## _wp1342

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---

### Introduction — background, research questions, and key quantitative findings
- Background:
  - Over 1970-2005, unemployment rates in Germany rose steadily; Hartz reforms implemented in 2003-2005, with Hartz IV in January 2005 overhauling the unemployment benefit system and substantially reducing long-term unemployment benefits.
  - A measurement change between January 2005 and March 2005 added more than half a million workers to the unemployed pool; more than 80 percent of these added unemployed workers lacked the equivalent of a high school degree.
- Research questions:
  - How much of the 2005-2008 decline in unemployment is permanently attributable to Hartz IV?
  - What are the consequences for economic growth, accounting for adjustment of physical and human capital?
  - What are the welfare effects for employed, short-term unemployed, and long-term unemployed households?
- Approach:
  - Develop a macro model with heterogeneous, risk-averse, long-lived households that choose search effort and invest in physical and human capital; combine incomplete-market human capital framework (Krebs, 2003) with a search unemployment model (Ljungqvist and Sargent, 1998).
  - Calibrate to match German economy features 2000-2004 and simulate Hartz IV (reduce long-term net replacement rate).
- Key quantitative introduction results:
  - Reform reduces long-run unemployment by 1.4 percentage points from a long-run value of 9 to 7.6 percent.
  - Quarterly job finding rate for long-term unemployed: 6.3 percent at beginning of 2004 → 9.3 percent at beginning of 2006 (and remained at higher level in data).
  - GDP growth: 2.5% in 2006 and 3% in 2007 vs average 1.1% in 1992-2011.
  - Annual long-run growth increases by about 0.1 percent.
  - Real wages fell about 4 percent in the period 2004-2009 (post-unification series 1992-2011 context).
  - Welfare (lifetime consumption equivalents): employed gain ≈ +0.4 percent; long-term unemployed lose ≈ −1.0 percent (baseline discussion).

### Model — structure, household problem, aggregation, and calibration
- Structure:
  - Time is discrete; unit mass of infinitely-lived households. Idiosyncratic state s_t = (s_1t, s_2t) with s_1t ∈ {E, SU, LU} and s_2t wage risk shocks. Search effort l unobservable; {s_t} is Markov with π(s_{t+1}|s_t, l_t).
- Households:
  - Preferences: u(c_t, l_t, s_t) = ln c_t − v(l_t) + d(s_1t); expected utility U = E[∑_{t=0}^∞ β^t (ln c_t − v(l_t) + d(s_1t)) | s_0].
  - Returns: employed receive r_{kt} k_t and r_{ht} h_t; unemployed receive benefits B_t = b(s_1t) h_t and income (1 + b(s_1t))(k_t + h_t).
  - Sequential budget constraints specified for employed and unemployed (see model).
- Firms and government:
  - Aggregate production Y_t = F(K_t, H^e_t) with constant returns to scale; firms maximize profits F − r_k K − r_h H^e.
  - Unemployment benefits financed by linear tax on labor; government balanced budget each period (equation (4)).
- Aggregation and equilibrium:
  - Wealth w_t = k_t + h_t; portfolio share θ_t = k_t / w_t; budget in wealth terms w_{t+1} = (1 + r(θ_t, s_t)) w_t − c_t.
  - Market clearing: K_t = E[θ_t w_t]; H^e_t = E[(1 − θ_t) w_t | s_{1t} = e]; aggregate resource constraint (8).
  - Proposition 1: consumption and next-period wealth linear in wealth: c = (1 − β)(1 + r(θ, s)) w; w' = β(1 + r(θ, s)) w; value function and intensive-form Bellman equation reduce dimensionality.
  - Proposition 2: stationary competitive equilibrium characterized by fixed points of intensive-form equations and laws of motion for wealth shares and unemployment rates.
- Calibration (quarter = one period) — selected parameter targets and values:
  - Search: p_{su,lu} = 0.25; p_{su,e} (data) = .06; p_{lu,e} (data) = .24; implied λ_{su} = 0.724; λ_{lu} = 0.229.
  - Disutility of search: v(l) = − v̄ l^γ with v̄ = 1; d = 0.294; γ = 2.774; average elasticity targets: −0.9 (chosen −0.6 short-term, −1.2 long-term).
  - Job separation and transitions: p_{e,su} = 0.0148 (matches unemployment rate 9% pre-reform); p_{lu,su} = 0.190 (matches long-term share 50%).
  - Wage risk: (1 − θ) σ = .075 (quarterly standard deviation).
  - Production: δ_k = δ_h = 0.015; F(K,H^e)=A K^α (H^e)^{1−α}; α = 0.36; A = 0.0656; β = 0.9847 (matches output growth 1% and saving rate 20%).
  - Unemployment benefits calibration targets (2000-2004 OECD net replacement rates): short-term 0.63; long-term 0.57.

