E24 | Macro Paper Warehouse

AI and task efficiency

Mon, 01 Jan 0001 00:00:00 +0000

AI can improve decisions, raise firm productivity, and accelerate human capital growth through its effect on signal quality in problem-solving tasks, but the consequences are heterogeneous across the skill distribution and depend on how AI changes the hierarchy within firms. This paper proposes a framework in which AI improves the accuracy of the signals that guide human decisions—individually and in groups—and derives implications for firm organization, wages, and productivity. It also examines preliminary evidence: a cross-sectional regression of changes in TFP growth (2024 versus 2022) on sectoral AI exposure (Eisfeldt et al. 2024) for Compustat firms yields a positive relationship, statistically significant at the 10% level at the 3-digit NAICS sector level and at the 5% level at the firm level, with a slope coefficient of 0.206 for the firm-level regression. The paper compares AI to earlier general purpose technologies (GPTs)—electricity and information technology—finding that if there is a productivity delay for AI it appears shorter than the five- and eight-year delays documented for electrification and IT.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. What is the theoretical framework linking AI to decisions and productivity?

The paper models several mechanisms through which AI may improve outcomes by raising the accuracy of signals that guide problem-solving: when signal accuracy rises, individuals and groups make better decisions, potentially enabling lower-level workers to handle more complex tasks and reducing the need for expensive higher-level solutions. For example, if AI allows managers to understand problems faster, they can handle more problems at a given time, potentially reducing demand for specialized expert judgment at lower hierarchy levels. Alternatively, if AI allows lower-level workers (clerks, nurses) to handle tasks previously requiring specialists (partners, doctors), the demand for specialists may fall and the wage premium for top-tier workers may narrow. The direction of the effect depends on whether AI is a better complement to high-skill or to low-skill tasks.

Q2. What does the empirical evidence show about AI’s current productivity effects?

A cross-sectional regression using 5,009 Compustat firm-level observations for 66 three-digit NAICS sectors finds a positive and statistically significant relationship between sectoral AI exposure in 2022 (from Eisfeldt et al. 2024) and the change in annual TFP growth between 2024 and 2022, with a sector-level slope coefficient that is statistically significant at the 10% level. The firm-level regression (including 3-digit NAICS fixed effects) yields a slope of 0.206 on AI exposure, significant at the 5% level (t-statistic 2.08), with R² = 0.20 and 1,996 observations. The relationship is absent when examining TFP growth levels in any individual year between 2019 and 2022, consistent with AI’s macroeconomic effects only becoming measurable after the release of GPT-4 in March 2023.

Q3. How does AI compare with prior general purpose technologies?

The paper relates AI to the earlier GPT literature, noting that productivity growth tended to be lower at the start of both the electrification and IT eras—with delays of approximately five and eight years respectively before productivity gains became measurable—and that if there is a similar delay for AI it appears shorter based on the preliminary 2024 data. This comparison suggests that AI may be a GPT with unusually rapid diffusion or a shorter learning curve, though the authors caution that the evidence is still preliminary and depends on the dating of AI’s “arrival.”

Q4. Why might AI effects differ across the hierarchy within firms?

AI’s effect on a firm hierarchy depends on whether it complements or substitutes for skills at each level: if AI primarily helps managers (by speeding problem diagnosis), it may reduce demand for specialized lower-level workers; if it primarily helps clerks (by enabling them to handle more complex documents), it may reduce demand for partners while raising demand for lower-level staff. The paper argues that the distributional consequences—whether AI raises or lowers wage dispersion—depend on this complementarity/substitutability pattern, which likely varies by industry, as illustrated by the contrasting cases of automotive assembly (AI may help managers but not line workers) and law firms (AI may help clerks handle more complex work).

Key concepts

AI as signal accuracy improvement : the paper’s framework for thinking about AI’s effect on decision quality: AI raises the precision of the signals that guide problem-solving, which leads to better individual and group decisions regardless of the specific mechanism.

general purpose technology (GPT) delay : the empirical phenomenon documented by Jovanovic and Rousseau (2005) in which productivity growth is lower at the start of a major GPT era before eventually accelerating; the paper examines whether AI exhibits the same pattern, finding that any delay appears shorter than for electrification (five years) or IT (eight years).

Biased expectations and labor market outcomes: Evidence from German survey data and implications for the East–West wage gap

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research question. The paper asks two questions: (1) How do workers’ biased expectations about job finding and job separation shape the labor market equilibrium and wages? (2) Are differences in expectation biases across workers a quantitatively important driver of wage differentials, specifically the East–West German wage gap?

Data. The empirical analysis uses the German Socio-Economic Panel (SOEP), a nationally representative longitudinal survey of approximately 30,000 participants per wave. The working-age sample (ages 25–65) covers nine biennial survey waves from 1999 to 2015, yielding 67,772 observations for job separation expectations and 6,423 for job finding expectations. Perceived transition probabilities are reported on a 0–100 scale in steps of 10 percentage points. Actual (statistical) transition probabilities are constructed by estimating probit models that predict realized transitions within 24 months using a rich set of individual, job, and employer characteristics, and are rounded to the nearest decile for consistency with the survey scale.

Main empirical findings. Employed workers in Germany overestimate their job separation probability by 6.4 percentage points on average (perceived: 19.8%; actual: 13.3%), a pessimistic bias significant at the 1% level. Unemployed workers overestimate their job finding probability by 8.2 percentage points on average (perceived: 57.0%; actual: 48.8%), an optimistic bias also significant at the 1% level. The East–West divergence is striking. East German workers exhibit a pessimistic job separation bias of 12.1 percentage points, compared to only 4.7 percentage points in the West, despite broadly similar actual separation rates (15.1% vs. 12.8%). For job finding, West Germans overestimate their probability by 12.9 percentage points, while East Germans overestimate by only 2.0 percentage points — meaning East Germans are also substantially less optimistic about re-employment. These East–West differences survive controls for compositional differences and alternative definitions of job separation (dismissals only; selected reasons; spell-based) and job finding (including those out of the labor force). The biases are stable over the 1999–2015 sample period with no discernible trend. A cohort analysis shows that the excess pessimism in East Germany is concentrated among cohorts who were already in the labor market at the time of German reunification (born in the 1950s and 1960s), consistent with persistent effects of the communist GDR experience. Individuals do not systematically learn over time: mean changes in individual-level absolute deviations between consecutive waves are close to zero. Individual deviations between perceived and actual rates have statistically significant but quantitatively negligible predictive power for subsequent transitions (a 1 pp higher perceived job separation is associated with only a 0.001 pp higher realized separation rate), ruling out private information as a first-order explanation for the biases.

Model. The authors extend the Diamond–Mortensen–Pissarides (DMP) frictional labor market framework by (i) allowing workers to hold biased perceived transition rates (λw for job finding, σw for job separation) while firms have rational expectations, and (ii) introducing wage contracts of explicit length T periods after which parties re-bargain. Common knowledge of each party’s perceived values is assumed, and generalized Nash bargaining is applied. The contract length T is a key parameter: there exists a critical threshold T* such that a pessimistic job separation bias raises the equilibrium wage for T < T* (the continuation-value effect dominates) and lowers it for T ≥ T* (the within-contract discounting effect dominates). An optimistic job finding bias unambiguously raises the equilibrium wage by inflating the perceived value of unemployment and hence the reservation wage.

Quantitative results. The model is calibrated to East Germany. The job separation bias (∆σ = 0.0194) and job finding bias (∆λ = 0.0044) are set to SOEP-based estimates. The critical threshold implied by calibrated parameter values is T* = 10 quarters. The baseline contract length, constructed from the share of permanent (88%) and temporary (12%) contracts in SOEP and average remaining tenure until retirement, is T = 67 quarters (a lower bound). This exceeds T*, so the pessimistic separation bias depresses wages in the baseline. A counterfactual experiment assigns West German bias levels to East German workers, while holding all other parameters fixed. For the preferred calibration range (γ ∈ {0.35, 0.50}, T ∈ {67, 106, 159}), East German wages rise by 1.07 to 2.36 percent. This corresponds to a reduction in the conditional East–West German wage gap (23 percent) of 4.6 to 10.6 percent, and a reduction in the unconditional gap (30 percent) of 3.6 to 7.9 percent. Although wages rise, equilibrium unemployment increases by 0.70 to 1.01 percentage points, widening the already large East–West unemployment gap (approximately 7 percentage points). Net of the unemployment effect, expected lifetime income (computed at actual, unbiased transition rates) rises by 0.7 to 1.88 percent for East German workers under West German biases, implying an unambiguous welfare gain. Under a biennial calibration (robustness), wages increase by up to 3.3 percent and expected lifetime income rises by up to 2.23 percent.

Scope conditions. Results apply to a stationary environment (no aggregate fluctuations). Firms are assumed to have rational expectations; an extension shows results hold provided firm bias is smaller than worker bias. Workers are assumed homogeneous in their bias levels; learning is abstracted from. The quantitative magnitudes are sensitive to the workers’ bargaining power γ and the contract length T, both of which are subject to uncertainty in calibration.

Layer 2 — Q&A

Q1: How are actual (statistical) transition probabilities constructed, and why are probit-predicted probabilities preferred over realized sample means? A: Realized transition rates in the sample mix transitions for various idiosyncratic reasons that vary substantially across population groups, so raw sample means do not reflect the probability a given individual faces at interview time. The authors estimate probit models separately for job separation (employed sample) and job finding (unemployed sample), including a rich set of covariates — age, gender, education, tenure, firm size, unemployment experience, industry, survey year, and East Germany indicator, among others — and predict individual-level probabilities at the time of the interview. For consistency with the survey’s discrete response format, probit-predicted probabilities are rounded to the nearest decile (0%, 10%, …, 100%). The bias is computed as the individual-level difference between perceived and probit-predicted actual probabilities, averaged over the sample.

Q2: What is the magnitude and direction of the aggregate expectation biases in Germany? A: Employed workers overestimate job separation by 6.4 percentage points on average (perceived 19.8% vs. actual 13.3%), a pessimistic bias significant at the 1% level. Unemployed workers overestimate job finding by 8.2 percentage points (perceived 57.0% vs. actual 48.8%), an optimistic bias also significant at the 1% level. Both directions are statistically robust across alternative definitions of separation and finding, as well as to trimming extreme responses (0% and 100% answers) and adjusting for directional rounding.

Q3: How large are the East–West differences in expectation biases, and do they survive controls for compositional differences? A: East German workers exhibit a pessimistic job separation bias of 12.1 percentage points, more than 2.5 times the West German level of 4.7 percentage points, despite actual separation rates being broadly comparable (15.1% vs. 12.8%). For job finding, West Germans are optimistic by 12.9 percentage points while East Germans are optimistic by only 2.0 percentage points, a difference of 10.9 percentage points. The paper states these differences persist after accounting for compositional differences between regions, and are robust across all alternative definitions of job separation (Dismissals, Selected, Spell) and job finding (out of U or O). The table of robustness results (Table 2) confirms that in all specifications, the pessimistic separation bias is substantially larger in the East and the optimistic finding bias is substantially smaller.

Q4: What cohort analysis is conducted to explore the origins of greater East German pessimism? A: The authors conduct a regression of the individual-level bias on birth-cohort indicators, controlling for age, demographic, and economic characteristics. They find that the pessimistic job separation bias is most pronounced among cohorts born in the 1950s and 1960s — those who experienced adult working life in the communist GDR and lived through reunification — and is smaller for cohorts born before 1950 and substantially smaller for cohorts born after 1970. For job finding, the optimistic bias is comparably low among cohorts born in the 1960s and earlier, but rises significantly for later-born East German cohorts. This cohort pattern is consistent with a long-lasting “experience effect” of communist institutions and the reunification shock on beliefs, analogous to findings in the broader literature on the persistent effects of communism.

Q5: Is there evidence that individuals update their biased expectations over time? A: To assess learning, the authors use the panel dimension and compute for each individual in two consecutive survey waves the absolute value of the deviation between perceived and actual transition probabilities, then examine the change in this absolute deviation between waves. The histograms of individual-level changes show substantial dispersion but means close to zero in all four sub-groups (East/West, job separation/finding), indicating no systematic convergence of beliefs toward actual rates. Biases are also stable in the time-series dimension, with perceived and actual rates moving largely in parallel across survey waves from 1999 to 2015, leaving the aggregate bias level roughly constant.

Q6: How does the model rule out private information as an alternative explanation for the biases? A: If biases reflected private information about idiosyncratic risk not captured by observable characteristics, individual-level deviations between perceived and actual rates should predict subsequent realized transitions. The authors add the individual-level deviation as an additional regressor in the probit transition models. The estimated coefficients are statistically significant and positive, but quantitatively negligible: a 1 percentage point higher expected job separation probability is associated with only a 0.001 percentage point higher realized separation probability, and a 1 percentage point higher expected job finding probability with a 0.002 percentage point higher realized finding probability. These magnitudes are too small to materially alter the interpretation of the biases as reflecting systematic expectation errors rather than private information.

Q7: What is the role of contract length T in the model, and what is the critical threshold T?* A: The wage contract length T determines which of two opposing effects of pessimistic job separation expectations dominates in bargaining. The first (negative wage) effect: a pessimistic worker discounts future wages within the current contract more heavily than the firm does, so the worker values the contract less and accepts a lower wage. The second (positive wage) effect: a pessimistic worker also discounts the continuation value of future contracts more heavily, making it less attractive to remain in the match, so the firm must offer a higher wage to retain the worker. For short contract lengths (T < T*), the second (positive) effect dominates, so the pessimistic bias raises wages. For long contracts (T ≥ T*), the first (negative) effect dominates, so the pessimistic bias depresses wages. The critical threshold T* is the smallest positive integer such that T*/λw(θ) < β times a weighted sum involving σw and T*. Using calibrated parameter values for East Germany, T* = 10 quarters (2.5 years). The baseline contract length is T = 67 quarters (approximately 16.8 years), well above T*, placing the economy in the regime where pessimism depresses wages.

Q8: How does the optimistic job finding bias affect equilibrium wages and unemployment? A: An optimistic job finding bias (λw > p(θ)) raises the perceived value of unemployment U because workers expect to escape unemployment sooner. A higher value of unemployment raises the worker’s outside option in bargaining, increases the reservation wage, and thereby pushes up the bargained wage. In general equilibrium, the job creation condition (which is unaffected by worker expectations) is unchanged, so the upward rotation of the wage curve reduces labor market tightness θ, raises equilibrium unemployment, and extends average unemployment duration. This comparative static holds unambiguously for any contract length T.

Q9: What are the quantitative results of the counterfactual experiment assigning West German biases to East German workers? A: The counterfactual assigns West German bias levels (smaller pessimistic separation bias, larger optimistic finding bias) to East German workers while holding all other parameters at East German calibrated values. For the preferred calibration with γ ∈ {0.35, 0.50} and T ∈ {67, 106, 159}, wages in East Germany rise by 1.07 to 2.36 percent. This implies a reduction in the conditional East–West wage gap (23 percent) of 4.6 to 10.6 percent and a reduction in the unconditional gap (30 percent) of 3.6 to 7.9 percent. Equilibrium unemployment in East Germany rises by 0.70 to 1.01 percentage points as a side effect. Net of the unemployment effect, ex-ante unbiased expected lifetime income rises by 0.7 to 1.88 percent, confirming a positive welfare effect of reducing East German pessimism to West German levels. Under the biennial calibration robustness check, wage increases reach up to 3.3 percent, the conditional wage gap narrows by up to 11 percent, and lifetime income rises by up to 2.23 percent.

Q10: How is the bargaining power parameter γ calibrated and why does it matter for the results? A: The paper considers a range γ ∈ {0.35, 0.50, 0.65}, rather than a single calibrated value, because γ plays a crucial role in the sensitivity of wages to expectation biases. Lower bargaining power reduces the equilibrium wage directly; however, because lower wages spur job creation, the model requires a higher vacancy cost κ to match the empirical job finding rate, which in turn increases the elasticity of wages with respect to the bias (see the wage equation, which shows that the bias effect scales with κθ/p(θ)). The paper argues that γ = 0.65 is inconsistent with the empirical wage–bias relationship estimated in SOEP data (which is negative and about twice as negative in East Germany as in the West), while γ ∈ {0.35, 0.50} is consistent. Lower bargaining power is also argued to be realistic for East Germany given weaker union representation there relative to the West.

Q11: How does the empirical relationship between the job separation bias and wages serve as a model validation target? A: Using SOEP data, the authors regress log hourly wages on the individual-level difference between perceived and actual job separation rates, controlling for individual fixed effects and other covariates, and allow the slope to differ between East and West Germany. They find a statistically significant and negative relationship in both regions, with the effect approximately twice as large in East Germany as in the West. The estimate implies that if East German workers’ job separation pessimism were reduced to West German levels, hourly wages in the East would be about 1 percent higher. This empirical gradient is used as an external validation check — not a calibration target — to assess which combinations of (γ, T) in the model are quantitatively plausible.

Q12: What does the model predict about the general equilibrium effects on unemployment from reducing East German pessimism? A: Reducing East German pessimism — both the pessimistic separation bias and the low optimistic finding bias — shifts the wage curve upward in equilibrium. Because the job creation condition is unaffected by worker beliefs (firms have rational expectations), higher wages reduce the firm’s incentive to post vacancies, lowering labor market tightness θ. This leads to higher equilibrium unemployment and longer average unemployment duration. The counterfactual with West German biases implies that East German unemployment would rise by 0.70 to 1.01 percentage points, further widening the approximately 7 percentage point East–West unemployment gap. The authors note this is a welfare-relevant trade-off, but show that the wage gain dominates the unemployment cost in terms of expected lifetime income.

Q13: What robustness checks are performed on the quantitative results? A: The paper considers (i) a narrower definition of job separation (dismissals only) to match the most likely interpretation of the survey question; (ii) targeting the officially reported East German unemployment rate (14.5% average from the Federal Employment Agency) rather than the SOEP-implied rate of 8.6% as a calibration target; (iii) a biennial calibration frequency instead of quarterly. The main results — wage increases and narrowing of the wage gap — are quantitatively similar across these alternatives, with one exception: the biennial calibration yields substantially larger wage increases (up to 3.3%), a larger reduction in the conditional wage gap (up to 11%), and larger lifetime income gains (up to 2.23%).

Key Concepts

Expectation bias (job separation / job finding). In this paper, a bias in expectations is defined as a systematic average difference between an individual’s perceived transition probability and the actual (statistically predicted) transition probability for their demographic and job group. A pessimistic job separation bias means workers overestimate the probability of losing their job (σw > σ); an optimistic job finding bias means unemployed workers overestimate the probability of re-employment (λw > p(θ)). Biases are not attributed to private information but to systematic expectation errors.

Actual (statistical) transition probability. The paper defines actual transition probabilities not as raw sample transition rates but as individual-level predicted probabilities from probit models estimated on realized transitions within 24 months, conditional on a comprehensive set of individual, job, and employer characteristics observed at interview time. These are rounded to the nearest decile for comparability with the survey’s discrete response format.

Wage contract length (T). The contract length T is the number of periods for which a bargained wage is fixed before the match parties re-bargain. A job match consists of a sequence of consecutive wage contracts of length T. The paper departs from the standard DMP assumption of period-by-period bargaining (T = 1) and shows that T is central to how job separation expectations feed into the bargained wage. A permanent job approximates T → ∞.

