## wp1787 ## Source details **Canonical URL:** [wp1787](https://www.imf.org/-/media/files/publications/wp/2017/wp1787.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2017/wp1787.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2017/wp1787.pdf.json) --- ### Overview and scope - Structure: empirical description of reforms; theoretical model; measures of recession cost (welfare and output); calibration strategy; quantitative results; robustness checks; conclusions. - Empirical focus: German Labor Market Reforms 2003–2005 (Hartz I–IV), with emphasis on Hartz III (JSA/placement) and Hartz IV (UI reduction). - Analytical components: model with search unemployment and incomplete markets; recursive equilibrium characterization; calibration to German data; decomposition of recession costs into permanent, transitory, job-destruction, and matching-efficiency components. ### Empirical findings on the Hartz reforms and labor-market patterns - Timing and core objectives: - Hartz I+II: January 2003; Hartz III: January 1, 2004; Hartz IV: January 1, 2005. - Objectives: increase matching efficiency (JSA), activate unemployed (labor supply), increase labor demand (temporary work deregulation, subsidies). - Hartz III (modeled as an 8 percent increase in search efficiency): - Evidence: restructuring and vouchers increased matching efficiency by at least 5 percent and perhaps up to 10 percent; vouchers improved job finding rates of affected workers by about 10−30 percent; with 20 percent of unemployed receiving vouchers, unconditional job finding rate increase implied 2−6 percent. - Paper simulates Hartz III as an 8 percent increase in search efficiency. - Hartz IV (modeled as an 11 percentage point reduction in net replacement rate for long-term unemployed): - Net replacement rate for long-term unemployed fell from 0.57 (2000–2004) to 0.46 (2005) — reduction by 11 percentage points; short-term net replacement rate essentially unchanged. - Paper simulates Hartz IV as reducing long-term net replacement rate by 11 percentage points. - Time series evidence (job finding rates 2000–2012): - Long-term unemployed: average job finding rate 2000–2003 = 6.3 percent; 2007–2012 = 9.3 percent (increase: almost 48 percent). - Short-term unemployed: average job finding rate 2000–2003 = 24 percent; 2007–2012 = 37 percent (increase: 54 percent). - Beveridge curve: substantial inward shift after Hartz III/IV; quantitative attribution in Section 6: the two reforms together account for most of non-cyclical rise in job finding rates and two-thirds of the shift in the Beveridge curve. - Unemployment rate: peaked near almost 11 percent in 2005, fell to 7.5 percent in 2008, reached 4.4 percent at end-2015; estimated non-cyclical decline since 2005 at least 3 percentage points and perhaps 5 percentage points. ### Theoretical framework and key analytical results - Model features: - Tractable incomplete-market model with search unemployment; unemployed choose search intensity l; unemployment can cause permanent skill scarring via skill depreciation δ_s. - Job destruction rates and job search efficiency vary exogenously with business cycle state S ∈ {R,N}. - Government provides JSA (x_s with cost λ_s(x_s)) and UI benefits b_s financed by linear labor income tax τ; b, x, τ do not depend on S. - When cost of financial intermediation α is large enough, equilibrium with no asset trade exists; aggregate state reduces to unemployment rates and human-capital shares (four-dimensional with short-term and long-term unemployment). - Main theoretical propositions: - Improvement in JSA (↑x) or reduction in UI (↓b) decreases the output cost of recessions ∆y (under specified assumptions). - Welfare cost of recessions ∆ is ambiguous with respect to JSA and UI changes because ∆ = ∆y + ∆r + ∆e (output cost + risk cost + effort cost); ∆r is generally positive, ∆e can be positive or negative. - In special-case settings (single unemployment type, linear job-finding in effort and x, i.i.d. S, β sufficiently small): ∂∆y/∂x < 0 and ∂∆y/∂b > 0. ### Calibration choices and baseline parameter targets - Period: one quarter; aggregate state S ∈ {R,N}. - Long-term unemployment definition: spells > 12 months; transition π_lu|su = 0.25. - Search technology (linear in l and x with cyclical factor Ψ(S)): - Data average quarterly transition probabilities (Federal Employment Agency, 2000–2004): ̄πe|lu = 0.06 → xlu = 0.084; ̄πe|su = 0.24 → xsu = 0.127. - πsu|lu = 0.190 to match long-term share = 50 percent (2000–2004). - Average job destruction rate ̄πu|e = 0.167 to match unemployment rate 10 percent (2000–2004). - Search disutility ds(l) = d0 l^γ + d1,s with d0 = 1, d1,e = 0, d1,su = d1,lu. - Target micro elasticity of job search w.r.t. UI for short-term unemployed: −0.7 ⇒ γ = 1.317 ⇒ implied Frisch-elasticity κ = 3.155 (via γ = 1 + 1/κ). - Skill depreciation during unemployment: - Baseline: δh,su = δh,lu = 2.5 percent quarterly. - Wage growth and risk: - Wage shock ln(1+ε) normal; μ set so average annual growth = 1 percent; σ = 0.075 quarterly. - Unemployment benefits (baseline): - Short-term net replacement targeted higher than OECD raw rate to avoid implausibly large consumption drops: bsu = 0.85 (baseline); blu = 0.79 to match short-term vs long-term net replacement difference target of 0.06 (OECD 2000–2004). - Discount factor and intermediation cost: - β = 0.99 quarterly; implied quarterly lending interest rate rf = 0.73 percent. - Minimal quarterly spread αmin = 0.36 percent yields no-asset-trade equilibrium. ### Quantitative results — Output cost of recessions (Section 6.4) - Baseline (Pre Reform) output cost ∆y = 2.014 percent of lifetime consumption. - Reform scenarios ∆y (values and percentage deviations from pre-reform): - Post Hartz-III-Reform: ∆y = 1.728 (14.2%). - Post Hartz-IV-Reform: ∆y = 1.745 (13.6%). - Post Hartz-III&IV-Reform: ∆y = 1.510 (25.0%). - Decomposition components (Percent) — Table 1 entries: - Pre Reform: ∆y 2.014, ∆perm y 0.651, ∆trans y 1.362, ∆des y 1.857, ∆eff y 0.156 - Post Hartz-III-Reform: ∆y 1.728, ∆perm y 0.550, ∆trans y 1.178, ∆des y 1.698, ∆eff y 0.030 - Post Hartz-IV-Reform: ∆y 1.745, ∆perm y 0.807, ∆trans y 0.939, ∆des y 1.600, ∆eff y 0.145 - Post Hartz-III&IV-Reform: ∆y 1.510, ∆perm y 0.515, ∆trans y 0.995, ∆des y 1.483, ∆eff y 0.027 - Key mechanisms and facts: - Majority of output cost driven by increase in job destruction rates during recessions: job-destruction component accounts for more than 90 percent of total cost. - Temporary component ≈ two thirds of total cost; permanent (scarring) ≈ one third. - Reform-induced increases in non-cyclical job finding rates drive reductions in ∆y; Hartz III and Hartz IV together reduce ∆y by 25.0 percent. ### Quantitative results — Welfare cost of recessions (Section 6.5) - Welfare cost ∆ and decomposition into ∆y (output), ∆r (risk), ∆e (effort) — Table 2 entries (Percent): - Pre Reform: ∆ 1.310, ∆y 2.014, ∆r 0.244, ∆l −0.947 - Post Hartz-III-Reform: ∆ 1.205 (8.0%), ∆y 1.728, ∆r 0.199, ∆l −0.722 - Post Hartz-IV-Reform: ∆ 1.277 (2.5%), ∆y 1.745, ∆r 0.209, ∆l −0.676 - Post Hartz-III/IV-Reform: ∆ 1.181 (9.8%), ∆y 1.510, ∆r 0.179, ∆l −0.508 - Interpretation: - Pre-reform welfare cost ∆ = 1.310 percent of lifetime consumption (smaller than output cost ∆y = 2.014 percent). - Risk cost ∆r positive (0.244 percent): recessions increase consumption volatility. - Effort cost ∆e negative (−0.947 percent): recessions reduce search effort relative to counterfactual, providing a large effort “gain” that offsets risk cost in baseline. - Reform impacts: Hartz III reduces welfare cost by 8.0 percent; Hartz IV reduces welfare cost by 2.5 percent; combined Hartz III&IV reduce welfare cost by 9.9 percent. Welfare reductions are substantially smaller than output-cost reductions because higher search effort induced by reforms raises the effort cost component. - Heterogeneity: - Pre-reform welfare cost by type: employed 1.313 percent; short-term unemployed 1.300 percent; long-term unemployed 1.271 percent. Reform-induced reductions similar across types. - Timing sensitivity: - If recessions eliminated starting in a recession (S0 = R), pre-reform welfare cost rises to 1.402 percent; combined reforms reduce it by 9.3 percent to 1.272 percent. ### Robustness analysis and model extensions (Section 7 and Appendix) - Sensitivity to key parameters: - Curvature γ (Frisch-elasticity) and skill depreciation δh have modest effects on percentage reductions from reforms; elasticity of job search is materially important. - Example alternatives: - γ = 2 (Frisch = 1): combined reforms reduce output cost by 22.6 percent (1.836 → 1.422) and welfare cost by 9.8 percent (0.954 → 0.861). - δh = 0.0125 quarterly (half baseline): combined reforms reduce output cost by 22.9 percent (1.313 → 1.013) and welfare cost by 3.1 percent (0.920 → 0.892). - Elasticity target −0.5 (vs baseline −0.7): combined reforms reduce output cost by 19.6 percent (1.832 → 1.473) and welfare cost by 8.2 percent (1.294 → 1.188). - DMP extension (vacancy posting, Nash bargaining): - Calibration: ψ = 0.5; bargaining power = ψ (Hosios condition); vacancy cost parameters chosen to match job filling rates and decline in job finding rates during pre-reform recessions. - Main quantitative effects: - Extension increases both output and welfare costs of recessions relative to baseline. - Extension amplifies Hartz IV effects (UI reduction) and attenuates Hartz III effects (JSA improvement) relative to baseline. - Table 3 (Diamond-Mortensen-Pissarides specification) — output and welfare costs (Percent): - Pre Reform: ∆DMPy 2.712, ∆DMP 2.178 - Post Hartz-III-Reform: ∆DMPy 2.646 (2.4%), ∆DMP 2.159 (0.9%) - Post Hartz-IV-Reform: ∆DMPy 2.108 (22.3%), ∆DMP 2.002 (8.1%) - Post Hartz-III/IV-Reform: ∆DMPy 2.069 (23.7%), ∆DMP 1.996 (8.4%) - Additional channels: - Wedge between micro- and macro-elasticities arises in extended model due to endogenous tightness Θ; for UI changes macro-elasticity can exceed micro-elasticity (example: −0.8 vs −0.7); for JSA