Abstract
In 2003–05 the German government implemented a number of farreaching labor market reforms, the socalled Hartz reforms. At the heart of the reform package was the Hartz IV law, which resulted in a significant cut in the unemployment benefits for the longterm unemployed. The paper develops a macroeconomic model with search and incomplete markets, calibrates the model economy to German data and institutions, and uses the calibrated model economy to simulate the effects of the Hartz reforms, and in particular Hartz IV, on the German labor market. The paper finds that the Hartz IV reform reduced the noncyclical unemployment rate in Germany by 1.4 percentage points. Employed workers benefited from the Hartz IV reform in welfare terms, but unemployed workers lost. It further finds that the Hartz I–III reforms reduced the noncyclical unemployment rate in Germany by 1.5 percentage points. Finally, the authors’ analysis suggests that the Hartz reforms contributed to the good performance of the German labor market during the Great Recession.
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Notes
 1.
The Hartz IV reform entailed a significant change in the official measurement of unemployment, which added more than half a million workers to the pool of unemployed between January 2005 and March 2005 (see Bundesagentur fuer Arbeit, 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 highschool degree.
 2.
We use a closedeconomy model with an aggregate resource constraint (market clearing) that determines wages and the interest rate endogenously. We think that it is desirable to include an analysis of possible real wage effects of the Hartz reform, something that would be missing if we had used a standard small open economy framework. Clearly, the Germany’s export sector is large (about half of GDP), and an extension of the current analysis that allows for current account effects of the Hartz reform is an important topic for future research.
 3.
Data on the job finding rates for shortterm and longterm unemployed before and after the reform support this prediction of the theory. See Section I for more details.
 4.
We use an endogenous growth model in which the labor market reform affects the longrun growth rate of the economy, including the longrun growth rate of real wages. The real wage decline we discuss here is a decline relative to the longrun trend. See Figure 8 for details.
 5.
Our results do not rule out the possibility that adopting other parts of the Hartz reforms (Hartz I–III) could prove more beneficial to France or Spain.
 6.
Franz and others (2012) analyze the Hartz IV reform using a microsimulation approach where households make a static labor supply decision.
 7.
A glance at Figure 4 shows that wage moderation has been taken place in Germany, but it also shows that this process of wage moderation started many years before the Hartz reforms. The wage evolution in Germany depicted in Figure 4 further suggests that in Germany, where union coverage is still relatively high, the bargaining power of unions in wage negotiations has been small for some time. Thus, our modeling assumption of a competitive labor market might be appropriate to a first approximation.
 8.
The fact that the German job finding rate has only a negligible cyclical component has also been documented in Jung and Kuhn (2012), a finding that stands in contrast to the findings for the United States (Shimer, 2005).
 9.
The OECD reports the fraction of longterm unemployed (the incidence of longterm unemployment). In accordance with the model prediction, in the data this variable decreased after the reform. However, the data on the incidence of longterm unemployed are not well suited to “test” the basic mechanism for two reasons. First, this variable is heavily influenced by movements into and out of the labor force, which can be very different for shortterm and longterm unemployed workers. Second, the variable has a strong cyclical component.
 10.
To gather public support for the reforms, the government took advantage of a scandal involving the Federal Employment Agency, which had grossly misreported the success of job placement.
 11.
Of course, most European countries introduced some type of labor market reform in the last 20 years, but they were either much more limited in scope or the implementation was much more gradual.
 12.
In addition, the eligibility period for shortterm unemployment benefits (Unemployment Benefit I) was reduced in February 2006, but this change was not officially a part of the Hartzlaws and had only a small effect on the average net replacement rate (see Figure 5).
 13.
In the model, the net replacement rate is not b, but b/((1−τ)r_{ h }), and we choose b so that the implied value of b/((1−τ)r_{ h }) matches the corresponding net replacement rate.
 14.
The results are similar, at least in terms of the effect of Hartz IV on net replacement rates, if we take couples instead of singles as long as we weigh the group without children and the group with two children the same way. The OECD does not report net replacement rates for households with one child. Hartz IV had a larger effect on the net replacement rate of households with one child than it had on the net replacement rate of households with two children, and our weighing scheme therefore understates the effect of Hartz IV on net replacement rates.
 15.
We also computed the benefits rate that maximizes social welfare and found that this rate is lower than the postreform benefit rate, but the welfare gains of this further benefit reduction are very small.
 16.
This effect is somewhat smaller than sum of the two individual effects because of nonlinearities.
 17.
Of course, this approach is somewhat crude, but seems appropriate given that the Hartz reforms mainly affected job finding rates and our interest is in analyzing how the Hartz reforms changed the dynamic response of the German labor market to macroeconomic shocks. Clearly, our approach is necessarily silent about the fundamental factors underlying the cyclical rise in job destruction.
 18.