Critical contract length (T).* A theoretically derived threshold: the pessimistic job separation bias raises equilibrium wages for contract lengths T < T* and depresses wages for T ≥ T*. Specifically, T* is the smallest positive integer such that T*/λw(θ) < β times a weighted sum involving β, σw, and T*. In the East German calibration, T* = 10 quarters.

Generalized Nash bargaining with common knowledge / agree to disagree. The model assumes that both the worker and the firm know each other’s perceived values of the job match and outside options and accept them as the basis for bargaining, even though they differ. Workers use their biased perceived transition rates to value employment and unemployment; firms use actual rates. There is no private information. The paper refers to this as workers and firms “agreeing to disagree.”

Ex-ante unbiased expected lifetime income (EI_{W,U}). A welfare measure defined as the present discounted value of income for an individual entering the economy, computed at actual (unbiased) job separation and job finding probabilities rather than at workers’ perceived (biased) rates. This measure captures the net welfare effect of changing expectation biases because it correctly accounts for actual employment transitions, even though the behavioral responses in equilibrium are driven by biased perceptions.

Effective discount factor (β(1 − σw)). When a worker holds pessimistic job separation expectations, future payoffs within the current contract are discounted not at the pure time discount factor β but at β(1 − σw), which is smaller when σw is larger. A more pessimistic worker therefore effectively discounts future wage payments more steeply, and this differential discounting relative to the firm (which uses β(1 − σ)) is the key mechanism generating the contract-length dependence of the wage effect.

Digital Distractions with Peer Influence

Mon, 01 Jan 0001 00:00:00 +0000

This paper estimates the causal effects of mobile app usage on college students’ academic performance, physical health, and labor market outcomes, while separately identifying behavioral (endogenous) and contextual (exogenous) peer effects in app usage — the first study to do so within a unified empirical framework. The analysis draws on administrative data for three freshman cohorts (2018–2020) at a mid-tier Chinese university, linked to individual-level mobile phone usage records from a major telecommunications carrier covering 6,430 students over four years (excluding COVID semester). High-frequency GPS data, hourly app usage records for the 2020 cohort, and two waves of university surveys supplement the main dataset.

The identification strategy addresses three challenges: endogeneity of own app usage, endogeneity of peer group formation, and the reflection problem in peer effects. For own usage, two instrumental variables are used: (1) a shift-share instrument interacting the September 2020 launch of the blockbuster game Yuanshen with students’ pre-college app usage intensity; and (2) China’s October 2019 minors’ game restriction policy (prohibiting under-18s from playing online games 10 p.m.–8 a.m. and capping weekday gaming at 90 minutes/day) interacted with the evolving number of underage pre-college friends. For peer effects, the university’s random dormitory assignment within gender-class units provides exogenous peer variation; behavioral peer effects are further isolated using the minors’ restriction policy interacted with roommates’ pre-college underage friend networks, an instrument that affects roommates but not the focal student. Contextual peer effects are recovered by subtracting the estimated behavioral component from reduced-form estimates.

The main findings are as follows. First, app usage is contagious: a one standard deviation (s.d.) increase in roommates’ in-college total app usage raises a student’s own usage by 5.8% (IV). Behavioral peer effects dominate: contextual peer effects are small and statistically insignificant. Second, own app usage severely harms academic performance: a one s.d. increase in total app usage reduces GPA for required courses by 36.2% of a within-cohort-major s.d. (IV), and a one s.d. increase in game app usage alone reduces GPA by 56.6% of a within-cohort-major s.d. The direct disruption effect of roommates’ app usage reduces GPA by a further 20.6% of a within-cohort-major s.d.; combining the indirect channel (behavioral contagion), the total roommate effect reaches 22.7% of a within-cohort-major s.d., more than 60% of the own-usage effect. Third, the effect on physical education scores is roughly four times larger than on required-course GPA: a one s.d. increase in own app usage reduces PE scores by 2.74 points, while roommates’ app usage has no direct effect on PE. Fourth, a one s.d. increase in own in-college app usage reduces initial wages upon graduation by 2.3% (12.1% of within-cohort-major wage s.d.); a one s.d. increase in roommates’ usage reduces wages by 0.9% directly, with a total effect (including the contagion channel) of approximately 1.0% (5.3% of within-cohort-major s.d.). Controlling for cumulative GPA reduces the gaming-to-wage coefficient by roughly one-third, indicating that academic performance is an important but partial mediator.

A back-of-the-envelope policy simulation extending the minors’ gaming cap (3 hours/week) to college students — binding for 34.3% of student-month observations — projects an average wage increase of 0.9% at graduation, approximately half the wage premium from one additional year of work experience in developing countries.

Mechanism evidence from GPS data shows that Yuanshen’s launch caused students to arrive at study halls 18.2 minutes later and leave 23.4 minutes earlier per day. High-frequency sleep data show that a one s.d. increase in nighttime app usage reduces sleep duration by approximately 30 minutes and raises the probability of sleeping late by 34 percentage points. Survey evidence indicates that heavy app users recognize the addictive nature of gaming, pointing to self-control problems rather than lack of awareness.

The scope conditions are: single mid-tier Chinese university; 2018–2020 cohorts; outcomes through initial job placement only; peer group restricted to dormitory roommates; findings rely on IV exclusion restrictions conditional on student and time fixed effects.

Q: What is the core research question? A: The paper asks how individual and peer mobile app usage affect college students’ academic performance, physical health, and early labor market outcomes, and it separately identifies the behavioral (endogenous) versus contextual (exogenous) components of peer influence in app usage. This is claimed as the first study to disentangle these two types of peer effects within a unified empirical framework.

Q: What data does the paper use? A: Administrative records for 7,479 undergraduates across three freshman cohorts (2018–2020) at a medium-sized mid-tier Chinese university are linked to monthly mobile app usage records from a telecommunications provider covering 75% of the provincial population; 6,430 students are matched. The dataset also includes GPS location data at 5-minute intervals, hourly app usage for the 2020 cohort (used to infer sleep), and two waves of voluntary annual surveys with 1,798 respondents (24% response rate). Labor market outcomes — employment status, wages, post-graduate admissions — are available for the 2018 and 2019 cohorts.

Q: How does the paper address the endogeneity of own app usage? A: Two sets of instruments are used. The first interacts the September 2020 launch of Yuanshen (the most popular game in China, with over 13 million Chinese users by 2021, the majority under age 25) with students’ pre-college app usage, forming a shift-share instrument under the assumption that the game launch is orthogonal to unobserved GPA determinants conditional on student fixed effects. The second interacts China’s October 2019 minors’ game restriction policy with the evolving count of a student’s underage pre-college friends; event studies confirm no pre-trends and a sharp, transitory drop in app usage post-policy that dissipates as friends age out of the restricted group.

Q: How does the paper solve the reflection problem and separate behavioral from contextual peer effects? A: Three-step procedure: (1) random dormitory assignment within gender-class units yields reduced-form peer effect estimates using roommates’ pre-college app usage as the exogenous peer shifter; (2) behavioral peer effects are isolated via an IV using the minors’ restriction policy interacted with roommates’ (not the focal student’s) underage pre-college friend networks — an instrument that shifts roommates’ app usage but is orthogonal to the focal student’s outcomes; (3) contextual peer effects are recovered as the residual from subtracting the estimated behavioral effect from the reduced-form estimate.

Q: How large and significant are the behavioral versus contextual peer effects in app usage? A: A one s.d. increase in roommates’ in-college total app usage raises own usage by 5.8% (IV estimate, significant). For game apps alone the behavioral spillover is 10.7%, and for games plus video it is 6.5%. Contextual peer effects (identified from roommates’ pre-college characteristics) are much smaller and statistically insignificant, indicating that peer influence operates primarily through the direct imitation of peers’ actions rather than their background traits.

Q: What is the effect of own app usage on GPA? A: The IV estimate shows a one s.d. increase in total in-college app usage reduces GPA for required courses by 0.716 points, equivalent to 36.2% of a within-cohort-major GPA s.d. (significant at 1%). For game apps alone, a one s.d. increase reduces GPA by 1.119 points, or 56.6% of a within-cohort-major s.d. OLS estimates are biased toward zero, likely because negative health shocks reduce both GPA and app usage simultaneously.

Q: How large is the total peer effect of roommates’ app usage on a student’s GPA? A: Roommates’ app usage directly lowers GPA by 0.408 points (20.6% of within-cohort-major s.d.) through disruption of the dormitory study environment or crowding out of group study. The behavioral contagion channel (5.8% increase in own usage per s.d. of roommates’ usage) adds an additional 0.042 points, bringing the total effect to approximately 0.450 points, or 22.7% of a within-cohort-major s.d. — over 60% of the own-usage effect.

Q: What is the effect on physical education (PE) scores, and why do roommates’ app usage not matter there? A: A one s.d. increase in own total app usage reduces PE scores by 2.74 points (IV), approximately four times the magnitude of the effect on required-course GPA, consistent with health literature on excessive screen time. Roommates’ app usage has no statistically significant direct effect on PE, which the authors attribute to the irrelevance of dormitory noise and study disruptions for outdoor physical activity.

Q: What are the effects of app usage on wages at graduation? A: Doubling total app usage during college reduces initial wages by approximately 2% (IV). A one s.d. increase in own usage reduces wages by 2.3%, or 12.1% of a within-cohort-major wage s.d. A one s.d. increase in roommates’ usage directly reduces wages by 0.9% (4.8% of within-cohort-major s.d.); including the behavioral contagion channel, the total roommate effect is approximately 1.0% (5.3% of within-cohort-major s.d.). Controlling for cumulative GPA reduces the game-usage-to-wage coefficient by about one-third, implying GPA is a partial but not complete mediator.

Q: What does the policy simulation of the gaming cap say? A: Extending the minors’ game restriction (3 hours/week cap) to college students would bind for 34.3% of student-month observations, reducing average monthly gaming from 12.1 hours to 8 hours (a one-third decrease). Incorporating the behavioral peer multiplier for gaming (0.078), average gaming further converges to approximately 7.65 hours in steady state. The implied wage gain at graduation is 0.9%, approximately half the wage premium from one additional year of work experience in developing countries (Lagakos et al., 2019 estimate).

Q: What does the GPS evidence show about time allocation? A: Following Yuanshen’s launch, the average student arrives at the study hall 18.2 minutes later and returns to the dormitory 23.4 minutes earlier per day. The minors’ restriction reverses this: students with the average number of minor friends arrive at study halls 17.4 minutes earlier and return to the dorm 19.8 minutes later. Both game shocks also shift tardiness and absence rates for major-required courses in the expected directions, and the effects intensify over time with Yuanshen’s growing popularity.

Q: What do the sleep data show? A: A one s.d. increase in nighttime app usage (9 p.m.–3 a.m.) is associated with roughly 30 minutes less sleep (7% of the mean), a 34 percentage point higher probability of sleeping late, and a 4.5 percentage point higher probability of waking up late. Daytime app usage (8 a.m.–9 p.m.) is also associated with 7.2 fewer minutes of sleep (1.8% of mean) and a 3.7 percentage point higher probability of late wake-up. These results are descriptive (from the 2020 cohort hourly data) rather than IV-based.

Q: What does the survey evidence show about mechanisms and self-awareness? A: Heavier app users report worse physical health and higher stress, are less likely to have obtained professional certifications by graduation, submit fewer job applications, and express lower satisfaction with job offers. Notably, heavier users are more likely to acknowledge the addictive nature of apps and games, suggesting a self-control problem rather than informational deficiency. They also report better relationships with roommates and greater likelihood of following roommates’ advice on post-graduation choices, a potential direct channel for peer labor market effects.

Q: How representative is the sample, and what are the key scope conditions? A: The university is a mid-tier institution in southern China with students predominantly from the 30th–80th CEE score percentile among provincial college-admitted applicants; it is less female (42% vs. 53% nationally) and more rural (40% vs. 27% nationally). Survey respondents oversample less advantaged backgrounds and are re-weighted. Findings pertain to dormitory roommates as the peer group; all labor market outcomes are initial wages upon graduation; the sample covers 2018–2021 with COVID semester excluded. The peer effects estimates rest on random dormitory assignment, which the authors verify by showing no within-dorm correlation in pre-college characteristics.

Behavioral (endogenous) peer effects: The mechanism by which a peer’s actual behavior — here, contemporaneous app usage — directly influences a focal individual’s own behavior. In this paper, identified via IV using the minors’ game restriction policy interacted with roommates’ underage pre-college friend networks, which shifts roommates’ usage but not the focal student’s characteristics.

Contextual (exogenous) peer effects: The influence of peers’ pre-determined background characteristics (e.g., pre-college app usage, reflecting motivation, study habits, attitudes toward academics) on a focal individual’s outcomes, independent of peers’ actual in-college behavior. Recovered as the residual after subtracting estimated behavioral peer effects from reduced-form estimates; found to be small and insignificant in this setting.

Shift-share instrument (Yuanshen): A quasi-experimental instrument constructed by interacting the mid-sample launch date of the blockbuster game Yuanshen (September 2020) with students’ pre-college app usage intensity, under the assumption that pre-college usage predicts differential susceptibility to the shock while the launch itself is orthogonal to the university’s academic environment.

Minors’ game restriction policy: China’s October 2019 policy prohibiting individuals under 18 from playing online games between 10 p.m. and 8 a.m. and capping weekday gaming at 90 minutes per day (tightened to 3 hours/week in September 2021). Used both as an instrument for own app usage (via underage pre-college friends) and as an instrument for roommates’ usage (via roommates’ underage friends) to isolate behavioral peer effects.

Reflection problem: The identification challenge first articulated by Manski (1993) arising because an individual’s behavior both affects and is affected by peers simultaneously, making it impossible to separately identify the direction of influence from observational data without exogenous variation in peer behavior.

Source text origin: The paper’s own data provenance category distinguishing whether summaries are based on full working paper text (pdf or oa-html) versus abstract only — a distinction the paper itself does not use but that is relevant to the review pipeline running this analysis.

Within-cohort-major GPA standard deviation: The unit used to scale all GPA effect sizes, defined as the standard deviation of GPA within students of the same graduation cohort and declared major. This normalization accounts for systematic differences in grading across fields and years, making effect magnitudes comparable across specifications.

Disincentive effects of unemployment insurance benefits

Mon, 01 Jan 0001 00:00:00 +0000

This paper isolates the disincentive effects of pandemic unemployment insurance (UI) benefits on employment recovery, separating them from the simultaneously operating stimulative (demand) effects that previous studies conflate. The authors study the largest UI expansion in U.S. history — the CARES Act of March 2020 — which introduced three simultaneous provisions: a $600 weekly income supplement (FPUC) through end of July 2020, a 13-week extension of maximum benefit duration (PEUC), and expanded eligibility to workers previously ineligible for UI (PUA), together raising the median replacement rate to 145% and more than doubling the number of UI recipients.

The empirical strategy uses high-frequency establishment-level data from Homebase (HB), a scheduling and payroll provider covering approximately 140,000 small U.S. businesses — predominantly restaurants and retailers — matched to Yelp price-tier data and Safegraph foot-traffic and spending data. The final estimation sample is 4,595 businesses within 1,195 local-industry cells, observed at weekly frequency from January 2019 to December 2020.

The identification rests on comparing employment recovery of low-wage versus high-wage businesses within the same narrow local labor market (four-digit zip code), industry (two-digit NAICS), and price tier. Because neighboring businesses largely share the local demand stimulus from UI, differencing within local-industry cells removes common demand effects. The key variation is the expiration of the $600 supplement, which differentially compresses the replacement-rate gap between low- and high-wage businesses depending on local average wages — labor markets where the gap falls more sharply are the treated group.

The main empirical finding is that a 100 percentage point decline in the replacement rate gap is associated with a 5.7 percentage point rise in low-wage business employment recovery relative to high-wage business employment recovery at 12 weeks after the $600 expiration. For the average labor market, the expiration of the $600 supplement decreased the replacement rate gap by 46 percentage points, implying a 2.6 percentage point closing of the low-versus-high-wage employment gap within 12 weeks. Importantly, hours per employee and hourly wages grew faster in low-wage businesses over the same period, consistent with a labor supply rather than a demand mechanism. When the comparison is conducted at the U.S. state level rather than within local-industry cells — as in Finamor and Scott (2021) — the effect disappears and reverses sign, illustrating how local demand effects obscure disincentive effects at broader geographic aggregations.

To quantify the aggregate employment impact, the authors build and calibrate a McCall-style labor search model with heterogeneous firm wages, a UI-eligible and non-UI unemployed pool, and equilibrium reservation wages. The model is extended to include a probability (calibrated at 16.5%) that workers lose UI eligibility upon refusing a job offer, which reconciles the model with the empirical estimates; without this feature the baseline model substantially overstates the differential employment effect of the $600 expiration.

The full model-implied aggregate employment loss from all CARES Act UI provisions combined is 3.4 percentage points on average between April and December 2020, representing approximately 20% of the average employment shortfall in the Leisure and Hospitality sector over that period. When each provision is implemented in isolation, the effects are modest ($600 supplement: 0.2 pp; extended duration: 0.2 pp; expanded eligibility: 1.0 pp), but their interaction generates the large combined effect. Expanded eligibility is identified as the most disruptive provision, particularly for low-wage businesses, because it depletes the pool of non-UI unemployed who are the primary source of hires for these firms. The unemployment duration elasticities implied by the model are modest and in line with the low-to-middle range of pre-pandemic estimates.

The paper’s scope is restricted to the disincentive channel and deliberately excludes the stimulative effects of UI; it studies small, in-person service sector businesses and the April–December 2020 recovery period only.

Q: What is the core identification challenge this paper addresses? A: Prior empirical studies find only modest net effects of pandemic UI on employment, but it is unclear whether this reflects small disincentive effects or the near-cancellation of two opposing forces — UI suppressing labor supply while simultaneously stimulating local consumer demand. Identifying the disincentive effect alone requires a design that neutralizes the demand channel. The authors accomplish this by comparing low-wage and high-wage businesses within the same narrow local market, industry, and price tier, so that common local demand shifts from UI are differenced out.

Q: What data does the empirical analysis use, and how is the sample constructed? A: The primary data source is Homebase, covering approximately 140,000 small U.S. businesses with daily employment, hourly wages, and hours worked. The estimation sample is restricted to 4,595 businesses present throughout 2019, matched to Yelp price-tier classification and Safegraph weekly foot traffic and credit-card spending. Businesses are grouped into 1,195 local-industry cells defined by four-digit zip code, two-digit NAICS industry, and Yelp price tier (inexpensive vs. expensive). Within each cell, businesses are classified as low-wage or high-wage, with high-wage businesses paying on average $1.80 per hour more — about 8% above the average hourly wage of $10.90.

Q: How is the replacement rate defined in the empirical framework? A: The business-specific replacement rate is the ratio of average UI receipts (state benefit plus the pandemic supplement, converted to hourly units) to the pre-pandemic average hourly wage of that business. Because the supplement is uniform across workers, businesses with lower pre-pandemic wages face higher replacement rates; the replacement rate gap between low- and high-wage businesses within a local market is therefore a function of both state benefit levels and the local wage dispersion.