changes macro response can be much smaller than micro response (example micro 0.41 vs macro 0.08). - Match-quality channel (UI affects productivity): modeling a productivity loss when unemployed workers find jobs after reductions in UI can weaken Hartz IV’s beneficial effect on recession costs (example: Hartz IV reduces ∆y from 2.014 to 1.877 percent when productivity loss introduced). ### Policy implications and interpretation - Primary quantitative conclusion: - Hartz III and Hartz IV reforms substantially increased labor-market fluidity in the calibration and reduced the output cost of recessions markedly (combined reduction of 25.0 percent in baseline), with a substantially smaller reduction in welfare cost (about 9.9 percent). - Mechanism: - Higher JSA (x) or lower UI (b) raise job finding rates across the cycle, reducing both temporary unemployment spikes in recessions and permanent scarring from long unemployment spells. - Welfare ambiguity and trade-offs: - Although output costs unambiguously decline with higher x or lower b under stated assumptions, welfare effects are ambiguous because increased search effort during recessions can generate welfare losses that offset output gains. - Model assumptions (moderate risk aversion: log-utility; absence of aggregate demand channel / automatic stabilizers) imply that cuts in UI could be more costly if risk aversion is higher or if UI provides automatic stabilization. - Recommendations for policy assessment: - Evaluations should consider both output-cost and welfare-cost channels, explicitly accounting for effort and risk costs. - Empirical priorities: better estimates of job-search elasticities and of matching technologies (vacancy posting responses and match-quality effects) are crucial to pin down magnitudes and the wedge between micro and macro elasticities. - Further research: apply framework to other countries; consider more general UI designs with incentive-compatibility; integrate short-run stabilization and long-run structural policy design. *Source: wp1787 - IMF Working Paper (sections 1–7, Appendix, and Tables/Figures listings).* ### 1. Introduction ........................................................................................................ ### wp1787 - 1. Introduction ........................................................................................................ ### Overview and scope - Presents the structure of the paper and main analytical components through numbered sections and subsections. - Organizes the study into empirical description of reforms, a theoretical model, measures of recession cost, calibration strategy, quantitative results, robustness checks, and conclusions. ### Empirical focus - Examines German Labor Market Reforms 2003-2005 with subtopics: - Historical Background - Hartz III Reform - Hartz IV - Time Series Evidence ### Theoretical framework - Develops a model with subsections: - Workers - Firms - Equilibrium - Equilibrium Characterization - Computation and Tractability ### Quantitative evaluation - Analyzes the Cost of Recessions with distinct treatments of: - Welfare Cost of Recessions - Output Cost of Recessions - A Decomposition - Labor Market Institutions and the Cost of Recessions - Provides Calibration details across multiple dimensions: - General Specifications - Search Technology and Mean Transition Rates - Search Preferences and Search Elasticity - Skill Loss During Unemployment - Wage Growth and Wage Risk - Unemployment Benefits - Discount Factor and Cost of Financial Intermediation - Cyclical Variations in Job Finding and Job Destruction Rates - Unemployment and Output Dynamics during Recessions - Reports Quantitative Results, including: - Reform Effects on Model Parameters - Long-Run Reform Effects on Job Finding Rates and Unemployment - Reform Effects on Dynamic Response to Recession Shock - Output Cost of Recessions - Welfare Cost of Recessions ### Robustness and validation - Contains Robustness Analysis with topics: - Changes in Calibration Targets - Search and Matching with Vacancy Posting - Wedge between Micro-and Macro-Elasticity - Unemployment Insurance and Match Quality ### Supporting materials - Lists Tables related to: - Output Cost of Recessions - Welfare Cost of Recessions - Output Cost of Recessions – Diamond-Mortensen-Pissarides - Lists Figures including time-series and diagnostic plots: - Output during Pre-Reform Recessions and Great Recession - Average Net Replacement Rate 201-2010 - Quarterly Job Finding Rates by Duration of Unemployment Spell 2000-2011 - Beveridge Curve 2000-2015 - Unemployment Rate 1970-2015 - Cyclical Unemployment during Pre-Reform Recessions: Data and Model - Output during Pre-Reform Recessions: Data and Model - Cyclical Unemployment during Pre-Reform and Post-Reform Recessions - Output during Pre-Reform and Post-Reform Recessions ### Conclusion - Concludes with section 8 and a References section. *Source: wp1787 - 1. Introduction (IMF working paper table of contents and lists of tables and figures).* ### 1. Introduction ### 1. Introduction ### Motivation and empirical patterns - The Great Recession generated intense debate about the economic and social cost of recessions; recent empirical contributions find that the output costs of recessions in the US and other advanced economies are large. - Figure 1 compares the output path during a typical pre-reform recession in Germany (before the 2003-2005 Hartz reforms) with the output path during the Great Recession in 2008/2009 and highlights two key differences: - The initial drop in output during the Great Recession was much larger than the initial output loss during previous (pre-reform) recessions. - The recovery following the Great Recession was very swift, whereas the rebound after the typical pre-reform recession was meager. - The paper argues that the Hartz reforms of 2003-2005 (notably Hartz III and Hartz IV) contributed to a more fluid German labor market and a swifter recovery after the Great Recession. ### Model and analytical approach - The paper develops a tractable incomplete-market model with search unemployment and provides a characterization of recursive equilibria. - Key model features: - Unemployed workers choose the intensity of job search; unemployment leaves permanent scars. - Job destruction rates and job search efficiency vary exogenously with business cycle conditions. - Government provides job search assistance (JSA) and unemployment insurance (UI) at levels independent of business cycle conditions. - Recessions are costly because they generate temporary and permanent output losses and have additional welfare consequences via distributional effects and costly search effort. - Analytical strategy: 1. Derive characterization of recursive equilibria in the model. 2. Use a simplified version for theoretical analysis of UI and JSA effects on recession costs. 3. Calibrate the model to German data and quantitatively assess Hartz III (improved JSA) and Hartz IV (reduced UI) reforms. 4. Conduct comprehensive robustness analysis including model extensions. ### Theoretical findings - An improvement in JSA or a reduction in UI leads to a decrease in the output cost of recessions (output cost defined as the present value output gain from eliminating recessions). - Economic intuition: higher JSA or lower UI increases job finding rates at all stages of the business cycle, making the labor market more fluid and the economy more resilient to adverse shocks. - Temporary output losses are diminished because higher job finding rates reduce the increase in unemployment during recessions. - Permanent output losses are reduced because higher job finding rates shorten unemployment spells and reduce scarring. - The effect of JSA or UI on the welfare cost of recessions is generally ambiguous despite the unambiguous effect on the output cost. - Representation result: the welfare cost of recessions equals the sum of three components: the output cost of recessions, the risk cost of recessions, and the effort cost of recessions. - The risk cost is generally positive; the effort cost may be positive or negative depending on changes in search effort during recessions. - UI has ambiguous effects on the risk cost; both JSA and UI have ambiguous effects on the effort cost. ### Calibration to the German Hartz reforms and quantitative results - Context: Hartz III improved the Public Employment Agency and JSA quality; Hartz IV substantially reduced UI for the long-term unemployed. - Empirical calibration evidence: the two reforms led to a substantial increase in the non-cyclical component of the job finding rate of unemployed workers. - Two main quantitative results: - The Hartz III and Hartz IV reforms together increased job finding rates by more than one-third at all stages of the business cycle, and this increased fluidity reduced the output cost of recessions by 25.0 percent—from 2.014 percent of lifetime consumption to 1.510 percent of lifetime consumption. - A substantial part of the reform-induced reduction in the output cost is driven by a reduction in permanent output losses (hysteresis) via shorter unemployment spells and reduced skill losses. - Welfare cost effects: - Both reforms reduced the welfare cost of recessions, but the reduction in welfare cost is significantly smaller than the reduction in output cost. - Quantitatively, the two reforms together reduced the output cost by roughly 25.0 percent, but reduced the welfare cost by 9.9 percent. - The smaller welfare gain reflects that one channel through which reforms reduce output cost—higher search effort during recessions—adversely affects welfare and increases the welfare cost of recessions. ### Model assumptions, limitations, and sensitivity - Two crucial modeling features: - Degree of risk aversion is moderate (log-utility). - The model does not incorporate aggregate demand fluctuations; it does not capture the potential automatic-stabilizer role of UI. - Implication: higher risk aversion and a non-negligible automatic