-Labor-Force 22.72 - From Out-of-the-Labor-Force: Employment 6.04, Unemployment 3.70, Out-of-the-Labor-Force 90.26 - HMM month1→month2: - From Employment: Employment 96.21, Unemployment 1.25, Out-of-the-Labor-Force 2.54 - From Unemployment: Employment 24.05, Unemployment 53.62, Out-of-the-Labor-Force 22.33 - From Out-of-the-Labor-Force: Employment 6.28, Unemployment 3.70, Out-of-the-Labor-Force 90.00 - One-year transition probabilities (Table 11; preserve values in percent): - Data (Pr(Y_12 | Y_1)): - If Y_0 = E: Employed 90.8, Unemployed 2.8, Out-of-the-Labor-Force 6.3 - If Y_0 = U: Employed 49.3, Unemployed 24.0, Out-of-the-Labor-Force 26.7 - If Y_0 = O: Employed 17.2, Unemployed 4.4, Out-of-the-Labor-Force 78.4 - FOM: - If Y_0 = E: Employed 73.9, Unemployed 3.9, Out-of-the-Labor-Force 22.2 - If Y_0 = U: Employed 60.6, Unemployed 4.9, Out-of-the-Labor-Force 34.6 - If Y_0 = O: Employed 50.5, Unemployed 5.6, Out-of-the-Labor-Force 45.0 - HMM: - If Y_0 = E: Employed 91.0, Unemployed 2.8, Out-of-the-Labor-Force 6.2 - If Y_0 = U: Employed 49.6, Unemployed 22.9, Out-of-the-Labor-Force 27.6 - If Y_0 = O: Employed 16.7, Unemployed 4.4, Out-of-the-Labor-Force 79.0 - Monte Carlo for P and observation matrix (Table 15; selected entries preserved): - Simulation: 500 samples, N = 2,420,463; MLE EM treating HMM estimates as data-generating process. - Initial distribution P: biases and SDs preserved as presented (e.g., Entry1 Bias -2.6 SD 1.6 CR(95%) [59.7 , 53.6], etc.). - Observation matrix: biases, SDs, CR(95%) preserved as presented in source. - Monte Carlo for Q (Table 16; selected entries preserved): - Bias and SD matrices (rows preserved as presented); CR(95%) preserved as presented. ### Separation from stable employment: long-run employment risk (Application 1) - Song and von Wachter (2014) (Social Security data, men <50, 1980–2005) findings: - Reduction in employment over next 20 years: 1.33 years (expansion), 1.48 years (recession). - HMM paper estimates (workers separated after 3 years continuous employment): - Even after 20 years, separated workers still have a 5 percent lower employment probability than controls. - Cumulative loss in years of employment over next 20 years (HMM): - 1.35 years in a recession - .97 years in a boom - HMM vs FOM implied employment-loss months (Figure 8; preserved values): - HMM Boom: 11.7 months lost - HMM Recession: 16.3 months lost - FOM Boom: 2.6 months lost - FOM Recession: 2.7 months lost - Cumulative loss in years implied by FOM: - .23 years during recessions - 0.22 years during booms - Sample and estimation for comparability: - Sample restriction: male workers 25–50 between 1980–2008 with 3 years continuous employment prior to displacement. - Recessions per NBER; boom defined as nonrecessionary with unemployment rate <6 percent. - HMM reestimated separately for expansions and recessions; annual averages from monthly series computed. - Comparability notes: - Social Security data annual; HMM monthly CPS (8 months of history over 16 months). - Song and von Wachter sample limited to men in large firms with mass-layoffs; HMM sample broader (no mass-layoff restriction). - Despite differences, HMM using 8 months of CPS history predicts persistent employment reductions similar to Social Security estimates. - Extensions: - HMM reestimated by sex×age×education groups to compute 20-year employment risk; results reported in Table 18 (Appendix). ### Expected years in employment lost from separation (selected exact statistics) - Within attachment statistics (Table 17; selected): - Employment types: - Full Time: E1 85.1, E2 76.3, E3 56.4; Share in E 81.8 - Part-Time for Economic Reasons: E1 2.7, E2 6.4, E3 5.4; Share in E 3.4 - Part-Time for Non Economic Reasons: E1 12.2, E2 17.3, E3 38.2; Share in E 14.8 - Unemployment reasons: - Temporary Layoff: U1 19.3, U2 7.4, U3 5.2; Share in U 13.2 - Job Loser: U1 36.6, U2 44.4, U3 19.3; Share in U 34.2 - Re-Entrant/New-Entrant: U1 24.6, U2 30.8, U3 63.0; Share in U 10.5 - Out of the Labor Force: - Marginally Attached: O1 15.0, O2 24.4, O3 11.4; Share in O 2.1 - Others: O1 85.0, O2 75.6, O3 88.6; Share in O 97.9 - Expected years in employment next 20 years after 3 years continuous employment (Table 18; selected entries preserved): - Men, High School and Less: - Age 16-24: - If stayed employed: 1980s 16.1, 1990s 15.9, 2000s 14.5 - If became unemployed: 1980s 15.1, 1990s 15.2, 2000s 13.3 - Employment lost: 1980s 3.9, 1990s 8.7, 2000s 31.24 (table formatting preserved) - Age 25-39: - If stayed employed: 1980s 18.2, 1990s 17.9, 2000s 16.9 - If became unemployed: 1980s 17.2, 1990s 16.1, 2000s 51.02 (preserved) - Employment lost: 1980s 1.8, 1990s 61.8, 2000s 1.84 (preserved) - Age 40-54: - If stayed employed: 1980s 16.7, 1990s 16.7, 2000s 16.4 - If became unemployed: 1980s 14.6, 1990s 14.6, 2000s 13.1 - Employment lost: 1980s 2.11, 1990s 2.15, 2000s 3.33 - Men, Some College: - Age 25-39: If stayed employed: 1980s 18.9, 1990s 18.6, 2000s 18.4; Employment lost: 1980s 1.1, 1990s 1.1, 2000s 1.61 - Men, College+: - Age 40-54: If stayed employed: 1980s 18.9, 1990s 18.9, 2000s 18.5; If became unemployed: 1980s 14.6, 1990s 16.2, 2000s 14.9; Employment lost: 1980s 3.25, 1990s 1.64, 2000s 1.95 - Women, College+: - Age 25-39: If stayed employed: 1980s 18.5, 1990s 19.1, 2000s 14.6; If became unemployed: 1980s 17.3, 1990s 18.1, 2000s 12.6; Employment lost: 1980s 1.17, 1990s 1.06, 2000s 2.01 - Summary from source: - More-educated prime-age workers enjoy more stable future employment; expected years lost due to separation are generally greater for less-educated older workers. ### Detailed employment stability analysis (8.6): evolution by gender, age, education, and recessions - Overview: - Use HMM applied to eight-month labor force histories to document percent of employed workers in E1 across decades (three-year averages: 1977-1979, 1987-1989, 1998-2000, 2012-2014). - Age profiles smoothed by averaging workers ±2 years; averages for workers older than 22. - Employment rates patterns: - Higher for more educated across ages; inverse U-shape over age peaking 25–50. - Men: employment rates fell across education groups since late 1970s; declines more pronounced for older men with less education; example 1977-79 → 1987-89: less than high school 82% → 74%; college 92% → 90%. - Women: employment rates rose across education groups since late 1970s; example 1977-79 → 1987-89: 30-year-old some college 65% → 76%; 30-year-old high school 56% → 65%. - Stable-employment rates (percent employed in E1): - Age profiles: for men with high school or less, stability peaks later (ages 45–50) than employment incidence. - Men with some college+ enjoy higher employment rates starting age 25 and more stable employment at younger ages. - Conditional on being employed, older workers more stable than younger. - Men: stable-employment rates changed little over decades (example: 1977-79 → 1987-89: men with high school -1.4 pp from 81% to 79%; men with college -0.8 pp from 84% to 83%). - Women: employment incidence rose substantially since late 1970s; stable-employment rates show milder improvements (example: 25-year-old women with some college stable rate +5 pp from 72% to 77% between 1977-79 and 1987-89); since late 1980s stability gains limited. - Recession dynamics: - Onset of recessions (1981, 2007/08): share in most stable employment E1 declines; share in less stable E2 rises during recessions; E1 share recovers toward end of recessions. - Among U-prone states, share in most unemployment-prone states increases as recession deepens and continues after official end. - Among O-prone states, share in O2 (more attached to unemployment) and O3 increases during downturns. - Synthesis: - Employment incidence vs stability divergence: - Men: employment incidence declined, but conditional stability remained relatively stable. - Women: employment incidence rose markedly, but stability gains were modest and limited after the 1990s. - Conclusion: incidence-only measures can exaggerate long-term deterioration for men and overstate improvement for women; stable-employment measures reveal subtler dynamics. *Source: wpiea2019282-print-pdf — Sections 3, 3.3, 5.2, 6.1, 8.4–8.6 and accompanying tables and appendices.