Unemployment, Hours, Taxation and the Welfare State– A Quantitative Assessment of Institutional Changes ∗
Philip Jung Universiteit van Amsterdam
March 14, 2007 First Version: April, 2006 Abstract This paper addresses, within a structural matching model with heterogeneous risk-averse agents, whether key mechanisms identified in the literature can quantitatively account for the different labor market experiences between the US and Germany. The set of facts a successful theory of the labor market should jointly explain are the strong increase in unemployment rates in Germany by five percentage points, the strong decline in average hours worked per person employed by fifteen percentage points, the decline in labor force participation rates relative to the US by six percentage points and the (almost) constancy of the German wage distribution relative to the big increase in wage inequality in the US. We focus on the role of taxation, the unemployment benefit system, union behavior, the increase in turbulence and the welfare state. We show that these explanations imply a positive relation between unemployment and hours worked. Therefore neither of the mechanisms can explain the rise in unemployment and the fall in hours worked jointly. We highlight that the increase in the social assistance level in Germany can quantitatively account for the wage compression as well as the labor force participation differential between the two countries. However, it cannot explain changes in unemployment rates or hours worked. JEL Classification System: E31,E32,E24,J64
Keywords: search theory, unemployment, hours worked ∗ I am indebted to my advisors Dirk Krueger and Wouter den Haan for very helpful comments and many discussions. I am grateful for comments by Keith Kuester, Christian Offermanns, Almuth Scholl and Gernot Mueller and by seminar and conference participants in Frankfurt, Mannheim, Amsterdam and Vienna. This paper is part of my thesis written with Dirk Krueger at the University of Frankfurt. All mistakes are my own. Correspondence: Jung: Universiteit van Amsterdam,e-mail:
[email protected].
1
Introduction
The US and Germany (and many other European countries) had remarkably different labor market experiences between the seventies and now. This difference is most evident in four stylized facts. First, in the US the unemployment rate fluctuates around a stable mean of 6% while in Germany there was a steady increase from very low rates to now 9%. Second, labor force participation rates were slightly higher in Germany in the seventies relative to the US, while they are 6% lower today. Third, average hours worked per person employed, being similar initially, stayed almost constant in the US, but declined dramatically in Germany by 15% for full time employed workers. Fourth, during the same time period the US experienced a strong increase in the spread of the wage distribution while the German wage distribution remained almost constant. A huge amount of research has been devoted to understanding the differences in unemployment rates from an empirical macroeconomic perspective, mainly focussing on interactions between macroeconomic shocks and institutions as in Blanchard and Wolfers (1999) and Nickell, Nunziata, and Ochel (1999). Typically either the extensive (employment) or the intensive (hours worked) margin has been used. The interaction between the two was hardly considered. More recently economists have tried to understand the big differences across countries in hours worked. Surveying the behavior of hours worked in 21 countries, Rogerson (2006) calls for models that can potentially explain the cross country differences as well as the time series pattern. He argues that hours worked are not just the flip side of the unemployment pattern but a distinct phenomenon. This paper extends this view and argues that a reasonable model of the labor market should ultimately explain the cross country differences in the four prime dimensions outlined above jointly. A general equilibrium approach can potentially provides restrictions on explanatory factors that can be used to disentangle the quantitative importance of different channels. To keep the analysis tractable we start by looking at two countries, Germany and the US. Within a general equilibrium matching model with risk-averse heterogenous agents facing a labor-leisure trade off, we address the quantitative importance of different mechanisms highlighted in the literature with respect to the four dimensions described above. The mechanisms refer to the role of taxation, to the importance of the unemployment benefit system, to the role of unions and to the interaction between the increase in the social assistance level and changes
1
in the composition of skill levels either due to an increase in turbulence, as defined in Ljungqvist and Sargent (2005), or due to skill-biased technical change. We find that the strong increase in labor taxation per se1 is quantitatively not an important cause of the increase in unemployment rates as proposed in Daveri and Tabellini (2000). But it can account for a significant fraction (around 50%) of the decline in average hours worked per person employed. This result is in contrast to Prescott (2004) who attributes 100% to tax rate changes alone but potentially consistent with the views expressed in Alesina, Glaeser, and Sacerdote (2005) who argue that other factors, in particular labor market institutions, might matter. However, changes in labor market institutions typically used to explain increases in unemployment differentials will lead to an increase in hours worked and can therefore not be made responsible for the increase in unemployment and the decline in hours worked at the same time. In particular we show that the increase in net replacement rates, as argued for in Mortensen and Pissarides (1999), has to be unreasonably large to explain the observed increase in unemployment rates. We need a seven percentage point increase in net replacement rates which is counterfactual. Additionally, an observed increase in unemployment benefits does not compress the wage distribution but increases averages hours worked per person employed. This is due to a composition effect that changes the skill distribution in favor of the high skilled who work more on average, and to a wealth effect that reduces consumption and increases incentives to work harder. Similarly, an increase in the strength of unions, captured by the relative bargaining position between workers and firms, can by construction ”explain” an increase in unemployment rates but is unable to explain the strong decline in hours worked at the same time. In particular ”unions” would opt for an increase in hours worked, which is counterfactual for Germany. Additionally, unions are likely not responsible for the compression of the wage distribution. To address the importance of the welfare state in Germany we look at the interaction between the social assistance level that provides an effective minimum wage requirement and the cut-off point for hiring low-skilled workers. Using the discipline imposed by the wage distribution we show that for the US the changes in the minimum wage2 is quantitatively not responsible for 1
Most papers implicitly relate tax rate changes to changes in say the net replacement rate, which we view as distinct phenomena
2
the change in the spread of the wage distribution. In contrast, for Germany the increase in the social assistance level might well be responsible for the observed wage compression relative to the US. Additionally it can quantitatively account for the observed increase in unemployed among the recipients of social assistance and the lower labor force participation rate of Germany relative to the US. However, it has problems in explaining the increase in unemployment rate differentials, given that the workers at the margin will drop out of the labor force. It also leads to an increase in hours worked, due to a composition effect. This finding might have implications for one of the most prominent explanations of the ”European Unemployment Dilemma” highlighted in Ljungqvist and Sargent (1998, 2005). They use the increase in the spread of the wage distribution in the US as evidence for an increase in ”turbulence”, that is, an increase in the variability of the idiosyncratic component of the skill level of an individual worker. In their model the interaction between (stochastic) changes in the skill level and the unemployment benefit system generates a diverging time path between high benefit countries like Germany and the US. However, an increase in the idiosyncratic component of the skill distribution should prima facie lead to an increase in the spread of the wage distribution for Germany also, something we do not observe in the data.
3
This either means
that there was no increase in turbulence in Germany, or, as our findings would suggest, that the interaction between the Welfare State and changes in the skill distribution can explain labor force participation rate differentials, but might not be able to explain unemployment differentials.
This paper abstracts from technological growth as an explanation of the phenomena described above as highlighted for example in Pissarides (2006). While a representative agent version of the model driven by technology shocks can reproduce the entire cyclical unemployment path for the US as shown in Jung (2005), our model, retaining a standard neoclassical growth structure, does not feature long run effects of growth on unemployment. However, the effects in Pissarides (2006) rely on a change in the spread of productivity relative to the outside option, a mechanism 2
The minimum wage restrictions works in our model similar to a guaranteed minimum earning. Both define an effective outside option or a minimum cut-off level, which prevents firms from opening up vacancy markets for particular skill groups.
3
The mechanism has been criticized by den Haan, Haefke, and Ramey (2005) who show nicely that the introduction of an endogenous destruction margin might destroy the quantitative implication of (Ljungqvist and Sargent, 1998, 2005). In addition their skill depreciation mechanism, which is hard to pin down, has to be in an equivalent order of magnitude as an observed increase in the outside option.
3
we discuss in detail and which is fully captured by the model.
4
The paper proceeds as follows. Sections 2 and 3 introduce the model and the equilibrium concept used. Section 4 describes part of the data and institutional arrangements for Germany and outlines our calibration strategy. Section 5 shows the results of different sets of policy experiments. Section 6 offers concluding remarks.
2
Description of the Model
The model economy consists of a large number of identical families, each family has a continuum of infinitely lived members. Each member of the family has a particular skill level Ai ∈ A. The distribution of skills is drawn from a continuous probability density function m defined over A ⊆ R+ which we take to be log-normal L(0,σ 2 ). Each worker can be in two states ee ∈ E = {u, e}, that is either unemployed or employed.
The families earn income from wages of their worker members, from unemployment benefits for their unemployed members, from their capital holdings, from general governmental transfers and from their shares in a mutual fund that redistributes all profits from firms arising in the economy. The family collects income of their members and distributes back consumption to its members. We assume that the family maximizes the sum of individual lifetime utilities where each member receives the same weight. Period utility is given by: u(c, h) = log(c) − Bhϕ
(1)
where B is a constant scaling parameter, c is consumption and h is hours worked. Given the form of the utility function this means that each member consumes the same.5 We now state f being a the family saving problem in recursive form where we denote the value function with W
function of the aggregate state S that includes the measure µ of the different skill tyeps. When
making their investment decision the family takes the distribution of skills and the corresponding 4
In his model this effect is reinforced by an endogenous search intensity, which we abstract from.
5
See Jung(2006) for the description of the general non-separable case in a similar model. We chose this particular form because it allows us to derive the Frisch-elasticity independent of the level of average hours worked h.
4
wage contracts and unemployment rates as given: f (S; µ) = max W ′ C,K
{ln(C) −
s.t.
c
C(1 + τ ) + K
′
Z
f (K ′ ; µ′ )} Bh(S; µ)ϕ dµ + β W
(2)
Z
= D(S; µ) + w(S; µ)h(S; µ)(1 − τ L (wh))dµ Z + b(S; µ)du + K + (r(S; µ) − δ)(1 − τ K )K + T (S; µ)
µ′ = H(µ)
(3) (4)
Taxes are denoted by τ where superscripts τ (c,K,L) refer to consumption, capital and labor tax respectively. We allow the labor tax code to be a function of labor income to discuss the role of progressiveness of taxes. K is the capital stock, D are dividends received from the firms sector, T are lump sum transfers from the government and C is aggregate consumption. Here r is the interest rate, δ the depreciation rate and b is the benefit level of an individual unemployed worker with particular skills. We denote with w(S),h(S) the wage and hour contracts of the individual skill types derived below, that are taken as given by the family when deciding on its optimal investment and aggregate consumption plan. H is the aggregate law of motion for the measure described below.6
2.1
The firms problem
There are two sectors in this economy, a final good producing sector that combines capital and a labor good to produce the final output good and the labor market firms that use labor to produce the labor good. We assume a perfectly competitive final good producing sector with a standard Cobb-Douglas technology solving the following problem: y = max K α L1−α − rK − P w L K,L
(5)
where K is capital and L is itself an aggregator of a differentiated, but homogenous labor service good lz : L= 6
Z
lz dµ
(6)
Given that we will focus on stationary distributions later on we will omit the dependence of all endogenous variables from the measure when it is innocent.