stabilizer would make cuts in unemployment benefits (Hartz IV) more costly. - Robustness analysis findings: - Results are robust to a wide range of parameter values and model specifications, but the strength of reform effects is sensitive to: - The elasticity of job search with respect to UI: effects weaken if the elasticity lies at the lower end of empirical estimates. - Inclusion of vacancy posting by firms (Diamond-Mortensen-Pissarides extension): this implies larger effects of UI (Hartz IV) and smaller effects of JSA (Hartz III) on the cost of recessions. - If a reduction in UI causes substantial productivity losses via worsened match quality, the Hartz IV effect on the cost of recessions becomes weaker. - Overall conclusion: available evidence suggests substantial reduction in the output cost of recessions from the Hartz reforms and a significantly weaker reduction in welfare cost; more empirical research on elasticities and matching technologies is needed to pin down magnitudes. ### Methodological contribution - The paper develops a tractable incomplete-market model with search unemployment and shows that when the cost of financial intermediation (the interest rate spread) is large enough, recursive equilibria exist with no asset trade and an aggregate state variable consisting of the vector of unemployment rates and human capital shares over employment states. - In the authors' model with short-term and long-term unemployment this is a four-dimensional aggregate state. - Consequently, neither the infinite-dimensional distribution of financial asset holdings nor the infinite-dimensional distribution of human capital are necessary state variables, which enhances tractability and avoids reliance on approximation methods. ### Relation to the literature - Connects to empirical work documenting large output losses and hysteresis from recessions (e.g., Ball, 2014; Blanchard, Cerutti, and Summers, 2015; Hall, 2014; IMF, 2015). - Extends structural, model-based welfare analyses of the Great Recession (e.g., Glover et al., 2014; Krueger et al., 2016) by studying how labor market institutions (UI and JSA) affect output and welfare costs of recessions and applying the analysis to the German Hartz reforms. - Relates to literature on labor market institutions and unemployment, including empirical and theoretical studies of UI, JSA, and labor market fluidity (e.g., Blanchard and Wolfers, 2000; Ljungqvist and Sargent, 1998; Davis and Haltiwanger, 2014). - Contributes to macro-labor structural studies of the Hartz reforms; complements but differs from existing structural studies by focusing explicitly on cyclical variation and the costs of recessions. *Source: wp1787 - 1. Introduction* ### 2. German Labor Market Reforms 2003-2005 ### 2. German Labor Market Reforms 2003-2005 ### Overview and policy objective - Timeframe and legislation: - Four laws implemented in three steps: January 2003 (Hartz I+II), January 2004 (Hartz III), January 2005 (Hartz IV). - Core policy objective: - Improve the process of moving workers from unemployment to employment. - Three core elements of the reform strategy: - Increase matching efficiency by providing job search assistance (JSA). - Increase labor supply by activating the unemployed. - Increase labor demand by deregulating the market for temporary work and providing employment subsidies. - Allocation of reforms to objectives: - Hartz III: mainly targeted matching efficiency/JSA. - Hartz IV: mainly targeted activation (labor supply) via benefit rules. - Hartz I and II: mainly addressed labor demand/deregulation and subsidies. ### Hartz III — restructuring Public Employment Agency and job search assistance - Institutional changes enacted January 1, 2004: - Public Employment Agency restructured into decentralized, customer-oriented job centers with higher responsibility and accountability. - Introduction of competition in placement services via voucher system allowing job seekers to choose private placement agencies. - Voucher system initially introduced in 2002 but Hartz III allowed for wider application. - Empirical evidence on effects: - Restructuring increased the efficiency parameter of the aggregate matching function by at least 5 percent and perhaps up to 10 percent (Fahr and Sunde, 2009; Klinger and Rothe, 2012). - Introduction of vouchers improved the job finding rate of affected workers by about 10−30 percent (Winterhager, Heinze, and Spermann, 2006). - On average, 20 percent of unemployed workers receive a voucher (Pfeiffer and Winterhager, 2006), which translates into an increase in the unconditional job finding rate by 2−6 percent for all unemployed workers. - Combined evidence implies Hartz III plus voucher system increased search efficiency by at least 7−16 percent. - Modeling choice for quantitative analysis: - The paper simulates Hartz III as an increase in search efficiency by 8 percent. ### Hartz IV — overhaul and reduction in unemployment benefits - Institutional changes enacted January 1, 2005: - Simplified two-tier unemployment insurance system: - Short-term unemployed (unemployment spell less than one year): Unemployment Benefit I — benefits proportional to earnings at last job. - Long-term unemployed (unemployment spell more than one year): Unemployment Benefit II — means-tested payments that heavily depend on household composition. - Reform also introduced new activation and monitoring measures for long-term unemployed/welfare recipients (not evaluated in the paper’s theoretical model). - Aggregate change in net replacement rates: - Long-term unemployed: net replacement rate reduced from 0.57 in 2000-2004 to 0.46 after the reform in 2005 — a reduction by 11 percentage points. - Short-term unemployed: Hartz IV had almost no effect on the net replacement rate. - International comparisons (comparable OECD methodology): - Long-term unemployed: Spain 27 percent, France 38 percent, Germany pre-reform 57 percent, Germany post-reform 46 percent. - Short-term unemployed: France 68 percent, Spain 66 percent, Germany 63 percent. - United States: short-term 55 percent, long-term 14 percent. - Conclusion: post-reform Germany remains relatively generous compared to the US. - Micro-econometric evidence: - Limited direct micro evidence on Hartz IV benefit reductions due to changes in official unemployment measurement affecting composition of the unemployed pool. - Engbom, Detragiache, and Raei (2015): difference-in-difference analysis finds workers with the largest reform-induced reduction in unemployment benefits experienced the largest increases in job finding rates — consistent with increased search incentives. - Modeling choice for quantitative analysis: - The paper simulates Hartz IV as reducing the net replacement rate for the long-term unemployed by 11 percentage points and leaving the short-term net replacement rate unchanged. ### Time series evidence on job finding rates, Beveridge curve, and unemployment - Job finding rates (2000–2012): - Long-term unemployed: - Average job finding rate 2000-2003: 6.3 percent. - Average job finding rate 2007-2012: 9.3 percent. - Increase: almost 48 percent. - Short-term unemployed: - Average job finding rate 2000-2003: 24 percent. - Average job finding rate 2007-2012: 37 percent. - Increase: 54 percent. - Temporal pattern: relatively stable pre-reforms, then steady rise until 2007, thereafter stable at a significantly higher level. - Note: the 2005 spike in official unemployment is a statistical artifact due to a change in measurement that added more than half a million workers to the unemployed pool (Bundesagentur fuer Arbeit, 2005); more than 80 percent of added unemployed lacked the equivalent of a high school degree, worsening pool quality and implying a larger quality-adjusted increase in job finding rates. - Beveridge curve (vacancy-unemployment relationship, 2000−2015): - The German Beveridge curve experienced a substantial inward shift shortly after Hartz III and Hartz IV implementation — consistent with higher matching efficiency and/or higher search effort. - Quantitative attribution: the two reforms together account for most of the non-cyclical rise in job finding rates and two-thirds of the shift in the Beveridge curve (per the paper’s Section 6 quantitative analysis). - Unemployment rate trend (1970–2015): - Unemployment peaked near almost 11 percent in 2005, fell to 7.5 percent in 2008, and reached 4.4 percent at end-2015. - Interpretation: long-run trend in unemployment reversed in mid-2000s. - Estimated non-cyclical decline in unemployment since 2005: at least 3 percentage points and perhaps even 5 percentage points. - Paper’s implication: Hartz III and Hartz IV made a substantial contribution to the decline in structural unemployment (see Section 6 for model-based quantification). ### Model implications and calibration choices (summary of approach) - Modeling framework: - Combines a tractable incomplete-market model (Constantinides and Duffie, 1996; Krebs, 2007) with a search-unemployment component (Hansen and Imrohoroglu, 1992; Ljungqvist and Sargent, 1998). - Baseline model assumes no search externalities: individual job finding rates are not affected by aggregate labor market tightness; micro elasticity equals macro elasticity of job search. - An extension with endogenous vacancies and matching technology (search externalities) is discussed in Section 7. - Key model implications and calibration points: - In baseline equilibrium, workers do not self-insure and the consumption response to income shocks is one-to-one (proposition 1). - Model chosen to match empirical evidence on the initial consumption drop upon becoming unemployed; robustness analysis shows main quantitative results are not sensitive to the size of this consumption drop. - For policy experiments: - Hartz III simulated as an increase in search efficiency by 8 percent. - Hartz IV simulated as an 11 percentage point reduction in the net replacement rate for the long-term unemployed, with short-term net replacement