* ### Section 3, I first describe the CPS and empirical transitions data over a one-year horizon. I ### Section 3 — Data, Empirical Transitions, and the Failure of the First-Order Markov Model ### CPS Description and Sample Construction - The Current Population Survey (CPS) conducts monthly interviews of approximately 60,000 households and 100,000 to 150,000 individuals since January 1976. - Households are interviewed for four consecutive months, rotated out for eight months, then interviewed four more months; this permits tracking labor force status for a maximum of eight months during a 16-month period. - Each CPS monthly file contains eight rotation groups defined by months in the survey. In month t, individuals in rotation group 1 are eligible to be matched for eight months spanning the next 15 months. - Matching approach: - Follow the algorithm in Madrian and Lefgren (2000) as in Shimer (2012). - Let τ be months elapsed since first entry into the survey. For a complete eight-month history observe τ ∈ {0,1,2,3,12,13,14,15}. - Match across months using household identifier, household replacement number, personal identifier, sex, age, and race. Age is allowed to differ by increment of one between consecutive months. - Matching outcomes and sample restrictions: - On average each monthly file contains around 18,000 individuals in rotation group 1. - More than 80 percent of these individuals can be matched within the next four months. - Around 65 percent can be matched for months 12 to 15. - Restrict sample to individuals between 16 and 64 years old with a complete eight-month labor force status history. - Final sample: 2,420,463 observations for the entire period and 6,320 average monthly observations. - Weighting correction for nonrandom attrition: - Reassign sample weights by multiplying original weights by the inverse of matching probability conditional on gender, age, race, education, and labor force status. - Predicted probabilities of matching are obtained from a logit model. - Rotation group bias: - Recognized as a potential issue (Bailar, 1975). Limiting first rotation group to respondents who responded in all eight months mitigates bias. - Verify unemployment rates in matched data against official Bureau of Labor Statistics series. - Classification errors: - CPS is subject to classification errors (misreported labor force status). - Prior approaches use reinterview surveys or latent-variable methods based on three months of history. - This paper does not mechanically adjust the CPS for classification errors; instead, the observation matrix of the HMM accounts for measurement errors. - The HMM allows for more than three unobserved states and interprets unobserved states as labor market attachments while still accounting for measurement errors. ### Empirical Transition Probabilities (Table 1 historical monthly averages, January 1976–July 2014) - Monthly sample size in Table 1: 6,320. - Distribution in month t=0 (counts in parentheses): - Employment (4,434) - Unemployment (312) - Out of the Labor Force (1,574) - Transitions from Employment (4,434) — counts and percentages: - Employment: 4,248 (95.8%) one month later; 4,159 (93.8%) three months later; 4,030 (90.9%) 12 months later. - Unemployment: 57 (1.3%) one month later; 93 (2.1%) three months later; 124 (2.8%) 12 months later. - Out of the Labor Force: 129 (2.9%) one month later; 182 (4.1%) three months later; 280 (6.3%) 12 months later. - Transitions from Unemployment (312) — counts and percentages: - Employment: 71 (22.9%) one month later; 112 (35.9%) three months later; 153 (49.3%) 12 months later. - Unemployment: 167 (53.5%) one month later; 119 (38.2%) three months later; 75 (24.0%) 12 months later. - Out of the Labor Force: 73 (23.5%) one month later; 80 (25.9%) three months later; 83 (26.7%) 12 months later. - Transitions from Out of the Labor Force (1,574) — counts and percentages: - Employment: 98 (6.2%) one month later; 162 (10.3%) three months later; 271 (17.2%) 12 months later. - Unemployment: 63 (4.0%) one month later; 69 (4.4%) three months later; 69 (4.4%) 12 months later. - Out of the Labor Force: 1,413 (89.8%) one month later; 1,343 (85.3%) three months later; 1,234 (78.4%) 12 months later. - Illustrative summaries from the data: - Among initially employed workers (4,434), 4,248 (96 percent) remain employed one month later; 4,030 (91 percent) remain employed after a year. - Among 312 initially unemployed, 267 (54 percent) are still unemployed one month later; after a year, 153 (24 percent) remain unemployed. - Among 1,574 nonparticipants initially, 98 (6.2 percent) move to employment and 1,413 (90 percent) remain out of the labor force one month later; after a year, 1,234 (78 percent) remain out of the labor force. ### First-Order Markov Model (FOM) and Its Failure to Fit Longer-Horizon Transitions - FOM setup: - Observed labor force statuses y_t ∈ {E, U, O}. - One-month transition probabilities are denoted π_{y_t,y_{t+1}}. - Two-month transition probabilities implied by FOM: - π_{y_t,y_{t+2}} = Σ_{y_{t+1}} π_{y_t,y_{t+1}} π_{y_{t+1},y_{t+2}}. - Define C as the 3 x 3 transition matrix with (i,j) element π_{ij} for i,j ∈ {E,U,O}. - Implied t+τ transition matrix is C^τ. - Empirical mismatch: - The FOM with homogeneous workers significantly misses empirical transition probabilities over horizons up to 15 months (Figure 1). - Example: using the FOM, the probability that an unemployed worker is unemployed two months later is computed as 30 percent, and after a year the FOM implies a less than 5 percent chance of being unemployed; in the data, 24 percent of initially unemployed workers are unemployed a year later — a large discrepancy. ### Causes of FOM Failure: History Dependence and Unobserved Heterogeneity - History dependence: - Transition probabilities depend on workers’ prior labor market history beyond the current state for all three statuses. - Job-finding probability declines with unemployment duration (Figure 2). - Example: Kudlyak and Lange (2018) find nonparticipants who were recently employed have job-finding probabilities of 25-30 percent, while those out of the labor force for three consecutive months have only a 2 percent chance of finding a job. - Job-separation probability for employed workers declines with tenure. - Heterogeneity (observable and unobservable): - Transition dynamics vary by observable characteristics (sex, race, age, education) and unobservable characteristics (human capital). - Exit rates differ by reason for separation: “laid off” workers have more than 45 percent chance of finding a job next month; “job losers” have less than 20 percent chance. - Two mechanisms that generate declining empirical hazards among unemployed: - Composition (heterogeneity): high-exit workers leave the unemployment pool, leaving a growing share of low-exit workers. - Genuine duration dependence: an individual’s exit rate may decline over the unemployment spell due to human capital depreciation, employer statistical discrimination, discouragement, etc. ### Empirical Strategy Motivation - The FOM’s assumption of homogeneous ex-ante workers and first-order Markov transitions is insufficient to capture observed history dependence and unobserved heterogeneity. - This motivates the introduction of a Hidden Markov Model (HMM) that: - Allows multiple unobserved labor market attachment states. - Captures duration dependence and unobserved heterogeneity. - Uses the observation matrix to account for classification errors in CPS responses. - Subsequent sections (described in the paper) will: - Introduce the HMM, estimation method, and identification results (Section 4). - Present the HMM’s fit to 15-month transition probabilities, duration dependence, and unobserved heterogeneity; relate unobserved states to observables (Section 5 and 5.3). - Present four applications of the HMM (Section 6) and conclude (Section 7). *Source: wpiea2019282-print-pdf — Section 3 (CPS description, empirical transitions, and discussion of FOM failure).