### Effects of Hartz IV Reform — calibration experiment, macro effects, transitional dynamics, growth, wages, and welfare
- Reform implemented in simulations:
  - Net replacement rate for long-term unemployed reduced from 0.57 to 0.46; short-term net replacement rate left unchanged.
- Macroeconomic long-run effects (stationary-equilibrium comparison):
  - Unemployment rate: 9 percent → 7.60 percent.
  - Share of long-term unemployment in total unemployment: 50 percent → 48 percent.
  - Job finding rates:
    - Short-term: Pre-Reform = 0.24 ; Post-Reform = 0.277.
    - Long-term: Pre-Reform = 0.06 ; Post-Reform = 0.077.
  - Growth: Pre-Reform annual = 1% ; Post-Reform annual = 1.07% (increase ≈ 0.07 percentage points reported in Table 2; narrative cites about 0.1 percent annual long-run growth increase).
  - Wages: initial decline in real wages driven by increased labor supply; model predicts initial real wage decline, with long-run dynamics influenced by endogenous human capital accumulation.
- Transitional dynamics:
  - Time to halfway adjustment of unemployment rate: about 8 quarters.
  - Dynamic adjustment of short-term and long-term unemployment rates reported as very similar.
- Welfare effects (expected lifetime utility translated into equivalent consumption changes):
  - Employed households: Net Effect = +0.44 percent of lifetime consumption (Table 3: +0.439%).
    - Insurance Effect (holding mean consumption growth unchanged) = −1.795%.
  - Short-term unemployed: Net Effect = −0.132% ; Insurance Effect = −2.354%.
  - Long-term unemployed: Net Effect = −.739% ; Insurance Effect = −2.948%.
  - Social Welfare (population-weighted average): Net Effect = +0.361% ; Insurance Effect = −1.873%.
  - Interpretation: Employed gain because tax-reduction gains outweigh insurance-losses; long-term unemployed lose because benefit cuts dominate tax gains; social welfare increases but distributional losses create political resistance.
- Insurance vs output effects:
  - Reform reduces insurance against unemployment risk (negative for unemployed), raises employment and output (positive for employed via lower labor income taxes).
  - The paper notes that reallocating more output gains to unemployed and less to employed could make reform Pareto-improving; computed welfare-maximizing benefit rate is lower than post-reform rate but further reductions yield very small additional welfare gains.

### Sensitivity analysis and robustness
- Sensitivity to pre-reform share of long-term unemployed:
  - If pre-reform share = 0.4 → unemployment reduction = 1.25%.
  - If pre-reform share = 0.3 → unemployment reduction = 1.0%.
- Sensitivity to average search elasticity:
  - If average search elasticity = −0.8 → unemployment reduction = 1.28%.
  - If average search elasticity = −0.5 → unemployment reduction = 0.87% (−0.5 noted as a lower bound for Germany pre-reform).
- Baseline summary reiterated:
  - Baseline calibration: reform reduced long-run unemployment rate by 1.4 percentage points.
- Numerical computation details:
  - Transitional-dynamics algorithm solves for sequence of aggregate states X=(Ωe,Ωsu,Ωlu,Usu,Ulu) iterating backward and forward until convergence.
  - Set T = 100 periods; algorithm converges within 5 iterations to tolerance tol = 1e−8.

### Key quantitative highlights (extracted)
- Long-term net replacement rate: 0.57 → 0.46 (post-reform).
- Unemployment rate: 9 percent → 7.60 percent.
- Share of long-term unemployment in unemployment: 50 percent → 48 percent.
- Time to halfway adjustment of unemployment rate: about 8 quarters.
- Job finding rates: short-term 0.24 → 0.277; long-term 0.06 → 0.077.
- Increase in annual long-run growth rate: about 0.1 percent (narrative) / Pre-Reform = 1% → Post-Reform = 1.07% (Table 2).
- Welfare changes (lifetime consumption equivalents):
  - Employed: +0.439%.
  - Short-term unemployed: −0.132%.
  - Long-term unemployed: −0.739%.
  - Social welfare: +0.361%.
- Calibration and computational parameters of note:
  - p_{e,su} = 0.0148; p_{su,lu} = 0.25; p_{lu,su} = 0.19; λ_{su} = 0.724; λ_{lu} = 0.229.
  - (1 − θ) σ = .075; δ_k = δ_h = 0.015; α = 0.36; A = 0.0656; β = 0.9847.
  - T = 100; convergence within 5 iterations; tol = 1e−8.

_ Source: _wp1342 _

### 1. Introduction

### 1. Introduction

### Background and context
- Over the period 1970-2005, unemployment rates in Germany had been steadily rising, making the country a leading example of Eurosclerosis.
- The German government implemented a number of wide-ranging labor market reforms in 2003-2005, the so-called Hartz reforms.
- Hartz IV was implemented in January 2005 and amounted to a complete overhaul of the German unemployment benefit system, resulting in a significant reduction in the level of unemployment benefits for the long-term unemployed.
- A measurement change added more than half a million workers to the pool of unemployed between January 2005 and March 2005 and resulted in a spike in the unemployment rate in 2005; more than 80 percent of these added unemployed workers lacked the equivalent of a high school degree.