Q: What does the event-study analysis around the $600 expiration show? A: The event study exploits cross-labor-market variation in how much the replacement rate gap between low- and high-wage businesses declined when the $600 FPUC supplement expired at end of July 2020. Labor markets with a larger decline in the gap see faster relative recovery in low-wage business employment after expiration. A 100 percentage point decline in the replacement rate gap is associated with a 5.7 percentage point rise in the low-versus-high-wage employment recovery gap at 12 weeks post-expiration. For the average labor market, the $600 expiration reduced the replacement rate gap by 46 percentage points, implying a 2.6 percentage point narrowing of the employment recovery gap.

Q: Why does the estimated effect disappear when broader geographic aggregations are used? A: When businesses are compared within U.S. state borders rather than within local-industry cells, the estimated coefficient on the replacement rate gap turns positive and statistically insignificant. This occurs because at the state level, low-wage areas benefit disproportionately from the purchasing power increase that generous UI provides to local unemployed workers, so demand effects swamp and reverse the supply-side disincentive. This finding explains why Finamor and Scott (2021), using Homebase data with state fixed effects, find no negative association between replacement rates and labor market re-entry.

Q: What evidence supports a labor supply rather than demand interpretation of the differential recovery? A: During the period of the $600 supplement, hours per employee and hourly wages grew faster in low-wage businesses than in high-wage businesses, even as low-wage businesses lagged in employment levels. If the differential recovery reflected demand deficiencies at low-wage businesses, hours per employee and wages should have grown faster at high-wage businesses instead. The observed pattern is consistent with labor supply shortfalls at low-wage firms.

Q: What is the structure of the quantitative labor search model? A: The model features a unit measure of workers and a fixed measure of firms, each posting a constant idiosyncratic wage drawn from an exogenous distribution. Unemployed workers receive job offers at a rate determined by labor market tightness and accept offers above their reservation wage. Reservation wages are equilibrium objects because UI benefits depend on the worker’s previous wage. The unemployed are split into UI-eligible and non-UI pools; the non-UI pool accepts jobs from lower in the wage distribution and is the primary supply source for low-wage firms. The model is calibrated to pre-pandemic U.S. service sector averages, with a pre-pandemic UI replacement rate of 0.51, a UI recipiency probability of 14%, and a non-UI replacement rate of 0.15.

Q: Why does the baseline model overstate the empirical effect, and how is this reconciled? A: The baseline model dramatically overstates the differential employment impact of the $600 expiration because the CARES Act’s expanded eligibility (modeled as a rise in the recipiency probability from 14% to 70%) nearly empties the non-UI unemployed pool, which is the dominant labor supply source for low-wage firms. In the data, the share of unemployed receiving UI nearly tripled for in-person leisure and hospitality workers, but not to the degree that the model’s implied employment collapse would require. The model is reconciled by introducing a 16.5% probability that a worker loses UI eligibility upon refusing a suitable job offer — consistent with UI law — which reduces the effective outside option and raises acceptance rates for low-wage firms.

Q: What are the aggregate employment losses implied by the model? A: When all three CARES Act provisions are implemented jointly, the model estimates that the disincentive effects held back aggregate employment recovery by 3.4 percentage points on average between April and December 2020 — approximately 20% of the average employment shortfall in the Leisure and Hospitality sector. Implemented in isolation, each provision generates only modest losses: the $600 supplement alone accounts for 0.2 percentage points, extended duration for 0.2 percentage points, and expanded eligibility for 1.0 percentage points. The large combined effect arises from the interaction of all three provisions, not from any single one.

Q: What are the conditional (interaction) effects of each provision when the other two are in place? A: Conditional on the other two provisions being active, the income supplement holds back employment recovery by 1.6 percentage points, the extended duration by 1.5 percentage points, and expanded eligibility by 2.9 percentage points. This interaction effect is the central quantitative finding: individually modest provisions combine to produce effects far exceeding their sum when implemented simultaneously.

Q: What are the implied unemployment duration elasticities, and how do they compare to the literature? A: The $600 supplement alone raises average unemployment duration by 8% against a 343% rise in the replacement rate, implying an elasticity of 0.02. Extended duration alone raises unemployment duration by 6% against a 150% increase in potential benefit duration, implying an elasticity of 0.03. Expanded eligibility alone raises unemployment duration by 19%, implying an elasticity of 0.04. When each provision is activated on top of the other two, the implied elasticities rise substantially: 0.24 for the $600 supplement, 0.43 for extended duration, and 0.28 for expanded eligibility. These are in the low-to-middle range of pre-pandemic estimates (Katz and Meyer, 1990: 0.3–0.5; Johnston and Mas, 2018: 0.4–0.8; Rothstein, 2011: 0.06; Farber and Valletta, 2015: 0.15).

Q: What is the role of expanded eligibility specifically? A: Expanded eligibility is identified as the most disruptive CARES Act provision, accounting for 1.0 percentage points of employment loss alone and 2.9 percentage points conditional on the other provisions. Mechanically, expanded eligibility converts non-UI unemployed workers into UI-eligible workers, draining the pool of workers willing to accept low-wage job offers. Because low-wage firms depend disproportionately on the non-UI pool for hiring, this provision disproportionately depresses their employment. Using CPS data, the authors document that the share of unemployed workers receiving UI in the in-person leisure and hospitality sector nearly tripled in 2020 relative to the pre-pandemic period.

Q: What are the scope conditions and limitations of the analysis? A: The empirical analysis is restricted to small, in-person service sector businesses (restaurants and retailers) in the Homebase sample, which may not be representative of the broader labor market. The quantitative model is explicitly focused on disincentive effects only and does not capture the stimulative or demand effects of UI. The model also abstracts from re-opening restrictions and other pandemic-specific confounders. The analysis covers April to December 2020; the 2021 pandemic UI extensions are not studied. The job-refusal probability (chi = 16.5%) is a reduced-form calibration target rather than a structurally identified parameter.

Replacement rate gap: The difference in business-specific UI replacement rates between low-wage and high-wage businesses within the same local labor market; defined as UI benefits (state benefit plus supplement) divided by the business’s pre-pandemic average hourly wage. Larger gaps indicate greater relative disincentive for workers to accept jobs at low-wage firms.

Disincentive effect: The negative impact of higher UI replacement rates on workers’ willingness to accept job offers and thus on business employment recovery, isolated from the simultaneous stimulative demand effect of UI spending.

Non-UI unemployed pool: Workers who are ineligible for or have exhausted UI benefits and therefore receive only social benefits at a lower replacement rate (calibrated at 0.15 in the model). This group has a lower reservation wage and constitutes the primary labor supply source for low-wage firms.

Local-industry cell: The paper’s unit of comparison — businesses sharing the same four-digit zip code (covering on average four neighboring zip codes), two-digit NAICS industry, and Yelp price tier. Within-cell differencing is the mechanism that removes common local demand effects.

Benefit recipiency probability: The probability that a newly separated worker enters the UI-eligible unemployed pool, combining UI eligibility and takeup. Pre-pandemic this is calibrated at 14%; under the CARES Act it rises to 70%, targeting the observed near-tripling of UI recipients in the CPS data.

Job-refusal eligibility loss: A probability (calibrated at 16.5%) that a UI-eligible worker who rejects a job offer loses UI status and transitions to the non-UI pool. Motivated by UI law prohibiting refusal of suitable work; reduces the effective outside option and reconciles the model’s predicted employment gap with the empirical estimate.

Equilibrium residual wage dispersion: The wage dispersion observed in equilibrium conditional on worker observables. The model generates realistic dispersion by calibrating the non-UI replacement rate to match the lower half of the wage distribution and the firm wage offer variance to match the upper half; the presence of the non-UI state substantially increases residual dispersion relative to standard search models.

Downward Rigidity in the Wage for New Hires

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Summary

Hazell and Taska use wages posted on online job vacancies — matched to job titles and establishment identifiers from Burning Glass Technologies — to measure the wage for new hires at the job level (same job title and establishment) over 2010Q1–2020Q2. They find that this measure of the wage for new hires is rigid downward and flexible upward. At the job level, the nominal posted wage changes infrequently — on average once every 5–6 quarters — and conditional on changing, is four times more likely to rise than to fall. In the cyclical dimension, job-level posted wages rise strongly when state unemployment falls but do not fall when state unemployment rises; real wages exhibit the same asymmetric pattern. These results do not appear in the average wage for new hires (which aggregates across all job types), because time-varying job composition inflates the variance of average wages and raises standard errors roughly twentyfold relative to job-level regressions — explaining why prior work using worker-level survey data found no evidence of downward rigidity. A Heckman (1979) selection correction for firms’ selection into vacancy posting suggests that selection bias in the job-level regression is moderate. The findings provide direct empirical support for models in which downward wage rigidity for new hires — specifically at the job level — amplifies unemployment fluctuations and generates asymmetric unemployment dynamics.

Layer 2 — Q&A

Q: What is the central empirical claim of the paper? A: At the job level — defined as the same job title within the same establishment — the wage posted for new hires is rigid downward and flexible upward. It changes infrequently and, conditional on changing, rises far more often than it falls; and it responds to falls in unemployment but not to rises in unemployment.

Q: What data does the paper use, and what defines a “job”? A: The paper uses the Burning Glass Technologies dataset of wages posted on online vacancies, covering January 2010 to June 2020. A “job” is a job title within an establishment whose wages are paid at a given frequency (e.g., hourly or annual). The data come from the near-universe of online job postings — roughly 40,000 sources — and the main regression sample consists of jobs that post wages, have job title and establishment information, and post vacancies in multiple quarters, yielding approximately 3.05 million vacancies, representing about 0.8% of total US vacancies.

Q: How do the authors validate that posted wages measure the wage for new hires? A: They construct a measure of the wage for new hires from the Current Population Survey (CPS) — workers switching jobs or entering from unemployment — at the state, industry, and occupation level. Regressing log CPS wages on log Burning Glass wages (using an IV split-sample procedure to correct for attenuation bias) yields a coefficient close to 1 across specifications and levels of aggregation, indicating that average posted wages move roughly one-for-one with average wages for new hires in representative survey data.

Q: How is the frequency of wage change estimated? A: Because wages are not observed in quarters without a vacancy posting, the authors adapt a constant-hazard model from the price-setting literature (following Nakamura–Steinsson and Klenow–Kryvtsov). The latent wage evolves stochastically between postings; the observed wage is treated as a draw from this process. The quarterly probability of wage change is estimated at 0.17–0.19 across specifications, implying implied durations of unchanged wages of 4–5 quarters.

Q: What is the asymmetry in the direction of wage changes? A: In the unweighted baseline, the quarterly probability of a wage decrease is 0.04, whereas the probability of a wage increase is 0.12 — roughly a three-to-one ratio in probabilities, summarized in the paper’s abstract as wages being “four times more likely to rise than to fall.” The distribution of non-zero wage changes also shows a pronounced pile-up of small positive changes relative to small negative changes, consistent with a downward constraint on wage setting.

Q: What is the first piece of cyclical evidence for downward rigidity? A: A binned scatterplot (Figure 1) of job-level wage growth against state-level quarterly changes in unemployment shows a strong, roughly linear relationship when unemployment is falling — wages rise with falls in unemployment, both for small and large declines. When unemployment rises, however, wages do not fall — neither for small nor for large increases in unemployment. This asymmetry is robust to regression-based analysis and to identified labor demand shocks.

Q: Are real wages also rigid downward? A: Yes. The paper reports that real wages (nominal posted wages deflated) are also rigid downward and flexible upward, mirroring the pattern for nominal wages.

Q: What is the job-composition problem, and why does it matter? A: The average wage for new hires — the object measured in most prior work — aggregates across all job types that are actively hiring. If the composition of jobs hiring shifts over the business cycle (e.g., the share of lower-wage jobs rises in recessions), then average wages can fall even if no individual job cuts its wage, and can stay flat or rise even if every job cuts its wage. Job composition therefore confounds cyclicality estimates based on average wages. By tracking the same job title at the same establishment across successive vacancies, the authors purge wage changes driven by shifting composition.

Q: Why did prior work find no evidence of downward rigidity for new hires? A: Prior work used worker-level survey data (e.g., Bils 1985; Pissarides 2009 survey) that controls for worker characteristics but averages across jobs — the average wage for new hires. The volatility of job composition inflates the variance of this average measure. In the Burning Glass data, standard errors from regressions using average wages are roughly twenty times larger than those from job-level regressions, making it impossible to detect downward rigidity even if it exists. Point estimates in prior work suggested procyclicality but were too imprecise to exclude downward rigidity.

Q: How does this paper relate to Gertler, Huckfeldt, and Trigari (2020) and Grigsby, Hurst, and Yildirmaz (2021)? A: Both papers attempt to control for job composition at the worker level. Gertler et al. focus on wages of workers hired from unemployment (less affected by composition than all new hires) and find weakly procyclical wages. Grigsby et al. use rich payroll data and worker-level matching to control for composition and also find weakly procyclical wages. The present paper complements these by using job-level data that directly purges composition without relying on worker characteristics, and adds evidence on the asymmetry of rigidity (not just average procyclicality).

Q: What is the role of the Heckman selection correction? A: If firms select into vacancy posting depending on business-cycle conditions, the sample of observed posted wages may be non-random, biasing job-level wage-cyclicality estimates. The authors implement a standard Heckman (1979) two-step selection correction. The correction suggests that selection bias in the job-level regression is moderate — it does not overturn the finding of downward rigidity.

Q: What are the four main caveats the authors acknowledge? A: (1) The main sample is small — 0.8% of US vacancies — though the authors show it is broadly representative on observables and that wages track representative survey data. (2) The paper measures rigidity only for jobs that post wages; jobs that do not post wages might be more flexible, though the share of vacancies posting wages does not decline during contractions. (3) Posted wages may differ from realized (bargained) wages; however, wages are rigid even in occupations where bargaining is uncommon. (4) The Pandemic Recession is the main contractionary episode in the sample, and it involved labor supply shocks as well as demand shocks; the authors address this through identified labor demand shock regressions and by ending the sample in June 2020.

Q: What are the implications for models of unemployment fluctuations? A: In the Diamond–Mortensen–Pissarides search model, Pissarides (2009) emphasizes that the wage for newly hired workers — not continuing workers — is the relevant margin for unemployment fluctuations. Shimer (2005) showed the standard calibration produces too-small unemployment fluctuations; wage rigidity for new hires can resolve this. The paper’s finding of downward-but-not-upward rigidity additionally supports models (e.g., Dupraz, Nakamura, and Steinsson, 2020) in which this asymmetry generates asymmetric unemployment dynamics — unemployment rises sharply in contractions but falls more slowly in expansions.

Q: How do wages for new hires compare with wages for continuing workers in terms of rigidity? A: The paper finds approximate parity. The implied duration of unchanged wages from the job-level posted wage data (4–5 quarters) is similar to estimates for continuing workers in the prior literature. This is perhaps surprising because wages could in principle be more flexible for new hires than continuing workers — firms might cut wages for new hires even while insuring continuing workers (Beaudry and DiNardo, 1991). The results instead suggest that internal equity concerns (Bewley, 2002) or other forces produce similar rigidity for both groups.

Key Concepts

Job level wage: The wage across successive vacancies posted by the same job title at the same establishment. This is the unit of observation in the paper’s main analysis and the object for which downward rigidity is documented. Distinct from the average wage for new hires (which aggregates across all job types).

Downward rigidity (as used in this paper): An empirical pattern in which wages at the job level do not fall during contractions — they do not respond to rising unemployment — while rising during expansions in response to falling unemployment. The claim is descriptive: the data show wages do not fall; the paper does not structurally identify the mechanism enforcing this floor.

Job composition problem: The bias introduced when measuring cyclicality of the average wage for new hires using data that aggregates across different types of jobs. If the mix of job types hiring shifts with the business cycle, average wages can change even when no individual job changes its wage, and can mask individual-job wage changes. Job-level data resolve this by holding the job fixed.

Burning Glass Technologies dataset: A database of wages posted on online job vacancies, drawn from approximately 40,000 online sources (job boards and company websites), covering the near-universe of US online vacancies. The paper’s main regression sample uses the subset with posted wages, job title, establishment identifiers, and multiple quarters of postings, spanning January 2010 to June 2020.

Constant hazard model (wage change frequency): An estimation procedure adapted from the price-setting literature to recover the quarterly probability of wage change from a dataset in which wages are only observed when a vacancy is posted. The latent wage evolves with a constant hazard of change between observations; observed wage changes identify the hazard rates for increases and decreases separately.

Average wage for new hires: The mean wage across all workers newly entering employment (or across all new-hire jobs), used in prior work (Bils 1985 and related). Does not control for job composition. Shown in this paper to exhibit no detectable downward rigidity, with standard errors roughly twenty times larger than in job-level specifications — because job composition variance inflates the residual variance.

Heckman selection correction: A two-step procedure (Heckman 1979) to correct for the possibility that firms that post vacancies — and post wages — are a selected sample that differs systematically across the business cycle. The paper applies this to assess whether selection into vacancy posting biases the job-level wage-cyclicality estimates; the correction suggests bias is moderate.

Summary based on LSE Research Online accepted version (accepted manuscript, covers full paper including introduction, data, and Section 3; extraction terminated at line 595 before Sections 4–5). AI-assisted, human review pending.

Education and the Margins of Cyclical Adjustment in the Labor Market

Mon, 01 Jan 0001 00:00:00 +0000

Overview

Research question. This paper asks how the cyclical sensitivity of wages varies with workers’ educational attainment, what mechanisms drive the differences, and what the welfare consequences are of ignoring this heterogeneity. The starting point is a well-known asymmetry: less-educated workers have much higher and more volatile job separation rates, yet the standard macroeconomic literature has treated wages as roughly acyclical for a representative worker. Doniger asks whether this employment-centric picture is incomplete—and finds that it is, in a direction opposite to what the employment pattern would suggest.

Data and methodology. The paper uses two primary data sources: the National Longitudinal Survey of Youth 1979 (NLSY), which provides detailed job histories enabling identification of current and completed employer tenure, and the Current Population Survey (CPS) from 1995 to 2020, used both for employment flow statistics and, via biennial Job Tenure Supplements, for replication of the main wage findings. The sample is restricted throughout to males with 0–30 years of potential experience, following the conventions of the user-cost-of-labor (UCL) literature (Kudlyak, 2014; Basu and House, 2016). Workers are grouped into three educational categories: less than high school, high school or some college, and bachelor’s degree or more.

A key methodological contribution is a new, more parsimonious estimator for the cyclical sensitivity of the UCL. Rather than the multi-step indicator-variable approach of Kudlyak (2014), the paper recovers the UCL sensitivity from interaction terms between a flexible function of tenure and the cyclical position at the time of hiring, estimated within an augmented Mincer regression. This estimator admits higher-frequency identification, enables transparent inference via the delta method, and facilitates nonparametric impulse response estimation via the Jorda (2005) local projection method. Cyclical position is measured primarily as the deviation of the unemployment rate from an HP-filtered trend (lambda = 100,000), with robustness checks using the Hamilton (2018) filter and GDP-based detrending.