unchanged. - Relevance of asset holdings: - Model implies zero asset holdings in equilibrium; empirical gaps exist (many households hold positive net wealth). - But empirical observations show large fractions of the population (especially unemployed and long-term unemployed) have no or negative net wealth: - Germany: 28 percent of all adults have no or negative net wealth; 39 percent of one-person households age < 60 have no or negative net wealth. - Germany: 65 percent of unemployed and close to 100 percent of long-term unemployed have no or negative net wealth. - Thus, for the target population of the study (unemployed and those most likely to become unemployed) the model’s asset implication is broadly consistent with available data. *Source: wp1787 - 2. German Labor Market Reforms 2003-2005* ### 3.1 Workers ### 3.1 Workers ### Employment states, wages, and search - Employment status s_t ∈ {e,su,lu}, where e = employed, su = short-term unemployed, lu = long-term unemployed. - Employed individuals work a fixed and common number of hours in each period (no labor-leisure choice). - Employed workers receive a before-tax wage w h, where h is individual human capital and w is the common wage rate per unit of human capital. - Unemployed workers search for jobs and choose search intensity l. - Unemployed worker who succeeds in search receives a job offer promising per period wage payment w h for human capital h; unemployed workers always accept job offers (conditions on fundamentals to ensure equilibrium acceptance are provided elsewhere). - Aggregate business cycle state S follows a Markov process with stationary transition probabilities π(S′|S). For simplicity S ∈ {R,N} with S = R (recession) and S = N (normal). - Business cycle effects on labor market: - Job destruction/loss rate: employed → unemployed with exogenous probability π_su|e(S). Job destruction is independent of effort (no moral hazard while employed). - Job finding rate: for an unemployed worker of type s ∈ {su,lu}, job finding rate is π_e|s(l,x_s,S), increasing and concave in (l,x_s) for given S. Search efficiency depends on individual search effort l, type-dependent efficiency parameter x_s, and cycle S. - Unemployed workers start as short-term unemployed and transition to long-term unemployed with exogenous probability π_lu|su. - Public job search assistance (JSA) determines x_s and costs government resources λ_s(x_s), with λ_s(.) increasing and convex. ### Human capital and wage dynamics - Human capital h_t aggregates characteristics determining labor productivity; employed workers receive after-tax income (1−τ) w h_t, where τ is a linear labor income tax (social security tax). - Human capital law of motion (equation (1)): - h_{t+1} = (1 + ε_{t+1}) h_t if s_{t+1} = e - h_{t+1} = (1 − δ_su) h_t if s_{t+1} = su - h_{t+1} = (1 − δ_lu) h_t if s_{t+1} = lu - {ε_t} is i.i.d. over time and across workers; E[ε] may be > 0 capturing learning-by-doing or on-the-job training. The mean of ε_{t+1} defines average growth rate of wages/earnings. - δ_su and δ_lu capture skill depreciation during unemployment (short-term and long-term). - Unemployment has permanent effects on wages if E[ε] > δ_su, δ_lu. Scarring can occur even if δ_su = δ_lu = 0 when E[ε] > 0. - δ_su, δ_lu, and E[ε] do not depend on aggregate labor market conditions S in the model. ### Assets, borrowing, benefits, and budget constraint - Workers begin life with zero financial wealth a_0 = 0, can save at risk-free rate r_t and borrow at rate r_t + α, where α is exogenous cost of financial intermediation (and equilibrium spread). - For long-term unemployed a fraction ψ of financial assets are confiscated (means-tested programs). - Unemployed workers receive unemployment benefits b(s_t) h_t with s_t ∈ {su,lu}. - Worker budget constraint (equation (2)), with explicit debt limit a_{t+1} ≥ − D̄ h_t, reads (cases reproduced exactly): - a_{t+1} = (1 + r_t) a_t + (1 − τ) w h_t − c_t if a_{t+1} ≥ 0 and s_t = e - a_{t+1} = (1 + r_t) a_t + b(su) h_t − c_t if a_{t+1} ≥ 0 and s_t = su - a_{t+1} = ψ(1 + r_t) a_t + b(lu) h_t − c_t if a_{t+1} ≥ 0 and s_t = lu - a_{t+1} = (1 + r_t + α) a_t + (1 − τ) w h_t − c_t if a_{t+1} < 0 and s_t = e - a_{t+1} = (1 + r_t + α) a_t + b(s_t) h_t − c_t if a_{t+1} < 0 and s_t = su, lu - a_{t+1} ≥ − D̄ h_t - c_t denotes consumption and a_t denotes financial asset holdings at beginning of period t. - Comment: equilibrium characterization remains valid if debt constraint is replaced by a_{t+1} ≥ − D̄ or a no-Ponzi scheme condition. - Each choice variable c_t, a_{t+1}, h_{t+1} is a function mapping histories of individual shocks s_t and aggregate shocks S_t into choices. ### Labor market institutions, financing, and incentives - Two types of labor market institutions considered: - Public Employment Agency providing JSA and job placement services, improving job finding rates via x = (x_su, x_lu), with resource costs λ_s(x_s). - Unemployment Insurance (UI) defined by benefit levels b = (b_su, b_lu). - Benefits b and JSA costs λ(x_s) are financed through the labor income tax τ. - b, x, τ affect job finding rates (search incentives) but do not affect job destruction rates; b, x, τ do not depend on aggregate state S (policy does not respond to business cycle by assumption). ### Preferences, disutility of search/working, and welfare - Workers are risk-averse with identical, time-additive expected utility. - One-period utility u_s(c,l) = ln c − d_s(l), where d_s is increasing and strictly convex in l. - Interpretation: there exists a type-independent disutility ˜d(l,n) over time spent searching l hours and working n hours; for unemployed l > 0, n = 0 so d_s(l) = ˜d(l,0); for employed l = 0 and n = n̄, d_e(0) = ˜d(0,n̄). - Expected lifetime utility (equation (3)): - W({c_t,l_t}|s_0) .= E[ Σ_{t=0}^∞ β^t (ln c_t − d(l_t,s_t)) | s_0 ], where β is workers' discount factor. - Expectations taken over joint distribution of idiosyncratic and aggregate shocks that depend on effort plan {l_t} through transition probabilities π. ### Initial conditions and aggregation - Initial type of a worker is (s_0, h_0) with a_0 = 0 for all workers. - Initial aggregate state is S_0 ∈ {N,R} and M_0 is joint distribution over initial s_0 and h_0; marginal over employment states gives initial unemployment rates U_0 = (U_{0,su}, U_{0,lu}). - For given (s_0,h_0,S_0,M_0) workers choose plans {c_t,l_t,a_t} to maximize (3) subject to (2). - Aggregate variables obtained by expectations over individual plans conditional on aggregate histories, e.g. C_t = E_t[c_t] = ∫_{h_0,s_0} Σ_{s_t} c_t(h_0,s_0,M_0,S_0; s_t,S_t) π_t(s_t,S_t|s_0,S_0) dM_0(h_0,s_0). - Aggregate variables depend on initial state (S_0,M_0) and partial history S_t: C_t = C_t(M_0,S_0,S_t). ### Firms (summary linked to workers) - Continuum of firms produce single consumption good using labor only. Firm productivity parameter Z takes values Z > 0 or 0; a firm with productivity 0 shuts down forever. - One firm matched with one worker; match produces Z × h or 0. - Job destruction π_u|e(S′) equals probability firm-level productivity changes from Z to 0 (exogenous). - Matching is random; aggregate output Ỹ_t = Z H_{t,e}, where H_{t,e} = E[h_t | s_t = e]. - Competitive labor market: wage per unit of human capital w = Z (marginal product); workers receive entire match surplus, firms zero profit. - Assumption ln Z − d_e(0) > ln b_s − d_s(0) for s = su, lu ensures unemployed workers accept job offers. - Despite common w = Z, endogenous cross-sectional distribution of wages/earnings arises from distribution of human capital and its stochastic evolution (logarithmic random walk with drift). ### Equilibrium, government budget, and aggregate resource constraint - Risk-free asset traded by workers is in zero net supply: A_t = 0 (equation (4)). Thus total debt A_t^- equals total assets A_t^+. - Output net of financial intermediation costs: Y_t = Ỹ_t − A_t^-. - Government spending and revenue induced by (b,x,τ): - G_t .= [b_su + λ_su(x_su)] H_{t,su} + [b_lu + λ_lu(x_lu)] H_{t,lu} (equation (5)) - T_t .= τ w H_{t,e} - A labor market institution (b,x,τ) is feasible if induced fiscal process {G_t, T_t} satisfies present value budget constraint PV_g(M_0,S_0) = 0, where - PV_g(M_0,S_0) .= E[ Σ_{t=0}^∞ ν_t (G_t − T_t) / Y_t | M_0,S_0 ] (deficit-to-output ratio used). - Sequential government budget constraint (7): D_{t+1} = (1 + r_w) (1 + D_t) + T_t − G_t, where D_t is government debt and r_w is world interest rate. For D_0 = 0, sequential constraint with no-Ponzi condition implies present-value constraint (6) with appropriate ν_t. - Discussion: equilibrium characterization holds if r_w = r (world rate equals domestic lending/saving rate). No-Ponzi scheme imposed at initial state (M_0,S_0). - For policies with potentially unbounded debt-to-output ratio, an alternative fiscal policy {G′_t, T′_t} with bounded debt-to-output and identical labor market institution can be constructed (details in Online Appendix) so that equilibrium effort choices are the same and welfare cost of recessions arbitrarily close; construction uses consumption tax/subsidy non-zero only when government debt very high. - Sequential equilibrium definition (for given (b,x,τ) and (M_0,S_0)): - A wage rate w, sequence of interest rates {r_t}, and family of worker plans {c_t,a_t,l_t} such that: - (i) For all worker types (h_0,s_0), individual plan maximizes expected lifetime utility (3) subject to (2). - (ii) Market clearing A_t = 0 holds in each period t. - (b,x,τ) is feasible if government budget constraint (6) is satisfied. - Aggregate resource constraint (expected present value form, equation (8)): - E[ Σ_{t=0}^∞ ν_t C_t / Y_t | M_0,S_0 ] + E[ Σ_{t=0}^∞ ν_t Λ_t / Y_t | M_0,S_0 ] = 1, - where Λ_t is aggregate spending on job search assistance for unemployed and C_t is aggregate consumption. Expectations taken over all histories S_t. *Source: wp1787 - 3.1 Workers* ### 3.4 Equilibrium Characterization ### 3.4 Equilibrium Characterization ### Recursive equilibrium with minimal state space - Recursive equilibria with minimal state space are characterized using only the exogenous aggregate state S; neither the cross-sectional distribution of assets nor the cross-sectional distribution of human capital are relevant state variables. - Worker maximization can be written as the dynamic programming problem in (9) with state (a,h,S). When workers do not trade the risk-free asset in equilibrium (a_t = 0) and consume current income (c_t = φ(s_t) h_t for all histories), the value function reduces to: - V_s(0,h,S) = v_s(S) + 1/(1−β) ln h (equation (10)) - The scalar coefficients v_s(S) and the optimal effort choice l = l(S) solve the intensive-form Bellman equation (11), which determines equilibrium effort and, given h_{t+1} = (1+η_{s′,ε′}) h_t, pins down the worker plan {c_t,a_t,l_t}. ### Intensive-form Bellman equation and effort choice - Intensive-form Bellman equation (11) (defines v_s(S)): - v_s(S) = max_l { ln φ_s − d_s(l) + (β/(1−β)) Σ_{s′,ε′,S′} ln(1+η_{s′,ε′}) π_{ε′} π_{s′|s}(l,S′) π(S′|S) + β Σ_{s′,S′} v_{s′}(S′) π_{s′|s}(l,S′) π(S′|S) } - Effort choice l = l(S) follows from solving (11); a_t = 0 and c_t = φ(s_t) h_t in equilibrium. ### Government budget constraint, law of motion for human-capital shares (Ω), and present-value deficits - Define Ω_s = H_s / H (human capital share vector). Equilibrium law of motion for Ω is (12): - Ω′_{s′} = [ Σ_s (1 + \barη_{s′}) π_{s′|s}(l(S),S′) Ω_s ] / [ Σ_{s,s′} (1 + \barη_{s′}) π_{s′|s}(l(S),S′) Ω_s ] - where \barη_{s′} = Σ_{ε′} η_{s′,ε′} π_{ε′}. - Present value of government deficits/surpluses PV_g = PV_g(Ω_0,S_0) solves recursive equation (13): - PV_g(Ω,S) = τ Z − (b_{su}+λ(x_{su})) (Ω_{su}/Ω_e) − (b_{lu}+λ(x_{lu})) (Ω_{lu}/Ω_e) + (1/(1+r_w)) Σ_{S′} (1 + g(Ω,S,S′)) PV_g( Φ(Ω,S,S′), S′ ) π(S′|S) - Discounting assumes ν_t = (1+r_w)^{−t} Π_{n=1}^t (1+g_n) and that the government can borrow/lend at world interest rate r_w. ### Equilibrium existence (Proposition 1) and key assumptions - Proposition 1 (summary): - If the cost of financial intermediation α (the interest rate spread) is greater or equal to α_min given in (A2), then the solution to (11) defines a recursive equilibrium with aggregate state S for given labor market institutions (b,x,τ). - A labor market institution (b,x,τ) is feasible if the government budget constraint (6) holds with PV_g given by the recursive equation (13) using law of motion (12). - Intuition and proof highlights: - Workers choose a_t = 0 (no-trade) when the borrowing–lending spread is sufficiently large. - The proof handles non-concavity issues in multi-period moral hazard settings and relies on three key assumptions: (i) homothetic preferences, (ii) non-asset income proportional to human capital, and (iii) human capital shocks proportional to human capital (proportional skill depreciation during unemployment). ### Special-case neutrality (one unemployed type, i.i.d. S_t) - In the special case with a single unemployment type (s=u,e), no wage shocks (ε = \barε), and i.i.d. {S_t}, (11) simplifies to (14): - v_u = max_l [ ln b − d(l) + (β/(1−β)) ( ln(1+\barε) \barπ_{e|u}(l) + ln(1−δ_h) (1−\barπ_{e|u}(l)) ) + β ( v_e \barπ_{e|u}(l) + v_u (1−\barπ_{e|u}(l)) ) ] - v_e = ln((1−τ) w) + (β/(1−β)) ( ln(1+\barε) (1−\barπ_{u|e}) + ln(1−δ_h) \barπ_{u|e} ) + β ( v_e (1−\barπ_{u|e}) + v_u \barπ_{u|e} ) - Here \barπ_{u|e} = π_{u|e}(N) π(N) + π_{u|e}(R) π(R) and \barπ_{e|u}(l) = π_{e|u}(l,N) π(N) + π_{e|u}(l,R) π(R). - Result: solution depends only on mean job destruction/finding rates, not volatilities; equilibrium effort l is constant over the cycle. ### Computation and tractability (Section 3.5) - Computational strategy (two steps): 1. For given labor market institutions (b,x,τ), solve worker problem (11) for v_s(S) and l_s(S). 2. Vary τ until government budget constraint (6) is satisfied using recursive equation (13) and law of motion (12). - Advantages: - Reduces the Bellman equation (9) with consumption-saving and effort choice to intensive-form (11) with only effort choice because a_t = 0 in equilibrium. - Removes the need to track infinite-dimensional cross-sectional distributions of assets and human capital; avoids approximation schemes like Krusell and Smith (1998) and allows solving exact equilibrium conditions. - Equilibrium objects computed from (11), (12), (13): - Search intensity and job finding rates, tax level τ ensuring budget feasibility, equilibrium law of motion for Ω. ### Equilibrium dynamics: unemployment and output growth - Law of motion for unemployment rate (15): - U′_{s′} = Σ_{s=su,lu} π_{s′|s}( l_s(S), S′ ) U_s + π_{su|e}(S′) (1 − U_{su} − U_{lu}) - Aggregate output: Y_t = Z H_{t,e}. Aggregate human capital H_t = (H_{t,e}, H_{t,su}, H_{t,lu}) evolves according to (16): - H_{t+1,s′} = Σ_s (1 + \barη_{s′}) π_{s′|s}( l_s(S_t), S_{t+1} ) H_{t,s} - Equilibrium growth rate of employed human capital (and output) from (17): - 1 + g(Ω,S,S′) = (1 + η_e) Σ_s π_{e|s}( l(S), S′ ) (Ω_s / Ω_e) - Special case: with s = u,e; δ_u = 0; ε = 0: - 1 + g = π_{e|e} + π_{e|u} ( U / (1−U) ), so output growth equals employment growth; steady-state g = 0 when U at steady state. - Non-neutrality arises when employed wage growth or skill depreciation during unemployment is present; these generate output costs of recessions discussed in Section 4. *Source: wp1787 - 3.4 Equilibrium Characterization* ### Section 6 for more details. ### wp1787 - Section 6 for more details. ### Labor Market Institutions and the Cost of Recessions - Welfare cost of recessions, ∆, and output cost of recessions, ∆y, depend on labor market institutions: ∆ = ∆(b,x) and ∆y = ∆y(b,x). Analysis focuses on signs and magnitudes of ∂∆/∂b, ∂∆/∂x, ∂∆y/∂b, and ∂∆y/∂x, holding government budget constraint (6) by adjusting τ when b or x change. - General result: effect of changes in (b,x) on welfare cost ∆ is ambiguous; effect on output cost ∆y can be signed under specific assumptions. - Proposition 3 (under assumptions: two employment states s = u,e; no wage shocks, ǫ = ̄ǫ; job finding rates independent of S and linear in effort πe|u(l,x,S) = x l; aggregate shock process {St} i.i.d.; and β sufficiently small): - i) Job search assistance (JSA) reduces the output costs of recessions: ∂∆y/∂x < 0 - ii) Unemployment insurance (UI) increases the output costs of recessions: ∂∆y/∂b > 0 - Intuition: increasing x or reducing b raises job finding rates across the cycle, making the labor market more fluid and the economy more resilient to adverse shocks by (a) reducing the rise in unemployment during recessions and (b) shortening unemployment spells and reducing skill losses, thus lowering both temporary and permanent output losses. - Caveats and robustness: assumptions that {St} is i.i.d. and β is sufficiently small are essential for the proof; other simplifying assumptions (single unemployment state, no wage shocks, linearity) simplify but are not essential. Formal global robustness proof is beyond scope. - Ambiguity for welfare cost ∆: - Although increases in x or reductions in b reduce ∆y, they can have offsetting effects on: - risk cost ∆r (reduction in x reduces ∆r; reduction in b generally increases ∆r) - effort cost ∆e (ambiguous for both x and b) - Calibrated model economy finding: both an increase in x or a reduction in b increase the effort cost of recessions, ∆e, and reduce the risk cost of recessions, ∆r. ### Calibration — overview and targets - Calibration uses German pre-reform data, matching mean values of macro variables before reform, focusing on period 2000-2004 for average pre-reform values of unemployment rate and job finding rate. - Calibrated model reproduces cyclical dynamics of job finding rate and job destruction rate during a typical pre-reform German recession. Cyclical components extracted via HP-filter on job flow rates from Jung and Kuhn (2014) for 1980−2004. - Additional calibration targets: German unemployment insurance system parameters before reform and empirical evidence about search elasticity w.r.t. unemployment benefits. ### 5.1 General specifications - Model period: one quarter. - Aggregate shock process two-state: S ∈ {R,N} where R = recession and N = normal. - Long-term unemployment defined as spells > 12 months. Transition probability πlu|su from s = su to lu set to 0.25. ### 5.2 Search technology and mean transition rates - Job search technology functional form: - πe|su(lsu,xsu,S′) = Ψ(S′) xsu lsu - πe|lu(llu,xlu,S′) = Ψ(S′) xlu llu - Ψ(S′) normalized to mean one; cyclical variation in Ψ chosen to match observed fluctuations in job finding rates. - Calibration targets and implied parameter values: - Data average quarterly transition probabilities (Federal Employment Agency, 2000-2004): ̄πe|lu = 0.06 and ̄πe|su = 0.24, which yield xsu = 0.127 and xlu = 0.084. - Transition from long-term to short-term unemployment πsu|lu chosen to match long-term share in unemployment pool: OECD share long-term unemployment = 50 percent for 2000-2004 ⇒ πsu|lu = 0.190. - Average job destruction rate ̄πu|e chosen to match average unemployment rate 10 percent (OECD definition) for 2000-2004 ⇒ ̄πu|e = 0.167. ### 5.3 Search preferences and search elasticity - Disutility of search specification: ds(l) = d0 l^γ + d1,s. - Normalizations and imposed equalities: - d0 normalized to 1. - d1,e = 0. - d1,su = d1,lu so disutility differences between employed and short-term unemployed derive from consumption paths only; same (dis)-utility for short-term and long-term unemployed. - Target for micro elasticity of job search w.r.t. UI: - Target elasticity for short-term unemployed: −0.7 (partial equilibrium elasticity computed numerically for a 1 percent change in bsu). - Resulting curvature parameter: γ = 1.317. - Corresponding implied Frisch-elasticity κ = 3.155 via γ = 1 + 1/κ. - Context: target elasticity −0.7 lies between values used in literature (examples: −0.9, −0.5). Robustness analysis in Section 7 explores alternatives. - Empirical evidence on search elasticity (micro) summarized: - US micro studies: Moffitt (1985) and Meyer (1990) ≈ −0.9; Krueger