Contrary to popular belief, this shows that the German job destruction rate increased during the Great Recession (relative to trend), though the increase was probably less pronounced than what one would expect given that GDP contracted by 5 percent in 2009. Jung and Kuhn (2012) and Gartner, Merkl, and Rothe (2012) compute the cyclical component of the job destruction rate (flow rate from employment to unemployment) using IAB data for the time period before the Hartz IV reform, and find that the job destruction rate in Germany is in general highly volatile.
 19.
Different assumptions about the implied search elasticities are another possible explanation for the different findings in the macro literature on Hartz IV. However, neither Krause and Uhlig (2012) nor Launov and Waelde (2013) report the respective microlevel search elasticity that their calibrated macro models imply, and it is therefore difficult to analyze the issue further.
 20.
Thus, B_{ W } is the set of all functions, V, with L(x)≤V(x)≤U(x) for all x∈X.
 21.
Alvarez and Stokey (1998) provide a different, but related argument to prove the existence and uniqueness of a solution to the Bellman equation for a class of unbounded problems similar to the one considered here, though without moral hazard.
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Additional information
^{*}Tom Krebs is Professor of Economics at Mannheim University and Martin Scheffel is Assistant Professor of Economics at Cologne University. The authors thank seminar participants at various institutions and conferences for useful comments. They thank the editors of this journal, two referees, and their discussant, Roman Duval, for many suggestions and insightful comments. The authors also thank the Center for European Research (ZEW), Mannheim, for supporting their work on labor market reform. Tom Krebs also thanks the German Science Foundation (DFG) for support under SFB884.
Appendix I
Appendix I
Proof of Proposition 1
The household maximization problem we consider in this paper has the feature that probabilities depend on choices, in contrast to the class of problems analyzed in Stokey and Lucas (1989). However, the standard argument for the principle of optimality still applies. Similarly, another standard argument shows that the Bellman equation (9) has a unique solution in an appropriately defined function space (contraction mapping theorem). Guessandverify then shows that the value function (equation (11)) with coefficients determined by Equation (12) solves Equation (9) with optimal policy function defined in Equation (10).
There is a technical issue regarding the construction of the appropriate function space as the economic problem is naturally an unbounded problem. To deal with this issue, one can, for example, follow Streufert (1990) and consider the set of continuous functions B_{ W } that are bounded in the weighted supnorm , where x=(w, θ, s) and the weighting function W is given by W(x)=L(x)+U(x) with U an upper bound and L a lower bound, and endow this function space with the corresponding metric.^{Footnote 20} A straightforward but tedious argument shows that confining attention to this function space is without loss of generality. More precisely, one can show that there exist functions L and H so that for all candidate solutions, V, we have L(x)≤V(x)≤H(x) for all x∈X. This completes the proof of Proposition 1.^{Footnote 21}
Proof of Proposition 2
From Proposition 1 we know that individual households maximize utility subject to the budget constraint. Thus, it remains to be shown that the intensiveform marketclearing condition (equation (14)) is equivalent to the marketclearing conditions (equation (7)) and that Equations (15) and (16) are the equilibrium law of motions for Ω and U.
First, note that the solution to the household problem only depends on the first component s_{1}, but not on the i.i.d. component s_{2}. Recall that and let be total wealth in period t after production and depreciation has taken place. The aggregate stock of physical capital held by households in period t+1 is
The second line in Equation (A.1) uses the equilibrium law of motion for the individual state variable w, the third line is simply the law of iterated expectations, the fourth line follows from the fact that the portfolio choices only depend on s_{1}, and the last line is a direct implication of the definition of Ω. A similar expression holds for the aggregate stock of human capital held by all households, E[h_{ t }]=E[(1−θ_{ t })w_{ t }], and the aggregate stock of human capital held by employed households, E[h_{ t }s_{1t}=e]=E[(1−θ_{ t })w_{ t }s_{1t}=e]. Dividing the expression for E[k_{ t }] by the expression for E[(1−θ_{ t })w_{ t }s_{1t}=e] proves the equivalence between Equations (7) and (14).
Define r(s_{1t}, s_{1,t+1}) as the investment return after the expectation over s_{2t} and s_{2,t+1} has been taken. The law of motion for Ω can be found as
where the second line uses the equilibrium law of motion for the individual state variable w, the third line is simply the law of iterated expectations, the fourth line follows from the fact that portfolio choices only depend on s_{1} in conjunction with the definition of r, and the last line is a direct implication of the definition of Ω. This shows that the law of motion for Ω is Equation (15). The law of motion (equation (16)) for U is obvious. This completes the proof of Proposition 2.
Computation
To compute stationary equilibria, we use Proposition 2, that is, we solve the equations (12), (13), (14), (15), (16) with Ω′=Ω and U′=U. The max problem (equation (12)) is solved using the firstorder conditions approach for portfolio choice and effort choice. Thus, we find a stationary equilibrium by solving a lowdimensional nonlinear equation system.
For the computation of the transitional dynamics, we iterate over the sequence of aggregate wealth shares and unemployment rates, that is, over sequences of the relevant aggregate state variable. Specifically, if we denote the aggregate state by X=(Ω_{ e }, Ω_{ su }, Ω_{ lu }, U_{ su }, U_{ lu }), then the solution algorithm proceeds as follows:
Step 1:

Compute the prereform and postreform stationary equilibrium allocation and the respective lifetime utilities.
Step 2:

Set the number of periods T the economy needs to converge to the new stationary equilibrium. Guess a sequence of aggregate states, {X_{ t }}_{t=0}^{T}, where the initial aggregate state and the final aggregate state correspond to their pre and postreform equilibrium values, respectively.
Step 3:

Given the sequence of aggregate states and the households’ life time utility function in intensive form, we start at period T and solve backwards for a time series of individual households portfolio and effort choices, households’ intensiveform lifetime utility, the aggregate capitaltolabor ratio, and the consumption tax rate.
Step 4:

Given the time series for households’ portfolio choices and effort choices and aggregate capitaltolabor ratio, we use the recursive formula (equation (15)) and (equation (16)) for the aggregate state variable to solve forward for a sequence of aggregate state variables {X_{ t }}_{t=0}^{T}.
Step 5:

If max{X_{ t }^{B}}_{t=0}^{T}−{X_{ t }^{F}}_{t=0}^{T}<tol, the backward and forward solutions converged and we have solved for the transitional dynamics of the endogenous variables; otherwise, update the guess for the evolution of the aggregate state variable {X_{ t }^{B}}_{t=1}^{T−1}={X_{ t }^{F}_{}t=1}^{T−1} and go back to step 3.
Solving for the transitional dynamics, we find that setting T=100 is sufficient and that the algorithm converges within five iterations to a tolerance level tol=1e−8.
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Krebs, T., Scheffel, M. Macroeconomic Evaluation of Labor Market Reform in Germany. IMF Econ Rev 61, 664–701 (2013). https://doi.org/10.1057/imfer.2013.19
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JEL Classifications
 E21
 E24
 D52
 J24