Life-cycle worker flows and cross-country differences in aggregate employment

Layer 1 — Overview

Research question. The paper asks: what are the sources of cross-country differences in aggregate employment across European economies, and which types of worker flows — between employment (E), unemployment (U), and nonparticipation (N) — drive those differences? The authors pay particular attention to heterogeneity by gender and age, motivated by the observation that cross-country employment dispersion is concentrated among women, youth, and older workers, and that a large portion of the dispersion is traceable to differences in labor force participation rather than unemployment rates alone.

Data. The empirical analysis draws on microdata from the EU Statistics on Income and Living Conditions (EU-SILC), an annual survey covering 32 European countries for 2004–2019. Germany is covered using the German Socio-Economic Panel (GSOEP, 2003–2018) because GSOEP longitudinal coverage begins earlier. The combined sample contains 7,064,306 individual-year observations for 2,221,672 individuals. Labor force status is recorded monthly via a retrospective calendar; transition probabilities are estimated at the quarterly frequency after correcting for measurement error (a “de-NUN-ification” procedure following Elsby et al. [2015]) and time-aggregation bias (Shimer [2012]).

Methodology — empirical. Six quarterly transition probabilities among E, U, and N are estimated by gender and single year of age (16–65). The life-cycle profile of each probability is extracted nonparametrically by regressing age-time cells on age and time dummies, removing business-cycle variation. To decompose cross-country employment differences into contributions of the six transition rates while handling the path-dependence of the decomposition (6! = 720 possible orderings), the authors apply the Shapley-Owen decomposition, which assigns to each transition rate its average marginal contribution across all orderings. An initial first-pass decomposition allocates the aggregate employment gap between any two countries into three parts: demographics, initial conditions (distribution across E, U, N at age 16), and transition probabilities. Transition probabilities account for 93–105% of the cross-country variance in aggregate employment, while demographics and initial conditions together explain less than 10%.

Methodology — structural model. The authors build a life-cycle Diamond-Mortensen-Pissarides (DMP) model with three labor market states, calibrated separately by gender and country for France, Germany, Italy, Spain, and the U.K. — the five largest economies in the sample. A key feature is that all primitives (technology, search and matching) are age-independent; life-cycle variation in worker flows arises endogenously from the finite retirement horizon and from two search margins: (i) an intensive margin — variable search intensity s in [0,1] chosen optimally each period — and (ii) an extensive margin — the endogenous labor force participation decision modeled as a discrete choice with i.i.d. extreme-value utility shocks. The model also incorporates permanent match quality (an experience good revealed stochastically with probability alpha per period following Jovanovic [1979]), transitory match-quality shocks (persistent AR(1) process), exogenous job-destruction shocks (per-period probability delta), a two-tier UI system, a two-tier EPL system capturing temporary vs. permanent contracts, and proportional value-added and social-security taxes.

Main empirical findings.

1. For male workers, employment-to-unemployment (EU) transitions account for approximately half of the cross-country variance in aggregate male employment across all 32 countries, rising to about three-quarters when looking at the five largest economies, and exceeding 85% for prime-age males (ages 25–54). Transitions in the reverse direction (UE) explain less than 30% of the variance across all 32 countries and play almost no role among the five largest economies. The labor force participation margin (combining NE and EN transitions) explains a non-negligible 25–30% of the aggregate male employment gap.
2. For female workers, at least half of the cross-country variance in employment is explained by participation-related flows, primarily transitions from nonparticipation to employment (NE). In the full 32-country sample, NE alone explains 65% of the variance in female employment rates across all ages (16–65). Its role is somewhat smaller in the five largest economies, where EN transitions also play a larger role. Crucially, the sum of NE and EN variance contributions for women is at least as large as the sum of UE and EU contributions, underlining the indispensability of a three-state model.

Main quantitative (model-based) findings. The model decomposes cross-country employment differences into technology (the distribution of permanent match quality, job-separation risk delta, and information frictions alpha), search parameters (vacancy costs, non-work utility, search-cost parameters), and policies (UI generosity, firing costs, taxes). The total employment variance across the five economies and two gender groups is 0.36 percentage points squared. Technology differences over-explain this variance (contribution of 0.65), while policies play almost no role (contribution of -0.04) and search frictions have a negative variance contribution (-0.25). The negative sign of search and policy contributions reflects the negative cross-country correlation between these factors and technology: countries with high employment rates (e.g., France) tend to have more generous UI and higher taxes, which the model attributes to compensating technology advantages. For individual countries: France is about 4.4 percentage points above the cross-country benchmark, driven by technology and partly offset by the highest replacement ratios and labor tax rates in the sample (67% and 56%, respectively). Spain is about 7 percentage points below the benchmark, driven by the lowest measured labor productivity (78% of Germany’s level) and the highest employment outflow rates (~4–5% per quarter vs. ~2% in France).