* ### 3.3 FOM with Observable Heterogeneity ### 3.3 FOM with Observable Heterogeneity ### Extended first-order Markov (FOM) with observable heterogeneity - CPS allows finer classification: employed split into full-time, part-time for economic reasons, part-time for non-economic reasons; unemployed split by reason ((1) layoff, (2) job loser, (3) temporary job ended, (4) job leaver, (5) re-entrant, (6) new-entrant) and duration ((1) less than 5 weeks, (2) 5-14 weeks, (3) 15-26 weeks, (4) 27 or more weeks). - This results in: - 6 × 4 = 24 unemployed types; - plus marginally attached and other nonparticipants; - total of 29 types of workers. - Transition-matrix accounting: - 29 × 29 = 841 entries by construction; - many entries are zero by construction (e.g., employed → unemployed can only go to <5 weeks next month; laid off cannot transition to job leaver or new entrant; out of labor force cannot transition to unemployed with duration >5 weeks); - after removing zero/structural constraints and imposing row sums equal 1, the effective number of parameters reduces to 212. - Fit to data: - The extended 29-state FOM transition probabilities miss their empirical counterparts by 9 percentage points on average. - Conclusion: even an extended 29-state first-order Markov transition matrix incorporating observable characteristics and unemployment duration still fails to generate the persistent labor market dynamics observed over the 15-month horizon. ### Motivation for unobserved heterogeneity - Prior work finds behavioral differences among workers within the same observed labor force status but still fails to capture differences in degree of labor market attachment sufficient to match 15-month transitions. - The paper proposes introducing unobserved labor market attachment states to explain persistent dynamics. ### Hidden Markov Model (HMM) — Model specification - Time is discrete; economy with L workers, observable labor market statuses Y, and S unobserved labor market attachment states indexed s ∈ {1,...,S}. - X_t: worker’s unobserved labor market attachment state at time t. - Dynamics: - Initial distribution: p_s = Pr(X_0 = s). - Hidden-state transition: q_ss' = Pr(X_t+1 = s' | X_t = s); Q is S × S. - Observation (emission): σ_s(y) = Pr(Y_t = y | X_t = s); observation matrix is S × M. - For the paper: - Observed labor force statuses: employed (E), unemployed (U), out of the labor force (O) so M = 3. - Number of unobserved labor market attachment states chosen: S = 9. - AIC and BIC suggest S = 10, but Monte Carlo simulations show parameters are unstable for 10 states; S = 9 yields stable, economically meaningful states. - Notes: - HMM nests the FOM with homogeneous workers when S = M and observation matrix = I_M (then Q = C, the observed-state transition matrix). - Baseline estimation assumes common parameters {P, Q, σ} across individuals. ### Estimation approach - Maximum Likelihood Estimation (MLE) implemented via the Expectation-Maximization (EM) algorithm. - Likelihood for individual l’s employment history y_l expressed in matrix form using diagonal matrices of emission probabilities and Q; full-sample likelihood is product across individuals. - Parameters to estimate: P (1 × S), Q (S × S), σ (M × S). ### Identification - Identification relies on Allman, Matias, and Rhodes (2009) Theorem 6 using Kruskal’s results: - Theorem: Parameters of an HMM with S hidden states and M observable states are generically identifiable from the marginal distribution of T = 2k + 1 consecutive variables provided k satisfies (k + M − 1 choose M − 1) ≥ S. - With M = 3 and T = 7 (i.e., seven months of observation), up to S = 10 unobserved states can be identified. - Practical considerations: - Label swapping (permutations of Q, σ, P) implies identification only up to label permutations. - Tradeoff: longer T allows more S but increases the number of possible employment histories to target, complicating fit. ### Results — Fit of HMM versus FOM - HMM substantially improves fit to 15-month transition probabilities compared with FOM variants. - Key illustrative one-year transitions (data vs. FOM vs. HMM): - Data: 24 percent of unemployed workers are unemployed a year later. - Data: 16 percent of nonparticipants are employed a year later. - FOM predicted: <5 percent for unemployed → unemployed; approximately 50 percent for nonparticipant → employed. - HMM predicted: 20 percent for unemployed → unemployed; 17 percent for nonparticipant → employed (much closer to data). - Mean absolute deviation (MAD) metric: - Definition: average percentage point difference between model-implied and empirical transition probabilities for τ ∈ T = {0,1,2,3,12,13,14,15} across observed statuses y, y' ∈ {E,U,O}. There are 9 transitions × 7 months = 63 data points. - MAD results: - HMM (S = 9): MAD = 0.3 percentage points. - Extended 29-state FOM: MAD = 8.9 percentage points. - HMM reduces deviation by a factor of 30 relative to the extended FOM. - HMM with only three unobserved states and 14 parameters: MAD = 2.9 percentage points. - HMM with 3 states and 14 parameters vs. FOMbase: FOMbase MAD = 10.086 (baseline FOM uses first two months); FOMmle MAD = 9.536 (MLE over all eight months); FOMext MAD = 8.862 (extended 29-state FOM with 212 parameters). - Table 3 (selected entries reproduced exactly as in source): - HMM3 2.9 14 FOMbase 10.086 - HMM4 2.10 23 FOMmle 9.536 - HMM5 1.4534 FOMext 8.86212 - HMM6 1.3747 - HMM7 0.8962 - HMM8 0.5479 - HMM9 0.2998 - HMM10 0.26119 - Interpretation of parameter-parsimony: - The HMM’s superior performance is not solely due to more parameters: the extended FOM uses 212 parameters yet MAD = 8.9 pp; the HMM with S = 3 uses 14 parameters and MAD = 2.9 pp; S = 9 uses fewer parameters than the extended FOM and attains MAD = 0.3 pp. - The gain arises from allowing unobserved labor market attachment states that govern the distribution of observed statuses and permit workers to change unobserved types over time. ### Additional diagnostics and robustness - One-month transitions: - By construction, one-month transitions in FOM equal empirical probabilities; HMM one-month transitions differ from FOM by less than 0.3 percentage points on average. - The HMM’s conditional independence assumption (observed status depends only on current hidden state, not directly on previous observed status) is therefore not restrictive empirically. - Alternative heterogeneity models: - Finite mixture models and fixed unobserved heterogeneity FOM (Browning and Carro, 2014) produce higher MADs than the HMM with comparable parameter sizes and do not allow types to change over time. - Using more observed states: - Incorporating more detailed observed statuses (e.g., F, P, U, O) can further reduce MAD for transitions between E, U, O; using four observed states reduces MAD by a factor of 1.5–2.8 for those transitions, with diminishing gains as S increases. ### Economic interpretation enabled by HMM - HMM permits: - Two workers with identical observed labor force status to have different future transition probabilities (unobserved heterogeneity). - A worker to change unobserved attachment type over time even while observed status remains