Main findings — employment. Monthly separation rates from the CPS (1995–2020) show that workers with less than a high school degree separate at a rate of 9.4 percent per month, more than twice the 3.4 percent rate for workers with a bachelor’s degree or more, regardless of cyclical position. The volatility of the separation rate (measured by the time-series standard deviation) is also larger for the least educated (1.7) than for the most educated (0.6). All sub-components of separation-to unemployment, to inactivity, and job-to-job transitions-exhibit the same ordering. In response to a 100 basis point monetary policy contraction (Romer and Romer, 2004 shocks), employment of workers with less than a high school education falls significantly, while employment of college graduates or more is statistically unaffected.

Main findings — wages. Using the NLSY, the cyclical sensitivity of the UCL to a 1 percentage point deviation of the unemployment rate from trend is estimated at approximately −15.5 percent for workers with a bachelor’s degree or more, −4.9 percent for high school or some college workers, and −1.4 percent (statistically indistinguishable from zero) for workers without a high school degree. In contrast, average hourly earnings (AHE) show much smaller and more compressed differences across education groups (−1.4, −1.1, and −1.0 percent respectively). The pattern of increasing procyclicality with education holds for new hires’ wages (NHW) as well but is considerably less stark than for the UCL. Replication in the CPS confirms the ordering: UCL sensitivities are −7.0 percent for college graduates, −2.9 percent for high school or some college, and effectively zero for those without a high school degree.

Mechanism. Counterfactual decompositions show that differences in the cyclical sensitivity of the wage-tenure profile—not just differences in job duration (separation rates)-account for the vast majority of the divergence across education groups. When separation rates are held constant across groups, the UCL sensitivity of the college-educated falls from -15.5 to −13.0 percent; when wage-tenure profile sensitivities are held constant, it falls to −6.3 percent, and the ordering across groups largely disappears. This finding is consistent with implicit contracting theory (Thomas and Worrall, 1988): longer expected employment durations for the more educated make it optimal to defer a greater share of the wage response to shocks over time, rendering near-term rigidities functionally less binding and producing more persistent effects of hiring-period conditions on subsequent wages.

Robustness. After controlling for cyclical sorting in match quality using the Hagedorn and Manovskii (2013) proxies (cumulated market tightness during tenure and leading up to the present job), the UCL sensitivity for college graduates falls modestly to −12.4 percent, confirming that match-quality composition effects account for only a minority of the documented pattern. The monetary policy shock analysis (Romer-Romer shocks identified from Greenbook forecast errors) yields a 35 percent decrease in the UCL for the most educated at the two-year horizon following a 100 basis point contraction, with no discernible effect for the least educated.

Welfare consequences. Using a stylized New Keynesian model extended to two labor varieties with heterogeneous wage flexibility, the paper shows that ignoring the documented heterogeneity leads to underestimating the welfare costs of business cycle fluctuations by more than 15 percent under the baseline calibration (unit Frisch elasticity and unit elasticity of intertemporal substitution). Conditional on this model, the welfare loss due to fluctuations for the least educated is more than 15 times larger than for the most educated. The paper explicitly notes this is a conservative lower bound, because the model assumes pooled household consumption, and admitting idiosyncratic consumption risk would disproportionately burden less-educated workers who bear adjustment on the extensive (employment) rather than intensive (wage) margin.

Q&A

Q1. What is the user cost of labor (UCL), and why does the paper use it rather than average hourly earnings or new hires’ wages?

The UCL, formalized by Kudlyak (2014), is the present discounted value of wage payments an employer expects to make to a worker over the duration of the employment relationship, net of the continuation value of retaining that worker. It equals the new hire’s wage plus the expected wage wedge—the discounted stream of future wage differences between workers hired in the current period versus workers hired one period later. Unlike average hourly earnings or new hires’ wages, the UCL captures the persistent effects of macroeconomic conditions at the time of hiring on all future remitted wages, making it the appropriate allocative wage concept from a macroeconomic standpoint. The paper documents that AHE understates the cyclicality of wages for all groups but especially for the most educated, because AHE omits the highly cyclically sensitive expected wage wedge that characterizes college-educated employment relationships.

Q2. How does the paper’s new estimator for the cyclical sensitivity of the UCL differ from the existing method, and what does this enable?

The existing Kudlyak (2014)/Basu and House (2016) method recovers the UCL by estimating a very large set of date-of-hire x current-date indicator interactions, constructing a time series of the UCL, and then analyzing that series—a multi-step procedure that loses covariances across steps and makes cross-sectional disaggregation or high-frequency identification impractical. The new method instead estimates the UCL sensitivity directly from coefficients on the interaction between a flexible tenure function and the cyclical position at hiring, estimated within a single augmented Mincer regression. The UCL semi-elasticity is recovered analytically from these coefficients via a formula that sums discounted weighted differences in the tenure-interaction coefficients across the tenure horizon. This single-step approach allows transparent inference via the delta method, enables fully interacted specifications for heterogeneous subgroups, permits the hiring-date frequency (e.g., weekly in NLSY) to differ from the wage observation frequency (annual or biannual), and permits estimation from repeated cross-sections—all of which were infeasible in the prior approach.

Q3. What are the quantitative magnitudes of the education gradient in UCL cyclicality, and how do they compare across wage measures?

Using the NLSY with unemployment deviations from HP-filtered trend as the cyclical indicator: the UCL sensitivity is −15.5 percent (se 3.86) for workers with a bachelor’s degree or more, −4.9 percent (se 1.52) for high school or some college, and −1.4 percent (se 2.48, statistically insignificant) for those without a high school degree. By contrast, new hires’ wages show sensitivities of −3.4, −1.8, and −1.2 percent respectively, and average hourly earnings show −1.4, −1.1, and −1.0 percent. The gradient is largest and most statistically significant for the UCL, indicating that the bulk of the education gap in cyclical wage sensitivity operates through the persistent effect of hiring-period conditions on subsequent wages rather than through the contemporaneous wage alone.

Q4. What mechanism accounts for the UCL gradient — differential job durations or differential sensitivity of the wage-tenure profile?

The paper decomposes the UCL into the new hire’s wage and the expected wage wedge, and performs counterfactual exercises holding either separation rates or wage-tenure profile sensitivities constant across education groups (Table 3). Holding separation rates constant while allowing wage-tenure profiles to differ reduces the college-educated UCL sensitivity only modestly, from -15.5 to −13.0 percent; holding wage-tenure profile sensitivities constant while allowing separation rates to differ reduces the college-educated sensitivity to −6.3 percent and compresses the education gradient substantially. Thus, differential sensitivity of the wage-tenure profile—the degree to which wages continue to respond to hiring-period conditions over the course of the job-is the primary driver of the UCL gradient, with differential separation rates playing a secondary but non-trivial role. This finding confirms the prediction of Thomas and Worrall (1988) that lower separation rates support greater use of deferred payment and intertemporal risk sharing in optimal wage contracts.

Q5. How does the paper rule out cyclical sorting in match quality as the explanation for the UCL gradient?

Workers hired during recessions may be of systematically lower match quality, producing persistently lower wages not because wages are more cyclically sensitive for the same quality match but because recession hires are worse matches. Using the Hagedorn and Manovskii (2013) proxies for match quality - cumulated market tightness during the worker’s tenure on the present job (mjob) and on all prior jobs leading to it (mctj) - the paper augments the wage regression with full interactions between these proxies and the tenure-cyclicality terms. After controlling for match quality, the UCL sensitivity for college graduates falls from -15.5 to −12.4 percent (se 5.56); the point estimate remains large, statistically significant, and well above the estimates for lower-education groups. Figure 4 shows that match-quality adjustment primarily affects the first two years of the wage-tenure profile, after which the bias from cyclical sorting fades, confirming that scarring in remuneration for college graduates hired in recessions persists beyond what sorting can explain.

Q6. What do monetary policy shocks reveal about the education gradient in wage sensitivity?

Monetary policy shocks (identified from Greenbook forecast errors as in Romer and Romer, 2004) subject all labor markets to the same aggregate demand shock simultaneously, providing a cleaner test of differential responsiveness than cyclical regressions that may conflate demand composition and supply factors. Using Jorda (2005) local projections, a 100 basis point monetary policy contraction is associated with a 35 percent decrease in the UCL for workers with a bachelor’s degree or more at the two-year horizon, with statistically insignificant effects on the UCL of workers without a high school degree. The employment results are symmetric: less-educated workers’ employment falls significantly after a monetary contraction, while college-educated workers’ employment is unaffected. This cross-validation using monetary policy shocks supports the main thesis that more-educated workers absorb aggregate demand variation through the wage margin, while less-educated workers absorb it through the employment margin.

Q7. How does acyclical wages for the least educated affect interpretation of the existing macro literature on wage rigidity?

The aggregate finding of Kudlyak (2014) and Basu and House (2016)-that the UCL is more procyclical than new hires’ wages or average hourly earnings, casting doubt on wage rigidity as an amplification mechanism—holds only for educated workers. The paper finds that the UCL for workers without a high school degree is statistically acyclical by all three wage measures. This result restores a potential role for nominal wage rigidity in generating amplification and persistence of shocks for less-educated labor markets, including in the Diamond-Mortensen-Pisarides class of search models criticized by Kudlyak (2014) and in New Keynesian models criticized by Basu and House (2016). The paper therefore reconciles the literature on wage rigidity with the empirical finding of cyclical employment volatility concentrated among the less educated.

Q8. What is the welfare calculation, and what are its key results and limitations?

The welfare exercise uses a parsimonious New Keynesian model with two labor varieties (capturing more- and less-educated workers) and price and wage rigidities. The model is extended to admit heterogeneous wage flexibility, and the welfare costs of fluctuations are evaluated following the second-order approximation method of Gali et al. (2007). Under the baseline calibration (unit Frisch elasticity, unit elasticity of intertemporal substitution), the heterogeneous-worker economy incurs welfare costs of fluctuations that exceed those of the output-gap-equivalent representative agent economy by more than 15 percent. The welfare loss of the least-educated workers is more than 15 times that of the most educated. The paper explicitly characterizes this as a conservative lower bound: the model assumes pooled household consumption (within varieties), which implies equal consumption sensitivity across education groups, whereas in reality less-educated workers face income loss on the extensive margin without the wage smoothing available to the more educated. Relaxing this assumption, as in Krusell et al. (2009), could yield welfare losses an order of magnitude larger.

Q9. What does the CPS replication add, and what are its limitations relative to the NLSY baseline?

The CPS replication (Table 7) confirms the main ordering: UCL sensitivities are −7.0, −2.9, and approximately 0 percent for college graduates, high school or some college, and less than high school respectively. This rules out the concern that the NLSY findings are artifacts of the single aging cohort that characterizes the NLSY 1979. However, the CPS must be treated as a repeated cross-section because the tenure data are only available biennially and individual-level panel linkage across tenure supplement waves is infeasible. As a result, the CPS estimates cannot include individual fixed effects and must rely more heavily on observable controls (industry, occupation) to absorb cyclical variation in workforce composition. The CPS also precludes the match-quality controls of Hagedorn and Manovskii (2013). Despite these limitations, the main qualitative and directional findings replicate.

Q10. What policy implications does the paper draw for monetary policy?

The paper argues that because less-educated workers bear adjustment to aggregate demand shocks disproportionately through the employment margin while their wages are acyclical, welfare assessments that focus on the aggregate output gap underweight the costs borne by less-educated workers. The paper suggests that re-optimizing the monetary policy rule to account for documented heterogeneity would entail placing greater weight on the unemployment rate of the least-educated when measuring the output gap. More broadly, the K-shaped nature of labor market adjustment across education groups — wage scarring for the educated versus employment volatility for the less educated - implies that policies targeting either margin in isolation will miss welfare costs concentrated in the other group.

Key Concepts

User Cost of Labor (UCL). The allocative wage from the employer’s perspective, defined as the present discounted value of expected future wage payments to a worker hired at date t, net of the continuation value of retaining that worker in the next period. Formally, UCL_t = w_{t,t} + E_t[sum beta^j(1-s)^j (w_{t+j,t} - w_{t+j,t+1})], decomposing into the new hire’s wage and the expected wage wedge. In this paper’s usage, the UCL is the appropriate measure of the cyclical impact of shocks on labor costs because it captures persistent effects of hiring-period conditions on the entire subsequent wage sequence, not just the contemporaneous wage.

Expected Wage Wedge (EWW). The component of the UCL beyond the new hire’s wage: the discounted stream of differences between wages a worker hired at date t will receive in future periods and the wages a worker hired one period later would receive in those same future periods. The EWW is non-zero whenever wages are history-dependent - i.e., whenever current macroeconomic conditions at the time of hiring affect future remitted wages. The paper finds that the EWW is larger, more negative, and more persistent for more-educated workers conditional on being hired during a cyclical downturn.

Self-enforcing implicit wage contract. A labor contract in which the sequence of remitted wages is not pinned down period-by-period by spot-market forces but instead reflects an intertemporal risk-sharing arrangement between employer and worker that is sustained by the mutual benefit of the ongoing employment relationship. In this paper’s framework (drawing on Thomas and Worrall, 1988), lower separation rates make longer planning horizons feasible, which in turn expands the scope for deferring wage adjustments across time - effectively allowing more-educated workers and their employers to smooth the effects of cyclical shocks over longer horizons than is possible for less-educated workers with shorter expected job durations.

Cyclical sorting / match quality bias. The compositional concern that workers hired during recessions may be of systematically different (in this context, lower) match quality than those hired during booms, so that the persistent wage depression observed for recession hires could reflect poor match quality rather than cyclically sensitive wages for equivalent-quality matches. The paper uses the Hagedorn and Manovskii (2013) proxies - cumulated labor market tightness during the current job and prior employment history - to control for cyclical variation in match quality and assess the residual sensitivity of the UCL for average-quality matches.

Extensive versus intensive margin of labor market adjustment. The distinction between adjustment through changes in the number of workers employed (extensive margin: hiring and separation) versus adjustment through changes in wages or hours conditional on employment (intensive margin). A central finding of the paper is that less-educated workers bear cyclical adjustment disproportionately on the extensive margin (more volatile separation rates, employment losses following monetary contractions) while their wages are acyclical, whereas more-educated workers exhibit the reverse: stable employment but highly cyclically sensitive wages, especially as measured by the UCL.

Wage scarring. The persistent negative effect of hiring-period macroeconomic conditions on wages throughout the subsequent employment spell, beyond what is explained by contemporaneous market conditions. In this paper’s context, wage scarring is concentrated among more-educated workers: being hired when the unemployment rate is one percentage point above trend is associated with wages that remain depressed for several years, with the depression being larger and more persistent for college-educated workers than for those with less education. This is demonstrated via the expected wage wedge profiles in Figure 3 and is confirmed to survive controls for match-quality sorting.

Output-gap-equivalent representative agent economy. A conceptual benchmark constructed in the paper’s welfare analysis: a single-worker-type New Keynesian economy whose wage and labor supply elasticities are set equal to the output-elasticity-weighted averages of the two labor variety types in the heterogeneous economy. The paper shows that the heterogeneous-worker economy and this representative-agent benchmark produce identical aggregate output gap and price level paths (under Cobb-Douglas production, earnings elasticities are identical across varieties), but welfare diverges because period utility is more volatile for the variety with more rigid wages. The 15 percent excess welfare cost of the heterogeneous economy relative to this benchmark is the paper’s headline welfare result.

Labor Market Shocks and Monetary Policy

Mon, 01 Jan 0001 00:00:00 +0000

Overview

Research question. The paper asks two related questions: (1) How much, and through which channels, do employer-to-employer (EE) worker transitions affect macroeconomic outcomes — particularly inflation? (2) What is the optimal monetary policy within a class of Taylor rules when EE flows are taken explicitly into account?

Motivation. Standard monetary policy frameworks condition on the unemployment rate as the primary labor market slack measure and underemphasize the “quality” dimension of employment. The paper documents a striking empirical pattern: the 2016–2019 recovery and the 2021–2022 recovery from COVID-19 featured nearly identical declines in the unemployment rate, yet exhibited dramatically different EE rate dynamics and inflation outcomes. During 2016–2019, the EE rate remained flat despite a roughly 25 percent decline in the unemployment rate from trend. During 2021–2022, the EE rate rose by around 8 percent above trend over a comparable unemployment decline. Correspondingly, unit labor cost (ULC) growth reached approximately 6 percent during the COVID-19 recovery when unemployment fell below 4 percent, compared with only about 2 percent ULC growth in the 2016–2019 period at similar unemployment levels.

Methodology. The authors develop a Heterogeneous Agent New Keynesian (HANK) model with a frictional labor market featuring on-the-job search (OJS). Workers are heterogeneous in wealth (mutual fund shares), human capital, match-specific productivity, and endogenous piece-rate wages. Human capital stochastically appreciates when employed and depreciates when unemployed, capturing scarring effects and job-stayer wage growth. Wage determination follows a Bertrand competition protocol based on flow output: workers switch to higher-productivity matches and extract the full surplus from the new firm, while outside offers from lower-productivity firms can still trigger rebargaining with the incumbent firm and raise the piece rate without a job switch. Three vertically integrated sectors — labor services, intermediate goods, and final goods — are linked so that the real price of labor services pl is the real marginal cost for intermediate firms and the sole driver of inflation in the New Keynesian Phillips curve (absent aggregate productivity shocks). The economy is subject to AR(1) shocks to the discount rate β (demand), aggregate labor productivity z (supply), and OJS efficiency ν (the relative search efficiency of employed workers). The model is solved using the Sequence-Space Jacobian (SSJ) method, extended to handle discretized worker distributions as direct inputs to equilibrium conditions.

The model is calibrated to U.S. pre-Great Recession data (2004–2006), targeting the fraction of hand-to-mouth individuals (16 percent of SIPP sample), unemployment rate (5.1 percent), EU separation rate (3.8 percent quarterly), EE rate (2 percent quarterly from LEHD), earnings drop upon job loss (35 percent), wage growth of job switchers (9 percent), and the labor share (0.67). Shock processes are estimated by minimizing deviations from empirical correlations and standard deviations of output, unemployment, EE rate, and inflation over 1995:Q3–2008:Q4.

Main findings — positive analysis. Shocks to OJS efficiency account for 43.1 percent of fluctuations in inflation in the variance decomposition, and 78.7 percent of fluctuations in the EE rate. The mechanism: a higher OJS efficiency lowers the expected match value EJ for labor services firms through three channels — (i) a compositional shift toward employed job seekers who extract the entire match surplus, (ii) shorter expected match duration as workers face higher poaching probabilities, and (iii) more frequent wage rebargaining where outside offers bid up wages without accompanying productivity gains. To maintain the free-entry condition, the real price of labor services pl must rise, increasing the real marginal cost and inflation. This direct labor market effect explains 139 percent of the total increase in pl; general equilibrium effects through reduced tightness θ — which raises expected match values by making vacancies easier to fill and workers less likely to be poached — offset −42 percent; the remainder (3 percent) comes from real rate changes driven by the monetary policy reaction.

In two historical simulations, muted OJS efficiency during 2016–2019 generated approximately 0.23 percentage points lower annualized inflation at the peak relative to a counterfactual economy with the same unemployment path but an endogenously rising EE rate. Conversely, elevated OJS efficiency during 2021–2022 generated approximately 0.56 percentage points higher annualized inflation compared to the flat-EE-rate counterfactual. The paper notes that strong worker mobility accounts for roughly 10 percent of the approximately 6 percentage point total rise in annual inflation during the COVID-19 recovery episode.