5
The price of the labor good is denoted by P w . Each labor service lz is produced by individual firms, viewed as a match between a worker and a small firm. The match has a linear production technology: lz = Az hz
z ∈ [0, 1]
(7)
where h indicates hours worked of an individual worker. The labor goods are viewed as perfect substitutes, so labor firms take prices as given. Standard first order conditions of the final goods producing sector lead to: Pw = r =
Y (1 − α) L Y α K
(8) (9)
Note however that P w is not the wage, but denotes the price the labor firm obtains for its services. The wage a worker obtains for its labor is determined as the outcome of a bargaining game between the worker and the labor service firm, which we describe next.
2.2
Bargaining
The labor service firm produces an intermediate labor good, which exclusively depends on labor inputs and is needed to produce the aggregate output good as described above. Whenever a match is formed, the worker and the firm produce until they receive an exogenous separation rate shock λ. Having received this shock, the match terminates, the firm gets out of business and the worker becomes unemployed. The value of a firm that is matched to a worker with skill levels Ai is given by: Π(Si ) = P w Ai hi − wi hi + (1 − λ)q ′ Π(Si′ )
(10)
where Si indicates the dependence on the aggregate state variables and the individual productivity level. Here q ′ is the discount factor of the firm that is linked to the discount factor of the owner, i.e. the family, such that ′
q =β
∂u(c′ ) ∂c′ ∂u(c) ∂c
(11)
that is Π(S) is the stock market value of a particular match if there were trade between families. The thread point from the families perspective for a particular skill type taken all other wage
6
contracts as given is: L
∆V (Si ; µ) =
) w(Si )h(Si ) (1−τ − 1+τ C
b(Si ) 1+τ C
C
− Bh(Si )ϕ + β(1 − λ − π ue )∆V (Si′ ; µ′ )
(12)
It is the value to the family of having marginally one worker of a particular skill type employed relative to unemployed, taking as given the wage and hour contract this particular worker would obtain. The equation is derived in Jung (2005) for general balanced growth utility functions. We assume that wages and hours in the match are determined through Nash Bargaining: arg max ∆V ζ Π1−ζ w,h
(13)
where ζ is the bargaining power of the family and a parameter of the model. The first order conditions are given by: Π(Si ) =
(1 − ζ) ∆V (Si ) f ζ ∂U (1−τ L ) ∂C
P w Ai =
(ϕ−1) Bϕhi f ∂U (1−τ L ) ∂C (1+τ C )
(14)
(1+τ C )
(15)
L = τ L (wh) + whτ L′ (wh), that is average tax rates plus the derivative of the average where τf
tax rate evaluated at the bargained total wage.7
This bargaining setup has been criticized by Hall and Milgrom (2005) to rely on an unreasonable thread point. They derive a wage setting equation that is influenced only by the cost of delaying the bargaining for a small period, thereby shielding the wage equation from labor market influences. In our setup this would translate into an equivalent wage equation that is not influenced by unemployment benefits and not influenced by labor market tightness, but by an arbitrary parameter that reflects the cost of delaying instead. Pissarides (2006) takes a middle ground and defines a wage setting equation that relies on unemployment benefits, but not on labor market tightness. Given that we calibrate to small vacancy posting cost, the influence of market tightness at the calibrated parameter values will be small, so our quantitative results do not hinge upon this assumption.
8
7
The tax code of the government is described below. Most part of the paper will focus on proportional tax rates, so the derivative expression will be zero
8
Obviously, they do strongly depend on the assumption that unemployment benefits have an impact on unemployment. However, elasticity estimates appear to be small, see the summary in Costain and Reiter (2005), but clearly not zero. At our calibrated values, that is what we get.
7
2.3
Matching
We assume a CES matching technology that is differentiated for each skill type. That is firms can observe skill levels and can direct their vacancy posting activities to a particular skill submarket. In each sub-market i matching takes place according to: M (Si ) =
u(Si )v(Si ) 1
(u(Si )ξ + v(Si )ξ ) ξ
(16)
with corresponding probabilities: π ue (Si ) ≡ θ(Si ) ≡
Mi x(Si ) = 1 , 0 ≤ π ue ≤ 1 ui (1 + x(Si )ξ ) ξ Mi 1 = 1 , 0 ≤ θ ≤ 1 vi (1 + x(S )ξ ) ξ
(17) (18)
i
where x(S) defines the market tightness separated for each type: xi ≡
vi ui
(19)
Here vi is the number of vacancies posted in each sub-market and ui is the skill dependent unemployment rate. To close the model we assume free entry into the entrepreneurial market for labor such that the number of vacancies posted is given by a standard zero profit condition: κ = q ′ Π(Si′ ) θ(Si )
(20)
where κ is an exogenous per period cost of posting a vacancy and θ is the probability of being matched. For an interior solution we obtain after some manipulations: w(Si )h(Si )
1 − τL b (1 + τ C ) = ζ(κx(Si ) + P w Ai h(Si )) + (1 − ζ)( + BCh(Si )ϕ ) L L L) 1 − τf 1 − τf (1 − τg
(21)
This equation is similar to the standard wage equation of the search and matching literature. That is wage income is a convex combination of skill dependent productivity plus the savings from not having to repost the position and the value of the outside option. This outside option now depends additionally on the value of leisure expressed in marginal consumption units. Note that we have to take into account that θ is bounded by one. We therefore denote by Amin the cut-off level of the skill distribution. No firm will announce a vacancy for types below this 8
level since the cost for filling the vacancy, that is θ(SAmin ) = 1 and x(SAmin ) = 0 does not cover the costs.
9
From the free entry condition this defines the cut-off-level Amin which we report
for future reference in closed form for the case of proportional taxation under the assumption ′
that the economy has settled at a stationary equilibrium: (τ L = 0)10 : b(Amin )(1−ζ)
Amin
1 κ(1 − β(1 − λ) + 1−τ L = w( (ϕ−1) P (1 − ζ) ) ϕ
)
(ϕ−1) ϕ
∗(
1 (1 + τ C )CBϕ (ϕ) ) L (1 − τ )
(22)
We interpret individuals with skill levels to the left of the cut-off point as being out of the labor force, that is as workers who are not searching, while all skill levels right to the point who are not currently employed as being unemployed. Some remarks about this setup are in order. To generate different unemployment rates for different skill groups which is an empirical fact, one has basically two modeling choices. One way to generate the effect is by assuming a higher relative outside option for lower skilled workers than for higher skilled workers as done in Mortensen and Pissarides (1999), for example by fixing the outside option independent of the wage. This would mean that with a proportional benefit system in our model the unemployment rate differential between skill groups disappears. The other alternative, which we prefer, is to assume that the hiring cost varies less than proportional or not at all with skill levels. Note that the average amount spent to hire a manager relative to a low skilled will be higher in the model, just the unit cost per time is assumed to be the same.
2.4
Government
The government follows a balanced budget rule by adjusting transfers T period by period and keeps the exogenous spending g/y fixed at a specified level.11 The governmental budget constraint reads as: g y+ y
Z
b(wh)dµ + T =
Z
whτ L dµ + (r − δ)Kτ K + Cτ C
(23)
9
Conditional on having a job, the bargaining is well defined also for types left to the cut-off point (even though one cannot characterize it in closed form), but these types will not be observed in a (stationary) equilibrium, given that they exit with positive probability and will never receive an offer from that point on. All contracts to the left of the cut-off point are characterized by the property that the expected profits will be smaller than the vacancy posting cost κ < qΠ(SAmin ).
10
The derivation makes use of the free entry condition and the two first order conditions: Expressions for the general tax code follow immediately but cannot be given in terms of exogenous parameters and aggregate endogenous variables, because it depends on the particular functional form.
11
Alternatively g could be held fixed. Given that the government to output ratio was fairly constant, we view this rule as a better description than to fix g.
9
The rule for the benefits is skill dependent. We assume, that it is proportional to the wage earned by the particular skill type. However, there might be a cut-off level, viewed as social assistance payment, which defines a minimum earnings threshold. We think of it as the – in Germany – constitutionally guaranteed minimum income level.12 We let the skill dependent benefit code be given as: b(Si ) = max(bmin , b ∗ w(Si )h(Si )(1 − τ L (w(Si )h(Si )))
(24)
that is, the net replacement rate is proportional until a cut-off point is reached. This rule implicitly defines a minimum wage because wages and hours are monotonically increasing in the skill level and the government therefore chooses the minimum skill level (and by monotonicity the minimum wage rate) that will receive a job offer.13 To capture the effects of progressive taxation we use a simple log-specification for the tax rule: t(Si ) = ̺0 + ̺1 log(w(Si )h(Si )))
(25)
In the benchmark case we work with a proportional tax rule (̺1 = 0) and report changes to this assumption in the sensitivity section.
12
Alternatively, it is the outside option of home production. In this case, of course, there would be no payment flow from the government. Given that we treat transfers as lump sum to the family for individuals not in the labor force, this interpretation would also be consistent with the model.
13
The only difference to an explicit minimum wage law is that the budget constraint of the government is affected differently. This effect is very small, so we will approximate this cut-off point for the US by the minimum wage. For Germany there is no minimum wage laws in place, but bmin can be explicitly approximated by the minimum income guaranteed from the government.
10
3
Equilibrium
We are now ready to define a stationary equilibrium: Definition 1 A stationary equilibrium for the above economy for a given distribution m of skills f : S → R for the representative family and associated is a measure µ ∈ Θ, a value function W
policy functions C : S → R++ , K ′ : S → R, value functions ∆V : S → R and Π : S → R and associated policy functions w : S → R++ , h : S → R++ for the bargaining, vacancy openings v : S → R++ and associated probabilities θ : S → [0, 1] and π ue : S → [0, 1] for the matching market, Dividends D : S → R and transfers T : S → R, prices P W , r, a cut off level Amin such that f satisfies the household Bellman equation and C, K ′ are the associated policy functions, 1. W given r, P W , h, w, and π ue .