### Research questions and approach
- Key questions:
  - How much of the observed decline in the unemployment rate in the period 2005-2008 is a permanent reduction attributable to Hartz IV?
  - What are the consequences for economic growth, taking into account adjustment of physical capital and human capital?
  - What are the welfare effects of Hartz IV for different groups (employed, short-term unemployed, long-term unemployed)?
- Methodology:
  - Develop a macroeconomic model with heterogeneous households that emphasizes the trade-off between insurance and incentive.
  - Use a calibrated version of the model economy to simulate the effects of the Hartz IV reform.

### Model structure (summary)
- The model combines:
  - An incomplete-market framework with human capital (Krebs, 2003).
  - A search unemployment model along the lines of Ljungqvist and Sargent (1998).
- Agents and decisions:
  - A large number of risk-averse, long-lived households who can invest in risk-free physical and risky human capital.
  - Unemployed households choose search intensity; unemployment benefits are not conditioned on (unobserved) search effort.
  - Distinction between short-term and long-term unemployment; job search of the long-term unemployed is assumed less effective than that of the short-term unemployed.
- Aggregate closure:
  - Aggregate production function with constant returns to scale using physical and human capital as inputs.
  - Unemployment insurance is financed with a linear tax on labor.
  - Closed-economy model with an aggregate resource constraint (market clearing) that determines wages and the interest rate endogenously.

### Quantitative findings: unemployment, job finding, and labor supply
- Baseline calibration results:
  - The reform reduces the unemployment rate by 1.4 percentage points from a long-run value of 9 to a new long-run value of 7.6 percent.
  - Main mechanism: increase in search effort leading to higher job finding rates for both short-term and long-term unemployed, with a more pronounced effect for the long-term unemployed.
- Empirical job finding evidence:
  - For the long-term unemployed, the quarterly job finding rate increased from 6.3 percent at the beginning of 2004 to 9.3 percent at the beginning of 2006, and then stayed at this higher level.
  - Job-finding rates for the short-term unemployed also increased substantially, with most of the rise occurring in 2006-2008.
- Cyclical context and measurement:
  - GDP growth was 2.5% in 2006 and 3% in 2007, compared with an average growth rate of 1.1% in the period 1992-2011.
  - The paper notes that the observed job finding increases in the data, particularly for the short-term unemployed, exceed the increases implied by the calibrated model, suggesting Hartz III may also have contributed via improved matching efficiency.

### Quantitative findings: growth and wages
- Growth effects:
  - The reform leads to an increase in long-run growth and an initial decline in real wages.
  - Two channels for higher growth:
    - Increased employment raises output.
    - Higher return to human capital investment induces more human capital accumulation; labor tax reductions due to lower unemployment raise human capital returns and dominate the initial decline in pre-tax wages.
  - Baseline calibration: annual long-run growth increases by about 0.1 percent.
- Wage effects:
  - Wages initially decrease because the reduction in unemployment benefits increases labor supply.
  - Real wages fell about 4 percent in the period 2004-2009 (post-unification series 1992-2011 context).
  - The model is an endogenous growth framework in which the labor market reform affects the long-run growth rate of the economy, including the long-run growth rate of real wages; the real wage decline discussed is relative to the long-run trend.

### Welfare effects and distributional outcomes
- The Hartz IV reform creates winners and losers; gains and losses are unevenly distributed.
- Financing context:
  - Unemployment benefit payments are financed through contributions to the unemployment insurance system levied on labor income.
  - Reductions in unemployment benefits and/or unemployment lead to reductions in this labor tax.
- Welfare impacts (baseline calibration):
  - Employed households gain: welfare gain equivalent to an increase of around 0.4 percent of lifetime consumption (gain from reduced labor tax outweighs loss of unemployment insurance).
  - Long-term unemployed lose: welfare loss around one percent of lifetime consumption (due to large cuts in unemployment benefits).
  - Short-term unemployed also lose, but their welfare loss is significantly smaller than that of the long-term unemployed.
- Political economy implication:
  - The substantial welfare losses experienced by the unemployed could explain why the reform encountered resistance in large parts of the German population.

### Contribution and relation to literature
- Contributions:
  - Introduce a human capital channel and emphasize the distinction between short-term and long-term unemployed.
  - Develop a tractable framework with risk-averse households making search and saving decisions, and apply it to Hartz IV.
- Comparison to other studies:
  - Krause and Uhlig (2011) find unemployment effects of Hartz IV larger than reported here.
  - Launov and Waelde (2012) suggest relatively small unemployment effects.
  - The paper’s results align with cross-country empirical work finding significant effects of unemployment benefits on unemployment (Layard, Nickell, and Jackson, 2005).
- Limitations and future research:
  - The paper abstracts from macroeconomic shocks and therefore cannot speak to interactions between policy and aggregate shocks; incorporating aggregate shocks and allowing for current account/export sector effects are topics for future research.