and Meyer (2002) suggest −1.0; Chetty (2008) suggests −0.5. - Card et al. (2015): administrative Missouri data find elasticity ≈ 0.35 before the recession and between 0.65 and 0.9 after the recession (regression kink design). - Krueger and Mueller (2010): time-use evidence—benefit level negatively affects search time. - Farber and Valletta (2015), Rothstein (2011): limited effects of benefit extensions during Great Recession on individual job finding rates; Johnston and Mas (2016) find larger effects. - Germany-specific: Hunt (1995) aligns with US earlier estimates; Addison, Centeno and Portugal (2008) find elasticities −1.14 to −1.66; Hofmann (2012) and Mueller and Steiner (2008) find sanctions/reductions affect transitions. ### 5.4 Skill loss during unemployment - Empirical findings on skill depreciation and earnings loss: - Addison and Portugal (1989): 10% increase in unemployment duration reduces wages between 0.8% and 1.4%. - Neal (1995): additional week of unemployment reduces wages by 0.37% ⇒ monthly rate ≈ 1.5%. - Keane and Wolpin (1997): structural estimates indicate even higher depreciation rates. - Schmieder, Wachter, and Bender (2016) (Germany, middle-aged workers, RD design): each month out of work reduces reemployment wages by 0.8 percent ⇒ quarterly depreciation rate of 2.4%. - Calibration choice: - Assume equal skill depreciation for short-term and long-term unemployed: δh,su = δh,lu. - Set δh,su = δh,lu to a quarterly depreciation rate of 2.5%. ### 5.5 Wage growth and wage risk - Wage/earnings shock ǫ: ln(1 + ǫ) assumed normally distributed with mean μ and variance σ^2; log wages follow random walk with drift. - Targets and parameter choices: - Choose μ so average annual growth rate of the economy = 1 percent. - Choose σ to match empirical estimates of permanent component of individual earnings risk: σ = 0.075 (quarterly standard deviation), motivated by US annual value ≈ 0.15 and German evidence. ### 5.6 Unemployment benefits - Calibration of benefit parameters bsu and blu: - OECD average net replacement rate for short-term unemployed in Germany 2000-2004 = 0.63 suggests bsu = 0.63, but model without equilibrium asset holdings would imply a consumption drop of 37 percent upon job loss — deemed unrealistic. - Baseline calibration chooses bsu = 0.85 (consumption drop of 15 percent); extensive sensitivity analysis in Section 7. - Difference between short-term and long-term net replacement rates targeted: - OECD reports short-term net replacement rate = 0.63 and long-term = 0.57 for 2000-2004 ⇒ target difference 0.06 percentage points. - Calibration yields blu = 0.79 to match bsu − blu (1 − τ) w = 0.06 target. ### 5.7 Discount factor and cost of financial intermediation - Quarterly discount factor chosen: β = 0.99. - Implied quarterly lending interest rate using (A1): rf = 0.73%. - Minimal quarterly interest rate spread (cost of financial intermediation) that yields no-asset-trade equilibrium from (A2): αmin = 0.36%. - Interpretation: quarterly spread 0.36% is moderate relative to observed spreads; consistent with realism. Comparative reference: Mehra, Piguillem, and Prescott (2011) use annual spread 2 percent in a related calibration. *Source: wp1787 - Section 6 for more details.* ### 5.8 Cyclical Variations in Job Finding and Job Destruction Rates ### 5.8 Cyclical Variations in Job Finding and Job Destruction Rates ### Calibration targets and parameter identification - The job destruction process is defined by four parameters: the two transition probabilities, π(R|R) and π(N|N), and the two job destruction rates, π_su|e(R) and π_su|e(N). - One restriction comes from the already specified targets for the steady state unemployment rate and the steady state job finding rates (which determine the steady state job destruction rate). - Three additional restrictions are imposed by requiring the model to match: - the frequency of recessions, - the persistence of the hike in the job destruction rate during a typical recession in Germany, - the severity of the hike in the job destruction rate during a typical recession in Germany. - The matching efficiency parameters Ψ(N) and Ψ(R) are set so that Ψ(N)π(N) + Ψ(R)π(R) = 1 and the model matches the observed decline in the job finding rate during a typical pre-reform recession in Germany. ### Empirical identification of cyclical behavior (Germany, 1980–2000) - Data source: worker flow rates between employment and unemployment for the period 1980-2000 from Jung and Kuhn (2014). - Recession dating rule: recessions identified as times in which the job destruction rate falls below the HP-trend for at least two quarters. - Empirical targets for the typical pre-reform recession in Germany (1980-2000): - probability of being in a recession: 30 percent - typical recession length: 8 quarters - average increase in the job destruction rate during the typical recession: 9.43 percent - average decrease in the job finding rate during the typical recession: 6.55 percent - Calibrated parameter values that match these targets: - π(R|R) = 0.8750 - π(N|N) = 0.9464 - π_su|e(R) = 0.0182 - π_su|e(N) = 0.0160 - Ψ(N) = 1.0056 - Ψ(R) = 0.9869 ### Stylized facts and comparisons - In both the calibrated model and the German data, the job destruction rate is more volatile than the job finding rate; recessions in Germany are mainly characterized by an increase in job destruction accompanied by a mild decline in the job finding rate. - International contrast: - Germany: cyclical movements in the job destruction rate account for around 2/3 of the volatility of the unemployment rate. - US: cyclical movements in the job destruction rate account for about 1/3 of the volatility of the unemployment rate; job finding rates are strongly counter-cyclical in the US. - Model implication for search effort: - In the calibrated model economy, search effort is mildly pro-cyclical — it declines by 4.51 percent during a typical recession. - Literature on US-calibrated search models finds search effort strongly pro-cyclical; empirical evidence on cyclicality of search intensity is mixed: - Shimer (2004): measures either a-cyclical or (slightly) counter-cyclical. - Mukoyama, Patterson, and Sahin (2014): counter-cyclical. - DeLoach and Kurt (2013) and Gomme and Lkhagvasuren (2015): pro-cyclical. - No known empirical study of search intensity cyclicality based on German data is cited. ### Model fit for worker flows and labor market dynamics - The calibrated model matches the unemployment dynamics observed during the typical pre-reform recession in Germany almost perfectly when fed the observed recession paths of the cyclical components of job destruction rates and job finding rates. - Matching of worker flows between unemployment and employment implies flows into/out of the labor force are not an important driver of unemployment dynamics during recessions in Germany. - The model also matches employment dynamics during the typical pre-reform recession. ### Output dynamics and hysteresis - The calibrated model captures about two-thirds of the observed drop in output during the typical pre-reform recession. - Main driver of output dynamics during a typical pre-reform recession in Germany: the flow of workers between employment and unemployment. - Changes in labor productivity and hours worked per employed worker have smaller, but non-negligible, impacts. - The calibrated model implies a somewhat stronger recovery than observed in the data, i.e., the model understates the observed hysteresis effect in output. - Overall conclusion: the calibrated model matches unemployment dynamics almost perfectly and output dynamics reasonably well during pre-reform recessions in Germany. *Source: wp1787 - 5.8 Cyclical Variations in Job Finding and Job Destruction Rates* ### 6.4 Output Cost of Recessions ### wp1787 - 6.4 Output Cost of Recessions ### Output cost of recessions: baseline and reforms - Baseline (Pre Reform) output cost of recessions, ∆y: 2.014 percent of lifetime consumption (potential output). - Post Hartz-III-Reform ∆y: 1.728 (14.2%) — percentage deviation from pre-reform allocation shown in brackets. - Post Hartz-IV-Reform ∆y: 1.745 (13.6%). - Post Hartz-III&IV-Reform ∆y: 1.510 (25.0%). ### Decomposition of output cost (Table 1 components) - For each scenario Table 1 reports: - ∆perm y (permanent component) - ∆trans y (transitory component) - ∆des y (component due to changes in job destruction rates) - ∆eff y (component due to changes in matching efficiency) - Table 1 values (in Percent): - Pre Reform: ∆y 2.014, ∆perm y 0.651, ∆trans y 1.362, ∆des y 1.857, ∆eff y 0.156 - Post Hartz-III-Reform: ∆y 1.728 (14.2%), ∆perm y 0.550, ∆trans y 1.178, ∆des y 1.698, ∆eff y 0.030 - Post Hartz-IV-Reform: ∆y 1.745 (13.6%), ∆perm y 0.807, ∆trans y 0.939, ∆des y 1.600, ∆eff y 0.145 - Post Hartz-III&IV-Reform: ∆y 1.510 (25.0%), ∆perm y 0.515, ∆trans y 0.995, ∆des y 1.483, ∆eff y 0.027 ### Key findings on output decomposition and drivers - Most of the output cost of recessions is generated by the hike in job destruction rates during recessions; the job-destruction component makes up more than 90 percent of the total cost. - Decrease in matching efficiency contributes only a small part of the total output cost. - The temporary component (output losses due to temporary employment drop) is about two thirds of the total cost; the permanent (scarring) component is about one third. - Assuming recessions are eliminated in a recession (S0 = R) increases ∆y slightly from 2.014 percent to 2.043 percent of lifetime consumption; percentage reductions due to Hartz III and Hartz IV are almost identical in that case (not reported in table). ### Mechanism behind reform effects - The reductions in ∆y from Hartz III (improvement in JSA) and Hartz IV (reduction in UI) are driven by reform-induced increases in the non-cyclical component of the job finding rate and improved labor market fluidity. --- ### 6.5 Welfare Cost of Recessions ### Aggregate welfare cost and decomposition - Welfare cost of recessions, ∆, computed