unchanged, allowing for genuine duration dependence (e.g., moving from a less persistent attachment state to a more persistent one while remaining unemployed or employed). *Source: wpiea2019282-print-pdf - 3.3 FOM with Observable Heterogeneity (https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019282-print-pdf.pdf)* ### 5.2 HMM Estimates ### 5.2 HMM Estimates ### Key features of the HMM observation and six‑month outcome matrices - The observation matrix shows distributions of current labor force status conditional on unobserved labor market attachment states: iy = Pr(Y = y | X = i). - The six‑month outcome matrix shows Pr(Y_{t+6} | X_t), i.e., the probability distribution of observed labor force status six months later conditional on the unobserved labor market attachment state in month 0. - The Appendix (not reproduced here) contains the transition matrix for labor market attachment states, bootstrap standard errors, and Monte Carlo simulation results (Tables 13, 15, and 16). ### Characterization of attachment “prone” states - First dimension: current-month association (employment-prone = E-prone, unemployment-prone = U-prone, out-of-the-labor-force-prone = O-prone). - Second dimension: predicted future outcomes — states within each prone category are ordered by persistence or most-likely future status: - E1: the most persistent employment state; the highest chance of being employed six months later (99 percent). - E2: second-most persistent employment state; 83–percent chance of being employed six months later and 13 percent chance of becoming unemployed. - E3: E-prone state with the highest (42 percent) chance of moving out of the labor force among E-prone states. - U1: among U-prone states, the highest chance (70 percent) of being employed six months later. - U2: most persistent unemployment attachment state (highest chance of being unemployed six months later). - U3: U-prone state with higher (63 percent) chance of leaving the labor force. - O1: nonparticipants most likely to become employed six months later (45 percent). - O2: O-prone state more attached to the labor force (21 percent chance of being unemployed six months later). - O3: most persistent out‑of‑the‑labor‑force state (96 percent remain out-of-the-labor-force; 2.6 percent chance of employment six months later). ### Numerical HMM versus FOM monthly transition probabilities (preserving source values) - Job finding probabilities (in %): - HMM U1: 35.6 - HMM U3: 9.6 - HMM U2: 3.8 - FOM U: 23.0 - Job separation probabilities of E-prone states (in %): - HMM E2: 6.4 - HMM E3: 2.0 - HMM E1: .01 - FOM E: 1.3 ### Interpretation and examples from the matrices - The HMM captures substantial heterogeneity within the same observed labor force status: e.g., the FOM assigns a single monthly job‑finding probability of 23 percent to all unemployed, whereas HMM unemployed workers’ monthly job‑finding probabilities vary from 3.8 percent (U2) to 35.6 percent (U1). - Similarly, FOM’s single separation probability of 1.3 percent for employed workers masks HMM variation: E2 = 6.4 percent, E3 = 2.0 percent, E1 = .01 percent. ### Unobserved heterogeneity (Section 5.2.1) - HMM unobserved attachment states allow transition probabilities to vary across workers who share the same observed current labor force status. - Consequence: workers with identical observed status (E, U, or O) can have markedly different short‑run and medium‑run prospects depending on their attachment state. ### Duration dependence (Section 5.2.2) - HMM captures history (duration) dependence by allowing the unobserved attachment state to evolve dynamically (first‑order Markov). - Empirical patterns: - Observed unemployment‑to‑employment exit (job‑finding) probability declines with unemployment duration. - Observed employment‑to‑unemployment hazard also varies with duration. - The HMM reproduces the observed decline in exit probabilities over duration, unlike the FOM which implies constant transition probabilities independent of duration. - Method: Bayes rule is used to compute Pr(X_t = s | employment history), e.g., for a single month unemployed: - Pr(X_t = s | Y_t = U) = p_s·(jU) / Σ_{i=1}^S p_s·(iU) (equation (6) in source). - For τ months unemployed, the conditional probability evolves via the estimated matrices as in equation (7) of the source; under first‑order Markov the conditional distribution converges to a steady state implying a flattening hazard after sufficient duration. ### Distribution of E/U/O durations by attachment state (Section 5.2.3) - Employment durations: - Example: 90 percent of workers employed in month 0 remain employed for five consecutive months. - As employment duration increases, workers shift compositionally toward the most persistent employment state (E1) from E2 and E3. - Unemployment durations: - Around 20 percent of unemployed workers in month 0 remain unemployed after five months. - Composition shifts toward the most persistent unemployment state (U2) as duration increases. - Out‑of‑the‑labor‑force durations: - Approximately 70 percent of workers out of the labor force in the first month are in O3. - In month 6, 80 percent of them remain out of the labor force and the fraction in O3 increases to approximately 90 percent. - Summary implication: workers who remain in a given status for longer spells comprise an increasing share of the most persistent attachment state associated with that status. ### What the attachment states capture (Section 5.3) — core empirical mappings - Three main findings: - The unobserved labor market attachment states are associated with observable characteristics. - The mapping between unobservables and observables is not one‑to‑one; unobserved heterogeneity remains among workers with identical observables. - Attachment states capture persistent labor market dynamics and provide improved predictions of future outcomes relative to a FOM. - Average monthly earnings (2005 US$) by E-prone state (Table 6): - E1: 3,994 - E2: 3,118 - E3: 2,129 - Employment types and shares (selected figures from Table 6): - Full Time distribution across E-prone: E1 82.2, E2 13.2, E3 4.6 - Part-Time for Economic Reasons across E-prone: E1 63.0, E2 26.4, E3 10.6 - Part-Time for Non Economic Reasons across E-prone: E1 66.0, E2 16.8, E3 17.3 - Share in E-prone (in Percent): E1 78.9, E2 14.3, E3 6.8 - Unemployment reasons and shares (U-prone, Table 6): - Temporary Layoff: U1 73.3, U2 18.4, U3 8.3 - Job Loser: U1 49.5, U2 39.6, U3 10.9 - Re-Entrant / New-Entrant: U1 31.5, U2 26.1, U3 33.9 - Share in U-prone (in Percent): U1 48.8, U2 31.7, U3 19.5 - Out-of-the-labor-force characteristics and shares (O-prone, Table 6): - Marginally Attached: O1 29.1, O2 39.7, O3 31.2 - Others: O1 17.9, O2 8.9, O3 73.2 - Share in O-Prone (in Percent): O1 18.4, O2 9.4, O3 72.2 - Industry and demographic patterns (selected figures from Table 6): - Construction (E-prone): E1 7.3, E2 19.8, E3 6.3 (as listed) - Government (E-prone): E1 84.9, E2 10.9, E3 6.9 - Demographic group example (E1 U2 O3 columns in Table 6): - Men: 61.0, 1.8, 10.1 - College +: 68.9, 0.8, 9.1 - Married: 59.6, 1.0, 16.3 - Share in Population (in Percent): 54.1, 1.5, 16.6 - Behavioral interpretations: - Full‑time workers are concentrated in the most stable employment state (E1). - Part‑time for economic reasons concentrate in E2 and are more likely to transition to unemployment. - Part‑time for non‑economic reasons concentrate in E3 and are more likely to move out of the labor force. - Temporarily laid-off workers are concentrated in U1 and are more likely to return to employment. - Job losers are concentrated in U2 (about 40 percent of job losers are in U2). - Marginally attached non‑participants are more likely to be in O1 or O2; other non‑participants are concentrated in O3. ### Implications