The channels through which technology affects employment are predominantly the employment inflows, not outflows. The exogenous job-separation risk delta affects aggregate employment mostly through its impact on expected duration of future employment spells, which reduces search incentives and job-finding rates from both unemployment and nonparticipation, and lowers labor force attachment. Similarly, mean permanent match quality (mu_x) and labor taxes (tau_ss) operate mainly through the inflow margin. Technology effects are amplified by search effort margins, particularly for women and youth: women face higher non-work utility (interpreted as labor-market frictions or opportunity costs), implying a lower employment surplus and therefore a higher surplus elasticity; for young workers, the long remaining horizon amplifies the effect of technology variations on discounted lifetime earnings, generating relatively higher search-effort responses.

Scope conditions. The analysis is confined to European countries. The structural decomposition covers only the five largest European economies. The authors acknowledge that parameters labeled as “job-separation risk” may also capture employment protection and temporary contracts not explicitly modeled, or non-monetary quit motives, so the attribution to “technology” should be interpreted with that caveat in mind. The model operates in a complete-markets, no-savings environment without on-the-job search.

Layer 2 — Q&A

Q1: What fraction of cross-country employment variance is explained by transition probabilities vs. demographics and initial conditions?

A: In the full 32-country sample, transition probabilities account for 94.7% of the cross-country variance in aggregate male employment and 99.9% for female employment. In the five largest economies, the corresponding figures are 93.5% (men) and 104.9% (women) — the slight excess above 100% reflects the negative contribution of initial conditions for women. Demographics and initial conditions together explain less than 10% of the variance, with somewhat larger demographic effects in Baltic and Eastern European countries, plausibly due to emigration-driven changes in age composition.

Q2: For male workers, which specific transition probability dominates the cross-country employment variance, and how does this vary by age and across country groupings?

A: EU (employment-to-unemployment) transitions account for approximately 51% of the cross-country variance in aggregate male employment (ages 16–65) across all 32 countries, rising to 77% in the five largest economies, and to 89% for prime-age males (ages 25–54) in the same group. By contrast, UE (job-finding from unemployment) explains at most 29% across all 32 countries and virtually nothing in the five largest economies. For prime-age men, EU remains dominant throughout; toward the end of the working life, EN (employment-to-nonparticipation) transitions become the main driver as workers move into retirement.

Q3: For female workers, what is the primary driver of cross-country employment variance, and does the pattern differ from men?

A: For women, transitions from nonparticipation to employment (NE) explain 65% of the cross-country variance in female employment across all ages in the 32-country sample. This dominance is more concentrated at ages 20–30, when participation entry is particularly heterogeneous across countries, likely reflecting fertility and child-rearing patterns. The sum of NE and EN contributions for women equals or exceeds the combined UE and EU contributions in both country groupings, demonstrating a fundamentally different demographic structure of employment differences for women relative to men.

Q4: How does the model generate life-cycle variation in transition rates despite having age-independent primitives?

A: The model produces age-varying transition rates through two mechanisms operating on age-independent fundamentals. First, variable search intensity declines as workers age because the remaining time to retirement shortens, reducing the expected lifetime returns to job search — the “horizon effect” (Cheron et al. [2011, 2013]). This mechanism explains virtually all of the life-cycle variation in the NE job-finding rate and an overwhelmingly large share of the variation in the UE rate, as shown by counterfactual exercises that fix search intensity at its life-cycle average. Second, information frictions about permanent match quality generate declining separation rates over the working life: young workers disproportionately hold matches with unrevealed quality and thus face higher reallocation risk upon quality revelation; as workers age, their employment share shifts toward matches with revealed quality, which have lower separation rates due to sorting.

Q5: What does the structural decomposition (Table 7) reveal about the role of technology vs. policies in explaining cross-country employment differences?