*Source: _wp1342 - 1. Introduction*

### 3. Model

### 3. Model

### Overview
- Framework combines the incomplete-market model with human capital (Krebs (2003)) with a search model along the lines of Ljungqvist and Sargent (1998).
- Time is discrete and open-ended; unit mass of infinitely-lived households.
- Idiosyncratic shock s_t = (s_1t, s_2t) with:
  - s_1t ∈ {E, SU, LU} (E = employed, SU = short-term unemployed/good job seeker, LU = long-term unemployed/bad job seeker).
  - s_2t represents wage risk (i.i.d. shocks to individual stock of human capital).
- Search effort l is unobservable (moral hazard). Process {s_t} is Markov with transition probabilities π(s_{t+1}|s_t, l_t).

### Households (3.1)
- Preferences:
  - Utility u(c_t, l_t, s_t) = ln c_t − v(l_t) + d(s_1t).
  - Expected lifetime utility: U({c_t, l_t | s_0}) = E[∑_{t=0}^∞ β^t (ln c_t − v(l_t) + d(s_1t)) | s_0].
- Initial state at t = 0: (k_0, h_0, s_0) where k_0 physical capital, h_0 human capital.
- Income and returns:
  - Employed: capital and labor income r_{kt} k_t and r_{ht} h_t.
  - Risk-free return to physical capital: r_{kt} − δ_k.
  - Risky return to human capital: r_{ht} − δ_h + η(s_2t).
  - Unemployed receive benefits B_t = b(s_1t) h_t; unemployed income assumed (1 + b(s_1t))(k_t + h_t) to rule out large portfolio shifts.
- Sequential budget constraint (2):
  - c_t + k_{t+1} + h_{t+1} = (1 + r_{kt} − δ_k) k_t + (1 + (1−τ) r_{ht} − δ_h + η(s_2t)) h_t if s_{1t} = e;
  - c_t + k_{t+1} + h_{t+1} = (1 + b(s_{1t}))(k_t + h_t) if s_{1t} = su, lu.
- For given government policy {b_t, τ_{ct}}, households choose {c_t, l_t, k_t, h_t} to maximize (1) subject to (2).

### Firms (3.2)
- Aggregate production: Y_t = F(K_t, H^e_t) with constant returns to scale.
- Firms hire K_t and H^e_t competitively at rental rates r_k and r_h, maximizing profit:
  - F(K_t, H^e_t) − r_{kt} K_t − r_{ht} H^e_t. (3)

### Government (3.3)
- Pays unemployment benefits financed by linear tax on labor income.
- Balanced budget every period; government budget constraint (4):
  - τ E[r_{ht} h_t] = E[b(s_{2t}) h_t] − E[(r_{kt} − b(s_{2t})) k_t]. (4)

### Aggregation and Wealth Variables (3.4)
- Define household-level:
  - w_t = k_t + h_t. (5)
  - θ_t = k_t / w_t.
  - r(θ_t, s_t) = θ_t (1 + r_{kt} − δ_k) + (1 − θ_t)(1 + (1−τ) r_{ht} − δ_h + η(s_2t)) if s_{1t} = e; = b(s_{1t}) if s_{1t} = su, lu.
- Budget constraint in wealth terms:
  - w_{t+1} = (1 + r(θ_t, s_t)) w_t − c_t. (6)
- Market clearing:
  - K_t = E[θ_t w_t]. (7)
  - H^e_t = E[(1 − θ_t) w_t | s_{1t} = e].
- Aggregate resource constraint:
  - C_t + K_{t+1} + H_{t+1} = (1 − δ_k) K_t + (1 − δ_h) H_t + F(K_t, H^e_t). (8)
- Stationary competitive equilibrium defined by feasibility, household optimization, firm profit maximization, market clearing, and government budget constraint.

### Key equilibrium properties
- Stationary competitive equilibrium: aggregate ratio variables constant; aggregate variables grow at constant rate (unbounded growth implied by constant returns and unbounded accumulation).
- Equilibrium unemployment rates for short-term and long-term unemployed, U_g and U_b, defined through initial values and transition probabilities; law of motion given below.