relative to FOM and predictive performance - HMM provides more accurate measures than the FOM for individual conditions and aggregate dynamics by: - Capturing unobserved heterogeneity within observed labor force statuses. - Capturing duration dependence via evolving attachment states. - Producing substantially different short‑term transition probabilities across workers sharing the same observed status. ### Applications (Section 6) — illustrative uses of the HMM - Application 1: Long‑term consequences of separating from employment - The HMM improves on FOM and generates estimated reductions in earnings and future employment probabilities close to estimates from U.S. Social Security data. - Application 2: Evolution of employment stability by demographic group - Example findings: while men’s average employment rate declined, employment stability did not; women’s average employment stability rose until the mid‑1990s but only highly educated women experienced the improvement. - Application 3: Labor market attachment changes during recessions (Great Recession of 2007–09 and 1981 recession) - The slower recovery after the Great Recession is attributable to larger and more persistent inflows into: - the more‑persistent unemployment state (U2), - less stable employment states (E2), - nonparticipants more attached to unemployment (O2). - Application 4: Counterfactual “good” vs “bad” economies - Two economies with identical distributions of current observed status but different distributions of underlying attachment states show diverging future dynamics: a “good” economy can experience declining unemployment, while a “bad” economy can experience persistently high unemployment, highlighting the importance of the distribution of unobserved attachments. *Source: 5.2 HMM Estimates, wpiea2019282-print-pdf* ### 6.1 Separation from Stable Employment ### 6.1 Separation from Stable Employment ### Employment risk: long-run reduction in employment probabilities - Separation from stable employment results in a large and persistent reduction in employment probabilities relative to a control group who did not experience separation. - The reduction is more severe if separation happens during a recession than during a boom. - Song and Wachter (2014) (U.S. Social Security data, men younger than 50, 1980–2005) find: - reduction in employment over the next 20 years is 1.33 years during an economic expansion - reduction in employment over the next 20 years is 1.48 years during a recession - HMM estimates in this paper (workers separated after three years of continuous employment): - even after 20 years, separated workers still have a 5 percent lower employment probability than the control group who did not separate - cumulative loss in years of employment relative to a control group over the next 20 years: - 1.35 years in a recession - .97 years in a boom ### Comparison of HMM and FOM implications - HMM implies a persistent reduction in employment after separation; FOM implies a short-lived reduction. - Figure 8 reported employment-loss months (relative to counterfactual): - HMM Boom: 11.7 months lost - HMM Recession: 16.3 months lost - FOM Boom: 2.6 months lost - FOM Recession: 2.7 months lost - Cumulative loss in years of employment implied by FOM: - .23 years during recessions - 0.22 years during booms ### Sample restriction and estimation strategy (to compare with prior literature) - To make results comparable to Song and von Wachter (2014) and Davis and von Wachter (2011), the sample is restricted to: - male workers between 25 and 50 years old between 1980 to 2008 - three years of continuous employment prior to job displacement - Definitions: - recession based on NBER recession periods - boom defined as a nonrecessionary period where the unemployment rate is below 6 percent - Estimation details: - re-estimate the HMM separately for expansionary and recessionary periods - compute annual average of employment risk from the monthly series - HMM here uses monthly CPS data (8 months of labor force history over 16 months) ### Differences between data and samples across studies - Frequency of data: - Social Security data: employment reported annually - This paper (HMM): monthly CPS data (8 months of history over 16 months) - Sample composition: - Song and von Wachter (2014): men in large firms (50+ employees) who experienced mass-layoff events - This paper: no large-firm or mass-layoff restriction; workers could have job-to-job transitions as long as they were continuously employed for the last three years; separations may occur for reasons other than mass layoffs - Despite differences, HMM using only eight months of labor force transition history over 16 months can accurately predict the persistent reduction in employment probabilities observed in Social Security data. ### Extension: estimating long-run consequences by demographic groups - CPS contains more demographic information (such as education) than Social Security but only 8 months of labor force history over a 16 month period. - The extrapolative power of the HMM enables estimating employment risk over 20 years using 16 months of labor force history. - The HMM is reestimated for various sex×age×education groups to calculate employment risk for those demographic groups over recent decades. - Results for these demographic-group estimates are reported in Table 18 in the Appendix. *Source: wpiea2019282-print-pdf - 6.1 Separation from Stable Employment* ### References ### References ### Key bibliographic entries - Abowd, John M., and Arnold Zellner. 1984. “Estimating Gross Labor-force Flows.” Journal of Business & Economic Statistics 3(3): 254–283. - Ahn, Hie Joo. 2019. “The Role of Observed and Unobserved Heterogeneity in the Duration of Unemployment Spells.” mimeo. - Ahn, Hie Joo, and James D. 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Summers. 1986. “Reporting Errors and Labor Market Dynamics.” Econometrica 54 (6): 1319–1331. - Shimer, Robert. 2005. “The Cyclical Behavior of Equilibrium Unemployment and Vacancies.” The American Economic Review 95 (1): 25–49. - Shimer, Robert. 2008. “The Probability of Finding a Job.” The American Economic Review 98 (2): 268–273. - Shimer, Robert. 2012. “Reassessing the Ins and Outs of Unemployment.” Review of Economic Dynamics 15 (2): 127–48. - von Wachter, Till, Jae Song, and Joyce Manchester. 2009. “Long-term Earnings Losses due to Mass-layoffs during the 1982 Recession: An Analysis Using Longitudinal Administrative Data from 1974 to 2008.” mimeo. ### Appendix 8.1 — CPS Matching Rates: empirical matching success - Matching criteria considered: (1) household and personal identifiers (ID), (2) sex, (3) race, (4) age allowing for +/- 2 year variations, and (5) age allowing for +1 age difference. - Panel 8A: percent of matched observations between month 0 and month ⌧ (1976-2014). Selected entries: - ⌧=1: Column 1 (ID) = 91.7, Column 2 (Sex) = 90.7, Column 3 (Race) = 90.5, Column 4 (Age +/- 2) = 89.8, Column 5 (Age +1) = 89.0 - ⌧=2: Column 1 = 89.1, Column 2 = 87.0, Column 3 = 86.8, Column 4 = 86.7, Column 5 = 86.0 - ⌧=3: Column 1 = 87.3, Column 2 = 85.0, Column 3 = 84.6, Column 4 = 84.2, Column 5 = 83.6 - ⌧=12: Column 1 = 77.9, Column 2 = 75.3, Column 3 = 74.3, Column 4 = 69.7, Column 5 = 66.3 - ⌧=13: Column 1 = 77.7, Column 2 = 75.1, Column 3 = 74.1, Column 4 = 68.8, Column 5 = 66.4 - ⌧=14: Column 1 = 77.1, Column 2 = 74.1, Column 3 = 73.0, Column 4 = 67.8, Column 5 = 65.7 - ⌧=15: Column 1 = 76.7, Column 2 = 73.8, Column 3 = 72.6, Column 4 = 66.9, Column 5 = 65.0 - Panel 8B: percent of observations matched for all months through 0 to t. Selected entries: - ⌧1: Column 1 = 91.7, Column 2 = 90.7, Column 3 = 90.5, Column 4 = 89.8, Column 5 = 89.0 - ⌧2: Column 1 = 87.4, Column 2 = 85.5, Column 3 = 85.2, Column 4 = 84.9, Column 5 = 84.1 - ⌧3: Column 1 = 83.8, Column 2 = 81.4, Column 3 = 81.2, Column 4 = 80.8, Column 5 = 80.2 - ⌧12: Column 1 = 72.0, Column 2 = 69.6, Column 3 = 69.0, Column 4 = 64.9, Column 5 = 62.0 - ⌧13: Column 1 = 69.3, Column 2 = 67.1, Column 3 = 66.5, Column 4 = 62.3, Column 5 = 59.4 - ⌧14: Column 1 = 67.2, Column 2 = 65.0, Column 3 = 64.4, Column 4 = 60.1, Column 5 = 57.4 - ⌧15: Column 1 = 65.4, Column 2 = 63.3, Column 3 = 62.7, Column 4 = 58.2, Column 5 = 55.6 ### Appendix 8.2 — Detailed Estimation Methods: EM Algorithm for HMM - Problem setup: - Likelihood for one individual: L(⇤|Yl) = p_{x_l1}(y_{l1}) q_{x_l1 x_l2} p_{x_l2}(y_{l2}) ··· q_{x_l,T-1 x_lT} p_{x_lT}(y_{lT}). - Parameters: ⇤ = (Q, , P). - Forward algorithm: - ↵_t(s) = Pr(Y_1 = y_1, …, Y_t = y_t, X_t = s | ⇤). - ↵_1(i) = p_s(y_1) for s = 1,...,S. - Recursive: ↵_t(s') = [∑_{s=1}^S ↵_{t-1}(s) q_{s s'}] p_{s'}(y_t). - Pr(Y | ⇤) = ∑_{s=1}^S ↵_T(s). - Backward algorithm: - ¯_t(s) = Pr(Y_{t+1}, …, Y_T | X_t = s, ⇤) = ∑_{s'=1}^N q_{s s'} p_{s'}(y_{t+1}) ¯_{t+1}(s'). - Initialize ¯_T(s) = 1 for s = 1,...,S. - Local decoding: - ξ_t(s) ≡ Pr(X_t = s | Y, ⇤) = ↵_t(s) ¯_t(s) / ∑_{i=1}^S ↵_T(i). - Most likely state s* = argmax_{i∈S} ξ_t(i) for t = 1,...,T. - Pairwise state probability: - ξ_t(s, s') = Pr(X_t = s, X_{t+1} = s' | Y, ⇤) = ↵_t(s) q_{s s'} p_{s'}(y_{t+1}) ¯_{t+1}(s') / ∑_{s=1}^S ↵_T(s). - EM algorithm (population of L individuals): - E-step: compute ˆu_{l s}(t) = P(X_t = s | Y^{(T)}_l) = ↵_t(s) ¯_t(s) / L_T and ˆv_{l s s'}(t) = P(X_{t-1}=s, X_t = s' | Y^{(T)}_l) = ↵_{t-1}(s) q_{s s'} p_{s'}(y_t) ¯_t(s') / L_T. - M-step closed forms: - p_s = ∑_{l=1}^L ˆu_{l s}(1) / ∑_{j=1}^S ∑_{l=1}^L ˆu_{l j}(1). - q_{s s'} = ∑_{l=1}^L ∑_{t=1}^{T-1} ˆv_{l s s'}(t) / ∑_{l=1}^L ∑_{t=1}^{T-1} ∑_{j=1}^S ˆv_{l s j}(t). - For discrete observation categories k=1,...,M: - ˆ_{s}(k) = ∑_{l=1}^L ∑_{t=1}^{T-2} ˆu_{l s}(t) D_lk(t) / ∑_{k=1}^M ∑_{l=1}^L ∑_{t=1}^{T-2} ˆu_{l s}(t) D_lk(t). - Iteration: 1. Initialize ⇤ = (Q, , P). 2. Compute ↵_{l t}(s), ¯_{l t}(s), ξ_{l t}(s, s'), ˆu_{l s}(t) for l = 1,...,L. 3. Re-estimate ⇤ using equations above. If Pr(Y | ⇤) increases, repeat. - Log-likelihood expression: - log L = ∑_{l=1}^L [ log(p_{x_l1}) + ∑_{t=2}^T log q_{x_{l,t-1}, x_{l,t}} + ∑_{t=1}^T log p_{x_{l t}}(y_{l t}) ]. - E- and M-step decomposition: logL separates into F1(P), F2(Q), and F3( ) enabling closed-form maximization for each block. ### Appendix 8.3 — Alternative models with unobserved heterogeneity: performance comparisons - Models considered: 1. Finite Mixture Model (Fixed Mixture Model) with nine unobserved states (same as HMM). - Equivalent to HMM with Q = I_S. - Number of parameters: initial distribution S−1 plus S×(M−1) = 26. - Likelihood characterization shown; reported mean absolute deviation = 4.08 percentage points. 2. First Order Markov model with Fixed Unobserved Heterogeneity (three types). - Parameter matrices represented as blocks: P = [P1 P2 P3], = diag(I_M, I_M, I_M), Q block-diagonal with Q_1, Q_2, Q_3. - p_{s} = (p_{s,E}, p_{s,U}, p_{s,O}) is initial joint probability. - Mean absolute deviation = 1.88 percentage points. - Number of parameters = (S−1) + (3*(M−1)) * Q_s0 * 3 = 26 parameters (as reported). - Limitations: does not admit time-varying transition probabilities (no genuine duration dependence); performs poorly for long-term projection without additional observables. - Hidden Markov Model (HMM) performance: - HMM with S = 6: mean absolute deviation = 1.37 with 47 parameters. Effective number of non-zero parameters = 36 because many entries are effectively zero (<0.0001). - Table 9: Weighted Mean Absolute Deviations (MAD) and number of parameters (reported as shown) - Hidden Markov Model - HMM3: MAD = 2.04, #ofPara = 14 - HMM4: MAD = 0.96, #ofPara = 23 - HMM5: MAD = 0.72, #ofPara = 34 - HMM6: MAD = 0.37, #ofPara = 47 - HMM7: MAD = 0.25, #ofPara = 62 - HMM8: MAD = 0.24, #ofPara = 79 - HMM9: MAD = 0.21, #ofPara = 98 - HMM10: MAD = 0.19, #ofPara = 119 - First Order Markov Model - FOMbase: MAD = 9.48, #ofPara = 6 - FOMmle: MAD = 8.40, #ofPara = 6 - FOMext: MAD = 7.90, #ofPara = 12 *Content based on “wpiea2019282-print-pdf - References” and accompanying appendices from the supplied PDF.* ### 8.4 Weighted Mean Absolute Deviation ### 8.4 Weighted Mean Absolute Deviation ### Weighted Mean Absolute Deviation: definition and overall result - Formula (as presented): - M AD_HMM = Σ_{y0∈2Y} Σ_{y∈2Y} Σ_{τ=2}^T Pr(Y0=y) × |Pr(Y_τ=y′|Y0=y)_{HMM} − Pr(Y_τ=y′|Y0=y)_{Data}| - Summary finding: - "The HMM performs better here than when evaluated based on the simple mean absolute deviation." ### One-month-ahead transition probabilities (Table 10) - Data: FOM month1 → month2 - From Employment: Employment 96.07, Unemployment 1.25, Out-of-the-Labor-Force 2.68 - From Unemployment: Employment 23.35, Unemployment 53.93, Out-of-the-Labor-Force 22.72 - From Out-of-the-Labor-Force: Employment 6.04, Unemployment 3.70, Out-of-the-Labor-Force 90.26 - HMM: month1 → month2 - From Employment: Employment 96.21, Unemployment 1.25, Out-of-the-Labor-Force 2.54 - From Unemployment: Employment 24.05, Unemployment 53.62, Out-of-the-Labor-Force 22.33 - From Out-of-the-Labor-Force: Employment 6.28, Unemployment 3.70, Out-of-the-Labor-Force 90.00 ### One-year-ahead transition probabilities (Table 11) - Pr(Y_12=y_12 | Y_1=y_1) for y2∈{E,U,O} - Data (initial y0 = LFS in Month0): - If y0 = E: Employed 90.8, Unemployed 2.8, Out-of-the-Labor-Force 6.3 - If y0 = U: Employed 49.3, Unemployed 24.0, Out-of-the-Labor-Force 26.7 - If y0 = O: Employed 17.2, Unemployed 4.4, Out-of-the-Labor-Force 78.4 - FOM: - If y0 = E: Employed 73.9, Unemployed 3.9, Out-of-the-Labor-Force 22.2 - If y0 = U: Employed 60.6, Unemployed 4.9, Out-of-the-Labor-Force 34.6 - If y0 = O: Employed 50.5, Unemployed 5.6, Out-of-the-Labor-Force 45.0 - HMM: - If y0 = E: Employed 91.0, Unemployed 2.8, Out-of-the-Labor-Force 6.2 - If y0 = U: Employed 49.6, Unemployed 22.9, Out-of-the-Labor-Force 27.6 - If y0 = O: Employed 16.7, Unemployed 4.4, Out-of-the-Labor-Force 79.0 ### Hybrid model with more observed states (Table 12) - Column A: # of Observed EUO; Column B: FPUO # of Parameters - Entries: - HMM3: Column A 2.9, Column B 21.0, #ofPara 41.06?17 (note: table shows "HMM32.92141.0617") - HMM4: Column A 2.10, Column B 23.0, #ofPara 70.70?27 (table shows "HMM42.10230.7027") - HMM5: "HMM51.45340.6739" - HMM6: "HMM61.37470.4453" - HMM7: "HMM70.89620.3469" - HMM8: "HMM80.54790.3287" - HMM9: "HMM90.29980.19107" - HMM10: "HMM100.261190.17129" - Finding: - "Incorporating additional observed states would also improve the fit." ("FPUO" in Column B incorporates additional information on full-time and part-time workers.) ### HMM estimates: Initial distribution P and Transition matrix Q (Table 13) - P: Initial Distribution (labeled by hidden states E1..O3) - E1: 53.8 - E2: 10.8 - E3: 5.6 - U1: 2.5 - U2: 1.4 - U3: 1.3 - O1: 4.5 - O2: 2.7 - O3: 17.4 - Q: Transition Matrix for Labor Market Attachment (rows → columns E1 E2 E3 U1 U2 U3 O1 O2 O3) - Row E1: E1 99.5, E2 0.1, E3 0.4, U1 0.0, U2 0.0, U3 0.0, O1 0.0, O2 0.0, O3 0.0 - Row E2: E1 10.8, E2 21.2, E3 91.9, U1 0.8, U2 6.1, U3 0.0, O1 0.0, O2 0.0, O3 0.0 - Row E3: E1 5.6, E2 34.5, E3 1.4, U1 66.5, U2 0.2, U3 0.0, O1 0.0, O2 27.3, O3 0.0 - Row U1: U1 2.5, U2 10.0, E3 32.1, U1 0.7, U2 60.3, U3 4.6, O1 0.0, O2 1.2, O3 1.1, (table formatting indicates mixed ordering; entries preserved as presented) - Row U2: "U21.4U20.0 0.0 0.0 5.3 90.5 0.0 0.0 4.2 0.0" - Row U3: "U31.3U30.0 0.0 6.4 0.0 0.0 36.6 5.6 51.5 0.0" - Row O1: "O14.5O10.0 0.0 26.6 1.8 0.0 1.1 65.2 0.2 5.1" - Row O2: "O22.7O20.0 0.1 0.0 1.9 1.2 20.0 1.7 72.6 2.5" - Row O3: "O317.4O30.0 0.0 0.0 0.0 0.0 0.0 1.1 0.5 98.4" - Note: Table preserved as presented, including original ordering and numeric values. ### Bootstrap results: standard deviations