A: The variance decomposition in Table 7 shows that technology parameters (permanent match-quality distribution, job-separation risk delta, and match-quality revelation probability alpha) account for a variance contribution of 0.65 (against total employment variance of 0.36), over-explaining the cross-country dispersion. Labor market policies (UI benefits, firing costs, taxes) have a near-zero variance contribution of -0.04. Search parameters contribute -0.25. The result that policies explain little does not mean they have no level effect: in simple comparative statics, the model predicts that more generous UI and higher labor taxes lower employment. However, in the cross-country calibration, countries with higher employment rates tend to have more interventionist policies, so the cross-country correlation between policies and technology masks individual policy effects at the variance level.

Q6: How do technology effects propagate to employment differences through worker flows, and why is the inflow channel dominant?

A: Table 8 decomposes employment elasticities with respect to delta (job-separation risk), mu_x (mean log permanent match quality), and tau_ss (social security tax rate) into contributions from (i) the NE job-finding rate, (ii) the share of nonemployed in the labor force (labor force attachment, u-tilde), (iii) the differential between UE and NE rates, and (iv) the employment outflow rate (pEO). At the aggregate level, the separation risk delta has an employment elasticity of -0.28, of which the outflow contribution (dpEO = -0.08) is smaller in absolute magnitude than the sum of inflow contributions (dpNE = -0.06, du-tilde = -0.07, dpDelta = -0.06). Mean match quality mu_x has an employment elasticity of 0.53, primarily mediated through inflows. The mechanism is that changes in delta or mu_x alter expected lifetime earnings, which in turn change search incentives and participation decisions, generating correlated movements in job-finding rates and labor force attachment that amplify the employment impact beyond what a simple outflow change would imply.

Q7: Why do women and youth show larger search-effort responses to technology variations?

A: For women, the calibrated non-work utility yo is higher in all five countries than for men (interpreting this as extra costs and wedges on the returns to working), which implies a smaller employment surplus. A smaller surplus generates a higher elasticity of surplus with respect to parameter changes, and since search intensity and participation decisions depend on expected surplus, women exhibit larger employment elasticities to technology variations. The aggregate employment elasticity of delta is -0.39 for women vs. -0.19 for men; for mu_x, it is 0.78 for women vs. 0.33 for men. For youth (ages 20–29), the long remaining horizon amplifies the effect of technology changes on discounted expected lifetime earnings, which in turn amplifies participation incentives: the labor force attachment channel (du-tilde) contributes -0.13 for youth compared to -0.07 at the aggregate, while dE = -0.31 for youth vs. -0.28 aggregate for delta.

Q8: What is the quantitative role of individual technology sub-components (match quality, job-separation risk, information frictions)?

A: Panel B of Table 7 breaks down technology into three sub-components. Match quality (mean mu_x and variance sigma^2_x) and job-separation risk (delta) are the key drivers; the match-quality revelation probability (alpha, “match revelation”) plays almost no independent role (variance contribution approximately 0.00). For France, the primary positive technology contributor is mean match quality (consistent with France’s labor productivity slightly above the German benchmark). For Germany and the U.K., the low job-separation risk is the primary positive contributor. For Spain, the high job-separation risk — calibrated to match Spain’s employment outflow rate of around 4–5% per quarter versus 2% in France — is the main negative contributor, reflecting the widespread prevalence of temporary contracts.

Q9: What role do labor market policies play at the country-specific level, even though they explain little cross-country variance?

A: Panel C of Table 7 shows that employment protection legislation plays almost no role for any country. Labor taxes are quantitatively important: they explain the relatively high employment rate in the U.K. (the country with the lowest social security contribution rate, about 20%), contributing positively. In France, where labor taxes exceed 50% of the average wage, the policy contribution is strongly negative, roughly offsetting the large positive technology contribution. UI benefits lower aggregate employment — Italy, with calibrated UI benefits lower than France’s, has a smaller employment gap vis-a-vis the benchmark partly because of this. The finding that policies explain little variance while having large individual-country effects is explained by the negative cross-country correlation: countries with generous policies also tend to have favorable technology, so policy and technology contributions partially offset each other in the variance decomposition.

Q10: How does the model fit untargeted moments, particularly the empirical Shapley-Owen variance decomposition?

A: The model is calibrated to aggregate transition rates by gender, and to moments describing labor productivity, vacancy rates, and policy targets. Despite having age-independent primitives, the calibrated model captures the empirical life-cycle profiles of transition rates as untargeted moments: declining NE and UE rates with age, rising EN rates near retirement, and the hump-shaped patterns. More stringently, the model replicates the empirical Shapley-Owen variance decomposition: it correctly predicts that EU separations account for most of the employment variance for men, and that NE inflows are relatively more important for women and youth. A notable limitation is that the model overshoots the UN (unemployment-to-nonparticipation) transition rate for a significant share of data points — but the authors note that flows between U and N play almost no role in cross-country employment variance.