2. K, L satisfy, given h, r, P w : r = α ∗ K α−1 L1−α P w = (1 − α) ∗ K α L−α
3. Capital markets and markets for the labor good clear. 4. ∆V and Π satisfy the Bellman equations of the marginal worker and the profit function of the firm. 5. Given probabilities, value functions ∆V and Π, and assumed future individual labor contracts, w(S), h(S) are the solution to the Nash-Bargaining procedure: w(S), h(S) ∈ arg max ∆V (S)ζ Π(S)1−ζ w,h
6. Zero profits from posting a vacancy: κ = Eq ′ Π(S)′ θ(S)
11
7. Perceived probabilities are consistent with the actual, that is they satisfy the aggregate matching condition for each type. 8. Dividends paid to the household are consistent with overall profits in the society: Z Z w D = (P Ah − wh)(1 − u)dµ − κ vdµ 9. The cut of level solves b(Amin )(1−ζ)
Amin =
1 κ(1 − β(1 − λ) + 1−τ L ( w (ϕ−1) P (1 − ζ) )
)
(ϕ−1) ϕ
ϕ
∗(
1 (1 + τ C )CBϕ (ϕ) ) L (1 − τ )
10. The government balances its budget in each period, given its specified rule on taxes and on the minimum wage level bmin 11. Final goods market clear. 12. Define a transition function H : S × Θ → [0, 1] H((K, e, Ai ), (K, e, Ai )) = 1 − λ H((K, e, Ai ), (K, u, Ai )) = λ H((K, u, Ai ), (K, e, Ai )) = π ue ((K, u, Ai )) H((K, u, Ai ), (K, u, Ai )) = 1 − π ue ((K, u, Ai )), ∀Ai , K
hence, stationarity requires ′
µ =µ=
Z
Hdµ
For future reference we define some more variables here precisely. Let u e : S × Θ → [0, 1] denote
] = µ(K, u, A)). The only the measure of unemployed for a particular skill group, that is u(S)
dynamics we allow is the movement in and out of unemployment.
14
Given a current measure of unemployment u the state evolves according to: ′
] = u(S) ] + (1 − u(S))λ ] − π ue ∗ u(S) ] u(S) 14
It is straightforward to generalize the setup to allow for idiosyncratic shocks in skills, which we rule out to focus on the main effects of different mechanism.
12
Stationarity requires: ]= u(S)
λ , ∀S λ + π ue (S)
Given that our total measure of households is normalized to one, we define the labor force to be: µLF =
Z
∞
m(a)dA
Amin
that is the integral with respect to the skill distribution m that actually could get or would accept an offer in the labor market. Correspondingly, the measure of households out of the labor force are: µOLF =
Z
Amin
m(a)dA 0
Given that this assumption is important in interpreting the results, some comments are offered. In our model, the households to the left of the cut-off level are at most indifferent between searching and not searching for a job because they will never receive an offer, in the case when the minimum benefit level is not binding, or would never accept an offer, in the case when it is binding. This corresponds to the ILO definition of unemployed who must actively search. Correspondingly the labor force consisting of employed and unemployed in our model is just the fraction of workers to the right of the cut-off level. However, this concept crucially depends on the definition of search.15 Accordingly we define all averages with respect to our measure of the labor force. For example, average unemployment rate u and average hours worked per person employed h are defined as: u h =
15
= R
R
udµ µLF
h(K,e,Ai )dµ µLF (1−u)
The persons left to the cut-off level are able to work and willing if economic conditions would change, so they clearly should count to the potential labor force. Whether they do in the data depends on their answer to a survey question asking whether they have actively looked for a job. (Also some small idiosyncratic shocks would keep them looking at newspaper adds.) Given that part of the unemployment benefits are conditional on actively searching even though the worker has no incentives to do so it is likely to be misreported. We therefore focus our attention for Germany on total employment to population relative to the US and interpret the difference as non-employed, consisting of unemployed and discouraged workers. In the data we mainly think of them as some fraction of the people receiving social assistance but be in principle able to work (For a time series plot on the fraction of people receiving social assistance see the appendix). While part of the payment in this group is for people unable to work for a variety of reasons unrelated to the labor market like health problems etc., estimates from the official bureau of statistic count over 60% of these households to the potential labor force or as actually unemployed.
13
4
Calibration
This section describes key developments of the German labor market relative to the US that need to be explained by the model. We first give a description of important changes in unemployment rates, hours worked, labor force participation and distributional changes in wages. Given that labor markets are affected by many trends not captured by the model, in particular the rise in female labor force participation, we use the US as a benchmark and aim to describe the differences between the two countries in labor force participation rates. We then highlight institutional changes in tax rates and the unemployment benefit system that we use as (exogenous) explanatory factors. Finally we take a stand on the parameters of the model and give a justification for our calibration strategy.
4.1
Labor Market Facts
We take the seventies as our initial steady state and calibrate the model to match the outlined facts. Table 1 summarizes our main stylized facts. We will shortly describe our choices.
14
Table 1: Stylized Facts and Institutional Changes Country Initial Steady State
USA
Germany
Old
New
Old
New
(1974-1978)
(1998-2002)
(1974-1978)
(1998-2002)
Unemployment Rate
6.5%
5%
4%
9%
Hours worked per employed
1880
1865
1800
1460
Labor Force Participation
70%
78%
69%
72%
P9/P1
3.68
4.65
2.88
3.01
P9/P5
1.94
2.25
1.69
1.85
P5/P1
1.89
2.07
1.7
1.65
Government/GDP
18%
15%
19%
19%
Consumption/GDP
63%
69%
55%
58%
Investment/GDP
19%
19%
22%
20%
τC
6%
6%
14%
16%
τL
25%
27%
33%
46%
τ K (after depreciation)*
50%
51%
39.5%
34%
Tax Revenue/GDP
28%
29%
34%
41%
Transfers Unemployment Ben-
.3%
.23%
.5%
2.6%
8%
12%
14%
21%
Net replacement rate
30%
30%
55%
58%
Minimum hourly wage/Median
44%
35%
-
-
Minimum Earning (Social As-
-
-
14.5%
17.5%
3%
3%
2%
2%
Years* Key Labor Market Variables:
Aggregate Variables:
Institutional Changes:
efit/GDP Transfers Social Security/GDP
sistance) Destruction Rate (λ)
Notes: Data for unemployment, labor force participation and the wage distribution are from the OECD employment outlook. The wage distribution for the US refers to the years 1976 and 2000. For Germany it refers to the year 1984 (the first year available) and 2000. Aggregate and institutional variables are from the national accounts, see the appendix. The capital tax is model based and obtained residually, but is reported for completeness. Hours worked are from ”The Conference Board and Groningen Growth and Development Centre, Total Economy Database, May 2006, http://www.ggdc.net”.
15
4.1.1
Unemployment Rates
In the US standardized unemployment rates were on average 6.5% in the seventies and were even declining slightly in the nineties averaging 5% over the years 1998-2002. German rates in contrast started close to full employment in the seventies and increased steadily until now. We take as our benchmark an average rate (averaged over the years 1974-78) of 4%. Between 1998-2002 standardized unemployment rates (ILO definition) were 9%, so we are interested in explaining a 5 percentage point increase. According to the national concept unemployment rates are now 11.7%, where in western Germany the rate is 9.4% and in the eastern part it is 20.1%. Roughly one million unemployed receive social assistance with an average duration of unemployment in 2004 of 34.3 months, and, discarding people older than 50, with an average duration of 22.5 month. We view this group to be out of the labor force according to our model and take the difference between the national concept and the ILO definition of around 2.5% to be represented by this group.16 4.1.2
Labor Force Participation Rates
Participation rates were similar in the seventies but changed rather drastically afterwards. Given that our model cannot account for the increase in female labor force participation, we focus on the relative differences between Germany and the US. Table 10 provides a more disaggregate view on labor force developments. In the age group 15-64, Germany had around 67% labor force participation that remained constant or slightly declined until reunification and then jumped to 71% and slightly increased to 72% while the US, starting equally in 1970, had already 69% in 1975 and gained steadily to now 77.5%. Interestingly an age decomposition shows that the US has lower participation rates for the prime group between 25-54 in 1970 of 2% which is still the case in 2000. The US exclusively gains in two groups, the young (15-24) where they have 77.2% participation rate while Germany has 72.2, and the old, where the US has 59.2% while Germans have 44.7% in that age group.17 Given that a big fraction of the elderly were almost surely 16
In the seventies this group was essentially zero for Germany. In the US the BLS reports also marginally or discouraged worker that add around 1-1.5% to the unemployment rate between 1994 and 2006. A bigger mass of persons are workers that are employed but had to settle for part-time instead of full-time work. In our model we do not view these people as unemployed or out of the labor force, even though the national German unemployment concept treats part of the persons that work less than 15 hours the week as unemployed.
17
Even more dramatic are employment rates for this group, being 38.6% to 57.7% in 2000. While scaring in absolute terms this numbers seem not to cause a particular problem in theory, given that the extensive
16
affected by the extensive retirement laws of the Kohl legislation we view the actual participation rate gap of 6% as an extreme upper bound and argue for a more modest gap of around 4% the model should be able to explain. 4.1.3
Hours Worked per Person Employed
One of the more spectacular differences are hours worked per person employed, as pointed out by Prescott (2004), even though he focusses on hours worked per population 15-65. According to the Groningen database yearly hours worked per employee in Germany dropped by 20% overall from 1800 between 1974-78 to 1460 between 1998-2002, while it remained almost constant in the US, 1880 and 1865 for the same time periods. There is, however, a strong composition effect, see Table 11. Part time work has increased from 6% to 20%, in part related to the strong rise in female labor participation. However, this composition effect is also present in the US. According to data from the IAB, see Wanger (2003), the drop for full time workers is 15%, while in the US it has been almost constant. Although composition effects are clearly present and the model is not designed to capture part-time work particularly well, we argue for a drop in hours worked per person employed of 15% in absolute terms and relative to the US, similar to the results in Bell and Freeman (1995). 4.1.4
Wage Distribution
The US has witnessed a dramatic change in the wage distribution, showing a strong increase in the spread of the distribution while in Germany this increase has been more modest; or, according to some studies, is not existing at all. According to the OECD measure of gross earnings, see Table 12, for full time employed workers in the US the P9/P1 ratio was 3.68 in 1976 and increased to 4.65 in 2000. The P5/P1 and the P9/P5 ratio increased from 1.9 and 1.95 to 2.07 and 2.25 respectively. These numbers correspond to estimates from Katz and Autor (1999) who report a P9/P1,P9/P5 and a P5/P1 ratio of 3.7, 1.85 and 1.97 respectively, for full-time, full year employed from the CPS in the year 1971. retirement laws of the Kohl government can account for a big part of it, see Fitzenberger and Garloff (2005). This group also accounts for a substantial part of long term unemployed, given that the plans allow for a transition phase of unemployment and an early retirement scheme afterwards, so basically workers become unemployed when 55 earning between 67% and 80% net replacement rates for an extended period of 3-5 years and become early retired with 58-60, facing no essential discount in the retirement payments.