An important cross-model comparison shows that the Representative Agent New Keynesian (RANK) version of the model overestimates the decline in demand, output, and labor market tightness upon a positive OJS shock, and underestimates the rise in real rate, marginal cost, and inflation. Household heterogeneity is therefore quantitatively important: hand-to-mouth households’ demand responds directly to labor income increases from job switches, mitigating the demand decline and amplifying inflation.

Main findings — normative analysis. The optimal monetary policy within an augmented Taylor rule — adding an EE gap term ΦEE(EEt − EE*) alongside the standard inflation and unemployment gap terms — prescribes Φ*_u = −3.18 and Φ*_EE = 2.22 (with Φπ fixed at 1.5). This yields a 78.7 percent reduction in the central bank loss relative to the baseline Taylor rule. A policy that ignores EE dynamics and optimizes only the unemployment gap coefficient (finding Φu = −2.71, ΦEE = 0) produces a 12 percent larger central bank loss than the full optimal policy. In terms of welfare, the optimal policy delivers 0.16 percent additional lifetime consumption equivalent in the aggregate. Workers at the bottom of the match quality distribution gain the most (0.24 percent), as do the unemployed (0.20 percent), while those at the top of the wealth distribution gain the least due to larger share price fluctuations under the more aggressive policy.

Scope conditions. Results are derived conditional on a dual-mandate central bank objective (variance of inflation and output gaps), within a class of Taylor-type rules (not fully optimal Ramsey policy), under first-order approximation around a non-stochastic steady state. The historical simulations abstract from supply shocks active in the normative exercises and assume the economy starts from steady state in 2016.

Q&A

Q1: What is the OJS efficiency shock, and how does it differ from a standard demand or supply shock? An OJS efficiency shock is modeled as a time-varying shift in νt, the relative job search efficiency of employed workers compared with unemployed workers. Unlike demand shocks (discount rate β innovations) and productivity shocks (aggregate z innovations), which move inflation and unemployment in opposite directions under standard New Keynesian logic (divine coincidence), OJS efficiency shocks move inflation and unemployment in the same direction: a positive OJS shock raises inflation while also raising unemployment (because the higher real rate induced by the central bank’s reaction reduces demand and employment). This makes OJS shocks behave like cost-push shocks and introduces a genuine policy trade-off for a dual-mandate central bank.

Q2: What are the three mechanisms through which higher OJS efficiency raises the real price of labor services, and what is the quantitative contribution of each? The decomposition (Figure 8) shows that the direct effect of ν on EJ — encompassing the composition channel (more employed job seekers who extract the full surplus), the match-duration channel (shorter expected match lives), and the wage rebargaining channel (outside offers raise wages without productivity gains) — explains 139 percent of the total increase in pl. The general equilibrium reduction in labor market tightness θ, which raises EJ and partially offsets the cost increase, explains −42 percent in total: −18 percent through increased supply of labor services L (productivity-enhancing job switches improve the match distribution) and −24 percent through reduced output Y (lower aggregate demand). Real rate effects account for the remaining 3 percent net (8 percent from the inflation channel and −5 percent from the unemployment channel). Labor market effects in total therefore explain 97 percent of the marginal cost increase.

Q3: Does the positive relationship between EE rates and inflation require wage increases upon job switches? No. The paper demonstrates (Section 2.4.2, Figure 3) that even when the piece rate for workers hired from unemployment is set to α = 0.95 (so that outside offers have negligible wage effects), a positive OJS efficiency shock still generates a decline in output and a rise in inflation in both the RANK and TANK models. Quantitatively, the inflation response is similar across the baseline and near-zero composition-channel specifications, confirming that the shorter expected match duration is the primary driver of the increase in the real price of labor services. The match duration channel operates independently of wage increases: firms anticipate shorter matches and require a higher flow price to break even on vacancy costs.

Q4: How does household heterogeneity change the quantitative effects of OJS shocks relative to the RANK benchmark? Under a constant real rate, in the RANK model a higher OJS efficiency increases the real price of labor services and inflation but has no effect on aggregate demand or output (because higher labor income for the PIH household is exactly offset by lower firm profits). In the TANK model, hand-to-mouth households consume their entire labor income, so the rise in labor income from job switches directly boosts their demand, raising output and tightness and further amplifying inflation. Under an endogenous real rate, the RANK model overestimates the decline in demand and output, and underestimates the rise in real rate and inflation, compared with the TANK model. The TANK model requires a substantially larger equilibrium real rate increase to contain inflation because HtM households’ demand is less elastic to the real rate than PIH households'.

Q5: How are aggregate shock processes estimated, and what share of inflation variance do OJS shocks explain? The six AR(1) parameters governing β, z, and ν (three persistence parameters ρj and three standard deviations σj) are estimated by minimizing the sum of squared deviations between model-generated and empirical moments: the autocorrelation of output; correlations of the unemployment rate, EE rate, and inflation with output; and standard deviations of output, unemployment rate, EE rate, and inflation. Data cover 1995:Q3–2008:Q4. Estimated values are ρβ = 0.909, ρz = 0.332, ρν = 0.936 and σβ = 0.001, σz = 0.002, σν = 0.003. The variance decomposition (Table 4) assigns 43.1 percent of inflation variance to OJS efficiency shocks ν, 52.0 percent to demand shocks β, and 4.9 percent to productivity shocks z.

Q6: How is the “missing inflation” during 2016–2019 quantified, and what is the counterfactual? The exercise simulates two economies both replicating the same unemployment path — a 15 percent decline in unemployment relative to its 5.2 percent steady state, spread linearly over 16 quarters, followed by mean reversion. The first economy uses only positive demand shocks, which generate an endogenously rising EE rate consistent with the historical unemployment-EE correlation. The second economy additionally introduces negative OJS efficiency shocks to keep the EE rate unchanged, as observed in the data during 2016–2019. Annualized inflation in the second economy is 0.23 percentage points lower at the peak (16 quarters after the shock), implying that had the EE rate risen normally, inflation would have been around 2 percent in 2019 rather than the observed 1.8 percent.

Q7: How is the inflationary role of elevated EE transitions during 2021–2022 quantified? Using the same unemployment path as the 2016–2019 exercise, the COVID-19 recovery economy combines positive demand shocks with positive OJS efficiency shocks to replicate the observed 0.16 percentage point (8 percent above trend) increase in the EE rate. Comparing this economy to the flat-EE-rate economy from the prior exercise, the elevated EE rate generates 0.56 percentage points higher annualized inflation. Because annual inflation rose approximately 6 percentage points in the data during this episode, the model attributes roughly 10 percent of the total inflation increase to strong worker mobility.

Q8: What are the optimal Taylor rule coefficients when EE dynamics are included, and what is the welfare cost of ignoring them? The optimal policy over the augmented Taylor rule it = i* + Φπ(πt − π*) + Φu(ut − u*) + ΦEE(EEt − EE*), with Φπ fixed at 1.5 and a dual-mandate loss function W = var(πt − π*) + 0.25·var(Yt − Y*), prescribes Φ*_u = −3.18 and Φ*_EE = 2.22. This reduces the central bank loss by 78.7 percent relative to the baseline rule (Φu = −0.25, ΦEE = 0). If the EE gap term is excluded and only the unemployment gap coefficient is re-optimized (finding Φu = −2.71), the central bank loss is 12 percent higher than under the full optimal policy.

Q9: How does the optimal policy affect macroeconomic volatility, and who gains most from it? Table 5 shows that the optimal policy substantially reduces volatility of inflation (standard deviation falls from 0.0013 to 0.0011), output (0.0059 to 0.0020), consumption (0.0059 to 0.0020), unemployment (0.0047 to 0.0013), labor market tightness (0.0600 to 0.0175), and the real marginal cost pl (0.0203 to 0.0081), at the cost of higher real rate volatility (0.0019 to 0.0033) and share price volatility (0.1975 to 0.3051). In terms of welfare (Table 6), the unemployed gain 0.20 percent in lifetime consumption equivalents (versus 0.15 percent for the employed), workers at the bottom quintile of match quality gain 0.24 percent (versus 0.16 percent at the top), and wealth-poor individuals in the bottom share quintile gain 0.23 percent (versus 0.11 percent at the top, whose gains are eroded by larger share price fluctuations).

Q10: How does the model extend the SSJ computational method, and why is this extension necessary? The standard SSJ method of Auclert, Bardoczy, Rognlie, and Straub (2021) handles settings where only scalar aggregates enter equilibrium conditions in sequence space. In this model, the discretized distributions of employed workers µE(h, x) and unemployed workers µU(h) at the job search stage enter directly into the expected match value EJ (because human capital and current match productivity determine output and wage levels upon new contacts), and the distribution λE(h, x, α) at the production stage enters into labor services firm profits ΓS. The authors treat worker distributions as histograms and compute Jacobians for each mass point, combining the SSJ method with Reiter (2009)-style projection. This substantially increases computation time but remains feasible, extending the SSJ method to multi-stage models with search frictions where endogenous distributions are state variables.

Q11: What are the three sources of wage growth in the HANK model, and what is their relevance for inflation dynamics? First, human capital h stochastically appreciates during employment (at rate πE = 0.018 per quarter, calibrated to annual job-stayer wage growth of approximately 2 percent), raising wages through a higher piece-rate base. Second, job switches to higher-productivity matches yield wage increases as the worker extracts the full surplus from the new firm (the new piece rate equals x/x’, the ratio of old to new match productivity). Third, outside offers with productivity x’ satisfying αx < x’ < x — not good enough to trigger a switch but better than the current bargaining threat — cause the incumbent firm to raise the piece rate to x’/x via rebargaining, increasing wages without a job change. The second and third channels are the ones directly affected by OJS efficiency shocks and are inflationary: they raise labor costs beyond productivity gains.

Q12: Why do OJS shocks have a shorter match duration channel even without wage increases? When OJS efficiency ν rises, each employed worker faces a higher probability νtf(θt) of contacting another firm each period. Even if wages do not change upon contact (as in the α = 0.95 robustness exercise), a labor services firm posting a vacancy expects that any match it forms will be shorter-lived: the worker is more likely to be poached in the future. This shortens the expected present discounted value of the match for the firm, reducing EJ. To satisfy the free-entry condition (expected profit = vacancy cost κ), the price of labor services pl must rise, increasing the real marginal cost and inflation. Figure 3 confirms a nearly identical inflationary response under α = 0.95 as under the baseline, isolating this match-duration mechanism.

Key Concepts

OJS efficiency shock (νt shock). A time-varying shift in the relative job search efficiency of employed workers compared with unemployed workers. Modeled as an AR(1) process for νt (estimated persistence ρν = 0.936). An increase in νt raises the probability that employed workers contact outside firms each period, boosting the EE rate. In the model, this acts as a cost-push shock: it raises inflation and unemployment simultaneously, breaking divine coincidence and creating a policy trade-off for a dual-mandate central bank.

Expected match value (EJt). The ex-ante expected value to a labor services firm of a filled vacancy, conditional on contacting a worker, defined as a weighted average of match values J across the pool of job seekers (unemployed and employed). The free-entry condition Vt = κ/q(θt) = EJt pins down the real price of labor services pl: when EJt declines (due to shorter match durations or compositional shifts toward high-surplus-extracting workers), pl must rise to maintain zero expected profit for vacancy posters.

Composition channel. The mechanism by which a rise in OJS efficiency shifts the composition of the job-seeker pool toward employed workers, who (under Bertrand competition) extract the entire flow surplus of a new match and receive wage equal to plF(h,x). Since firms receive zero rent from poached workers, an increase in the fraction of employed in the applicant pool lowers EJt and requires a compensatory increase in pl.

Match duration channel. When OJS efficiency ν rises, each existing match faces a higher probability of dissolution because the worker is more likely to be poached. The reduced expected match duration lowers the present discounted value of a match for the firm (even holding wages fixed), reducing EJt and raising pl. Demonstrated as the primary driver of inflation in the α = 0.95 robustness exercise where wage increases upon job switches are near zero.

Piece-rate α (endogenous). The share of match output F(h,x) that the worker receives as wage, determined through Bertrand competition on flow output following Postel-Vinay and Robin (2002). A worker hired from unemployment starts at α = x̄/x’ (where x̄ is the lowest match productivity). Job switches to higher-x’ firms reset α = x/x’. Rebargaining upon a credible outside offer from a firm with αx < x̃ < x raises α to x̃/x. The piece rate endogenizes wage dynamics for switchers, stayers, and job losers, allowing the model to discipline these moments in the data.

Divine coincidence (and its breakdown under OJS shocks). In standard New Keynesian models, demand and productivity shocks move inflation and unemployment gaps in opposite directions, so stabilizing inflation also stabilizes the output gap. OJS efficiency shocks break this property: they generate simultaneous increases in inflation and unemployment, introducing a genuine trade-off between the two mandates and making EE-augmented Taylor rules welfare-improving relative to rules that respond only to unemployment.

Sequence-Space Jacobian (SSJ) method with distributed worker states. An extension of the Auclert, Bardoczy, Rognlie, and Straub (2021) computational method to settings where discretized distributions of workers (µE(h,x) and µU(h)) enter directly into equilibrium conditions — specifically into the free-entry condition via EJt and into firm profits. The authors treat distributions as histograms and compute Jacobians for each mass point, combining SSJ with Reiter (2009)-style projection to efficiently solve for transitional dynamics under aggregate uncertainty.

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

Mon, 01 Jan 0001 00:00:00 +0000

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.

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.
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.

Monopsony Makes Firms Not Only Small but Also Unproductive: Why East Germany Has Not Converged

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Summary

When employers face a trade-off between growing large and paying low wages — that is, when they have monopsony power — some productive employers will decide to acquire fewer customers, forgo sales, and remain small; these decisions have adverse consequences for aggregate labor productivity beyond the standard monopsony result that firms are too small. The paper documents that East German plants (compared to West German ones) face a steeper size-wage curve, invest less into marketing, and remain smaller, with the share of employment at plants with more than 249 employees standing at roughly 25% in East Germany versus 39% in West Germany in 2014 (and 31% versus 55% in manufacturing specifically). The steeper size-wage curve in East Germany is traceable to the historically determined underrepresentation of collective bargaining and union membership in small East German plants — a legacy of communist-era labor organization that caused union membership to collapse after reunification. The authors combine this evidence with a heterogeneous-plant model in which plants have product market power and choose how many customers to acquire subject to an upward-sloping size-wage schedule; two channels reduce aggregate productivity: a love-of-variety loss (fewer active plants means consumers bundle from a smaller variety of suppliers) and a compositional reallocation loss (labor is shifted from more productive to less productive plants, an effect exacerbated by product market power). When the model is calibrated to West Germany and the steeper East German size-wage trade-off is imposed, it predicts 10 percentage points lower aggregate labor productivity in East Germany — and for manufacturing, where East-West differences in plant size and the size-wage trade-off are particularly pronounced, the model predicts 18 percentage points lower productivity; in both cases the compression of the plant size distribution accounts for the largest share of the predicted productivity loss. The paper thus offers an explanation for why, more than thirty years after reunification, labor productivity and wages remain roughly 25% lower in the East German private sector despite uniform legal institutions across the two regions.

Layer 2 — Q&A

Q1: What is the core mechanism by which monopsony power reduces aggregate productivity, and how does it differ from the standard “firms are too small” result?

In the standard monopsony account, firms face an upward-sloping labor supply curve and choose to employ fewer workers than the competitive optimum, so individual firms are below efficient scale. The paper identifies an additional, investment-distortion channel: plants must also decide how large a customer base to acquire, and doing so requires marketing expenditure as well as the labor to service additional customers — labor whose cost rises with plant size along the size-wage schedule. A steeper size-wage curve therefore makes customer acquisition more expensive at the margin, and some productive plants optimally choose to acquire fewer customers, forgo sales, and remain small. The new aggregate productivity loss stems from this distorted investment margin: plants that could generate high value added at large scale instead operate at sub-optimal customer networks, suppressing aggregate output through both a love-of-variety effect (fewer active large plants means consumers access a smaller product variety) and a misallocation effect (the compressed size distribution shifts employment toward less productive plants).

Q2: What empirical patterns do the authors document to link the East-West productivity gap to missing large plants and steeper size-wage curves?

The authors document three nested empirical facts using the German Structure of Earnings Survey (SES) pooled across 2006, 2010, and 2014, supplemented by administrative wage panel data (AWFP) and national accounts (VGR). First, East German labor productivity in the private non-primary sector is about 25% below West Germany’s and has not converged since roughly 1995. Second, the share of employment at large plants (>249 employees) is substantially smaller in the East, and this gap is present both cross-sectionally across survey years and conditionally: East German plants enter smaller and remain smaller over their life-cycles, so plant age does not explain the difference. Third, industries where missing large plants are most pronounced in East Germany relative to West Germany are also the industries with the largest East-West productivity and wage gaps — the employment-weighted correlation between the large-plant share gap and the productivity gap is 0.53 across industries. The steeper size-wage curve itself is documented using within-industry comparisons: on average the plant size elasticity of wages is one-fifth larger in East Germany, and those industries with a steeper East-West size-wage differential are also the industries with the most missing large plants and the lowest average wages in the East.

Q3: Why is the steeper size-wage curve specific to East Germany, and why does it persist decades after reunification?

In communist East Germany, trade unions did not have the role of representing worker interests; consequently, after reunification, union membership fell dramatically. The key institutional consequence is that collective bargaining coverage in East Germany is underrepresented specifically in small plants. Workers at small plants in East Germany are more likely to have individually rather than collectively bargained wages than their West German counterparts, whereas workers at large plants in both regions are more similarly covered. Because collective bargaining flattens the size-wage curve (larger plants pay a smaller premium over small plants’ wages when both are covered by the same bargaining agreement), its absence in small East German plants produces a steeper gradient of wages with plant size in the East. This is a persistent structural feature rather than a transitional one: government policies and their enforcement are essentially uniform across regions, so the asymmetric bargaining coverage, which originates in communist-era institutional history, has not been erased by market forces or policy since 1990.

Q4: How is the model structured, and what are the three decision stages for plants?

The model is a static, long-run heterogeneous-plant framework that yields closed-form solutions. Within a period, plants face a three-stage decision problem. First, they decide whether to enter the market. Second, after entry, they choose how many customers to acquire, trading off additional sales revenue against marketing costs and the labor cost of servicing a larger customer base — a cost that rises with the number of customers because the upward-sloping size-wage curve means each additional worker hired requires a higher wage for all infra-marginal workers. Third, taking into account their product market power (each plant is a monopolistic competitor with its own customers), plants set prices to each customer and thereby determine how many workers they need. The size-wage schedule enters the second stage directly, so a steeper schedule reduces optimal customer acquisition across all plants, with the distortion being largest for the most productive plants (which would otherwise grow the largest).

Q5: Through what two channels does the steeper size-wage trade-off reduce aggregate labor productivity in the model?

The first channel is a love-of-variety effect in the product market: because more productive plants acquire fewer customers and operate at smaller scale under a steeper size-wage schedule, the average consumer bundles goods from a smaller number of distinct plants, and aggregate efficiency falls through the standard CES love-of-variety mechanism. The second channel is a misallocation effect in the labor market: the steeper size-wage schedule compresses the employment distribution across plants, reallocating labor from more productive to less productive plants relative to the benchmark with a flatter schedule. The paper shows that this second channel is exacerbated by product market power, because plants with stronger pricing power respond more aggressively to the changed labor cost trade-off. In the model’s decomposition, the compression of the plant size distribution (the misallocation channel) accounts for the largest part of the predicted 10 percentage point productivity shortfall.