### Law of motion and intensive-form representation
- Household problem reformulated with state (w, θ, s) and Bellman equation (9):
  - V(w, θ, s) = max_{c, θ', w', l} { ln c − v(l) + d(s) + β ∑_{s'} V(w', θ', s') π(s'|s, l) } s.t. w' = (1 + r(θ, s)) w − c.
- Closed-form properties (Proposition 1):
  - Consumption and next-period wealth linear in wealth:
    - c = (1 − β) (1 + r(θ, s)) w. (10)
    - w' = β (1 + r(θ, s)) w.
  - Value function:
    - V(w, θ, s) = Ṽ(s) + 1/(1 − β) ln(1 + r(θ, s)). (11)
  - Intensive-form Bellman equation for θ' and l (12):
    - Ṽ(s) = max_{θ', l} { B − v(l) + d(s) + [β/(1 − β)] ∑_{s'} ln(1 + r(θ', s')) π(s'|s, l) + β ∑_{s'} Ṽ(s') π(s'|s, l) }
    - where B = ln(1 − β) + [β/(1 − β)] ln β.
- Proposition 1: solution to household problem is given by (10), (11), and (12).
- Aggregate capital-to-labor ratio ˜K = K_t / H^e_t and intensive-form production function f(˜K) = F(˜K, 1).
- Pricing conditions under CRS and competition:
  - r_k = r_k(˜K) = f'(˜K). (13)
  - r_h = r_h(˜K) = f(˜K) − ˜K f'(˜K).
- Intensive-form market clearing condition (14):
  - ˜K' = [ ∑_s θ'(s, ˜K') Ω(s) ] (1 − U') / [ ∑_s (1 − θ'(s, ˜K')) Ω(s) ].
  - Ω(s) is share of aggregate total wealth held by type s; U' = U'_su + U'_lu unemployment rate next period.
- Law of motion for wealth shares Ω (15):
  - Ω'(s') = ∑_s (1 + r(θ'(s, ˜K'), s', ˜K')) Ω(s) / ∑_{s, s'} (1 + r(θ'(s, ˜K'), s', ˜K')) Ω(s).
- Law of motion for unemployment rates (16):
  - U'_su = p_{e,su} (1 − U_su − U_lu) + p_{lu,su} U_lu + (1 − p_{su,e}(l(su, ˜K')) − p_{su,lu}) U_su.
  - U'_lu = p_{su,lu} U_su + (1 − p_{lu,su} − p_{lu,e}(l(lu, ˜K'))) U_lu.
- Proposition 2: Any solution to (12)-(16) with Ω' = Ω and (U'_su, U'_lu) = (U_su, U_lu) is a stationary competitive equilibrium.

### Equilibrium Characterization (4)
- Proposition 1 reduces the household Bellman problem to the intensive-form Bellman equation (12).
- Portfolio choice θ and effort choice l are independent of wealth w; consumption linear in w — enables solving general equilibrium without the full wealth distribution.
- Proposition 2 provides characterization used for quantitative computation of equilibria and transitional dynamics.

### Quantitative Evaluation Setup (5, calibration summary)
- Basic model period: one quarter.
- Calibration targets: stationary equilibrium matching German economy features 2000-2004 (pre-Hartz IV).

Search (5.1.1)
- Long-term unemployment defined as spells > 12 months: p_{su,lu} = 0.25.
- Job search technology (exponential):
  - p_{su,e}(l) = 1 − e^{−λ_{su} l}. (17)
  - p_{lu,e}(l) = 1 − e^{−λ_{lu} l}.
- Quarterly transition probabilities from data (2000-2004):
  - p_{su,e} = .06.
  - p_{lu,e} = .24.
  - These yield λ_{su} = 0.724 and λ_{lu} = 0.229.
- Disutility of search:
  - v(l) = − v̄ l^γ. (18) with normalization v̄ = 1.
- Utility difference between employment and unemployment:
  - d(e) = 0, d(su) = d(lu) = d.
- Target search elasticities:
  - Average elasticity target −0.9.
  - Chosen elasticities: −0.6 for short-term unemployed, −1.2 for long-term unemployed.
  - Implied preference parameters: d = 0.294 and γ = 2.774.
- Job separation and transitions:
  - Job separation rate p_{e,su} chosen to match unemployment rate 9 percent (2000-2004): p_{e,su} = 0.0148.
  - p_{lu,su} chosen to match share of long-term unemployed in unemployment pool 50 percent (OECD 2000-2004): p_{lu,su} = 0.190.

Wage Risk (5.1.2)
- Human capital shock η ∼ N(0, σ^2).
- Approximation: log labor income follows random walk with innovation variance (1 − θ)^2 σ^2.
- Target for (1 − θ) σ = .075 in equilibrium (quarterly standard deviation).

Production (5.1.3)
- Quarterly depreciation rates: δ_k = δ_h = 0.015.
- Cobb-Douglas production: F(K, H^e) = A K^α (H^e)^{1−α}.
- Capital share α = 0.36.
- Technology parameter A and discount factor β chosen to match:
  - Output growth rate 1 percent.
  - Saving rate 20 percent.
  - This yields A = 0.0656 and β = 0.9847.

Unemployment Benefits (5.1.4)
- Calibration of b_{su} and b_{lu} to match net replacement rates for short-term and long-term unemployed (2000-2004) using OECD net replacement rates for single households with average earnings.
- Target net replacement rates (weighted average across single households without children and with two children):
  - Short-term unemployed: 0.63.
  - Long-term unemployed: 0.57.