17
In contrast the German wage distribution has been remarkable stable. Prasad (2004) even speaks from the ”unbearable” stability of the German wage structure. OECD data based on the GSOEP indicate even a decline in inequality over the eighties, and a modest increase in the nineties. In 1984, the first year available, the P9/P1 ratio was 2.88, the P5/P1 was 1.7 and the P9/P5 was 1.69. In 1990, the first two values dropped to 2.7 and 1.62 respectively, while the P9/P5 ratio remained constant. In the nineties inequality modestly increased to 3.02, 1.65 and 1.85 respectively.18 We follow Kohn (2006) and argue that there was a modest increase in the upper tail of the distribution and use the OECD data as an estimate.
4.2
Institutional changes
We now provide a description of institutional changes we want to use as explanatory factors. We start out by describing aggregate expenditure and revenue of the government and derive our tax rate measures. We then discuss differences in the benefit system and derive our choice of the minimum earning or the binding outside option. 4.2.1
Tax Rates, Governmental Benefits and Transfers
The US labor tax rate has been fairly constant, while Germany’s was steadily rising. We estimate a labor tax of 25% for the US, obtained from the NIPA by setting aggregate Compensation in proportion to wage taxes. This corresponds also to estimates following the approach of Mendoza, Razin, and Tesar (1994) as updated in Carey and Tchilinguirian (1999).19 We estimate the consumption tax rate τ C to be 6%, also consistent with their approach. We view the capital tax, defined as capital tax after depreciation, as the residual, which we estimate to match the ratio of total amount of taxes paid to output, which is 28%. For the benchmark parameterization this leads to a capital tax of 50%, which is also in line with the estimates obtained using the 18
However, the quality of the GSOEP is problematic. Fitzenberger (1999) provides evidence for the wage and employment trends in Germany for the period 1975-1990 from the IABS, a high quality governmental data set based on social security records. According to his study wage inequality increased for full-time working males. Given that the 90% decile is censored for his data set he reports an increase in P8/P2 from 1.52 in 1975 to 1.72, for the P8/P5 a change from 1.24 to 1.34 and for the P5/P2 from 1.21 to 1.24. In particular for the low skilled there appears to be just a modest increase in wage inequality over time, while for the two other skill groups the inequality increase is more pronounced. For the nineties Kohn (2006) reports an increase in P8/P2 by 9 log points, mainly caused by increases in the upper tail of the distribution.
19
Their revised methods lead to estimates slightly below the value above, being 22% using OECD data. However, we stick to the aggregate estimates but checked sensitivity.
18
Mendoza, Razin, and Tesar (1994) methodology.20 Labor tax rates increased at most by 2% over time, while aggregate tax revenue increased by 1%, so we can reasonably argue that there was essentially no tax rate change in the US. Transfers on social security, which in our model are general transfers to the family, started with 7% between 1974-1978 and increased to 11% for 1998-2002. According to O’Leary (2000) transfers to the unemployed started with 0.35% in the seventies and decreased to now 0.25%. For Germany we obtain a very different pattern. We estimate the consumption tax rate to be 14% for the years 1974-1978. We choose a labor tax rate, that in our model includes all social security contribution to be 33%, according to the data from the German bureau of labor statistic. They give the average wage rate per employee and the average income taxes and social security contributions, which are plotted in the appendix. For the years 1998-2002 we obtain an average labor tax of 46%.21 . This big change is also reflected in the increase of total tax revenue relative to GDP, that increased from 34% to 43%, which is spent mainly on transfers for social security that also increased from 14% to 21%. We again treat the capital income tax after depreciation allowances as the residual and obtain an estimate using our model of 39.5%, which slightly decreased to 34% over time, in our benchmark calibration, again in line with the estimates by Carey and Tchilinguirian (1999). 4.2.2
Replacement Rates and Minimum Earnings Level
Unemployment benefit systems differ across many dimensions, that is eligibility, duration and total amount, which makes a comparison across countries difficult. We will shortly describe both systems in turn. 20
Capital taxes are very hard to measure, so we treat them as the residual and use the model together with our governmental rule to balance the budget. This might lead to slightly different tax rates across experiments with respect to capital taxes, however, the differences are extremely small.
21
While for the eighties the data roughly correspond to the estimates of Carey and Tchilinguirian (1999) they do not for later periods. Their estimate is 42% for the late nineties, significantly below our estimates. However, social security contributions dramatically increased over time, and according to the data used reached an average labor tax of 46%, averaged over employees. Given that we use a bargaining model this appears to be the relevant group. We therefore need to assume that the self-employed face a similar tax rate
19
4.2.3
US Benefit System
For the US the OECD reports gross replacement rates to be between 11% in the seventies and 14% now. Given that tax rates have been almost constant this numbers translate into a net replacement rate of 20%. Net replacement rates in the initial phase are somewhat higher but the pick up rate for the US is very low, just 50% of the persons that are eligible actually apply. Also the duration of 26 weeks is fairly low compared to Germany. We use an estimate of a net replacement rate of 30% which is at the higher end of the estimates, and consider sensitivity in the range of 20-40%. More important than the level is the time series dimension. We argue that there were no big changes in the benefit system, so we treat the net replacement rate of the US as constant. To obtain an estimate of the cut off level Amin , we target the actual minimum wage laws, see Figure 4. According to OECD data the minimum wage expressed as wage per hour was around 44% of the median hourly wage in the seventies and declined to 35%. In the calibration we choose the outside option bmin such that the minimum wage is binding for the lowest skilled group. 4.2.4
German Benefit System
For Germany we shortly describe the benefit system following Hunt (1995). There are three parts to the system, Unemployment Insurance (UI), Unemployment Assistance (UA) and Social Assistance (SA). The latter two are funded by general governmental revenues, while the former is funded by contributions of the employed. Unemployment Insurance was paid up to one year with a net replacement rate of 68% of the previous net monthly wage, conditional that one has worked one year in the previous four years.22 Unemployment Assistance was paid after Unemployment Insurance was exhausted and paid a net replacement rate of 58%, but in contrast to UI was means tested. Between 1985 and 1987 the government extended the duration of unemployment insurance for experienced older workers up to 32 month for workers older than 54, and up to 20 month for workers older than 44. To construct an average, we take the weighted sum spent by the labor agency on unemployment assistance and unemployment insurance weighted by the proportions receiving the different kinds 22
Benefits are part of the tax base to determine average tax rates, but taxes are applied to income without the benefits. There is a cap on benefits which was applied to less than 1% of the recipient according to Hunt (1995).
20
of payment.23 Graph 7 in the appendix shows the result. While the series is highly cyclical, there is no strong increase in the average rate. We argue that it was initially 55% and at most increased by 3% points to 58% as an upper bound. This estimate is in line with the ones obtained from the OECD who estimates net replacement rates for the late nineties (no earlier numbers are available), controlling for different household types. Their estimate is on average 54%, see Martin (1996), but significantly higher for some household characteristics. Using the European Community Household Panel (ECHP) ?) find for the year 1993 a net replacement rate of 55% for Germany on average, though this number is higher for some low skilled groups. Both averages are pretty close to our aggregate measure.24 4.2.5
German Social Assistance Level
In contrast to the US, we can infer the German cut off level bmin directly from the data. We use the third pillar of the welfare state in Germany, the social assistance level. Figure 7 shows the time series plot of minimum net replacement rates where we take the official ”absolute” numbers (Regelsatz ) (which are not defined in relative terms) that define the constitutionally guaranteed existence minimum and relate it to the gross and the net wage.25 While the gross rates were kept almost constant, the net replacement rate increased from 14.5 to 17.5. Given that there is no formal minimum wage, we target this numbers as our effective minimum earning, assuming that nobody is working as full employed below this cut-off level. However, these numbers constitute an extreme lower bound, given that the agency provides means tested subsidies for housing, 23
We do not include payments for skill upgrading, bad weather money for construction worker or bureaucratic spending. These numbers do however include spending on health and retirement that the agency directly transfers to the health and retirement companies/agency.
24
Even though there might be a debate about the precise number of the net replacement rate, being a crude approximation of the actual tax/benefit system, my reading of the social political chronicles (actual law changes as documented in Steffen (2005)) show a systematic increase over the seventies, in particular payment for unemployment education or skill updating was dramatically increased, which was paid at 75% up to 87% of the last netto wage. These years coincide with social democratic influenced coalitions, so it appears unlikely that there was a decrease in the net replacement rates in the seventies. Starting with the conservative Kohl government there were a couple of labor market reforms that would indicate a decrease in the net replacement rate. These are of course counteracted by the strong increase in net replacement rates for older worker. However, as was pointed out by Fitzenberger and Garloff (2005) these changes appear to have effected the drop-out-of-labor-force rate for old age persons, while not significantly affecting the unemployment duration. They are included in our average numbers however. For the nineties it appears to be likely that the net replacement rate in particular for the eastern part has increased in the beginning of the nineties while some very modest reforms were implemented in the later part of the nineties.
25
We also use the total amount spent divided by the number of persons receiving help and come to similar conclusions.
21
durable good consumption and the like. However, since part of these transfers can also be obtained when working, we stick to the official ”Regelsatz ” as a lower bound.