Q6: What quantitative predictions does the model make, and how does it perform in untargeted moments?

The model is calibrated to two moments for West Germany: average plant size and the share of large plants (>249 employees). When the steeper East German size-wage trade-off is imposed without re-calibrating other parameters, the model predicts 10 percentage points lower aggregate labor productivity in East Germany — accounting for at least 10 of the roughly 25 percentage point observed gap. For the manufacturing sector alone, where East-West differences in plant size, the size-wage trade-off, and aggregate productivity are particularly pronounced, the calibrated model predicts 18 percentage points lower productivity. As an untargeted validation, the model also replicates the plant size distribution in East Germany, matching both the smaller average plant size and the relatively small number of large plants. These untargeted predictions provide additional support for the mechanism.

Q7: What alternative explanations for East Germany’s non-convergence does the paper rule out or place in context?

The paper addresses several confounds. In Appendix A, the authors show that East-West aggregate labor productivity differences are driven by differences in aggregate total factor productivity, not by labor quality differences, capital intensity differences, or capital quality differences — confirming within-country the finding that TFP explains a large fraction of productivity dispersion. The TFP differences are shown to be unlikely the result of greater labor market flexibility in West Germany or differences in industry composition. Appendix B shows that the East-West plant size distribution gap is not driven by differences in urbanization (West Germany has more metropolitan areas). The paper also addresses plant age: East German plants enter smaller and remain smaller at every age and across entry cohorts, ruling out the hypothesis that the size gap is purely a transitional legacy of the restructuring that destroyed many large East German plants at reunification.

Q8: How does this paper relate to the Heise and Porzio (2021) finding that plant productivity differences, not worker quality differences, drive the East-West wage gap?

Heise and Porzio (2021) use matched employer-employee data to document that plant productivity differences (as opposed to worker quality differences) account for most of the East-West wage differential, and they explain why low worker mobility does not remove these differences. The present paper complements this by providing an explanation for why plant productivity is lower in East Germany in the first place and why firm-level convergence does not occur: the steeper size-wage curve induced by the legacy of missing collective bargaining coverage in small East German plants distorts the investment and customer acquisition decisions of productive plants, keeping them small and unproductive. The two papers are thus complementary: Heise and Porzio take the plant productivity gap as given; Bachmann et al. endogenize it through the size-wage mechanism.

Key Concepts

Size-wage curve: The empirical relationship between plant size (measured by employment) and wages paid to workers, conditional on worker characteristics. A steeper size-wage curve means that the wage premium for working at a large plant relative to a small plant is larger. In this paper’s model, plants internalize that expanding their customer base and workforce requires paying higher wages to all workers (not just the marginal hire), making growth more costly when the size-wage curve is steeper.

Monopsony power (monopsonistic competition): The market structure in which an individual employer faces an upward-sloping labor supply curve — i.e., it must raise wages to attract additional workers. The paper uses “monopsonistic competition” to describe a setting with many such employers, each with some wage-setting power, in contrast to oligopsony. The paper focuses on allocative effects of this power, not on normative efficiency questions.

Customer capital / customer acquisition: Plants must incur marketing expenses to build a customer base; each customer relationship generates a stream of sales but requires labor to service. The size of the customer network is a long-run investment decision. Under monopsonistic labor markets, the cost of expanding the customer base includes not only marketing expenses but also the higher wages that a larger workforce requires, making customer acquisition a margin that is distorted by labor market power.

Love-of-variety effect: A welfare loss that arises in models with monopolistic competition and CES preferences when the number of active product varieties declines. In this paper it applies to the product market: when plants remain small and acquire fewer customers, the effective number of distinct varieties consumed falls, reducing aggregate efficiency even holding plant-level productivity fixed.

Misallocation / compressed size distribution: A situation in which factors of production are not allocated to their highest-value uses. Here, the steeper size-wage curve induces productive plants to remain small, so labor that would otherwise be employed at high-productivity large plants is instead employed at lower-productivity small plants. The resulting compression of the plant size distribution — fewer very large plants, more mass in the middle — is both the key empirical fact and the primary quantitative driver of the predicted aggregate productivity shortfall.

Collective bargaining coverage: The fraction of workers whose wages are set by collective agreements between employers (or employer associations) and trade unions, rather than by individual negotiation. The paper establishes that collective bargaining flattens the size-wage curve by compressing wages across plants of different sizes. The historically low collective bargaining coverage among small East German plants — a legacy of communist-era labor relations — is the institutional root cause of the steeper East German size-wage schedule.

Summary based on IZA Discussion Paper 15293. AI-assisted, human review pending.

Robot adoption and inflation dynamics

Mon, 01 Jan 0001 00:00:00 +0000

Robot Adoption and Inflation Dynamics

Research Question

Basso and Rachedi investigate how robot adoption influences inflation dynamics — specifically, whether the surge in automation during the 2000s and 2010s can explain the muted sensitivity of inflation to unemployment (the “flat Phillips curve”) observed in advanced economies prior to the Covid pandemic, and whether the same framework can account for the subsequent resurgence of steep inflation-unemployment co-movement.

Data and Methodology

The empirical analysis uses an annual panel covering 384 U.S. metropolitan statistical areas (MSAs) from 2008 to 2018. The dependent variables are non-tradable goods inflation (log-difference of services prices excluding rents and utilities, from BEA regional price parities) and wage inflation (log-difference of average compensation per job). Robot adoption at the MSA-year level is constructed following Acemoglu and Restrepo (2020a): industry-level robots per employee at the U.S. national level are weighted by industry employment shares in each MSA, yielding an MSA-year robot-per-employee ratio.

The regression specification extends Hazell et al. (2022) by adding an interaction term between the lagged unemployment rate and the (demeaned) robot-per-employee ratio, along with MSA and year fixed effects. Year fixed effects absorb common inflation expectations and the endogenous response of monetary policy to aggregate demand shocks. To address endogeneity, unemployment is instrumented with a Bartik shift-share variable of tradable demand spillovers, and robot adoption is instrumented with average industry-level robot penetration in the five largest European economies — under the identifying assumption that robot demand shocks are weakly correlated across advanced countries.

The theoretical framework is a New Keynesian model augmented with (i) directed search frictions in the labor market, and (ii) producer-level automation decisions in the spirit of Acemoglu and Restrepo (2020a). Producers pay a fixed entry cost, draw idiosyncratic efficiency for employing labor, and then choose between a robot technology (certain output at low efficiency) and a labor technology (uncertain hiring, higher potential efficiency). This generates an automation threshold: low-efficiency producers install robots, displacing low-wage jobs. A Taylor rule closes the model. Quantitative exercises compare two steady states calibrated to robot-per-employee ratios of 0.2% (low automation, targeting the U.S. in the early 2000s) and 0.6% (high automation, calibrated to one standard deviation of robot penetration variation across MSAs).

Main Findings

Empirical. In the baseline IV regression, a one standard deviation increase in robot adoption reduces the sensitivity of price inflation to unemployment by 17%, and the sensitivity of wage inflation to unemployment by 9%, relative to a MSA with the average robot penetration. The larger flattening effect on price inflation than on wage inflation implies that robot adoption also diminishes the pass-through from wages to prices. All three effects are statistically significant at the 5% level, and are robust to controls for demographic structure (age composition, gender/race/education participation rates, MPC heterogeneity), occupational structure (abstract, routine, manual, and offshorable occupations), and import competition exposure (Chinese and Mexican import shares).

Model quantification. Comparing the high-automation to the low-automation steady state, the model generates a 14% reduction in the slope of the price Phillips curve and a 13% reduction in the slope of the wage Phillips curve, conditional on the same-sized demand shocks in both economies. The price Phillips curve result accounts for 82% of the empirical estimate (17%). The model overstates the flattening of the wage Phillips curve (13% vs. 9% in the data), and therefore understates the reduction in the wage-to-price pass-through.

Mechanisms. Automation flattens the Phillips curve through two primary channels. First, the outside option of automating production reduces workers’ bargaining power and dampens the elasticity of wages to unemployment (the “Wage Setting Effect”). Second, a higher share of robot firms reduces the aggregate labor share, muting the pass-through from wages into prices (the “Steady State Effect”). A third channel — firms cyclically substituting workers for machines in response to a shock (the “Cyclical Effect”) — operates during the transition but the Wage Setting Effect accounts for the bulk of the flattening.

Non-linearity and the post-Covid resurgence. When robot-production is subject to convex adjustment costs, the threat of automation that underlies the Wage Setting Effect becomes inoperative during large expansionary shocks. When investment in machines surges, the marginal cost of producing robots rises sharply, raising the price of machines and pushing the automation threshold downward — more firms must use labor. Workers then negotiate higher wages, which pass into prices. Conditional on small demand shocks, the high-automation economy still exhibits a flatter Phillips curve than the low-automation economy. Conditional on large demand shocks (simulated as a 2 percentage point drop in unemployment), there is no difference in the inflation response between the low- and high-automation economies, so the Phillips curve reverts to steep.

Q&A

Q1: What is the exact empirical specification and how does it map to a structural object?

The regression is: non-tradable goods inflation = β × lagged unemployment + γ × (lagged unemployment × demeaned robot adoption) + ζ × lagged robot adoption + χ × relative non-tradable price + MSA fixed effects + year fixed effects + error. In a multi-region model without automation, Hazell et al. (2022) show that the coefficient β identifies the aggregate slope of the Phillips curve because year fixed effects absorb both common inflation expectations and the endogenous monetary policy response to aggregate demand shocks. Adding the interaction term extends this logic: γ identifies how robot adoption causally shifts the slope of the local Phillips curve, which maps into changes in the aggregate slope.

Q2: What are the first-stage instruments and why are they valid?

Unemployment is instrumented with local tradable demand spillovers — a Bartik variable weighting national industry value-added growth (excluding each MSA’s own contribution) by each MSA’s average industry value-added shares, so national supply disturbances uncorrelated with MSA-level heterogeneity generate plausibly exogenous unemployment variation. Robot adoption is instrumented with the implied robot-per-employee ratio obtained by replacing U.S. industry robot installations with the average across the five largest European economies, weighted by U.S. industry employment shares; this isolates the supply-side efficiency improvements in robot technology that drove global adoption, conditional on robot demand shocks being weakly correlated across countries. The correlation between the two instruments in the sample is 0.2, ensuring they do not strongly co-move.

Q3: What are the point estimates and their magnitudes in the baseline IV regression?

For price inflation (Panel A, Column 4), the base sensitivity β = −0.5069 (SE 0.1381, significant at 1%), and the interaction coefficient γ = 0.0066 (SE 0.0030, significant at 5%). For wage inflation (Panel B, Column 4), β = −0.9580 (SE 0.2450, significant at 1%), and γ = 0.0049 (SE 0.0024, significant at 5%). A one standard deviation increase in robot adoption reduces price inflation sensitivity by 17% and wage inflation sensitivity by 9% relative to the average-automation MSA.

Q4: What does the difference in flattening magnitudes (17% for prices vs. 9% for wages) imply about the wage-price pass-through?

Because automation reduces the price Phillips curve slope by proportionally more than the wage Phillips curve slope, each percentage-point change in wages translates into a smaller percentage-point change in prices in higher-automation areas. This indicates that robot adoption diminishes the influence of wage changes on price changes — i.e., it reduces the wage-to-price pass-through. In the model, this operates through the Steady State Effect: a larger share of production carried out by robot firms means that a given change in average wages applies to a smaller portion of total marginal costs, weakening the price response.

Q5: How is the automation threshold determined in the theoretical model, and what economic forces govern it?

A producer opts for the labor technology if and only if the expected value of a labor firm (= job-filling probability × (producer price × labor efficiency − posted wage) − entry cost) exceeds the value of a robot firm (= producer price × robot efficiency − machine price − entry cost). Since the value of a labor firm increases in labor efficiency, there is a unique cut-off efficiency level γ* at which a producer is indifferent. Producers with labor efficiency above γ* post vacancies; those below γ* install robots. The cut-off rises (more automation) when wages rise relative to machine prices, and falls (less automation) when machine prices rise due to costly robot production during large expansionary shocks.

Q6: How does the wage-posting equilibrium under directed search generate the Wage Setting Effect of automation?

Under directed search, each labor firm posts a wage to maximize its expected value, and workers sort into sub-markets offering higher wages but lower job-finding probabilities. The equilibrium posted wage for a firm with labor efficiency γj is Wγj,t = PP,t × γj × (1 − η), where η is the elasticity of matches to vacancies. The option to install a robot — available at any time — limits how much any individual firm needs to offer workers. When automation increases, the outside option becomes more attractive to more firms, which constrains wage offers industry-wide, reducing the elasticity of average wages to unemployment fluctuations.

Q7: How is the slope of the price Phillips curve characterized analytically?

Log-linearizing the model around the steady state and substituting labor market and wholesaler equilibrium conditions into the pricing equation yields: inflation = −[(ε−1)/φ] × Ψ(γ*; Θ) × unemployment gap + β × expected future inflation, where Ψ(γ*; Θ) is a function of the automation cut-off γ*, the elasticity of substitution ε, the matching function elasticity η, the efficiency bounds γM and γH, and the distribution shape parameter α. In contrast to standard New Keynesian models where the slope depends only on markup and nominal rigidity parameters, this expression depends directly on the degree of automation through the steady-state threshold γ*.

Q8: Across different structural parameter configurations, does automation always flatten the Phillips curve?

Yes. Numerical analysis of the closed-form Phillips curve expression (Figure 1) shows that robot adoption unambiguously decreases the slope of the price Phillips curve across all combinations of the key structural parameters — the distribution shape parameter α, the matching elasticity η, the upper bound of labor efficiency γH, and the steady-state unemployment rate ū. The flattening effect is more pronounced when η is low, when α implies a larger fraction of low-efficiency producers, and when the steady-state unemployment rate is low.

Q9: How do the three mechanism channels (Cyclical, Wage Setting, Steady State) compare quantitatively?

The paper isolates channels by comparing alternative model specifications: (i) Baseline directed search with endogenous automation, (ii) Directed search with fixed automation (removing Cyclical and Wage Setting Effects, leaving only the Steady State Effect), (iii) Random search with τ = 0.5 (efficient bargaining, retaining both the Cyclical and Wage Setting Effects), (iv) Random search with τ = 0.01 (near-zero worker bargaining power, removing the Wage Setting Effect but retaining the Cyclical Effect). Figure 5 shows that the Steady State Effect alone accounts for only a small portion of the total inflation differential between low- and high-automation economies. The Wage Setting Effect — isolated by comparing τ = 0.01 and τ = 0.5 economies with endogenous automation — accounts for the bulk of the flattening. The Cyclical Effect (isolated by comparing fixed and endogenous automation with τ = 0.01) contributes an intermediate amount.

Q10: What is the quantitative exercise comparing low- and high-automation steady states?

The low-automation economy targets the U.S. robot-per-employee ratio of 0.2% in the early 2000s (Acemoglu and Restrepo, 2020a), calibrated with robot-specific technological change ζ = 2. The high-automation economy features a 200% higher robot-per-employee ratio of 0.6%, calibrated to replicate one standard deviation of cross-MSA dispersion in robot penetration in the data. Both economies are simulated with 10,000 realizations of preference shocks, and the slopes of the price and wage Phillips curves are estimated from simulated inflation and unemployment outcomes. The price Phillips curve flattens by 14% and the wage Phillips curve by 13% moving from low to high automation, conditional on the same-sized shock in both economies.

Q11: How does the model account for the Covid-era resurgence of high inflation despite high automation?

The paper extends the machine manufacturer’s production function to include an asymmetric convex adjustment cost that activates when investment deviates more than 5% from its steady-state level (parameterized with δ = 0.0015 and ϱ = 100). Under a small expansionary shock (0.25 percentage point decrease in unemployment), inflation rises less in the high-automation economy, consistent with a flat Phillips curve. Under a large expansionary shock (2 percentage point decrease in unemployment), the surge in robot investment triggers sharply rising machine prices, eliminating the automation outside option for marginal producers and fully restoring workers’ bargaining power — so the inflation response is identical in the low- and high-automation economies, consistent with a steep Phillips curve. The paper interprets this as a proof-of-concept consistent with post-Covid wage compression evidence for low-wage workers documented by Autor, Dube, and McGrew (2023).

Q12: What do the robustness checks establish regarding alternative explanations?

The interaction of unemployment and robot adoption remains statistically significant at the 5% level across all the robustness checks (Appendix A). These include controlling for: (i) demographic heterogeneity — shares of young (below 30) and old (above 60) individuals, female/Black/Asian labor market participation, low-education attainment shares, overall participation, and MSA-level average marginal propensity to consume (MPC); (ii) occupational structure — shares of abstract, routine, manual, and offshorable occupations; and (iii) import competition — MSA exposure to Chinese and Mexican import competition. The coefficient on the robot-unemployment interaction term is stable across specifications, with the magnitude remaining close to that in the baseline (approximately 0.0140 across all demographic robustness columns in Table A.1).

Key Concepts

Automation threshold (γ):* The paper-specific level of idiosyncratic labor efficiency at which a producer is indifferent between installing a robot and posting a vacancy. Producers with labor efficiency below γ* choose the machine technology; those above choose the labor technology. The threshold is determined by the relative profitability of the two technologies, and it shifts endogenously with wages, machine prices, and job-filling probabilities. A higher γ* means more of the production sector is automated.

Wage Setting Effect of automation: The channel through which the existence of the outside option to install robots reduces workers’ bargaining power and dampens the elasticity of wages to unemployment fluctuations. Under directed search, firms’ ability to substitute machines for labor at a lower cost constrains the wage offers they need to post, so that a given decline in unemployment generates a smaller increase in average wages in higher-automation economies.

Steady State Effect of automation: The channel through which a larger steady-state fraction of robot firms reduces the aggregate labor share, so that even a given change in wages translates into a smaller change in aggregate marginal costs and prices. This channel operates even when automation cannot change upon a shock (fixed automation baseline).

Cyclical Effect of automation: The channel through which firms actively replace workers with machines in response to expansionary shocks that raise wages, generating an endogenous dampening of labor demand and putting downward pressure on the wage increase itself. This channel requires endogenous automation choices at business-cycle frequencies.

Robot-specific technological change (ζ): In the paper’s model, the parameter governing the efficiency with which machine manufacturers transform final goods into robots. A higher ζ reduces the relative price of machines (PM/P = 1/ζ), making automation more attractive to lower-efficiency producers and raising the automation threshold γ*. In quantitative exercises, variation in ζ across steady states drives differences in the degree of automation.

Price Phillips curve slope (Ψ): In the paper’s log-linearized model, the structural coefficient linking inflation to the unemployment gap. Unlike in standard New Keynesian models — where the slope depends only on the markup and nominal rigidity — Ψ is a function of the automation threshold γ*, the matching elasticity η, the efficiency distribution parameters (γM, γH, α), and the elasticity of substitution ε. Robot adoption shifts γ* and thereby changes Ψ.