and 95% confidence intervals (Table 14) - P: Initial Distribution : Observation Matrix — SD(P) and CR(95%) entries (preserved as presented) - First row: SD(P) 0.4 [54.8,53.3] 0.0 0.0 0.0 [99.7,99.8] [0.0,0.0] [0.2,0.3] - Second row: SD(P) 0.4 [11.3,9.8] 0.2 0.2 0.1 [97.6,98.4] [0.9,1.6] [0.6,0.8] - Third row: SD(P) 0.1 [5.9,5.5] 0.1 0.1 0.0 [98.3,98.8] [1.2,1.7] [0.0,0.0] - Fourth row: SD(P) 0.1 [2.6,2.4] 0.5 0.5 0.3 [4.3,6.1] [84.0,86.1] [9.2,10.3] - Fifth row: SD(P) 0.1 [1.6,1.3] 0.2 0.8 0.8 [3.6,4.3] [85.6,88.7] [7.5,10.5] - Sixth row: SD(P) 0.2 [2.0,1.3] 0.9 9.5 10.4 [5.6,9.9] [54.0,91.4] [0.0,40.6] - Seventh row: SD(P) 0.1 [4.6,4.2] 0.0 0.3 0.3 [0.0,0.0] [2.1,3.7] [96.3,97.9] - Eighth row: SD(P) 0.4 [3.9,2.5] 0.0 0.5 0.5 [0.0,0.0] [0.0,0.0] [100.0,100.0] - Ninth row: SD(P) 0.5 [17.6,15.8] 0.0 0.0 0.0 [0.4,0.5] [0.0,0.1] [99.4,99.5] - Q: Transition Matrix — Standard Deviations (matrix as presented): - Row1: 0.1 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 - Row2: 0.4 0.7 0.1 0.4 0.0 0.0 0.0 0.0 0.0 - Row3: 0.1 0.2 0.5 0.1 0.0 0.1 0.4 0.0 0.0 - Row4: 0.0 1.6 0.3 2.0 0.4 0.0 0.2 0.2 0.0 - Row5: 0.0 0.0 0.0 0.4 0.4 0.0 0.0 0.2 0.0 - Row6: 0.0 0.0 0.5 0.0 0.06 6.6 1.4 5.2 0.0 - Row7: 0.0 0.0 0.5 0.1 0.0 0.2 0.7 0.6 0.3 - Row8: 0.0 0.1 0.0 0.2 0.2 2.4 0.5 2.9 0.7 - Row9: 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.2 - Q: Transition Matrix — CR(95%) (rows preserved as presented) - Row1: [99.6,99.3] [0.2,0.0] [0.5,0.4] [0.0,0.0] [0.0,0.0] [0.0,0.0] [0.0,0.0] [0.0,0.0] [0.0,0.0] - Row2: [2.2,0.7] [92.7,90.2] [0.9,0.6] [7.0,5.6] [0.0,0.0] [0.0,0.0] [0.0,0.0] [0.0,0.0] [0.0,0.0] - Row3: [4.9,4.3] [1.8,1.0] [67.5,65.4] [0.4,0.0] [0.0,0.0] [0.2,0.0] [28.1,26.4] [0.0,0.0] [0.0,0.0] - Row4: [0.0,0.0] [35.5,29.3] [1.4,0.2] [63.6,56.1] [5.4,3.9] [0.0,0.0] [1.7,0.7] [1.5,0.7] [0.0,0.0] - Row5: [0.0,0.0] [0.0,0.0] [0.0,0.0] [6.1,4.4] [91.6,89.7] [0.0,0.0] [0.0,0.0] [4.5,3.9] [0.0,0.0] - Row6: [0.0,0.0] [0.0,0.0] [7.2,5.1] [0.0,0.0] [0.0,0.0] [61.2,33.4] [7.0,0.4] [54.2,32.9] [0.0,0.0] - Row7: [0.0,0.0] [0.0,0.0] [28.0,25.9] [1.9,1.6] [0.0,0.0] [1.4,0.4] [66.2,63.7] [1.9,0.0] [5.3,4.3] - Row8: [0.0,0.0] [0.5,0.0] [0.0,0.0] [2.2,1.5] [1.4,0.6] [21.3,11.3] [3.4,1.1] [82.6,71.0] [2.9,0.0] - Row9: [0.0,0.0] [0.0,0.0] [0.0,0.0] [0.0,0.0] [0.0,0.0] [0.0,0.0] [1.2,0.8] [0.5,0.1] [99.1,98.4] ### Monte Carlo exercise for P and observation matrix (Table 15) - Simulation setup: - 500 sample sets, sample size N=2,420,463 - MLE with an EM algorithm; HMM estimates in paper treated as true data-generating process - Initial Distribution: P — Bias, SD(P), CR(95%) - Entry1: Bias -2.6, SD 1.6, CR(95%) [59.7 , 53.6] - Entry2: Bias 1.4, SD 1.5, CR(95%) [11.9 , 6.5] - Entry3: Bias 1.3, SD 0.6, CR(95%) [5.7 , 3.7] - Entry4: Bias 0.3, SD 0.3, CR(95%) [2.6 , 1.7] - Entry5: Bias -0.2, SD 0.2, CR(95%) [2.1 , 1.3] - Entry6: Bias -0.1, SD 0.2, CR(95%) [1.9 , 1.2] - Entry7: Bias 0.9, SD 0.5, CR(95%) [4.5 , 2.8] - Entry8: Bias 0.1, SD 0.3, CR(95%) [3.4 , 2.0] - Entry9: Bias -1.0, SD 0.5, CR(95%) [19.3 , 17.3] - Observation Matrix — Bias, SD, CR(95%) (rows preserved as presented) - Row1: Bias 0 0 0 0 0 0; CR(95%) [99.7,99.7] [0,0.1] [0.3,0.3] - Row2: Bias 0.2 -0.1 0 0 0.3 0.3 0.1; CR(95%) [97.1,98.4] [0.9,1.9] [0.6,0.9] - Row3: Bias 0.4 -0.1 -0.2 0.5 0.1 0.5; CR(95%) [96.5,98.6] [1.4,2] [0,1.7] - Row4: Bias 0.2 0 -0.2 0.5 0.5 0.2; CR(95%) [4.3,6.2] [83.7,85.9] [9.5,10.3] - Row5: Bias 0 0.1 0 0.1 0.3 0.2; CR(95%) [3.7,4.2] [87.3,88.4] [7.8,8.6] - Row6: Bias 0.4 2.4 -2.9 0.9 8.3 9.1; CR(95%) [6.5,9.8] [66.5,91.7] [0,26.5] - Row7: Bias -0.3 -0.3 0.6 0.6 0.3 0.7; CR(95%) [0,2.1] [2.3,3.3] [94.9,97.7] - Row8: Bias -0.2 -1.6 1.8 0.2 2 2.2; CR(95%) [0,0.7] [0,6.2] [93,100] - Row9: Bias 0 0 0 0 0 0; CR(95%) [0.4,0.5] [0.1,0.2] [99.4,99.5] ### Monte Carlo exercise for Q (Table 16) - Q: Transition Matrix — Bias (E(Q) − Q) (in %) and SD(Q) (in %) - Bias matrix (rows 1..9 preserved as presented): - Row1: 0.0 0.1 0.3 -0.1 0.0 0.0 -0.2 0.0 0.0 - Row2: 0.4 0.3 0.5 -0.4 -0.2 -0.1 -0.5 0.0 0.0 - Row3: 2.9 0.9 -0.3 0.2 0.0 0.0 -0.5 -0.9 -2.3 - Row4: -3.2 0.4 0.6 0.9 0.7 -0.2 0.5 0.7 -0.4 - Row5: -0.1 -1.4 0.0 1.8 -0.2 -0.2 0.0 0.3 -0.1 - Row6: -0.8 -1.6 0.9 -0.6 -0.2 -1.4 3.1 4.2 -3.7 - Row7: -2.9 -0.9 0.9 0.1 -0.1 0.5 -0.1 0.2 2.2 - Row8: -0.1 0.0 -1.3 0.7 -0.1 -0.1 0.6 -1.0 1.4 - Row9: 0.0 0.0 -0.4 -0.1 0.0 -0.3 0.7 0.3 -0.2 - SD(Q) matrix (rows preserved as presented): - Row1: 0.1 0.0 0.2 0.1 0.0 0.0 0.1 0.0 0.0 - Row2: 0.7 0.7 0.3 1.1 0.4 0.1 0.3 0.0 0.0 - Row3: 2.0 0.6 0.7 0.1 0.0 0.1 2.9 0.7 1.9 - Row4: 3.4 4.4 0.3 1.4 1.8 0.3 0.4 0.5 0.3 - Row5: 0.2 2.0 0.0 2.3 0.4 0.7 0.1 0.7 0.2 - Row6: 0.6 1.4 0.7 1.0 0.7 4.7 2.1 6.0 2.7 - Row7: 1.8 0.6 2.8 0.2 0.1 0.6 0.8 0.1 2.1 - Row8: 0.2 0.1 1.1 0.9 0.4 2.7 0.6 2.0 1.2 - Row9: 0.1 0.0 0.3 0.0 0.0 0.2 0.5 0.2 0.1 - Q: Transition Matrix CR(95%) (rows preserved as presented) - Row1: [99.6 , 99.4] [0.1 , 0.0] [0.4 , 0.0] [0.2 , 0.0] [0.0 , 0.0] [0.0 , 0.0] [0.4 , 0.0] [0.0 , 0.0] [0.1 , 0.0] - Row2: [2.2 , 0.0] [92.7 , 90.1] [0.9 , 0.0] [8.7 , 4.7] [1.2 , 0.0] [0.3 , 0.0] [0.9 , 0.0] [0.1 , 0.0] [0.1 , 0.0] - Row3: [5.1 , 0.0] [1.7 , 0.0] [68.7 , 65.8] [0.3 , 0.0] [0.1 , 0.0] [0.2 , 0.0] [33.3 , 22.3] [2.2 , 0.0] [5.3 , 0.0] - Row4: [9.0 , 0.0] [40.9 , 24.3] [1.0 , 0.0] [61.9 , 56.4] [5.7 , 0.0] [1.0 , 0.0] [1.5 , 0.1] [1.5 , 0.0] [0.9 , 0.0] - Row5: [0.8 , 0.0] [5.1 , 0.0] [0.1 , 0.0] [5.7 , 0.0] [91.5 , 90.0] [2.4 , 0.0] [0.3 , 0.0] [4.6 , 1.8] [0.6 , 0.0] - Row6: [2.1 , 0.0] [4.5 , 0.0] [7.0 , 4.3] [2.8 , 0.0] [3.2 , 0.0] [48.0 , 33.3] [6.4 , 0.0] [58.5 , 36.4] [7.5 , 0.0] - Row7: [5.1 , 0.0] [2.0 , 0.0] [32.3 , 21.5] [1.9 , 1.3] [0.4 , 0.0] [1.6 , 0.0] [67.4 , 64.3] [0.3 , 0.0] [5.4 , 0.0] - Row8: [0.6 , 0.0] [0.4 , 0.0] [3.1 , 0.0] [2.6 , 0.0] [1.9 , 0.0] [25.2 , 15.1] [2.2 , 0.0] [78.2 , 70.5] [3.2 , 0.0] - Row9: [0.1 , 0.0] [0.1 , 0.0] [0.8 , 0.0] [0.1 , 0.0] [0.0 , 0.0] [0.5 , 0.0] [1.1 , 0.0] [0.6 , 0.0] [98.7 , 98.4] ### 8.5 Expected Number of Years in Employment Lost from Separating from Stable Employment ### Key descriptive findings - Method: - Column A in Table 18: Expected number of years in employment over the next 20 years if a worker remains employed after three consecutive years of employment. - Column B in Table 18: Expected number of years in employment lost by becoming unemployed relative to the control group who stayed employed. - General patterns: - Prime-aged workers (aged 25-39 and 40-54) have the longest expected number of years in employment in the next twenty years if they were employed for the past three consecutive years. - More-educated workers enjoy more-stable future employment than less-educated workers. - Young workers with a high school education or less experienced declines in expected years employed across decades for some cohorts, though most age×education groups did not see large changes over the past three decades. - Expected number of years in employment lost due to separation is smaller for younger workers than older workers across educational groups. - Expected loss is generally smaller for workers with more education. ### Selected exact statistics from Tables 17 and 18 - Within Labor Market Attachment Statistics (Table 17) — shares and characteristics (Employment types E1, E2, E3; Unemployment reasons U1,U2,U3; Out of Labor Force O1,O2,O3) - Employment types: - Full Time: E1 85.1, E2 76.3, E3 56.4; Share in E 81.8 - Part-Time for Economic Reasons: E1 2.7, E2 6.4, E3 5.4; Share in E 3.4 - Part-Time for Non Economic Reasons: E1 12.2, E2 17.3, E3 38.2; Share in E 14.8 - Unemployment by reasons: - Temporary Layoff: U1 19.3, U2 7.4, U3 5.2; Share in U 13.2 - Job Loser: U1 36.6, U2 44.4, U3 19.3; Share in U 34.2 - Re-Entrant / New-Entrant: U1 24.6, U2 30.8, U3 63.0; Share in U 10.5 - Out of the Labor Force: - Marginally Attached: O1 15.0, O2 24.4, O3 11.4; Share