4.3
Parameter Choices
We choose parameters such that our model meets the aggregate statistics of the initial steady state outlined above. Table 2 summarizes the parameter choices together with the targets and Table 9 in the appendix gives the implication of the model for key endogenous variables. Table 2: Basic Calibration Variables
Value
Target (US)
Value
Target (GER)
α
0.35
labor share
0.35
Labor-share
β
0.9975
K/Y=2.6
0.9979
K/Y=3
δ
0.0062
I/Y=.19
0.0062
I/Y=.22
σ2
0.3513
P9/P5=1.95
0.2750
P9/P5=1.7
b
0.3000
data(range)
0.5500
data
bmin
0.1200
MinWage/Median
0.1450
.145*Average Wage
̺0
0.2500
τL
0.3300
τL
̺1
0.0000
proportional
0.0000
proportional
τK
0.5000
Total Taxes=.28
0.3950
Total Taxes=.34
τc
0.0600
data
0.1400
data
ζ
0.4378
U=.065
0.1504
U=.04
B
15.9577
H=.25
14.1486
H=.25
ϕ
3.0000
Estimates
3.0000
Estimates
λ
.03
Data
.02
Data
ξ
1.5408
θ = .7
1.4633
θ = .7
κ
0.3697
prof it = .015
0.5168
prof it = .015
G/Y
0.1800
G/Y =.18
0.19
G/Y =0.19
Notes: This table gives the parameters of the model together with the calibration targets.
Our model period is one month. We choose α, the discount factor β and the depreciation rate δ to match the labor share, the capital to output ratio and the investment to output ratio. We set the institutional variables, that is tax rates und the benefit system to match the stylized facts described above. We choose the dis-utility of work parameter to match a steady state 22
average hour choice of one quarter of available time, an innocent normalization in our setup. To set the cost of posting a vacancy we target an average profit-share for both countries to be 1.5% relative to the labor share, in line with the estimates of Hagedorn and Manovskii (2005). This parameter is crucial for business cycle fluctuations as shown in Jung (2005), but does not influence our steady state comparison significantly.26 We estimate the probability of finding a match to be 0.7, also in line with Hagedorn and Manovskii (2005) to pin down the elasticity of the matching function. Given our parametric assumption on the log-normality of the skill distribution we target the P9/P5 for both countries to fix the variance of the distribution. We also match closely the P9/P1 and P5/P1 ratio. The most controversial parameter is the intratemporal elasticity of substitution.27 Prescott (2004) uses a log specification, so his elasticity estimate is 3. As pointed out by Alesina, Glaeser, and Sacerdote (2005) this number does not correspond to most of the micro-evidence. However, Prescott (2004) uses a labor supply model of a family that consists of the entire population 15-65, not the labor force or even an individual person employed. So in some sense his estimates reflects a very different object. In our model we condition on the labor force and treat the hour choice as hours worked per person employed. Note that for elasticity estimates in the range proposed by Prescott there do not exist equilibria with unemployment rates and outside options in observable ranges. To show the importance of this parameter, Figures 1 and 2 plot the semi-elasticities of the unemployment rate with respect to changes in the outside option for different parameter values of the outside option and the intra-temporal elasticity. As pointed out by Costain and Reiter (2005) the elasticity is highly influenced by the overall surplus of the match which in turn is a function of the two components of the outside option, the benefits and the utility gain from not having to work. We follow Heathcote, Storesletten, and Violante (2005) and set the elasticity to 0.5 using the 26
Given that the micro-evidence on this parameter is weak, we checked sensitivity to this choice by considering values in the range of 1-3%, with no essential change in the conclusion.
27
The intra-temporal elasticity is given by: εF risch =
∂u dh dw (1 − h) (1 − ϕ(1 − σ)) ∂h / | ∂u =const = = ∂u h ∂c∂h h w ∂c h σ ∂u h ∂h∂h − ∂u
(26)
∂c∂c
for general balanced growth utility, depending on leisure and for our model is given by: εF risch =
23
1 ϕ−1
(27)
most recent estimates by Domeij and Floden (2004). Given the choices on α, β, τ L , τ C we then solve the model iteratively in the space of τ K , δ,σ 2 ,bmin ,τ K ,ξ,κ,B and ̺ to match the targets described above.
24
5
Policy Experiments
Once the model is calibrated it can be used for policy experiments. We consider six experiments, which are summarized in Table 3. Table 3: Experiment Results Instruments/Endogenous
∆u
∆h
∆ LFP
∆ Wage
∆ τ (tax rate)
+
--
nil
nil
∆ b (benefits)
++
+
nil
nil
∆ bmin (cut-off)
+
+
++
--
∆ σ (skill variance)
+
+
++
++
∆ ̺ (bargaining)
++
+
nil
nil
∆ ϕ (preference)
++
--
nil
nil
This tables summarizes our main findings. +/- means a positive/negative effect, but small in magnitude. ++/- - means a positive/negative effect that is quantitatively important. Nil means that the effect is almost zero. On the x axis we consider changes in unemployment rates, hours, labor force participation (LFP) and some statistics of the spread of the wage distribution. As instruments we use the change in taxation ∆ τ , change in net replacement rates ∆ b, change in the minimum outside option, change in the spread of the skill distribution, change in the bargaining power and a change in preferences.
The first two experiments are related to observed changes in the institutions as described above. We show how much of the change in the German data can be attributed to changes in the tax and transfer structure and how much can be attributed to changes in the outside option. We then look at experiments related to unions bargaining position and the preferences for leisure, both unobserved changes. We then discuss the role plaid by the increase in the German minimum benefit level relative to the US. We use the US data to identify the potential increase in the variance of the skill distribution, our measure of an increase in turbulence. Finally, we ask whether the observed changes in the minimum benefit level can account for the relative constancy of the German wage distribution and the relative decline in labor force participation rates.
25
5.1
Change in Tax Rates
We fix all parameters to the benchmark case and change average labor taxes from 33% to 46% and the average consumption tax from 14% to 16%. We adjust capital taxes to be consistent with total tax revenue that increased from 34% to 43% measured in percentage to GDP, which leads to a decline of -4.5 percentage points.28 The minimum wage earned is also kept at 14.5% of the average wage. Note that we also define governmental spending in relative terms given that the government to output ratio remained almost constant over time and let the transfers adjust. We see that the strong increase in taxes can explain a drop in average hours worked per Table 4: Policy Experiment – Tax Rate Change Variables
Old Steady State
New Steady State
Data (1998-2002)
̺0
33%
46%
46%
τK
39.5%
34%
-
14%
16%
16%
1
0.94
-
TRANSFER
15%
22%
21%
Total Taxes /GDP
34%
41%
41%
U
4%
4.3%
9%
H
25%
23.17%
21.25%
Exogenous Change:
τc Endogenous Change: Y
person employed by 8% percent, while the data even for full time employed require a decline of around 15%. So roughly half of the decline is explained by a 12% point increase in the average labor tax29 from 41% to 53%. With respect to unemployment the strong tax increase accounts for a 0.3 percentage point rise in unemployment, that is the observed increase in unemployment cannot be attributed to tax rate changes. All other dimensions are virtually unaffected by the change in tax rates. The precise decline in hours worked is an increasing function of the Frisch elasticity estimate. 28
This decline is in line with the findings of Carey and Tchilinguirian (1999)
29
The average labor tax is defined as τ =
(τ c +τ l ) . 1+τ c
26
Prescott (2004) is able to generate a decline in hours consistent with the data even by using a change in the tax rate that is half the one we argued for by choosing a very high Frisch elasticity.30 However, once an extensive and an intensive employment margin is introduced, a Frisch elasticity as the one proposed in Prescott (2004) leads to a break down of the equilibrium for observable outside options because the unemployment state becomes too attractive and agents would stop working. Most papers analyzing effects of tax rates like Daveri and Tabellini (2000) implicitly or explicitly interact tax rate changes either with changes in the net replacement rate, by fixing the gross replacement rate, or by fixing the minimum level of social assistance in brutto terms. Given that these are policy choices we look at them separately. Before turning to these issues we shortly discuss sensitivity of our results with respect to the progressiveness of the tax rate. However, given that the increase in tax rates was mainly due to proportional changes in indirect taxes related to health and retirement, we view the focus on proportional tax changes as a good approximation.
5.2
Tax Rate Changes under a progressive Tax Code
The German tax code is a very complex object. Given a huge amount of loop holes and deductibility opportunities the official tax brackets cannot simply be used. In this sensitivity section we do not aim to provide a close approximation to the German tax code but provide evidence that in our model changes towards a more progressiv tax code will reduce average hours worked and decrease unemployment rates. As will be shown for the unemployment benefit system and union bargaining the effects move in the opposite direction. Explanations for the decline in hours worked that rely on an increase in progressive taxation will therefore severe the problem in explaining unemployment differentials. The intuition is very simple. A more progressiv tax code effectively weakens the bargaining position of the worker given that the government introduces an additional non-linear wedge between the gross and the net wage. So each individual extra euro the worker obtains increases his surplus under-proportional relative to a proportional tax system. To illustrate this point we use a simple log-linear tax rule as outlined above. We keep the 30
He also treats the consumption to output ratio as exogenous which explains roughly half of the tax impact.
27
average tax rate at its benchmark level, as well as the minimum earning level, and consider a (counterfactual) tax rate change towards a highly progressiv system with a marginal tax rate for the highest skilled worker of around 50%, which was the highest tax bracket in the seventies, see Figure 3.31 We see in Table 5 that this extreme change reduces the unemployment rate by 1.5%, while hours drop strongly. Table 5: Policy Experiment – Progressive Tax Rate Change Variables
Old Steady State
New Steady State
̺0
.33
0.43
̺1
0
0.18
14.5%
14.5%
1
0.9
33%
33%
U
4%
2.5%
H
25%
22.5%
Exogenous Change:
Minimum Wage/Mean Endogenous Change: Y Average Tax
31
The results are meant to be illustrative, not a close approximation of the German tax code.