*Source: _wp1342 - 3. Model*

### 5.2 Effects of Hartz IV Reform

### _wp1342 - 5.2 Effects of Hartz IV Reform

### Overview of the reform's direct effect on replacement rates
- The Hartz IV reform left the net replacement rate of the short-term unemployed unchanged.
- The net replacement rate for the long-term unemployed was reduced from 0.57 in the period 2000-2004 to 0.46 after the reform in 2005.
- The simulations assume the reform reduced the long-term net replacement rate from 0.57 to 0.46 and left the short-term net replacement rate unchanged.

### Macroeconomic effects
- Long-run unemployment:
  - Unemployment rate falls from 9 percent before the reform to 7.60 percent after the reform (stationary-equilibrium comparison).
  - The model implies a permanent reduction in the unemployment rate attributable to Hartz IV.
- Job-finding rates:
  - Job finding rates for both short-term and long-term unemployed increase after the reform due to higher search effort.
  - In percentage terms, the increase in the job finding rate for the long-term unemployed exceeds that for the short-term unemployed.
  - Hartz IV explains a large portion, but not all, of the observed increases in job finding rates; improvements in matching efficiency (e.g., Hartz III) are cited as a candidate to explain remaining increases.
- Transitional dynamics:
  - It takes about 8 quarters for the unemployment rate to reach halfway to the new stationary equilibrium.
  - The share of long-term unemployment in total unemployment declines from a long-run value of 50 percent before the reform to 48 percent after the reform.
  - The dynamic adjustment of the unemployment rates for short-term and long-term unemployed is reported as very similar.
- Growth and wages:
  - The reform leads to an increase in long-run growth and an initial decline in real wages.
  - Initial wage decline is driven by increased labor supply after benefit reduction.
  - Long-run growth rises because (i) higher employment raises output, and (ii) the return to human capital investment increases, inducing more human capital investment; the increase in human capital returns arises because the labor tax can be reduced following lower unemployment, and this effect dominates the initial decline in pre-tax wages.
  - The increase in the annual long-run growth rate of the economy is about 0.1 percent.

### Welfare effects (individual and social)
- Method:
  - Welfare is measured as expected lifetime utility for each group (employed, short-term unemployed, long-term unemployed) computed in the pre-reform stationary equilibrium and for the transitional path to the post-reform stationary equilibrium.
  - Social welfare is defined as the population-weighted average of the welfare of the three groups.
  - Welfare changes are translated into equivalent consumption units via the change in certainty consumption that makes households indifferent between no-reform and reform.
- Distributional outcomes:
  - Employed households: welfare increases by 0.44 percent of lifetime consumption.
    - For employed households, tax-reduction gains outweigh insurance-losses.
  - Long-term unemployed: welfare decreases by 0.74 percent of lifetime consumption.
    - For long-term unemployed, loss of unemployment benefits dominates tax-reduction gains.
  - Short-term unemployed: welfare falls (magnitude reported as losing, intermediate between employed and long-term unemployed).
- Insurance vs. output effects:
  - The reform reduces insurance against unemployment risk (negative welfare effect), especially for long-term unemployed.
  - The reform raises employment and output, and employed households benefit via lower labor income taxes (positive welfare effect).
  - Table 2 (as described) isolates the welfare loss due to insurance loss by computing welfare changes holding mean consumption growth unchanged.
- Social welfare:
  - The reform increased social welfare (population-weighted average).
  - The paper notes that redistributing more of the output gains to the unemployed and less to the employed would make the reform Pareto-improving, but in practice employed households receive the output gains through reduced contributions to unemployment insurance.
  - A computed benefits rate that maximizes social welfare is reported to be lower than the post-reform benefit rate, but welfare gains from further reduction are "very small."

### Sensitivity analysis
- Robustness: main results are surprisingly robust to moderate changes in parameter values; substantial changes to key targets matter.
- Examples:
  - If the pre-reform share of long-term unemployed is decreased to 0.4, the Hartz IV reform reduces the unemployment rate by 1.25%.
  - If the pre-reform share of long-term unemployed is 0.3, the unemployment reduction is 1.0%.
  - If average search elasticity with respect to unemployment benefits is −0.8, the unemployment reduction due to Hartz IV is 1.28%.
  - If average search elasticity is −0.5, the unemployment effect is 0.87%. (The text notes −0.5 is a lower bound for the average elasticity in Germany before the reform.)
- Baseline summary:
  - In the baseline calibration, the reform reduced the German long-run unemployment rate by 1.4 percentage points.

### Numerical and computational details (selected)
- Transitional-dynamics computation:
  - The algorithm solves for a sequence of aggregate states X=(Ωe,Ωsu,Ωlu,Usu,Ulu) iterating backward and forward until convergence.
  - Setting T = 100 periods is sufficient for convergence.
  - The algorithm converges within 5 iterations to a tolerance level tol = 1e−8.