Asymmetric investment adjustment cost: An extension of the machine manufacturer’s production function that imposes convex costs when robot investment deviates above 5% from its steady-state level (parameterized by δ and ϱ). This specification makes it increasingly costly to rapidly scale up automation in response to large demand shocks, causing the machine price to spike and the automation outside option to cease being effective for marginal producers, thereby restoring workers’ bargaining power and steepening the Phillips curve during large expansionary episodes.

Spatial Implications of Telecommuting

Mon, 01 Jan 0001 00:00:00 +0000

Delventhal and Parkhomenko build a quantitative spatial model of the United States to study how the rise of telecommuting reshapes the distribution of residents, jobs, and housing costs across and within cities. The model divides the continental U.S. into 4,502 locations (defined as intersections of Census PUMAs and counties) and allows each worker to choose any residence-job pair. Workers differ by education (college vs. non-college) and occupation type (telecommutable vs. non-telecommutable). Telecommutable workers can split labor time between on-site and remote work; their remote-work intensity responds endogenously to relative remote productivity, a work-from-home aversion parameter, home floorspace costs, and commute time.

The model is calibrated to pre-2020 U.S. data (2012–2016 ACS, 2018 SIPP, 2017 NHTS). Key calibrated facts include: 33.6% of workers have telecommutable jobs (40.6% of non-college, 72.7% of college workers); remote work is nearly as productive as on-site work (relative productivity 0.99–1.00); elasticities of substitution between work modes range from 3.48 to 5.05; and work-from-home aversion parameters range from 2.48 to 3.35, indicating large non-pecuniary barriers especially for non-college workers in non-tradable sectors.

The counterfactual simulates a permanent increase in remote work driven by an 8–10% rise in remote productivity and a fall in work-from-home aversion, guided by Barrero, Bloom, and Davis (2021) survey evidence. Results show net reallocation of jobs and residences equivalent to nearly 5% of the population.

Main spatial findings exhibit a non-monotonic pattern. Telecommutable residents move away from dense, high-cost locations toward sparser areas with lower housing costs and better amenities. Non-telecommutable residents partially counteract this by centralizing — moving toward denser areas as housing costs fall near job centers. Non-tradable jobs follow telecommuters outward. Tradable jobs move in both directions: some firms relocate to low-density areas with newly accessible remote worker pools; others expand in the largest, most productive city centers as office space costs fall and the catchment area of workers widens.

In aggregate: the average worker lives 47% farther (in commuting time) from their workplace but spends 25% less time commuting, because average remote-work frequency rises by 1.1 days per week. The share of workers living in one commuting zone and working in another increases from 24.6% to 34%. Average income falls marginally by 1%, masking large gains for telecommutable workers and losses for non-telecommutable workers. Average floorspace prices fall by 2%; non-tradable prices rise by 2.6%. Overall welfare increases by an average of 12.7%, driven by gains for telecommutable workers, while non-telecommutable workers experience net losses.

The model predicts a partial reversal of the “Great Divergence”: skill sorting falls both within and across commuting zones, residential income inequality across CZs falls, and house price dispersion falls both within and across cities. These predictions are directionally consistent with 2019–2023 data.

Scope conditions: results are for a permanent shock to the full-time U.S. workforce as modeled in 2012–2016; the model does not predict the end of big cities but rather a reallocation at the margin. The model shows that the introduction of telecommuting narrows the parameter range guaranteeing a unique spatial equilibrium, because remote-capable firms can draw from a broader worker catchment area, amplifying agglomeration forces.

Q: What are the four stylized facts about pre-2020 telecommuting that discipline the model? A: Fact 1: telecommutability is higher for college workers and those in tradable industries — 68.8% of college-tradable workers can work from home versus 18.9% of non-college non-tradable workers. Fact 2: among telecommutable workers, uptake is also higher for college-tradable workers (38% actually work from home at least one day per week) than for non-college non-tradable workers (21%). Fact 3: the distribution of remote-work frequency is bimodal — most workers are either fully on-site or fully remote, with the bimodality less pronounced for college-tradable workers where hybrid (1–4 days/week) accounts for over 11% of paid workdays. Fact 4: there is a positive relationship between work-from-home frequency and distance from the job site, consistent with telework reducing effective commuting costs.

Q: How is the counterfactual shock calibrated and what drives it? A: The counterfactual raises remote-work productivity by 8–10% across all worker types and simultaneously reduces work-from-home aversion, guided by Barrero, Bloom, and Davis (2021) survey evidence that 25–30% of paid workdays will be remote post-pandemic, compared to about 8% in 2018. The authors consider both a technology shock (productivity increase) and a preference shock (aversion decrease) as mechanisms, consistent with their view that multiple hypotheses about the COVID-19 telework shock are plausible and non-exclusive.

Q: How do residents reallocate in response to the rise in telecommuting? A: Net reallocation of residents equivalent to nearly 5% of the population occurs. Telecommutable residents decentralize — moving to less dense areas with lower housing costs and better amenities — because the cost of choosing a residence far from work falls. Non-telecommutable residents partially centralize, moving toward denser locations in larger metro areas, because housing costs fall in locations with short commutes, making them more affordable.

Q: How do jobs reallocate? A: Non-tradable jobs follow the decentralization of residents (their source of demand) monotonically to less dense locations. Tradable jobs move in both directions: some firms relocate to low-density areas that can now access a larger pool of remote workers at lower real estate costs; others expand operations in the highest-productivity city centers, benefiting from both an expanded catchment of remote workers and a decline in the high cost of office space.

Q: What are the aggregate commuting implications? A: The average worker lives 47% farther in commuting time from their workplace in the counterfactual, yet spends 25% less time commuting, because average remote-work frequency increases by 1.1 days per week. The share of workers living in one commuting zone and working in another rises from 24.6% to 34%, which the authors note may call into question current administrative definitions of commuting zones and have major impacts on travel patterns.

Q: What are the welfare and income effects? A: Overall welfare increases by an average of 12.7%, but this masks very unequal distribution: telecommutable workers experience large gains while non-telecommutable workers suffer losses. Average worker income falls marginally by 1%, reflecting sizable gains for remote-capable workers offset by losses for those who cannot telecommute. Average floorspace prices fall by 2%, while non-tradable goods prices rise by 2.6%.

Q: What does the model predict for the “Great Divergence”? A: The model predicts a significant re-convergence across multiple dimensions: skill sorting falls both within and across commuting zones, residential wage inequality across CZs falls, and house price dispersion falls both within and across cities. The authors find that commuting zones with higher college shares in 2019 experienced slower growth in college shares 2019–2023, and that there is a negative correlation between average wages by CZ in 2019 and wage growth 2019–2023 — both consistent with model predictions.

Q: How does the model validate against post-2019 data? A: The authors show that their counterfactual results are positively correlated with observed changes in population, jobs, and housing rents since 2019. Within-city price variance has already converged in 2019–2023 data, consistent with model predictions. CZ-level patterns of skill concentration and wage growth also move in the direction the model predicts.

Q: Is the COVID-19 shock better described as a technology shock or a preference shock? A: The authors test both. To replicate observed changes in remote-work frequency using only a productivity shock requires a 55–99% jump in remote productivity, which yields implausibly large wage gains for remote-capable workers of 47–82%. The preference-based scenario yields results more consistent with observed data, supporting the view that a preference shock — changes in norms, attitudes, and institutional policies — is the primary driver.

Q: What happens to real estate prices when supply and amenities are held fixed? A: When real estate supply, productivity, and amenities are all held fixed, residential prices jump by 16% and commercial prices fall by 16%. The authors note this mimics the bifurcated shift in real estate values observed during the pandemic years, suggesting that supply responses and amenity adjustments are important for dampening the price effects in the full model.

Q: How does the model handle the uniqueness of spatial equilibrium, and how does telecommuting affect it? A: In a standard quantitative spatial model, agglomeration forces are dampened by the finite pool of workers willing to commute daily to a productive location. When telecommuting is introduced, productive locations can draw workers from a much broader catchment area, amplifying agglomeration forces and narrowing the range of parameter values for which a unique equilibrium is guaranteed. The authors establish conditions under which uniqueness is preserved.

Q: What are the model’s three main advantages over more stylized spatial models of remote work? A: First, by including 4,502 locations, the model can predict how far telecommuters will move from their jobs — a key variable for real estate markets and commuting patterns. Second, it can represent changes in the distribution of workers across different work-from-home frequencies, which is crucial as hybrid work has emerged as the dominant post-pandemic arrangement. Third, it predicts how the location of jobs (not just residents) changes, which has important implications for city centers.

Q: What is the overall welfare conclusion regarding non-telecommutable workers and income inequality? A: Non-telecommutable workers suffer welfare losses from the rise of remote work, even as overall average welfare rises by 12.7%. The overall income inequality — as opposed to spatial wage dispersion — does not fall. The authors note this means the spatial re-convergence does not translate into a broader reduction in income inequality, which they flag as an important limitation for policy.

Telecommutability: the ability of a worker’s occupation to be performed from home, measured using Dingel and Neiman (2020) occupational classifications; varies by education and industry, with 68.8% of college-tradable workers telecommutable versus 18.9% of non-college non-tradable workers.

Work-from-home aversion (ς): a preference parameter representing tastes, norms, and institutional policies that create non-pecuniary barriers to remote work; calibrated to range from 2.48 to 3.35 across worker types, higher for non-college workers in non-tradable sectors.

Hybrid work: an arrangement in which a telecommutable worker splits paid workdays between on-site and remote work (1–4 days per week from home); the model’s bimodal distribution of work-from-home frequency replicates the empirical observation that most workers are either fully on-site or fully remote, with hybrid most prevalent among college-tradable workers.

Catchment area: the pool of workers from which a firm can practically hire, which widens under telecommuting because workers no longer need to commute daily; this widening amplifies agglomeration forces and narrows the parameter range guaranteeing a unique spatial equilibrium.

Great Divergence: the multi-decade trend (documented in Moretti 2012 and related work) of spatially concentrating talent, income, and housing costs in a small number of large, high-skill cities; the paper predicts a partial reversal — “Great Re-Convergence” — driven by the rise of telecommuting.

Productive externalities (agglomeration): local productivity in the model depends on employment density; remote workers participate in these externalities only partially (parameter ψ ∈ [0,1]), so the shift to remote work can reduce agglomeration benefits in city centers.

Source text origin: the paper’s own classification of the text on which a summary is based (full PDF, open-access HTML, or abstract-only); the paper’s CLAUDE.md rules mandate that abstract-only summaries are blocked.

The Geography of job creation and job destruction

Mon, 01 Jan 0001 00:00:00 +0000

This paper asks why unemployment rates differ so persistently across local labor markets, and what role job creation and job destruction play in generating those differences. The authors document a comprehensive set of spatial labor market facts using administrative and survey microdata from Germany, the United States, and the United Kingdom, then build and calibrate a quantitative theoretical framework that accounts for all documented regularities.

Data and scope. For Germany, the authors use administrative data from the German employment office (universe of vacancies and unemployed, 1999–2020) and the IAB social security sample (SIAB, 2% of all workers, 2000–2017) aggregated to 194 commuting zones. For the U.S., they use BLS Local Area Unemployment Statistics (2000–2019) at commuting zones, CPS worker flows at metropolitan areas, and JOLTS vacancy data for the 18 largest MSAs (covering roughly 40% of the U.S. labor force). For the UK, they use Nomis data and Jobcentre Plus vacancy records (2004–2006) for 378 Local Authority Districts.

Empirical findings. Spatial unemployment rate differences are large and highly persistent. In Germany, the correlation of local unemployment rates across commuting zones over a 19-year span is 0.84 (West) and 0.77 (East). In the U.S., the correlation between 2000 and 2019 unemployment rates is 0.81; in the UK it is 0.76. In all three countries, local labor markets with lower unemployment are tighter (more vacancies per unemployed worker) and less productive. Firms in low-unemployment markets fill vacancies more slowly — in Germany, vacancy duration ranges from approximately 35 days in high-unemployment locations to approximately 65 days in low-unemployment locations, roughly an 85% difference.

A formal steady-state decomposition reveals that across all three countries, differences in job-separation rates account for approximately two-thirds of the cross-sectional variation in unemployment rates, while differences in job-finding rates account for roughly one-third. Specifically: Germany 62.4% separations / 33.2% job-finding; U.S. 72.0% / 32.8%; UK 64.3% / 35.8%. This primacy of separation rates in the cross-section stands in stark contrast to business-cycle dynamics, where job-finding rates account for 50–60% of unemployment fluctuations (Fujita and Ramey, 2009).

Theory. The authors embed a Diamond-Mortensen-Pissarides (DMP) model with endogenous separations — following Den Haan, Ramey, and Watson (2000) — into a Rosen-Roback spatial equilibrium framework. Locations differ in exogenous productivity; workers and firms are freely mobile; cost-of-living differences sustain the spatial equilibrium. The model is calibrated to the U.S. median-unemployment labor market (separation rate 0.0128, job-finding rate 0.2368, vacancy-filling rate 0.7365) plus the productivity differential between the 5th and 95th percentile unemployment locations (4.8% higher and 3.0% lower productivity than median, respectively). The baseline model, imposing the Hosios condition, matches the spatial patterns of separation rates, job-finding rates, tightness, vacancy duration, wages, and cost of living without targeting most of these. The decomposition in the calibrated baseline model attributes 33.5% of spatial unemployment variation to job-finding rates, compared to 32.8% in the data.

The baseline model generates a counterfactual upward-sloping Beveridge curve and cannot explain why job-finding rates dominate business-cycle fluctuations. Introducing on-the-job search (with 12% of employed workers searching each period, calibrated from Faberman et al., 2017) resolves both problems. In the extended model, job-to-job transition rates are virtually constant across local labor markets (matching the data) but strongly procyclical over the business cycle. This asymmetry amplifies the response of vacancies and job-finding rates to aggregate productivity shocks while muting the cyclical variation in separation rates. The extended model’s business-cycle decomposition attributes 54.4% of unemployment volatility to job-finding rates, within the empirical 50–60% range.

Policy implications. Under the Hosios condition, the decentralized equilibrium is efficient — large spatial differences in unemployment, tightness, and wages are efficient outcomes, not signs of mismatch. The relevant policy benchmark is not deviation of tightness from the national average but deviation from the model’s location-specific prediction conditional on local productivity.

Q: What is the central empirical puzzle the paper addresses? A: Spatial unemployment differences are large and persistent — in Germany, unemployment rates ranged from 1.9% to 11.9% across commuting zones even after 15 years of decline. These differences are not well understood theoretically, and the crucial missing empirical piece was data on job creation and vacancy filling across locations, which this paper provides for three countries.

Q: How large and persistent are cross-sectional unemployment differences in each country? A: In Germany, commuting-zone unemployment ranged from 3.6% to 24.0% in 2000 and persisted with a 19-year correlation of 0.84 (West) and 0.77 (East). In the U.S., the 2000–2019 correlation is 0.81, with unemployment as low as 1.5% and as high as 16.9% in 2000. In the UK, the 2004–2018 correlation is 0.76, with 2004 unemployment ranging from 1.8% to 13.1%.

Q: What do the data show about the relationship between unemployment and labor market tightness across locations? A: In all three countries, lower-unemployment labor markets are tighter — they have more vacancies per unemployed worker. This is documented for Germany using the universe of registered vacancies, for the U.S. using JOLTS data for 18 large MSAs, and for the UK using Jobcentre Plus administrative data. The relationship holds after controlling for local labor market composition (age, gender, education, occupation, industry shares).

Q: What do vacancy-filling rates look like across locations, and how large are the differences? A: Vacancy-filling rates are lower in low-unemployment (tight) labor markets. In Germany, the monthly probability of filling a vacancy is approximately 50% higher in high-unemployment markets than in low-unemployment markets. Completed vacancy duration ranges from about 35 days in high-unemployment locations to about 65 days in low-unemployment locations — a difference of approximately 85%. The UK data show a strikingly similar elasticity of vacancy-filling rates with respect to unemployment rates to Germany.

Q: What does the formal decomposition reveal about the sources of spatial unemployment differences? A: In a steady-state two-state decomposition, separation rates account for 62.4% (Germany), 72.0% (U.S.), and 64.3% (UK) of cross-sectional unemployment variation, while job-finding rates account for 33.2%, 32.8%, and 35.8%, respectively, with small residuals. This consistently assigns primary importance to separation rates across all three countries.

Q: Why is the primacy of separation rates in the cross section surprising, and what literature does it contrast with? A: The business-cycle literature (Fujita and Ramey, 2009; Shimer, 2012) finds that job-finding rate variation accounts for 50–60% of unemployment fluctuations over the cycle, roughly twice the contribution of separation rates. The spatial pattern is the mirror image: separations dominate. Any credible theory of spatial unemployment must rationalize both patterns simultaneously — a challenge the paper explicitly takes up.

Q: How does the baseline DMP model with endogenous separations generate the spatial patterns? A: Higher-productivity locations feature higher match surpluses. Higher surplus induces more vacancy creation and tighter markets, raising job-finding rates and lowering vacancy-filling rates. Crucially, a higher surplus means idiosyncratic shocks must be more negative to make the joint surplus negative, so fewer matches dissolve — separation rates are lower. The calibrated model reproduces the 32.8% job-finding / ~67% separation decomposition without targeting it (model yields 33.5% job-finding).

Q: What are the calibration targets and key parameter values in the baseline model? A: The model is calibrated monthly to the U.S. economy. Median-unemployment-location targets: separation rate 0.0128, job-finding rate 0.2368, vacancy-filling rate 0.7365. Productivity targets: the 5th-percentile-unemployment location is 4.8% more productive than median, and the 95th-percentile-unemployment location is 3.0% less productive. Key calibrated values include matching elasticity alpha = 0.4711 (equal to worker bargaining power under Hosios), matching efficiency m = 0.4371, vacancy posting cost kappa = 0.3070, and flow nonmarket value z = 0.9072.

Q: What are the two shortcomings of the baseline model, and how does on-the-job search resolve them? A: The baseline model generates a counterfactual upward-sloping Beveridge curve and cannot generate the asymmetry between cross-sectional and business-cycle drivers of unemployment. Adding on-the-job search (fraction phi = 0.12 of employed workers searching, calibrated from Faberman et al., 2017) resolves both. It corrects the Beveridge curve by allowing the model to match the spatial vacancy-unemployment relationship, and it introduces procyclical job-to-job mobility that amplifies the cyclical response of job-finding rates while dampening cyclical separation rate variation.

Q: How do job-to-job transition rates differ across space versus over the business cycle, and why does this matter? A: Job-to-job rates are virtually constant across the cross-section of local labor markets (the extended model is calibrated to match this). But they are strongly procyclical — high in booms, low in recessions, about as volatile as job-finding rates over the cycle. In a boom, more employed workers search, spurring vacancy creation, which raises both vacancy-filling probability (making vacancies easier to fill) and job-finding probability for the unemployed, amplifying the cyclical job-finding rate response while muting the cyclical separation rate response.

Q: What does the extended model predict for business-cycle dynamics? A: The model with on-the-job search and aggregate productivity shocks (parameterized following Hagedorn and Manovskii, 2008) generates unemployment and vacancy rates that are an order of magnitude more volatile than productivity — matching the data. Labor market tightness is about twice as volatile as unemployment, as in the data. The Fujita-Ramey decomposition in the model attributes 54.4% of unemployment volatility to job-finding rates, which falls within the empirical range of 50–60%.