28
5.3
Unemployment Benefits
As was argued in Daveri and Tabellini (2000), part of the increase in social security taxation might have led to an increase in net replacement rates.32 As was shown above the reaction to a change in the benefit system crucially depends on the level of the outside option and on the estimate of the intra-temporal elasticity. The following table gives the change in key endogenous variables with respect to a change in the outside option by 3%, the upper bound we argued for in the data, and a counterfactual 6.8% change, the amount needed to increase the unemployment rate by 5%. In the experiment considered we change the tax structure simultaneously as outlined in the last section to be in line with observed values. Table 6: Policy Experiment – Basic Calibration Variables
Old Steady State
3% Change
6.8% Change
Data (2000)
̺0
33%
46%
46%
46%
τK
39.5%
34%
34%
-
14%
16%
16%
16%
58%
61.8%
58%
Exogenous Change:
τc Outside Option
55%
Endogenous Change: Y
1
93.5%
91.2%
U
4%
5.3%
9%
9%
H
25%
23.2%
23.47%
21.25%
Benefits
0.9%
1%
1.8%
2.1%
Aggregation Effect:
-
U-percentile(1)
5.3%
7.4%
13.62%
-
U-percentile(2)
4.6%
6.3%
11.08%
-
U-percentile(9)
2.8%
3.3%
4.81%
-
Notes: Benefits include payments of the unemployment system, not the social assistance level which is included in general transfers. 32
Most evidence presented in the empirical literature is based on OECD gross replacement rates which is a problem. Note that viewed through the structure of this model, that is if we fix the functional form of the utility function to be the same across countries, cross sectional regressions are not identified. The reason is that just the joint setting of the bargaining parameter and the outside option can be interpreted as a labor market institution to guarantee existence of the equilibrium.
29
The reaction to a net replacement rate increase is quite strong at German parameter values while for the US a similar increase would be much weaker. In the US a seven percentage point increase would lead to an increase in the unemployment rate by 0.7 percentage points while in Germany it is 5 percentage points.33 As shown in Costain and Reiter (2005), the reason for the stronger reaction in Germany is related to the total surplus of a match which is much smaller in Germany than in the US due to the higher outside option. However, this argument has also implications for interpreting cross-sectional regression results related to net replacement rates. Conditional on a search and matching model once a homogeneity assumption on the utility function between countries is made, the only way the model can sustain different steady state unemployment rates given strongly different net replacement rates are different bargaining power parameters across countries. That is the bargaining power is the residual explanation that necessarily has to be different to sustain different equilibria once controlled for observable variables. Therefore elasticity estimates with respect to net replacement rates based on cross-sectional regressions appear hard to interpret. Interestingly, an increase in the outside option leads to an increase in average hours worked per person employed, a result we also obtain when considering changes in the union bargaining power as shown in the next section. Even though modest in magnitude, it clearly causes the problem that prime candidates for weak labor market performance might not be responsible for the decline in the extensive and the intensive margin at the same time. Two effects generate this result. The first is a composition effect. Low skilled worker are hit by the changes more heavily than higher skilled as can be seen from the table. We report unemployment rates for the two lowest skill percentiles and the highest skill percentile. We see that unemployment rates increase over-proportionally for low skilled types leading to the strong composition effect. The second effect is a wealth effect. The family earns less income and would prefer to compensate this by extending their work hours.
34
33
Note that the increase in benefits, that is total resources spent by the government on unemployment benefits and unemployment assistant is still lower in the model than in the data. So the model does not create a counterfactually high spending on unemployment benefits.
34
To quantify the composition or heterogeneity effect consider a representative agent version of the model, where all agents have the same skill level. In this case output would decline by approximately 2.3% more to .891, which is quite substantial. We compare the steady state of output to the steady state obtained under the pure tax rate change. Relative to this steady state in a homogenous agent version output is linear in labor, given that the capital-labor ratio stays constant. So the relative changes can be directly quantified back of the envelope, even though we also looked at it numerically.
30
5.4
Unions
One big actor in the German labor market are unions. In the political debate this wage setting institution is often blamed to be responsible for the bad performance of the German labor market. In our model we capture the role of unions in one parameter, the bargaining power ζ and interpret the family that does the bargaining as a union.35 The parameter captures in a reduced form the bargaining strength of the union, typically approximated in empirical work by union related indices as member share and coverage density.36 One of the explicitly stated goals of unions during the eighties and nineties up until now was to reduce hours worked per person employed, see Hunt (1999) for a description. The goal of a 35 hour week for all is still on our agenda...37 The principal stated argument is that an increase in hours worked will increase unemployment, given that there is, in the unions view, a fixed amount of total work. So an increase of the workweek for the current employed would decrease the chances for the current unemployed. While it is hard to disentangle whether this is the typical believe of union leaders or pure propaganda, it is clear that at least in the political debate there is a close perceived linkage between the average time worked and unemployment.38 In this section we ask whether changes in the union bargaining position can explain the increase in unemployment and the decrease in hours worked jointly. We show that the model cannot. We look for an increase in the bargaining power that generates the right increase in unemployment rates. Table 7 summarizes our results. The bargaining power would have to be more than doubled to generate the observed increase in unemployment-rates. Note however, that a uniform increase of the bargaining power has very 35
In our model the family/union aggregates the preferences of their members in a consistent fashion if we assume that each worker receives equal weights in the welfare function. In this sense the objective of the family/union is a micro-founded description of union behavior.
36
See Nickell, Nunziata, and Ochel (1999) for empirical results along these lines.
37
Free translation (emphasize added by author) from the homepage of the biggest union (DGB) in Germany, see http://www.dgb.de/themen/tarifpolitik/arbeitszeit.htm from the year 2006. Note that many industries officially already have the 35 hours work week. They also provide evidence of the development of the average work week in graphical form and the achievements of their policies.
38
Note that the federation of employers argues the other way around and claim that an increase in hours worked, fixing wage per hour, will decrease unemployment. Both parties at least see a strong link between hours and unemployment.
31
Table 7: Policy Experiment – Bargaining Power Change (Germany) Variables
Old SS
Change in ζ
Change in ϕ
Data (1998-2002)
̺0
33%
46%
46%
46%
τK
39.5%
34%
34%
-
τc
14%
16%
16%
16%
ζ
.15
0.325
.15
-
ϕ
3
3
2.8
-
Y
1
0.91
0.86
-
U
4%
9%
5.5 %
9%
H
25%
23.5%
21.3%
21.3%
U-percentile(1)
5.3%
13.2%
7.8%
-
U-percentile(2)
4.6%
11.1%
6.5%
-
U-percentile(9)
2.8%
5.1%
3.3%
-
Benefits
0.9%
1.7%
1.0%
2.1%
Exogenous Change:
Endogenous Change:
different effects for different skill levels of the worker. Given our homogeneity assumption the increase in the bargaining position increases unemployment of the highest skill group by a factor of 1.8 while the unemployment rate of the lowest skilled percentile is increased by a factor of 2.5. This is due to our assumption that vacancy posting costs for different types are similar. Interestingly an increase in the bargaining position of the union would lead, by construction, to an increase in unemployment but also to an increase in hours worked (relative to the pure tax rate decline). Given that unions receive a bigger part of the overall surplus, the wealth effect, that is the loss in aggregate income and consumption, would lead to a compensating effect in hours worked. This effect is quantitatively small. However, we conclude that within the setup of this model it is hard to make unions responsible for the decline in hours and the increase in unemployment at the same time. The only change within the model that ”explains” the change in hours worked is a change in preferences. We see from Table 7 that a fairly modest change in the Frisch elasticity39 from 0.5 39
Recall that the Frisch elasticity is given by
1 (ϕ−1)
32
to 0.555 generates a big decline in hours worked. Intuitively, an increase in the Frisch elasticity gives more weight on the value of leisure and increases implicitly the overall outside option. This in turn leads to a modest increase in unemployment rates and via the optimality condition on hours to a strong decline in average hours worked. This explanation of course relies on an unobservable change in the Frisch elasticity and is reported only because it might mimic part of the union behavior during the eighties and nineties. Bell and Freeman (1995) provide evidence for the different preferences reflected in the desire to work based on survey questions between Germans and Americans. They show that in the US a great number of workers would even like to work more hours while in Germany, already working 15% less hours, a significant number of worker would still like to work less. Their labor supply model as well as ours is unable to explain these differences in preferences endogenously.
33
5.5
Turbulence
As argued nicely in Ljungqvist and Sargent (2005), an increase in the variance of the idiosyncratic risk component combined with bad institutions might be responsible for the sharp increase in unemployment rates. The key mechanism used is the assumption that unemployed workers might experience a depreciation of their human capital, when unemployed, relative to their employed counterparts. If benefits are linked to last period wages their mechanism translates, in the setup of our model, into an increase in the outside option relative to a particular skill level. Having shown the reaction curve of unemployment to an increase in the observed outside option in the last paragraph, the added feature of the Ljungqvist and Sargent (2005) approach is that their model works even without an observable change in the outside option, given that the skill depreciation creates the same effect.40 While it would be possible to introduce idiosyncratic shocks into the model, for the purpose at hand it might be sufficient to focus on the implications of the mechanism for observable variables. If there was an increase in turbulence, the steady state wage distribution would become more skewed (given the monotonic relation between wages and skills), a counterfactual observation for Germany. Given that an observable increase in the outside option will not compress the wage distribution as shown in the last section, (at least) two explanations are possible: either there was no increase in turbulence in Germany, that is the skill/efficiency distribution remained constant, or there was also a more turbulent time period in Germany, but labor market institutions or other factors prevented a big change in the wage distribution. To address this issue we first show that for the US the changes in the skill distribution were likely not caused by changes in the minimum wage laws and argue that the increase in turbulence was exogenous with respect to the dimensions we consider. We then use the US to back out the quantitative change in the skill distribution, our measure of turbulence, and ask whether there was a change in the distribution in a similar order of magnitude in Germany. The decline in the minimum wage from 44% of median hourly wages to 35% in the US just accounts for a mild increase in the wage distribution and is quantitatively not responsible for the increase in the spread of the wage distribution. Fixing all other parameters at the benchmark case the increase in the P9/P1 and P5/P1 ratio is from 3.7 to 3.87 and from 1.9 to 1.96 40
Note however that their assumed increased mismatch or skill depreciation effect has to be in the same order of magnitude as the increase in the actual outside option of 7%.