### Key quantitative highlights (extracted)
- Long-term net replacement rate: 0.57 → 0.46 (post-reform).
- Unemployment rate: 9 percent → 7.60 percent (stationary equilibrium comparison).
- Share of long-term unemployment in unemployment: 50 percent → 48 percent.
- Time to halfway adjustment of unemployment rate: about 8 quarters.
- Increase in annual long-run growth rate: about 0.1 percent.
- Welfare changes (lifetime consumption equivalents):
  - Employed: +0.44 percent.
  - Long-term unemployed: −0.74 percent.
- Sensitivity scenarios:
  - Pre-reform long-term unemployed share 0.4 → unemployment reduction 1.25%.
  - Pre-reform long-term unemployed share 0.3 → unemployment reduction 1.0%.
  - Search elasticity −0.8 → unemployment reduction 1.28%.
  - Search elasticity −0.5 → unemployment reduction 0.87%.
- Computational parameters:
  - T = 100; convergence within 5 iterations; tol = 1e−8.

*Source: _wp1342 - 5.2 Effects of Hartz IV Reform*

### References

### _wp1342 - References

### References (Selected citations)
- Acemoglu, D., and R. Shimer (2000) “Productivity Gains from Unemployment Insurance,” European Economic Review 44: 1145-1224.
- Addison, J., Centeno, M., Portugal, P. (2008) “Unemployment Benefits and Reservation Wages: Key Elasticities from a Stripped-Down Job-Search Model,” IZA Discussion Paper.
- Alvarez, F., and N. Stokey (1998) “Dynamic Programming with Homogeneous Functions,” Journal of Economic Theory 82: 167-189.
- Ball, L., Leigh, D., and P. Loungani (2012) “Okun’s Law: Fit at 50?” IMF Working Paper.
- Blanchard, O., and J. Wolfers (2000) “The Role of Shocks and Institutions in the Rise of European Unemployment: The Aggregate Evidence,” Economic Journal 100: 1-33.
- Bois, R., Causa, O., Demmon, C., Duval, R., and A. Zdziemicka (2012) “The Short-term effects of Structural Reform: An Empirical Analysis,” OECD Working Paper.
- Bundesagentur fuer Arbeit (2005) “Der Uebergang von der Arbeitslosen- und Sozialhilfe zur Grundsicherung fr Arbeitssuchende,” Sonderbericht.
- Bundesagentur fuer Arbeit (2011) “Der Arbeitsmarkt in Deutschland: Sockel- und Langzeitarbeitslosigkeit,” Arbeitsmarktberichterstattung.
- Burda, M. and J. Hunt (2011) “What Explains the German Labor Market Miracle in the Great Recession?” NBER Working Paper.
- Chetty, R. (2008) “Moral Hazard vs Liquidity and Optimal Unemployment Insurance,” Journal of Political Economy 116: 173-234.
- Fahr, R., and U. Sunde (2009) “Did the Hartz Reforms Speed Up the Matching Process? A Macro-Evaluation Using Empirical Matching Functions,” German Economic Review 10, 284-316.
- Hansen, G., and A. Imrohoroglu (1992) “The Role of Unemployment Insurance in an Economy with Liquidity Constraints and Moral Hazard,” Journal of Political Economy 100: 118-142.
- Hopenhayn, H., and J. Nicolini (1997) “Optimal Unemployment Insurance,” Journal of Political Economy 105: 412-438.
- Hunt, J. (1995) “The Effect of Unemployment Compensation on Unemployment Duration in Germany,” Journal of Labor Economics 13: 88-120.
- Jacobi, L., and J. Kluve (2006) “Before and After the Hartz Reforms: The Performance of Active Labor Market Policy in Germany,” IZA Discussion Paper.
- Jung, P., and M. Kuhn (2011) “The Era of US-Europe Labor Market Divide: What Can We Learn?”, Working Paper.
- Krause, M., and H. Uhlig (2011) “Transitions in the German Labor Market: Structure and Crisis,” Deutsche Bundesbank Working Paper.
- Krebs, T. (2003) “Human Capital Risk and Economic Growth,” The Quarterly Journal of Economics 118: 709-744.
- Krebs, T., and Y. Yao (2010) “Labor Income Risk in Germany,” Working Paper.
- Krueger, D., and N. Fuchs-Schuendeln (2009) “Inequality Trends for Germany in the Last Two Decades: A Tale of Two Countries,” Review of Economic Dynamics 13: 103-132.
- Landais, C., Michaillat, P., and E. Saez (2010) “Optimal Unemployment Insurance over the Business Cycle,” NBER Working Paper.
- Launov, A., and K. Waelde (2012) “Estimating Incentive and Welfare Effects of Non-Stationary Unemployment Benefits,” Working Paper.
- Layard, R., Nickell, S., and R. Jackman (2005) Unemployment: Macroeconomic Performance and the Labour Market 2nd. edition, Oxford University Press, 2005.
- Lentz, R. (2009) “Optimal Unemployment Insurance in an Estimated Job-Search Model with Savings,” Review of Economic Dynamics 12: 37-57.
- Lucas, R. (2003) “Macroeconomic Priorities,” American Economic Review 93: 1-14.
- Ljungqvist, L., and T. Sargent (1998) “The European Unemployment Dilemma,” Journal of Political Economy 514-550.
- Meyer, B. (1990) “Unemployment Insurance and Unemployment Spells,” Econometrica 58: 757-782.
- Meyer, B., and W. Mok (2007) “Quasi-Experimental Evidence on the Effects of Unemployment Insurance from New York State,” NBER Working Paper.
- Shimer, R., and I. Werning (2008) “Liquidity and Insurance for Unemployed Workers,” American Economic Review 98: 1922-1942.
- Shimer, R. (2005) “The Cyclical Behavior of Equilibrium Unemployment, Vacancies, and Wages: Evidence and Theory,” American Economic Review 95: 25-49.
- Streufert, P. (1990) “Stationary Recursive Utility and Dynamic Programming under the Assumption of Biconvergence,” Review of Economic Studies 57: 79-97.
- Stokey, N., and R. Lucas (1989) Recursive Methods in Economic Dynamics Harvard University Press, 1989.