Q11: What is the “horizon effect” and how does it operate in this model?

A: The horizon effect, coined by Cheron et al. [2011, 2013] in a two-state (E/U) DMP model, refers to the phenomenon that as workers approach retirement, the expected returns to job search fall because the remaining period of employment is shorter. This reduces search intensity from both unemployment and nonparticipation, lowering job-finding rates, and in the present model also affects the match-acceptance probability: workers near retirement find it optimal to remain in unemployment to collect UI benefits rather than accept a job offer, further reducing the UE rate. The current paper generalizes this effect to a three-state setting by incorporating the labor force participation margin alongside search intensity, generating plausible declining job-finding rates and increasing EN rates at older ages from age-independent parameters.

Q12: How does the paper handle the gender dimension in the model calibration?

A: The model assumes that men and women share the same production and matching technology parameters within a country (A, cv, delta, alpha, mu_x, sigma^2_x, sigma^2_z), but allows the search-cost and non-work-utility parameters (ceu, cnu, cu, kappa_u, kappa_n, yo) to differ by gender. The gender-specific search parameters are identified from the gender-specific transition rates: for example, kappa_u (marginal search cost in unemployment) for women is inferred from the female UE transition rate, relative to the normalization for men. The non-work utility yo is consistently higher for women in all five countries, rationalizing lower female employment through a lower employment surplus. This generates a higher surplus elasticity for women, which in turn explains why women’s employment is more responsive to technology variations across countries.

Key Concepts

Shapley-Owen Decomposition. A method from cooperative game theory (Shapley [1953], Owen [1977]) used here to decompose cross-country differences in employment into contributions of individual worker-flow transition rates (or structural parameters). It computes the marginal contribution of each component averaged over all 6! = 720 orderings of the six transition rates, yielding a unique, symmetric, exact decomposition that sums to the total employment gap. Unlike sequential decompositions, it is path-independent.

Extensive Margin of Search Effort. The binary labor force participation decision: whether a nonemployed worker enters the unemployment state (and thus accesses the superior search technology at a flow cost) or remains in nonparticipation. In the paper’s model, this is captured as a discrete choice between states U and N, governed by i.i.d. extreme-value utility shocks, yielding a closed-form logit participation probability.

Intensive Margin of Search Effort. The continuous choice of search intensity s in [0,1] by nonemployed workers (both unemployed and nonparticipants), which scales the probability of meeting a vacancy per period. The optimal intensity equates the marginal cost of search (convex in s) to the marginal benefit (the expected surplus from meeting a firm times the contact rate). Search intensity declines with age because the remaining working life shortens, reducing the discounted value of a job.

Permanent Match Quality (x). A time-invariant, match-specific productivity component drawn from a log-normal distribution upon meeting a firm, but initially unobserved by both worker and firm (an experience good). With per-period probability alpha, the quality is revealed; prior to revelation, the parties form expectations over the distribution. Revelation triggers reallocation of bad matches, generating a negative relation between job tenure and separation probability (following Jovanovic [1979]).

Horizon Effect. The mechanism by which workers reduce search effort as they approach retirement because the expected present value of future employment spells shortens. In this paper the concept, coined by Cheron et al. [2011, 2013] in a two-state DMP setting, is extended to include the labor force participation margin: near-retirement workers not only search less intensively but also become more likely to choose nonparticipation (or to remain unemployed to collect benefits rather than accept a job), generating the observed life-cycle decline in job-finding rates from age-independent parameters.

Technology Parameters (theta). In the paper’s structural decomposition, “technology” refers specifically to the vector (mu_x, sigma^2_x, alpha, delta) — the mean and variance of log permanent match quality, the match-quality revelation probability, and the exogenous job-destruction probability. These are contrasted with search-cost parameters (phi) and policy parameters (psi). The label “technology” is acknowledged to potentially also capture employment protection and quit motives not explicitly modeled.

Life-Cycle DMP Model. A finite-horizon version of the Diamond-Mortensen-Pissarides search-and-matching framework in which workers live for J periods, all primitives are age-independent, and life-cycle variation in worker flows arises endogenously from the interaction of the finite horizon with search intensity, labor force participation, and match-learning mechanisms. The model distinguishes three labor market states (E, U, N) and uses Nash bargaining to split the employment surplus.