34
respectively, so it does not, according to this model, contribute much to the observed inequality increase. We therefore take the increase in the US as exogenous and not related to labor market policies, either caused by an exogenous event that increased the volatility of the idiosyncratic risk component as in Heathcote, Storesletten, and Violante (2005), or caused by changed returns to human capital acquisition as in Guvenen and Kuruscu (2005).41 We target the increase in the P9/P1 ratio from 3.7 in the seventies to 4.6 in the end of the nineties to estimate the increase in the variance of the skill distribution for the US. We find an increase from .35 to .4. This is similar to the increase in the permanent component of the processes calibrated by Heathcote, Storesletten, and Violante (2005). The variance increase has almost no influence on all endogenous variables, except, of course, the wage distribution in the US. For Germany we then look at the effects of an observed increase in the minimum social assistance level by 3% from 14.5% to 17.5%, entertaining two alternative hypothesis. One assumes that the skill distribution remained constant in Germany (no turbulence), the other assumes that there was a spreading in the skill distribution in a similar order of magnitude as in the US (increase in turbulence). Table 8 shows that an increase in the skill distribution when fixing the cut off level relative to the mean wage to be 14.5% already leads to an increase in the drop out-of-labor-force rate by around 1.7%. This is due to the fact that the effective minimum wage to the median increases. There is essentially no effect on the unemployment rate. However, an increase in turbulence alone leads to a strong change in wage inequality, which is counterfactual. Alternatively, we increase the minimum cut-off level to 17.5%, assuming that there was no change in wage inequality. This has a similar effect on the drop out of labor force rate, but compresses the German wage distribution too strongly. Finally we look at a joint change in the skill distribution, assuming that Germany was effected in a similar order of magnitude by changes in the underlying skill distribution as the US, but counteracted this change by an increase in the welfare state, that is by an increase in the minimum existence level granted to the workers. This joint change increases the P9/P1 ratio and the P9/P5 ratio slightly while leaving the P5/P1 ratio almost unaffected. According to Fitzenberger (1999) and Kohn (2006) this is what has happened at least in the nineties, while according to Prasad (2004) there was 41
We are agnostic with respect to the cause of this increase in the US, as long as it is not related to labor market policy, which we show with respect to the minimum wage laws, and assume with respect to all other dimensions.
35
Table 8: Turbulence (Germany) Old SS
Change in σ 2
Change in bmin
Change in σ 2 +bmin
0.2750
0.3250
0.2750
0.3250
b
55%
55%
55%
55%
̺0
33%
46%
46%
46%
Minimum Wage/Mean
14.5%
14.5%
17.5%
17.5%
MinWage/Median
49.9%
50.8%
56.1%
57.1%
Y
1
95.3%
90.8%
94.5%
U
4%
4.6%
4.5%
5.8%
0.76%
2.5%
2.4%
4.9%
H
25%
23.2%
23.3%
23.5%
P9/P1
2.87
3.34
2.78
3.14
Variables: Exogenous Changes: σ2
Endogenous Change:
Out of LF
(Data: 3.01) P5/P1
1.69
1.80
1.65
1.71 (Data: 1.65)
P9/P5
1.70
1.85
1.69
1.83 (Data: 1.85)
Benefits
0.90%
0.84%
0.88%
0.98%
no change overall. Even though we slightly over-predict the P9/P1 ratio we view the result as evidence in favor of the hypothesis that Germany faced a similar increase in turbulence as the US but used a different labor market policy to respond to this change. This labor market policy though appears to come at a price. The drop out of labor force is in the order of magnitude similar to the difference between Germany and the US in the labor force participation rate and around 5%. It is also consistent with the strong increase in social assistance payment observed in the data (roughly an increase by 5 percentage points). The influence on the unemployment rate however is practically zero. Interestingly the increase in the minimum wage has also the effect of increasing the average hours worked per person employed counteracting again the drop through the tax regime change. This is a pure aggregation effect, given that the low-skilled low hours drop out of the labor market while there is more mass 36
at the top. Even though small in magnitude explanations related to increases in turbulence, endogenous creation or destruction will likely not solve the puzzling fact why Germans decided to choose to work less. Having argued that in the German data unemployment and the model theoretic concept of out of the labor force might be related, we can at least argue that this group is not the registered unemployed, given that there was a strong increase in the amount of benefits paid, from .001 to .021% in the data
42 ,
while it remained almost constant in the model. However, it might well
capture the proportion of unemployed who are not eligible for unemployment assistance, mainly the young, who never paid into the system or the workers that worked below the social security threshold. This group makes roughly 20% of the unemployed according to the national concept. Overall the influence of the minimum wage for the US appears to be modest, while for Germany it appears to be quite strong. Quantitatively there is a lot of mass at the cut-off value, so the change towards more generous social assistance level in Germany might significantly account for part of the wage compression.
42
Note that the data just include payment from the unemployment benefit and unemployment assistant system, not the social assistance level.
37
6
Conclusion
This paper describes the implication of different labor market mechanisms with respect to four important dimensions, namely unemployment rates, hours worked, labor force participation rates and the wage distribution. We ask quantitatively how much of the changes in the different labor market variables can be accounted for by changes in labor market institutions. We show that tax rate changes can explain roughly half of the change in hours worked per person and nothing in terms of unemployment rates. The increase in unemployment benefits in turn explains at most one third of the increase in unemployment rates. In addition an increase in unemployment benefits or the union bargaining strength increases average hours worked per person. We conclude that key mechanism highlighted in the literature cannot account for the increase in unemployment rates and the decline in hours worked at the same time. In particular, increases in unemployment benefits or union bargaining strength lead to an increase in hours worked. We show that the increase in the welfare state interpreted as an increase in the social assistance level, might have had important implications for the compression of the wage distribution in Germany relative to the US. It can also account for over 80% in labor force participation rate differentials. However, the impact on the (OECD) unemployment rate is small and the effect on average hours worked is positive, due to a composition effect. In summary our results suggest that many mechanism proposed in the literature can not fully account for the differences in hours worked or unemployment rates for Germany. Maybe elements we have abstracted from so far, like productivity growth or product market competition as in Ebell and Haefke (2004) might provide ”the missing link.” The results presented are purely descriptive and simply account in a quantitative manner for changes in exogenous institutions. No welfare implications are given because, in our view, the model is too stylized to interpret the results in a normative way. The main problem of the model is its assumption of a family that insures each workers with respect to consumption. This assumption is convenient to derive a wage setting equation that is independent of individual capital holding. Even though we share this assumption with most of the literature it is problematic with respect to welfare because the model does not attribute any positive role to the unemployment benefit system. The welfare maximizing outside option is zero. Given that the
38
steady state effects of the described mechanism at least on output are big, it appears an important next step to derive a model that can address the welfare implications within a framework that attributes a positive role to the unemployment benefit system.
39
References Alesina, A., E. Glaeser, and B. Sacerdote (2005): “Work and Leisure in the U.S. and Europe: Why so different?,” Working paper. Bach, H.-U., and S. Koch (2003): “Working Time and the Volume of Work in Germany- The IAB Concept of Measurement -,” IAB Labour Market Research Topics. S. 1-27;, 53, 1–27. Bell, L., and R. Freeman (1995): “Why Do Americans and Germans Work Different Hours?,” in Institutional Framework and Labor Market Performance: Comparative Views on the U.S. and Germany, ed. by F. Butler, W. Franz, R. Schettkat, and D. Soskice, New York, Ruttledge. Blanchard, O., and J. Wolfers (1999): “The Role Of Shocks And Institutions In The Rise Of European Uunemployment: The Aggreagte Evidence,” Working paper. Carey, D., and H. Tchilinguirian (1999): “Average Effective Tax Rates on Capital, Labour and Consumption,” Working paper. Costain, J. S., and M. Reiter (2005): “Business Cycle, Unemployment Insurance, and the Calibration of Matching Models,” Working paper. Daveri, F., and G. Tabellini (2000): “Uemployment, Growth and Taxation in Industrial Countries,” Economic Policy, pp. 48–104. den Haan, W. J., C. Haefke, and G. Ramey (2005): “Turbulence and Uunemployment In a Job Matching Model,” Working paper. Domeij, D., and M. Floden (2004): “The labor-supply elasticity and borrowing constraints: Why estimates are biased.,” Working paper. Ebell, M., and C. Haefke (2004): “The Missing Link: Product Market Regulation, Collective Bargaining and the European Unemployment Puzzle,” Working paper. Fitzenberger, B. (1999): Wages and Employment Across Skill Groups: An Analysis for West Germany. Physica-Verlag, Heidelberg. Fitzenberger, B., and A. Garloff (2005): “Descriptive Evidence on Labor Market Transitions and the Wage Structure in Germany,” Working paper. Guvenen, F., and B. Kuruscu (2005): “Understanding Wage Inequality: Ben-Porath Meets Skill-Biased Technical Change,” Working paper. Hagedorn, M., and J. Manovskii (2005): “The Cyclical Behavior of Equilibrium Unemployment and Vacancies Revisited,” Working paper. Hall, R. E., and P. R. Milgrom (2005): “The Limited Influence of Unemployment on the Wage Bargain,” Working paper.
40
Heathcote, J., K. Storesletten, and G. L. Violante (2005): “Insurance and Opportunity: The Wlefare Implications of Rising Wage Dispersion,” Working paper. Hunt, J. (1995): “The Effects of Unemployment Compnesation on Unemployment Duration in Germany,” Journal of Labor Economics, pp. 88–120. (1999): “Has Work-Sharing Worked in Germany,” Quarterly Hournal of Economics, pp. 117–148. Jung, P. (2005): “Capital, Unemployment and Hours - On the Quantitative Performance of a DSGE Labor Market Model,” Working paper. Katz, L. F., and D. Autor (1999): “Changes in the Wage Structure and Earnings Inequality,” in Handbook of Labor Economics, ed. by O. Ashenfelter, and D. Card, vol. 3, pp. 1463–1555. North Holland, Amsterdam. Kohn, K. (2006): “Rising Wage Dispersion After All,” Working paper. Ljungqvist, L., and T. Sargent (1998): “The european Unemployment Dilemma,” Journal of Political Economy, 106, 514–550. (2005): “Jobs and Unemployment in Macroeconomic Theory: A Turbulence Laboratory,” Working paper. Martin, J. P. (1996): “Measures of Replacement Rates for the Purpose of International Comparisons: A Note,” OECD Economic Studies, 26, 99–115. Mendoza, E., A. Razin, and L. Tesar (1994): “Effective Tax Rates In Macroeconomics: Cross Country Estimates Of Tax Rates On Factor Income and Consumption,” NBER Working Paper. Mortensen, D. T., and C. A. Pissarides (1999): “Unemployment Responses to ”SkillBiased” Technological Shocks: The Role of Labor Market Policy,” The Economic Journal, 109(455), 242–265. Nickell, S., L. Nunziata, and W. Ochel (1999): “Unemployment in the OECD since the 1960s. What Do We Know?,” The Economic Journal, 115, 1–27. O’Leary, C. J. (2000): “U.S. Unemployment Insurance: Progress and Prospects,” Working paper. Pissarides, C. A. (2006): “Unemployment and Hours of Work: The North Atlantic Divide Revisited,” Working paper. Prasad, E. S. (2004): “The Unbearable Stability of the German Wage Structure: Evidence and Interpretation,” Imf stuff report vol.51, no.2. Prescott, E. C. (2004): “Why Do Americans Work So Much More Than Europeans?,” Working paper. 41
Rogerson, R. (2006): “Understanding Differences in Hours Worked,” Review of Economic Dynamics, 9, 365–409. Steffen, J. (2005): “Sozialpolitische Chronik,” Working paper. Wanger, S. (2003): Arbeitszeit und Arbeitsvolumen in der Bundesrepublik Deutschland 19701990. Bundesanstalt f¨ ur Arbeit, N¨ urnberg.