assuming S0 = N and welfare weights μs = Ω0,s. - Table 2 reports ∆ and its decomposition into: - ∆y (output cost of recessions) - ∆r (risk cost of recessions) - ∆e (effort cost of recessions) - Table 2 values (in Percent): - Pre Reform: ∆ 1.310, ∆y 2.014, ∆r 0.244, ∆l −0.947 - Post Hartz-III-Reform: ∆ 1.205 (8.0%), ∆y 1.728, ∆r 0.199, ∆l −0.722 - Post Hartz-IV-Reform: ∆ 1.277 (2.5%), ∆y 1.745, ∆r 0.209, ∆l −0.676 - Post Hartz-III/IV-Reform: ∆ 1.181 (9.8%), ∆y 1.510, ∆r 0.179, ∆l −0.508 Notes drawn from Table 2: - All welfare changes are expressed in percent of equivalent variations in lifetime consumption and welfare weights are μsu = Ωsu, μlu = Ωlu, and μe = 1−Ωsu−Ωlu. - The values in brackets are the percentage deviation from the pre-reform allocation. ### Interpretation of welfare components - Pre-reform: total welfare cost ∆ = 1.310 percent of lifetime consumption, which is smaller than the output cost ∆y = 2.014 percent. - Risk cost ∆r = 0.244 percent: recessions increase consumption volatility (positive risk cost). - Effort cost ∆e = −0.947 percent: recessions reduce search effort (negative, interpreted as an effort gain relative to higher effort); the effort component dominates the risk component in magnitude. - The welfare cost ∆ is the sum of ∆y, ∆r, and ∆e according to decomposition (25). ### Reform impacts on welfare cost - Hartz III reduces welfare cost by 8.0 percent: from ∆ = 1.310 to ∆ = 1.205 percent of lifetime consumption. - Hartz III reduces risk cost but increases effort cost (higher search effort), so the net welfare reduction is smaller than the reduction in output cost. - Hartz IV reduces welfare cost by 2.5 percent: from ∆ = 1.310 to ∆ = 1.277 percent. - Hartz IV reduces output cost substantially but increases effort cost pronouncedly, leading to a small net welfare effect. - In the calibrated model, reduction in UI reduces the risk cost of recessions because increased search effort and job finding rates reduce consumption volatility; the second effect dominates. - Hartz III and Hartz IV together reduce welfare cost by 9.9 percent: from ∆ = 1.310 to ∆ = 1.181 percent. - Combined effect on welfare cost is non-negligible but substantially smaller than combined effect on output cost; combined effect is somewhat lower than sum of individual effects (non-linearity present but not large). ### Heterogeneity across worker types - Welfare cost ∆ by worker type (pre-reform): - Employed workers: 1.313 percent of lifetime consumption. - Short-term unemployed workers: 1.300 percent of lifetime consumption. - Long-term unemployed workers: 1.271 percent of lifetime consumption. - Reform-induced reductions in welfare cost are very similar across worker types. ### Sensitivity to timing assumption - If recessions are eliminated in a recession (S0 = R), pre-reform welfare cost increases to 1.402 percent of lifetime consumption. - The two reforms together reduce this cost by 9.3 percent from 1.402 to 1.272 percent of lifetime consumption. --- ### 7 Robustness Analysis — main messages ### 7.1 Changes in calibration targets (summary) - Many calibration targets, including pre-reform levels of unemployment benefits bsu and blu, have only small effects on main results. - bsu and blu substantially affect welfare difference between employment and unemployment, but only very small effect on output cost of recessions and modest effect on welfare cost of recessions. - Effects of Hartz III and Hartz IV on output and welfare cost barely change with these benefit parameter variations. - Three parameter dimensions materially affect quantitative results: 1. Curvature parameter of the disutility function (γ). 2. Level of skill depreciation during unemployment, δh. 3. Target value of the elasticity of job search. ### Effects of specific parameter changes (examples) - Curvature parameter γ: - Baseline γ = 1.317 implies Frisch elasticity = 3.155. - Alternative γ = 2 implies Frisch elasticity = 1 (micro-level evidence). - For γ = 2 calibration: - Combined Hartz III and Hartz IV reduce output cost of recessions by 22.6 percent from 1.836 percent to 1.422 percent of lifetime consumption. - Combined reforms reduce welfare cost by 9.8 percent from 0.954 percent to 0.861 percent. - Percentage reductions are very similar to baseline. - Skill depreciation δh: - Baseline δh = 0.025 (quarterly). - Alternative δh = 0.0125 (half baseline) reduces the overall cost of recessions (smaller scarring), but reform-induced percentage reductions remain similar. - Example: combined reforms reduce output cost by 22.9 percent from 1.313 percent to 1.013 percent; reduce welfare cost by 3.1 percent from 0.920 percent to 0.892 percent. - Target elasticity of job search: - Baseline target elasticity = −0.7. - Alternative target elasticity = −0.5 (Landais, Michaillat, and Saez (2015)). - With −0.5 elasticity: - Combined reforms reduce output cost by 19.6 percent from 1.832 percent to 1.473 percent. - Combined reforms reduce welfare cost by 8.2 percent from 1.294 percent to 1.188 percent. - Conclusion: elasticity of job search with respect to unemployment benefits is an important summary statistic affecting magnitudes. ### 7.2 Extension: Search and matching with vacancy posting (DMP-Model) — overview - Extension introduces vacancy posting and matching à la Diamond-Mortensen-Pissarides. - Worker side (labor supply) identical to baseline. - Firms post vacancies and incur posting and filling (training) costs. - Match surplus split by Nash bargaining. - Productivity of producing firms Z remains constant over the cycle (only exogenous variations in job destruction rates drive fluctuations). - Firms’ job filling rate πf(Θ) = Θ−η with Θ as tightness index. - Matching function with endogenous search effort: - Job finding rates specification becomes πe|s(l, xs, S, Θ) = xs l Θ1−η, s = su, lu, where η is elasticity of job matching w.r.t. Θ. - Labor market tightness index Θ = V / (xsu Lsu Usu + xlu Llu Ulu) as used in the model. - The extension preserves comparability with baseline by keeping Z constant and thus isolating effects of vacancy posting and search externalities. *Source: wp1787 - 6.4 Output Cost of Recessions (excerpt).* ### Appendix specifies the matching function that is associated with ourspecification of job ### wp1787 - Appendix specifies the matching function that is associated with our specification of job ### Matching function, calibration, and model structure - The extended model associates the matching function with job-finding rates (27) and job filling rates πf(Θ) = Θ−η using (28) as a measure of labor market tightness. - The model endogenously links aggregate shocks and labor market tightness, giving an equilibrium relationship Θ = Θ(S). - Equilibrium conditions for the extended model (search and matching, matching described by (27) and (28), firms post vacancies) are discussed in the Online Appendix; in equilibrium workers do not self-insure and neither the asset distribution nor the human capital distribution are relevant state variables. - Calibration approach: - Most parameters are taken from the baseline model (see Section 5 for baseline calibration). - Four new parameters in the extended model: the elasticity of job matching with respect to labor market tightness, ψ; the bargaining power of workers; and two parameters defining the cost of posting and filling job vacancies. - ψ is set to 0.5 following Petrongolo and Pissarides (2001). - Bargaining power is chosen equal to ψ to satisfy the Hosios condition. - Vacancy cost parameters are chosen to match the observed average job filling rate and the observed decline in job finding rates during a typical pre-reform recession in Germany (decline from 24.67 percent in normal times to 22.43 percent during recessions). ### Main quantitative findings for the extended Diamond-Mortensen-Pissarides specification - Extension effects (summary of Table 3 results): - The model extension increases the output cost and welfare cost of recessions relative to the baseline model. - The output cost of recessions remains substantially larger than the welfare cost of recessions. - The extension increases the effect of the Hartz IV reform (reduction in UI) on the output cost and welfare cost of recessions. - According to the extended model, the effect of the Hartz III reform (improvement in JSA) on the output cost and welfare cost of recessions is small, whereas in the baseline model this reform has a substantial impact. - Table 3: Output Cost of Recessions (in Percent) – Diamond-Mortensen-Pissarides - ∆DMPy ∆DMP - Pre Reform 2.712 2.178 - Post Hartz-III-Reform 2.646 (2.4%) 2.159 (0.9%) - Post Hartz-IV-Reform 2.108 (22.3%) 2.002 (8.1%) - Post Hartz-III/IV-Reform 2.069 (23.7%) 1.996 (8.4%) - Notes: ∆DMPy is the output cost of recessions in percent of lifetime consumption (potential output) and ∆DMP is the welfare cost for the Diamond-Mortensen-Pissarides specification. The values in brackets are the percentage deviation of the respective cost from the pre-reform allocation. ### Vacancy-posting channel — economic intuition - In the extended model with costly vacancy posting and Nash wage bargaining: - Changes in labor market institutions or job destruction rates change wages and thus firm profits. - Profit changes alter vacancy posting, affecting labor market tightness Θ and job-finding rates. - Recession shock (exogenous increase in job destruction rate): - Expected present discounted value of firm profits falls → bargaining position of firms weakens → wages go up → vacancy posting declines → labor market tightness declines → job finding rates fall. - Vacancy-posting channel adds to the cost of recessions, raising output and welfare costs relative to baseline. - Hartz IV reform (reduction in UI): - Lifetime utility of workers declines → worker bargaining position weakens → wages fall → profits and vacancy posting rise → job finding rates increase. - Extension amplifies the effect of Hartz IV on labor market fluidity and reduces recession costs more than in baseline. - Hartz