### Table 1. Calibration (Parameter values)
- p_e,su : transition probability E→SU = 0.0148
- p_su,lu : transition probability SU→LU = 0.25
- p_lu,su : transition probability LU→SU = 0.19
- λ_su : search efficiency of short-term unemployed = 0.724
- λ_lu : search efficiency of long-term unemployed = 0.229
- ̄v : utility parameter (normalization constant) = 1
- d : disutility of work = 0.293
- γ : curvature of disutility function = 2.774
- β : discount factor = 0.985
- σ : standard deviation of wage shocks = 0.075
- δ_k : depreciation rate of physical capital. = .015
- δ_h : depreciation rate of human capital. = .015
- α : capital’s share in output. = .36
- A : total factor productivity = 0.0656
- b_su : net replacement rate for short-term unemployed = 0.628
- b_lu : net replacement rate for long-term unemployed = 0.572

### Table 2. Macroeconomic Effects (Pre-Reform vs Post-Reform)
- unemployment rate: Pre-Reform = 9% ; Post-Reform = 7.760%
- unemployment rate (short-term unemployed): Pre-Reform = 4.5% ; Post-Reform = 3.92%
- unemployment rate (long-term unemployed): Pre-Reform = 9% ; Post-Reform = 3.67%
- job finding rate (short-term unemployed): Pre-Reform = 0.24 ; Post-Reform = 0.277
- job finding rate (long-term): Pre-Reform = 0.06 ; Post-Reform = 0.077
- growth: Pre-Reform = 1% ; Post-Reform = 1.07%

### Table 3. Welfare Effects in Percent of Lifetime Consumption
- Net Effect / Insurance Effect
- Employed: Net Effect = +0.439% ; Insurance Effect = -1.795 %
- Short-term Unemployed: Net Effect = −0.132% ; Insurance Effect = -2.354 %
- Long-term Unemployed: Net Effect = −.739% ; Insurance Effect = -2.948 %
- Social Welfare: Net Effect = +0.361% ; Insurance Effect = -1.873 %

### Figures (captions and data notes)
- Figure 1: Unemployment Rate, Germany 1970 - 2011
  - Source: OECD: 1970 - 1990, annual unemployment rate for West Germany; 1991 - 2011, annual harmonized unemployment rate for Germany.
- Figure 2: Quarterly Job Finding Rates by Duration of Unemployment Spell, Germany 2000 - 2011
  - Series: short term; long term.
  - Source: Bundesagentur für Arbeit (2011).
- Figure 3: Real Wage and Real GDP per Capita (1992 = 100), Germany 1992 - 2011
  - Series: real wage; real gdp per capita.
  - Sources: Statistisches Bundesamt: annual real wage index (series: Reallohnindex) and annual real GDP per capita (series: Bruttoinlandsprodukt) normalized to 1992.
- Figure 4: Average Net Replacement Rate, Germany 2001 - 2010
  - Series: short term; long term.
  - Sources: OECD. (1) net replacement rates: OECD Tax-Benefit Models, (2) population weights: OECD Family Database.
- Figure 5: Unemployment Rate (plot axis labeled −100102030405060 and percent axis showing values including 7.4 through 9.4)
- Figure 6: Unemployment Rate by Duration of Unemployment Spell (short term; long term) (plot axis labeled −100102030405060 and percent axis showing values including 3.6 through 4.6)
- Figure 7: Annualized Growth Rate of Aggregate Output (no reform; reform) (plot axis labeled −100102030405060 and percent axis showing values including 0.9 through 1.6)
- Figure 8: Annualized Growth Rate of Average Wage (no reform; reform) (plot axis labeled −100102030405060 and percent axis showing values including 0.4 through 1.1)

*Content derived from _wp1342 - References (PDF).*

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