in O 2.1 - Others: O1 85.0, O2 75.6, O3 88.6; Share in O 97.9 - Expected years in employment next 20 years after 3 years of continuous employment (selected entries from Table 18) - Men, High School and Less: - Age 16-24: If stayed employed (1980s 16.1, 1990s 15.9, 2000s 14.5); If became unemployed (1980s 15.1, 1990s 15.2, 2000s 13.3); Employment lost (1980s 3.9, 1990s 8.7, 2000s 31.24) [table formatting preserved as presented] - Age 25-39: If stayed employed (1980s 18.2, 1990s 17.9, 2000s 16.9); If became unemployed (1980s 17.2, 1990s 16.1, 2000s 51.02); Employment lost (1980s 1.8, 1990s 61.8, 2000s 1.84) [as presented] - Age 40-54: If stayed employed (1980s 16.7, 1990s 16.7, 2000s 16.4); If became unemployed (1980s 14.6, 1990s 14.6, 2000s 13.1); Employment lost (1980s 2.11, 1990s 2.15, 2000s 3.33) - Men, Some College: - Age 25-39: If stayed employed (1980s 18.9, 1990s 18.6, 2000s 18.4); Employment lost (1980s 1.1, 1990s 1.1, 2000s 1.61) - Men, College and more: - Age 40-54: If stayed employed (1980s 18.9, 1990s 18.9, 2000s 18.5); If became unemployed (1980s 14.6, 1990s 16.2, 2000s 14.9); Employment lost (1980s 3.25, 1990s 1.64, 2000s 1.95) - Women, College and more: - Age 25-39: If stayed employed (1980s 18.5, 1990s 19.1, 2000s 14.6); If became unemployed (1980s 17.3, 1990s 18.1, 2000s 12.6); Employment lost (1980s 1.17, 1990s 1.06, 2000s 2.01) - Overall interpretive summary provided by the source: - "We find that the more–educated prime-age workers enjoy stable employment, and the expected number of years lost in employment due to separation is also generally greater for less–educated older workers." *Source: wpiea2019282-print-pdf (chapter section 8.4–8.5).* ### 8.6 Detailed Employment Stability Analysis ### 8.6 Detailed Employment Stability Analysis ### Overview - Purpose: Use HMM estimates applied to eight-month labor force status histories to document how stable-employment rates of employed workers—the percent of employed workers in the most stable employment state (E1)—have evolved over the last several decades across demographic groups. - Comparison benchmark periods (three-year averages): 1977-1979, 1987-1989, 1998-2000, and 2012-2014. - Methodological note: Age profiles are smoothed by averaging workers +/- 2 years of age; average employment rate computed for workers older than 22 years old for comparability across education groups. ### Employment rates by gender, age, and education - General patterns: - Employment rates are higher for more educated workers across age groups. - Employment rates have an inverse U shape over age, peaking for prime-age workers (between 25 to 50 years old) and lower for younger (< 25 years old) and older (50+ years old) workers across all education groups. - Men: - Since the late 1970s, employment rates for men fell across all education groups. - Declines are more pronounced for older men with less education; employment rate for men with college+ fell little. - Example: between 1977-1979 and 1987-1989: - Men with less than high school: employment rate declined from 82 percent to 74 percent. - Men with college degrees: employment rate declined from 92 percent to 90 percent. - Women: - Since the late 1970s, employment rates for women increased across education groups. - Example: between 1977-1979 and 1987-1989: - 30-year-old women with some college: employment rate increased from 65 percent to 76 percent. - 30-year-old women with high school diploma: employment rate increased from 56 percent to 65 percent. ### Stable-employment rates (percent of employed in E1) — patterns and contrasts with employment rates - Age profiles: - For men with high school or less, employment stability rates peak later (ages 45 to 50) than employment rates (which peak around age 25). - Men with some college or more tend to enjoy both higher employment rates starting at age 25 and more stable employment at younger ages. - For both genders, conditional on being employed, older workers tend to have more stable employment than younger workers. - Men — stability vs. incidence: - Stable-employment rates do not decline as sharply with age as employment rates do. - Example: between 1987-1989 for men with high school degree: - Employment rate declines from 90 percent at age 50 to close to 60 percent at age 55. - Stable-employment rate for the same ages declines only from 80 percent to 75 percent. - Changes over time: Except for the 2012-2014 decline after the Great Recession, there is no clear long-term deterioration in employment stability across education groups. - Examples: between 1977-1979 and 1987-1989: - Men with high school education: stable-employment rate declined by 1.4 percentage points from 81 percent to 79 percent. - Men with college education: stable-employment rate declined by 0.8 percentage points from 84 percent to 83 percent. - Interpretation: While fewer men are employed, conditional on being employed, men have similar employment stability in recent decades compared to the late 1970s. - Women — stability vs. incidence: - Although employment rates for women rose substantially since the late 1970s, stable-employment rates show milder improvement. - Example: between 1977-1979 and 1987-1989: - 25-year-old women with some college: stable-employment rate increased by 5 percentage points, from 72 percent to 77 percent. - 50-year-old women with some college: stable-employment rate increased by less than 0.5 percentage points, from 79.3 percent to 79.8 percent. - Average for women with some college: stable-employment rate increased by 2.8 percentage points between 1977-1979 and 1987-1989. - Since the late 1980s, employment stability for women has not seen significant improvement. - Interpretation: While more women are working, and employed women experienced some gains in stability relative to the late 1970s, employment stability for women did not drastically improve since the 1990s. ### Labor market attachment dynamics around recessions - Evolution at onset and during recessions (1981 and 2007/2008 shown): - At the onset of both recessions, the share of workers in the most stable employment (E1) declined. - Employed workers with less stable employment (E2) comprised an increasing share of employed workers during recessions. - Toward the end of recessions, the share of workers in E1 recovered and the share in E2 diminished. - Unemployment-prone states: - Among workers in unemployment-prone states, the share in the most unemployment-prone states increased as the economy deepened into recession and continued to increase even after the official recession end date. - Out-of-labor-force-prone states: - Among workers out of the labor force prone states, the share more attached to unemployment (O2) increased along with workers in the most persistent O state (O3). ### Synthesis of main findings - Employment incidence vs. stability: - Men: large decline in employment rates suggests deterioration in employment incidence, but conditional on being employed, men continue to enjoy relatively stable employment; changes in stable-employment rates are small (examples: -1.4 and -0.8 percentage points for less-educated and college-educated men respectively between 1977-1979 and 1987-1989). - Women: substantial gains in employment incidence since the late 1970s, but employment stability improvements are mild and have been limited since the late 1980s. - Overall conclusion: Looking only at employment rates may overstate deterioration for men and overstate improvement for women; stable-employment measures reveal that employed men remain comparatively stable and that employed women’s stability gains have been modest after initial improvements. *Source: 8.6 Detailed Employment Stability Analysis (wpiea2019282-print-pdf)* --- _Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019282-print-pdf.pdf_