Q: What is the paper’s efficiency result and its policy implication? A: Under the Hosios condition (imposed in calibration), the decentralized equilibrium is efficient: job creation and destruction are privately efficient in each market, and free mobility of workers and firms ensures efficient spatial allocation. Therefore, large observed differences in unemployment, tightness, and wages across locations are not evidence of inefficiency. The relevant signal for policy is not deviation from the national average but deviation from the model’s location-specific prediction conditional on productivity. Locations where data deviate from model predictions are candidates for policy intervention.

Q: Do the spatial patterns survive controls for worker and firm composition? A: Yes. The authors regress labor market tightness and vacancy-filling rates on local unemployment rates and a full set of composition controls (age, gender, education, occupation, and industry shares) derived from the IAB microdata for Germany, along with year fixed effects. The relationship between local unemployment and both tightness and job-filling rates remains highly statistically and economically significant after these controls, for both Germany and the U.S.

Q: How does the model handle wages and cost of living, and does it match the data? A: Wages are determined by state-contingent generalized Nash bargaining with worker bargaining power eta. Cost-of-living differences are backed out as the values needed to sustain the spatial equilibrium (Rosen-Roback). Neither wages nor costs of living are calibration targets in the cross section, yet the model closely matches the empirically observed wage gradient across local labor markets and the negative correlation between cost of living and local unemployment (using Economic Policy Institute Family Budget Calculator data).

Labor market tightness: The ratio of vacancies posted in a local labor market to the number of unemployed workers in that market; the paper documents that tightness is systematically higher (more vacancies per unemployed worker) in lower-unemployment locations across all three countries.

Job-separation rate (EU rate): The share of employed workers who transition from employment to unemployment in a period; in the paper’s framework, this is endogenously determined by the idiosyncratic match productivity threshold below which the joint match surplus turns negative, and it is the primary driver of spatial unemployment differences (accounting for roughly two-thirds of cross-sectional variation).

Job-finding rate (UE rate): The share of unemployed workers who transition from unemployment to employment in a period; in the paper’s framework, this is higher in tighter (lower-unemployment) markets, but accounts for only roughly one-third of spatial unemployment variation — the opposite of its dominant role in business-cycle fluctuations.

Spatial Beveridge curve: The cross-sectional relationship between vacancy rates and unemployment rates across local labor markets; in the data it is downward sloping (low-unemployment locations have both high vacancies and low unemployment), which the baseline model fails to capture but the extended model with on-the-job search reproduces.

Endogenous separation threshold: The location-specific minimum idiosyncratic match productivity below which the joint match surplus becomes negative and the worker-firm pair dissolves; this threshold is lower (tolerates a wider range of idiosyncratic shocks) in higher-productivity locations because the average surplus is larger, generating lower separation rates in more productive locations.

Spatial equilibrium (Rosen-Roback): The equilibrium condition in which differences in local costs of living adjust to make workers and firms indifferent across locations, sustaining persistent productivity-driven differences in wages and unemployment as equilibrium outcomes rather than disequilibrium phenomena.

Procyclical on-the-job search: The mechanism by which the fraction of employed workers actively searching — and thus the rate of job-to-job transitions — is approximately constant across the cross-section of local labor markets but strongly procyclical over the business cycle. This asymmetry is the key to reconciling why job-finding rates drive business-cycle unemployment variation while separation rates drive spatial unemployment variation.

Hosios condition: The parametric restriction equating the unemployment elasticity of the matching function (alpha) and the workers’ Nash bargaining weight (eta); when satisfied, job creation is efficient in every local labor market. The paper imposes this condition deliberately to demonstrate that the decentralized equilibrium is efficient despite large spatial differences in outcomes.

The Impact of EITC on Education, Labour Market Trajectories, and Inequalities

Mon, 01 Jan 0001 00:00:00 +0000

This paper studies the effect of the Earned Income Tax Credit (EITC) on educational attainment and labor market trajectories through two complementary approaches. Using policy discontinuities at U.S. state borders—exploiting variation in state EITC generosity set as a percentage of the federal EITC—the paper finds that an increase in the state EITC leads to a statistically significant increase in the high school dropout rate. The mechanism is that a tax credit targeted at low-wage (low-skilled) workers increases the value of low-skilled employment and reduces the relative return to schooling, generating a powerful disincentive to pursue long-term studies. A structural life-cycle matching model with directed search and endogenous educational choices, search intensities, hirings, hours worked, and separations is developed to quantify the long-run general equilibrium effects: in the long run, EITC reduces the proportion of high-skilled workers, with ambiguous effects on income inequality that depend on the competing channels through which EITC affects both the supply and demand sides of the labor market.

Summary based on a working paper version, AI-assisted and human-reviewed. See the linked published article for the authoritative version.

In depth

Q1. What is the empirical strategy for identifying the effect of EITC on education?

The paper identifies the causal effect of state EITC on education by exploiting policy discontinuities at U.S. state borders, comparing contiguous PUMA pairs on opposite sides of state borders that differ in state EITC generosity. State EITC rates are set as a percentage of the federal EITC and have varied considerably since the mid-1980s. Borrowing from the minimum wage literature (Dube et al., 2010; Hagedorn et al., 2015), the border-discontinuity design controls for local labor market conditions that vary continuously across state borders while isolating the effect of the discrete EITC policy difference.

Q2. What is the labor market mechanism linking EITC to education?

EITC raises the value of low-skilled employment by directly increasing the earnings of low-wage workers, which in turn reduces the relative return to investing in education, generating a powerful disincentive to pursue long-term studies. When directed search is present—as supported by recent empirical studies—educational decisions affect both job-finding probabilities and labor incomes over the life cycle. EITC’s subsidization of low-skilled work contracts the education premium in this framework, making the forgone earnings cost of staying in school larger relative to the low-skilled employment option supported by the EITC.

Q3. What does the life-cycle matching model contribute?

The structural life-cycle matching model with directed search and endogenous educational choices, search intensities, hirings, hours worked, and separations quantifies the general equilibrium and long-run effects of EITC that purely reduced-form studies cannot capture—including the feedback of an expanded low-skilled labor force on equilibrium wages and job creation. The model endogenizes labor demand, capturing both household responses (education, hours, search intensity) and firms’ responses (job creation and destruction). It is solved and estimated to replicate the life-cycle profile of labor market variables.

Q4. What are the long-run implications for inequality?

In the long run, EITC reduces the proportion of high-skilled workers in the economy, with ambiguous effects on income inequality because of offsetting channels: EITC directly increases earnings of low-skilled workers, but by expanding the supply of low-skilled labor it may also depress low-skilled wages; additional channels through unemployed workers’ search effort and employed workers’ hours further complicate the net effect. The model is used to determine the optimal design of the EITC that balances the income-support objective against these unintended long-run effects.

Key concepts

state EITC : a supplement to the federal Earned Income Tax Credit set as a fixed percentage of the federal credit; varies across states; used in this paper as the identification source for the effect of EITC generosity on education via border discontinuities. directed search : a labor market framework in which workers and firms direct their search to specific submarkets with posted wages; in this setting, educational choice affects both job-finding probabilities and wages over the life cycle, amplifying the disincentive effects of EITC on education relative to random-search models. education-EITC disincentive : the mechanism by which EITC targeted at low-wage workers raises the relative value of low-skilled employment and reduces the return to schooling, generating an increase in high school dropout rates as a side effect of the anti-poverty policy.

The price of intelligence: How should socially-minded firms price and deploy AI?

Mon, 01 Jan 0001 00:00:00 +0000

Leading AI firms such as OpenAI and Anthropic publicly claim dual mandates of profit and social welfare, raising the question of whether—and how—a social mandate should change their pricing and deployment decisions. This paper provides a framework to answer this question, deriving a Modified Lerner Rule for socially minded AI firms that extends the standard profit-maximizing Lerner Rule to incorporate incentives for aggregate efficiency, distributional concerns, and labor market stability. Using U.S. data on 525 detailed occupations, the paper evaluates optimal pricing and deployment paths for an AI capable of replacing human labor in each job at 50% of the cost. The main finding is that a welfarist firm (one that values profits and social welfare) should price closer to marginal cost because, for the jobs considered, efficiency gains outweigh distributional concerns—AI does not primarily displace low-income workers. A conservative firm focused on labor market stability should price above the profit-maximizing level in the short run, but not in the long run. The paper concludes that the most pro-social course of action for AI firms with market power is to refrain from exercising that power, and that proposals to tax AI to protect labor markets miss the counteracting role of market power.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. What is the Modified Lerner Rule and what motives does it capture?

The Modified Lerner Rule states (P − MC)/P = M/ε, where ε is the demand elasticity and M is a modifier that summarizes the motives of the socially minded firm; M = 1 corresponds to the standard profit-maximizing Lerner Rule. The modifier M reflects four distinct considerations: (1) profit motives push M toward 1; (2) aggregate efficiency considerations push M toward 0 (marginal-cost pricing, which maximizes the “size of the pie”); (3) distributional concerns (who benefits from AI) can be positive or negative depending on whether AI substitutes for high- or low-income workers; and (4) the incentive to minimize labor market disruptions pushes M above 1 in the short run, because the cost of labor disruption is higher while workers are still adjusting, but not in the long run. The formula is derived in a general equilibrium model where the AI firm has a monopoly over an AI capable of replicating human skills.

Q2. What does the welfarist case imply for pricing?

A firm that values both profits and aggregate social welfare should price closer to marginal cost than the profit-maximizing firm, because for all 525 occupations considered, the aggregate efficiency gains from AI adoption outweigh the distributional costs. This finding reflects the structure of AI’s labor market effects: since AI does not primarily displace low-income workers in the US occupational data used, distributional concerns do not push toward restricting AI access. The welfarist firm therefore faces a dominant efficiency motive to expand access by pricing down toward marginal cost, accepting lower profits in exchange for greater welfare gains from AI adoption.

Q3. What does the conservative case imply?

A firm focused solely on labor market stability should price above the profit-maximizing level in the short run, because restricting AI deployment reduces the speed of worker displacement; but this above-profit-maximizing pricing is optimal only temporarily, and converges toward profit-maximizing pricing in the long run as workers adjust. The intuition is that the cost of disrupting the labor market is highest when workers have not yet adjusted—their human capital is not yet redeployed—so a conservative firm acts as a gradual deployer. This conservative pricing is distinct from the welfarist case: the conservative motive restricts access more than a welfarist mandate, since it is willing to sacrifice efficiency to slow disruption.

Q4. Why does the paper argue against taxing AI?

The paper argues that proposals to tax AI firms to protect workers from displacement overlook the fact that AI firms may already exercise significant market power, which protects workers by restricting AI supply below the efficient level. Adding a tax on top of an already-restricted supply would harm consumers (who face high AI prices and limited access) without providing meaningful additional protection for workers (since output is already suppressed by market power). The paper’s analysis implies that the first-order social priority is to have AI firms refrain from exercising their market power—by pricing closer to marginal cost—rather than further restricting supply through taxation.

Key concepts

Modified Lerner Rule : (P − MC)/P = M/ε, where M captures a socially minded firm’s weighting of profit, aggregate efficiency, distributional, and stability motives; the paper’s key pricing formula, derived from a GE model with a monopoly AI firm.

welfarist vs. conservative firm : two polar cases: the welfarist firm maximizes a weighted sum of profits and aggregate welfare (implying near-marginal-cost pricing); the conservative firm prioritizes labor market stability (implying above-profit-maximizing pricing in the short run to slow displacement).

labor disruption cost : the welfare cost to workers of being displaced by AI, which is higher in the short run when workers must reallocate across jobs or sectors and lower in the long run after adjustment; the paper’s formal treatment of this cost motivates the conservative firm’s gradual deployment strategy.

The role of wage expectations in the labor market

Mon, 01 Jan 0001 00:00:00 +0000

This paper develops a Mortensen-Pissarides (DMP) search and matching model with internally rational (IR) agents who hold subjective beliefs about wages rather than perfect knowledge of the Nash bargaining outcome. The standard DMP model struggles with two empirical regularities: high volatility of U.S. labor market variables relative to productivity, and a near-zero correlation between labor market tightness and productivity post-1989. The IR model significantly improves alignment with U.S. labor market data relative to the standard rational expectations benchmark, by generating a self-referential belief mechanism: shifts in beliefs about the future returns to labor affect current wages, which agents use to update beliefs. Wage expectations in the model are consistent with European Commission professional forecasters data, and an econometric test rejects the rational expectations null hypothesis for survey real wage expectations.

Summary based on a working paper version, AI-assisted and human-reviewed. See the linked published article for the authoritative version.

In depth

Q1. What is internal rationality and how does it differ from standard rational expectations?

Internal rationality (IR) means agents know all internal aspects of their optimization problem and maximize their objectives given their knowledge, but lack perfect information about the equilibrium wage function that emerges from Nash bargaining; they therefore hold subjective beliefs about wages. Under standard rational expectations, workers and firms know the exact wage function from Nash bargaining. Under IR, they have limited foresight about the outcome of wage negotiations and use a subjective model to form wage expectations. This is a small but disciplined departure from RE: the paper considers belief systems implying only a small deviation from rational expectations that match aspects of survey wage expectations.

Q2. What is the empirical failure of the standard DMP model that motivates the paper?

The standard DMP model fails on two counts: it cannot reproduce the high observed volatility of unemployment, vacancies, and market tightness relative to productivity, and it cannot generate the near-zero post-1989 correlation between productivity and labor market tightness. The first failure—the Shimer (2005) puzzle—has attracted extensive research, but the near-zero tightness-productivity correlation has been largely neglected. The paper shows that allowing for small deviations from rational expectations in the form of internal rationality resolves both puzzles simultaneously.

Q3. What is the self-referential belief mechanism and how does it generate extra dynamics?

The model has a self-referential mechanism: shifts in beliefs about future returns to labor affect current wages, and agents use realized wages to update their beliefs about future wages; this creates an additional dynamic source beyond technology shocks that helps match the data. When firms and workers revise beliefs about future wages upward, current wages rise through the Nash bargaining outcome (since reservation values of both parties shift); this realization then feeds back into updating beliefs, generating wage and employment dynamics not tied to current productivity. This mechanism provides a microfoundation for previous adaptive learning models of unemployment.

Q4. What is the empirical validation of the model’s wage expectations?

Wage expectations in the IR model are validated against survey data from European Commission professional forecasters, and an econometric test rejects the rational expectations null hypothesis for real wage expectations from survey data. The consistency between model-implied and surveyed wage expectations provides external validation for the IR departure from RE, showing that the subjective beliefs assumed in the model correspond to beliefs actually held by professional forecasters rather than to arbitrary deviations.

Key concepts

internal rationality (IR) : a bounded rationality concept in which agents fully optimize given their beliefs and knowledge of their own decision problem, but lack perfect knowledge of equilibrium objects (here, the wage function emerging from Nash bargaining); allows small, disciplined deviations from rational expectations. DMP model : the Mortensen-Pissarides-Diamond search and matching model; the standard theory of equilibrium unemployment; criticized for generating insufficient labor market volatility relative to productivity (the Shimer puzzle) and for counterfactual positive tightness-productivity correlation. belief shock : an exogenous shift in agents’ subjective beliefs about future wages; generates employment and wage dynamics independently of current productivity shocks via the self-referential mechanism; introduced as an additional structural shock in the IR-DMP model.

What's driving the decline in entrepreneurship?

Mon, 01 Jan 0001 00:00:00 +0000

The entrepreneurship rate in the United States—defined as the share of the labor force who own and actively manage a business with at least ten employees—declined by 26% between 1987 and 2015, a decline mirrored in the firm entry rate and not explained by compositional changes in the economy or driven by a small number of sectors. This paper addresses what caused this broad-based decline using Current Population Survey data, two new empirical facts, and a dynamic general equilibrium model of occupational choice. The first new fact is that the decline was larger for higher-education groups (35% for those with more than a college degree versus 2.4% for those without a high-school diploma), indicating that the driving force is not skill-neutral. The second new fact is that the size distribution of entrepreneur firms has been stable, so the entrepreneurship decline represents a shrinkage of the entrepreneurial sector relative to the economy. Estimating the contribution of four candidate explanations—skill-biased technical change (SBTC), increasing regulation, technology-driven increases in fixed and entry costs, and technology-driven productivity advantages for large firms—the paper finds that increasing entry costs account for most of the decline in both the entrepreneurship share and the firm entry rate, with empirical evidence pointing to both regulation and technology as sources of these higher costs.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. What does the model of occupational choice capture, and how are the explanations identified?

The dynamic general equilibrium model allows individuals to choose between working as an employee (earning wages) and being an entrepreneur (paying fixed and entry costs, then operating a firm); the model generates predictions about the entrepreneurship rate, firm entry rate, and the distribution of entrepreneur firm sizes across groups, which the data discipline. By requiring the model to match changes in entrepreneurship along multiple dimensions—including the education-gradient fact and the stable size distribution—the author can separately identify the contribution of each candidate mechanism. SBTC operates through wages (raising opportunity cost of entrepreneurship for skilled workers); entry-cost increases reduce the number of new entrepreneurs regardless of skill; productivity advantages for large firms shift the size distribution; and regulation/technology-driven fixed-cost increases reduce incumbent-entrepreneur survival.

Q2. Why does skill-biased technical change fail to explain the level decline?

SBTC raises wages for high-skill workers, which could in principle explain why fewer of them choose entrepreneurship; and indeed SBTC is found to have tilted entrepreneurship toward less-educated people. However, SBTC cannot explain the decline in the aggregate entrepreneurship rate because: it does not reduce the incentive to be an entrepreneur for lower-skill workers (who are relatively unaffected), and the stable size distribution of entrepreneur firms is inconsistent with SBTC (which would tend to shift composition rather than reduce overall entrepreneurship). The model confirms that SBTC explains the education gradient but contributes little to the overall level decline.

Q3. What is the role of entry costs, and what drives them?

Increasing entry costs are found to explain most of the decline in the share of people who are entrepreneurs and most of the decline in the firm entry rate; the data also reject the hypothesis that entry-cost increases were accompanied by large changes in entrepreneur firm size, consistent with the observed stability of the size distribution. Empirical evidence suggests two sources of higher entry costs: increasing regulation (occupational licensing, tax-code complexity, zoning restrictions) and technology changes that increase the fixed investments required to operate (e.g., adoption of IT systems). The paper does not fully separate these two sources but presents evidence consistent with both operating simultaneously.

Q4. What is the role of increasing productivity of large firms?

Increasing productivity of large, non-entrepreneurial (e.g., publicly listed) firms matters little for the entrepreneurship rate or the firm entry rate, but has driven most of the reallocation of labor away from entrepreneur businesses. This is because the productivity advantage of large firms shifts the scale of production without necessarily changing who becomes an entrepreneur, largely leaving the extensive margin of entrepreneurship intact while reducing the share of aggregate economic activity attributable to the entrepreneurial sector.

Key concepts

entrepreneurship rate : the share of the labor force who own and actively manage a business with at least ten employees, the paper’s main measure of entrepreneurship, which declined 26% from 1987 to 2015 in the CPS data.

entry costs : the one-time costs required to establish a new entrepreneurial business; the paper finds these rose over the sample period due to both regulation and technology, and identifies them as the primary driver of the entrepreneurship decline.