III reform (improvement in matching efficiency): - Lifetime utility of workers increases → worker bargaining position strengthens → wages rise → profits and vacancy posting fall → job finding rates decline. - Vacancy-posting channel reduces the positive impact of improved matching efficiency on labor market fluidity; thus extended model implies smaller effects of Hartz III than baseline. - Empirical notes related to vacancy posting and wages: - Extended model implies Hartz IV reduced non-cyclical unemployment by 1.72 percentage points; Hartz III reduced long-run unemployment by 0.22 percentage points. - Time series evidence: vacancy posting by firms remained constant from January 2004 to January 2005 and rose thereafter, suggesting Hartz III and related matching-efficiency increases did not reduce job finding rates, though more empirical evidence is needed. ### Wedge between micro- and macro-elasticity - Baseline model: micro-elasticity and macro-elasticity with respect to UI or JSA coincide. - Extended model: equilibrium effects on labor market tightness Θ generate a wedge between micro- and macro-elasticities. - For a change in UI (Hartz IV reform), three equilibrium effects on job finding rates: - Increase in U reduces job finding rates. - Reduction in L increases job finding rates. - Increase in vacancy posting increases job finding rates. - Calibrated model: effect of variations of U×L is small; positive effect through variations in V dominates. Macro-elasticity of job search is larger than micro-elasticity: −0.8 vs−0.7. - For a change in JSA (Hartz III reform), three equilibrium effects: - Improvement in matching efficiency reduces U and increases job finding rates. - Increases L and reduces job finding rates. - Reduces vacancy posting and reduces job finding rates. - Calibrated model: effect of variations of U×L is small; negative effect through variations in V dominates. Large wedge: micro-elasticity of job search with respect to JSA is 0.41, macro-elasticity is 0.08. - Implication: the wedge between micro- and macro-elasticities is an important determinant of recession costs and the effects of UI and JSA on those costs. - Empirical literature is mixed on the wedge: some studies find macro-elasticity exceeds micro-elasticity; others find differing results. Additional empirical work needed. ### Unemployment insurance and match quality channel - Extended model variant: UI affects productivity and wages by encouraging search for high-productivity jobs (Acemoglu and Shimer (1999, 2000) channel). - Modeling choice: after the Hartz IV reform (reduction in UI), unemployed workers who find a job lose x percent of their productivity (human capital h); x set to match Acemoglu and Shimer (1999) calibration. - Rationale: Acemoglu and Shimer find a 10 percent reduction in unemployment benefits b leads to a productivity increase somewhat more than 1 percent. Hartz IV reduced benefits for half of unemployed by roughly 20 percent; modeled as a 1 percent productivity loss occurring when an unemployed worker finds a job. - Quantitative implications: - Hartz IV reform reduces the output cost of recessions from 2.014 percent of lifetime consumption to 1.877 percent of lifetime consumption (smaller cost reduction than in the baseline model because productivity losses increase output cost). - The productivity channel raises the welfare cost of recessions from 1.310 percent to 1.338 percent in the extended model. - Conclusion: endogenous match-quality effects can significantly alter the effect of UI on recession costs. Empirical literature on UI effects on post-displacement wages is mixed. ### Conclusion and directions for future research - Main paper contributions: - Developed a tractable incomplete-market model with search unemployment to analyze UI and JSA effects on output and welfare costs of recessions. - Theoretical result: an improvement in JSA or reduction in UI decreases the output cost of recessions; effect on welfare cost is generally ambiguous. - Calibration to German data: both Hartz III (improvement in JSA) and Hartz IV (reduction in UI) substantially improved labor market fluidity and reduced output costs of recessions in Germany; welfare cost reductions are weaker than output cost reductions. - Suggested topics for future research: - Apply analysis to other countries (several European countries implemented reforms; US labor market fluidity may have diminished). - Broaden government policy instruments beyond the simple parametric UI systems studied; analyze more general unemployment insurance systems with incentive-compatibility and resource feasibility. - Joint analysis of optimal stabilization policy and optimal long-run (structural) policy in one framework to study interaction between short-run and long-run policy choices. *Source: wp1787 - Appendix specifies the matching function that is associated with our specification of job (IMF Working Paper wp1787).* ### References ### References (wp1787) ### Major thematic concentrations - Labor market institutions, unemployment insurance (UI), and policy evaluation - Key works on UI design, moral hazard, duration effects, and optimal UI: Acemoglu and Shimer (1999, 2000); Chetty (2008); Hopenhayn and Nicolini (1997); Hansen and Imrohoroglu (1992); Lentz (2009); Mitman and Rabinovich (2015); Pavoni (2009); Landais, Michaillat, and Saez (2015). - Empirical evidence on UI effects on durations, wages, and search behavior: Addison et al. (2008); Card et al. (2015); Farber and Valletta (2015); Gruber (1997); Krueger and Mueller (2010); Schmieder, Wachter, and Bender (2016); Mueller and Steiner (2008). - Studies of UI extensions and macro effects during recessions: Hagedorn et al. (2013); Lalive, Landais, and Zweimueller (2015); Mitman and Rabinovich (2014, mimeo). - Job search, matching frictions, and unemployment dynamics - Theoretical and empirical matching literature: Pissarides (1979, 1992, 2009); Mortensen and Pissarides (1994); Petrongolo and Pissarides (2001); Shimer (2004); Mortensen and Nagypal (2007); Davis and Haltiwanger (2014). - Search intensity, matching function estimation, and search effort amplification: Cho, Cooley, and Kim (2015); Gomme and Lkhagvasuren (2015); Fahr and Sunde (2009); Mukoyama, Patterson, and Sahin (2014); Hairault, Lagot, and Osotimehim (2010). - Costs of business cycles, welfare, and redistribution - Quantification of welfare costs and redistribution across agents: Lucas (1987, 2003); Atkeson and Phelan (1994); Krusell and Smith (1998, 1999); Storesletten, Telmer, and Yaron (2001); Guvenen, Ozkan, and Song (2014); Glover et al. (2014); Krueger, Mitman, and Perri (2016). - Endogenous growth and human capital considerations in business cycle costs: Barlevy (2004); Krebs (2003, 2007); Pavoni (2009); Heisz, Oreopoulos, and Wachter (2012). - German labor market reforms, Hartz reforms, and country-specific studies - Macro- and micro-evaluations of Hartz reforms and German labor market performance: Burda and Hunt (2011); Fahr and Sunde (2009); Hertweck and Sigrist (2012); Engblom, Detragiache, and Raei (2015); Krause and Uhlig (2012); Klinger and Rothe (2012); Jacobi and Kluve (2006); Winterhager, Heinze, and Spermann (2006). - Evidence on displaced workers, wage losses, and hiring costs in Germany: Burda and Mertens (2001); Muehlemann and Pfeifer (2013); Grabka and Westermeier (2014); Mueller and Steiner (2008). - Financial crises, macroeconomic recoveries, and secular stagnation - Analyses of the global financial crisis and long-term damage to output: Atkinson, Luttrell, and Rosenblum (2013); Ball (2014); Blanchard, Cerutti, and Summers (2015); Hall (2014); Reinhart and Rogoff (2014); Wolf (2015). - Discussions of secular stagnation and potential output: VoxEU (2014); IMF (2012); IMF (2015, Chapter 3). - Methodological and asset-pricing approaches related to macro and labor topics - Dynamic programming, recursive methods, and heterogeneous-agent asset pricing: Alvarez and Stokey (1998); Stokey, Lucas, and Prescott (1989); Constantinides and Duffie (1996); Alvarez and Jermann (2004); Mehra, Piullelm, and Prescott (2011). - Risk-sensitive, stochastic, and finite-life formulations: Tallarini (2000); Streufert (1990); Bohn (1995); Uhlig (1996). ### Representative empirical and theoretical contributions (selected entries with emphasis) - Empirical UI and search studies: - Addison, Centeno, and Portugal (2008) — IZA Discussion Paper No. 3357 on unemployment benefits and reservation wages. - Card, Chetty, and Weber (2007) — The Quarterly Journal of Economics122: 1511-1560 on cash-on-hand and intertemporal behavior. - Schmieder, Wachter, and Bender (2016) — American Economic Review106: 739-777 on UI and non-employment duration effects on wages. - Theoretical optimal policy and welfare analyses: - Hopenhayn and Nicolini (1997) — Journal of Political Economy105: 412-438 on optimal unemployment insurance. - Jung and Kuester (2014) — American Economic Journal: Macroeconomics7: 124-156 on optimal labor market policy in recessions. - Landais, Michaillat, and Saez (2015) — NBER Working Paper16529 presenting a macroeconomic theory of optimal unemployment insurance. - Matching, job creation, and labor market flows: - Mortensen and Pissarides (1994) — Review of Economic Studies61: 397-415 on job creation and destruction. - Pissarides (1979) — Economic Journal89: 818-833 on job matching with state agencies and random search. ### Cross-cutting empirical settings and data contexts - Recessions and recovery episodes studied across multiple papers, including the Great Recession (2007-2009) and country episodes (Germany, US, and cross-country analyses). - Use of administrative, firm-level, and experimental designs: randomized experiments and clustered randomized experiments cited (Crepon et al. 2013); time-use and microdata studies (Krueger and Mueller 2010; Card et al. 2015). *References list extracted from the wp1787 PDF (References section).* --- _Source: https://www.imf.org/-/media/files/publications/wp/2017/wp1787.pdf_