42
A
Appendix Table 9: Key Endogenous Variables Variables
Value (US)
Data (US)
Value (GER)
Data (GER)
Y 1 1 C/Y 61.4% 63% 57% 55% I/Y 19.2% 19% 22% 22% G/Y 18% 18% 19% 19% H 0.25 0.25 0.25 0.25 Out of LF 1.5% 0.76% U 6.5% 6.5% 4% 4% U percentile(1) 8.6% 5.3% U percentile(2) 6.8% 4.6% U percentile(9) 3.9% 2.7% π ue 42% 47% TRANSFER 9.5% 8% 15% 14% Total Taxes /GDP 27.5% 28% 34% 34% Average Labor Tax 25% 25% 33% 33% MinWage/Median 44% 44% 49.1% bmin 14.9% 14.5% 14.5% P9/P1 3.70 3.65 2.86 2.88 P5/P1 1.9 1.9 1.69 1.7 P9/P5 1.95 1.95 1.7 1.69 This table gives the implications of some key endogenous. The first box describes the big aggregate ratios. The second box refers to implication for the labor market. The percentile distributions are taken with respect to the skill distribution of the labor force, showing that the person at the lowest 10% skill level has a 2 times higher unemployment rate than the high skilled at the 90% percentile. The P ratios refer to total earnings of the employed workers at the corresponding percentiles. The Minimum Wage is defined as the gross hourly compensation of the worker with the lowest skill that actually works to the median. Given that hourly wages are monotonically increasing in wages, this is th only type where the constraint binds. bmin refers to the cut off earnings level relative to the mean. Note that this level is binding not just for the lowest skilled type.
43
Figure 1: Semi-elasticity of unemployment rate with respect to the outside Option - US 0.22 intratemporal=2.6 intratemporal=2.8 intratemporal=3.0 intratemporal=3.3 intratemporal=3.5 intratemporal=3.7 intratemporal=4
0.2
Unemployment Rate
0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.25
0.3
0.35
0.4 0.45 Outside−Option
0.5
0.55
0.6
The figure shows the semi-elasticity of the unemployment rate with respect to changes in the outside option for different levels as a function of ̺ evaluated at the US benchmark 1 parameters. Note that the Frisch elasticity is given by ̺−1 .
44
Figure 2: Semi-elasticity of unemployment rate with respect to the outside Option - Germany 0.11 intratemporal=2.8 intratemporal=3 intratemporal=3.2 intratemporal=3.4 intratemporal=3.6 intratemporal=3.8 intratemporal=4
Unemployment Rate
0.1
0.09
0.08
0.07
0.06
0.6
0.605
0.61 Outside Option
0.615
0.62
The figure shows the semi-elasticity of the unemployment rate with respect to changes in the outside option for different levels as a function of ̺ evaluated at the German benchmark 1 parameters. Note that the Frisch elasticity is given by ̺−1 .
45
Figure 3: Progressiv Taxation 0.6 proportional progressive
0.55 0.5
Average tax rate
0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.4
0.6
0.8
1
1.2
1.4 1.6 Skill level
1.8
2
2.2
Notes: The figure shows the change in the tax code. On the x-axis we plot the range of the skill level and on the y-axis we report the average tax code. Both tax codes have the same average tax rate, averaged over all skill groups according to the same skill distribution function.
46
Table 10: Labor Force Data by Sex and Age Country
GER 1970 44.2 30.3 59.6 69.5 48.0 92.6 69.1 66.9 70 71.4 49.6 69.5 67.3 70.3 71.7 50.3 0.6 0.6 0.5 0.4 1.4 0.8 -
Total Labor Force % of POP Female Male Total Labor Force % of POP(15-65) Female Male Employment/Population Employment/Population(15-64) Employment/Population(15-24) Employment/Population(25-54) Employment/Population(55-64) Labor Force Participation Rate Labor Force Participation Rate(15-64) Labor Force Participation Rate(15-24) Labor Force Participation Rate(25-54) Labor Force Participation Rate(55-64) Unemployment Rate Unemployment Rate(15-64) Unemployment Rate(15-24) Unemployment Rate(25-54) Unemployment Rate(55-64) Standardized U-rate Destruction Rate
2000 48.1 41.4 55.2 71.3 63.6 78.8 67 66.3 48.4 80.2 38.6 72.9 72.2 52.5 86.5 44.7 8.1 8.1 7.7 7.3 13.5 8.44 .02
US 1970 41.9 30.2 54.2 67.7 48.9 87.1 67.7 64.9 53.3 65.9 57.6 68.6 67.7 65.6 68.9 60.1 5.3 5.4 10.0 4.4 4.2 7.7 .03
2000 51.0 46.3 56.0 77.1 71.0 83.2 76.4 74.1 59.8 81.5 57.7 79.6 77.2 65.9 84.1 59.2 4.0 4.0 9.3 3.1 2.5 4.9 .03
Notes: This table shows data from the OECD labor market statistics for the earliest available year 1970 and for 2000, disaggregated by age and sex.
Table 11: Hours Worked for Dependent Worker in Germany, disaggregated Year Percentage Part Time Average Hours Worked Average Hours Worked (Full) Percentage of (1970 Hours) Average Hours Worked (Part) Percentage (1970 Hours) Ratio (Part/FULL)
1970
1990
2000
6.26 1868.1 1925.2 1068.7 0.56
17.2 1489.2 1664.8 0.87 680.4 0.64 0.41
24.6 1400.2 1654.5 .86 674.8 .63 0.41
Notes: This table gives hours worked data for Germany, disaggregated by full-time and part time workers. The data have been obtained for the years 1970-1990 from Susanne Wanger, see Wanger (2003). For the years 1991 to 2000 they have been taken from Bach and Koch (2003).
47
Table 12: Gross Wage Distribution (OECD) P9/P1
P5/P1
P9/P5
P1/Mean
Incidence=2/3 Mean
GER (1984) 2.88 1.70 1.69 0.54 14.80 GER (1998) 3.04 1.65 1.85 0.55 12.90 US (1976) 3.68 1.90 1.95 0.48 22.80 US (1984) 4.11 2.00 2.05 0.45 21.60 US (2000) 4.65 2.07 2.25 0.39 24.70 Notes: This table shows OECD gross wage distribution before tax. Incidence describes the percentage of persons with earnings income less than 2/3 of the mean. The years for Germany reflect the first and last year available.
Table 13: Aggregate Statistics Aggregate Data Investment/Y Government/Y C/Y Compensation/Y
GER 1974-1978 0.22 0.19 .55 0.55
1998-2002 0.2 0.19 0.58 0.54
US 1974-1978 0.19 0.18 0.63 0.6
1998-2002 0.19 0.15 0.69 0.58
Notes: This Table gives aggregate data from the NIPA and the German statistical office averaged over the respective periods.
Table 14: Tax rates and social spending Taxes Transfers on Social Security/(Y) Transfers on Unemployment System (Total)/Y Transfers on Unemployment Benefits/Y Tax Revenue (Nipa, Bundesamt fuer Statistik)/Y Labor Tax Consumption Tax
GER 1974-78 14% 0.5%
1998-2002 21% 2.6%
US 1974-78 8% .3%
1998-2002 12% 0.2%
0.1% 34%
2.1% 43%
.3% 28%
0.2% 29%
33% 14%
47% 15%
25% 6%
25% 6%
Notes: This table shows the total tax revenue and our estimate of the consumption and labor tax. For Germany, data refer to the Bundesamt f¨ ur Statistik, for the US data are from the NIPA. Transfers of Unemployment Benefits are from O’Leary (2000) for the US, for Germany they are from statistical source at the ministry of social affairs, (”Bundesministerium f¨ ur Soziales”). Output is adjusted for the consumption tax payments.
48
Figure 4: Average Hourly Minimum Wage As Percentage of the Median 0.65
0.6
0.55
0.5
0.45
0.4
0.35
1960
1965
1970
1975
1980
1985
1990
1995
2000
Notes: The figure shows the development of the minimum wage, defined as average hourly wage rate in percentage to the median. Data are from the OECD.
Figure 5: Percentage of persons receiving labor market related transfers - Germany 0.1 Percentage Unemployment Insurance to Labor Force Percentage Unemployment Assistance to Labor Force Percentage Social Assistance to Labor Force Combined national Unemploymentrate
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0 1970
1975
1980
1985
1990
1995
2000
2005
Notes: The figure shows the development of the three pillars of the German compensation system, unemployment benefits, unemployment assistance, and social assistance. Data are from the German statistical office. All numbers are expressed relative to the German labor force (=Erwerbspersonen) as a normalization.
49
Figure 6: German Tax Rates with social security contributions 0.5 0.48 0.46 0.44 0.42 0.4 0.38 0.36 0.34 1970
1975
1980
1985
1990
1995
2000
2005
Notes: The figure shows the German tax rate as obtained from the ministry of social affairs, statistical yearbook. We use their estimate of the average brutto and netto wage and relates it to the average tax payments.
50
Figure 7: German Net Replacement Rates, constructed 0.72 0.7 0.68 0.66 0.64 0.62 0.6 0.58 0.56 0.54 0.52 1970
1975
1980
1985
1990
1995
2000
2005
Notes: The figure shows our estimate of the German net replacement rates. It is a weighted average of the two unemployment benefit system total payments divided by the persons receiving benefits in each group relative to the net wage. Data are from the ministry of social affairs, statistical yearbook.
51
