Explaining Interregional Differences in LaborMarket Participation

Joachim MÖLLER 1

Alisher ALDASHEV 2

Keywords:Regional participation behavior, search models, wage inequality, German unifi-cation, spatial econometrics, spatial weight matrix.

JEL-classification: J21, R23

This version: 03 February 2005

Acknowledgements:We would like to thank the participants of the annual meeting of the “Aus-schuss für Regionaltheorie und -politik” in Kiel, October 2004 and the IAB Re-search Seminar in Regensburg, especially Jörg Lingens, Gianmarco Ottaviano,Uwe Blien and Johannes Ludsteck for their many helpful comments and sug-gestions. All remaining errors are our own. Financial support of the DeutscheForschungsgemeinschaft (DFG) through the research project MO523/41 “Flex-ibilität der Lohnstruktur, Ungleichheit und Beschäftigung - Eine vergleichendeMikrodatenuntersuchung für die USA und Deutschland” is gratefully acknowl-edged. The data used in this paper were made available by the Institute forEmployment Research (IAB) at the Federal Labor Office of Germany, Nürnberg.

Correspondence:Joachim MöllerUniversitätsstraße 3193053 Regensburg, GermanyTel: +49-941-943-2550, Fax: +49-941-943-2735,E-mail: joachim.moeller@wiwi.uni-regensburg.de

1University of Regensburg, Department of Economics2University of Regensburg, Department of Economics

Abstract

The paper analyzes the variation of gender-specific labor-market participation

rates at the regional level. We first develop a search-theoretical model with inter-

temporal optimization behavior of agents. The model suggests that a higher regional

wage level fosters participation, while higher job insecurity as measured by the un-

employment rate discourages workers. Moreover, a high wage dispersion increases the

value of search and should lead to higher participation rates.

Using a spatial econometric approach we investigate the determinants of gender-

specific participation in a comprehensive empirical model where differences between

West and East Germany are explicitly accounted for. We generally find that variation

in regional participation rates is driven by economic forces. Unemployment depresses

labor-market participation of male and female workers in both parts of the country,

while a higher wage level stimulates it. This is in line with theoretical predictions.

However, contrary to the implications of a model with risk-neutral individuals, our

results show that higher wage dispersion in the left tail of the wage distribution tends to

lower participation. We conclude that the inter-temporal search-theoretical framework

assuming risk-neutral individuals is not able to cover all major aspects of participation

behavior.

1 Introduction

At the time of unification, labor market participation rates in West and East

Germany differed remarkably. When the German Democratic Republic (GDR)

collapsed, 86.0 percent of the male and 77.2 of the female population aged be-

tween 15 and 65 belonged to the active workforce. The corresponding figures

for West Germany (the so-called “old laender”) were 82.7 percent and 58.5 per-

cent, respectively. Even compared to international standards, the East German

labor-force-to-population ratio of women was high.

In West Germany labor market participation of male workers followed a declining

trend after the overheated labor market situation of the late sixties. The share

of the active population steadily came down from 88.2 percent in 1970, 84.4 in

1980 and 82.7 in 1990 to 80.0 percent in the year 2000 (see Figure 1). At the

same time, the active share of the female population increased step-by-step from

46.2 percent in 1970, 50.2 in 1980 and 58.5 in 1990 to 62.1 percent in 2000.

In the early nineties there was some indication that participation behavior in East

Germany (the “new laender”) would quickly adapt to West German standards.

In fact, after unification the new laender witnessed a sharp decline in the labor-

force-to-population ratio. From 1991 to 2000 the share of the active population

fell by 6.2 percentage points for males. With participation rates in the year 2000

being almost identical in both parts of the country (80.0 versus 79.8 percent), the

hypothesis of rapid adaptation is supported for the male population. The same

is not true for females, however. Although the initial differences in participation

indicators between the western and eastern part of the country were much higher

for women, the observed changes in the transition period during the nineties

were quite lower (minus 4.2 percentage points). As a result, a substantial gap

of more than 10 percentage points in participation rates is still visible for the

female population (62.1 versus 72.2 percent in 2000). Hence there is evidence for

the view that a more active labor market behavior of females was inherited from

the past and still persists in the new laender even more than a decade after the

unification.

1

Taking German unification as a natural experiment, the aim of the present paper

is to analyze the development of labor market participation in the new and old

laender more thoroughly at the regional level. Using highly disaggregated data,

we are able to control for various influences on participation behavior. In our

view there are good reasons to analyze the interactions of labor market partici-

pation with other labor market variables in more detail. The German economic

policy debate mainly concentrates on the unemployment problem, thereby of-

ten neglecting the remarkable features in the gender-specific levels and trends of

participation. Taking up an argument that Lindbeck (1996) has used in the con-

text of international comparisons, the regional employment-to-population ratio

is a more reliable indicator of labor market performance than the unemployment

rate.

Despite a huge literature studying participation behavior at the micro level, there

are only few contributions investigating the phenomenon for spatial units as a

whole. A major exception is the early study by Clark and Summers (1982) dealing

with female participation behavior in the U.S. during and after World War II.

These authors argue that persistence effects and path-dependency are crucial

for understanding labor market participation. From this angle it seems likely

that these effects are equally important for explaining the obvious differences in

labor market behavior patterns between West and East Germany. One should,

however, stress the fact that there are not only strong differences between the

new and the old laender, but also within the two parts of the country. At a more

disaggregated regional level, not only unemployment rates but also participation

rates scatter widely. Moreover, there seem to be systematic patterns between

neighboring regions as well as differences between types of regions defined by

centrality and population density. The idea of the present paper is to use the

considerable cross-regional variation in participation, wages, unemployment and

other key labor market indicators to gain insight into the functioning of regional

labor markets and to assess the relevance of competing economic theories. As an

alternative to macro-oriented approaches following Clark and Summers (1982),

we sketch a search-theoretical explanation in the tradition of McCall (1970),

Pissarides (1974), Mortensen (1977), Mortensen and Pissarides (1994) and others.

2

The remainder of the paper is organized as follows. In section 2 we consider the

theoretical background. Section 3 introduces basic empirical concepts, describes

our data base and reports some descriptive evidence. Section 4 discusses spatial

econometric issues and outlines the econometric model. Section 5 contains the

estimation results. Section 6 concludes.

2 Theoretical background

2.1 The search-theoretical framework

A standard search-theoretical model can be referred to as the urn model. In the

urn model a job offer is considered as a random drawing. For simplicity rea-

sons the wage distribution in this approach is often assumed to be a one-point

distribution (see, among others, Pissarides (1979)). Even under this unrealistic

setting, the model has been successfully applied to real data sets (cf. Burda and

Profit (1996)). Other models like Burdett (1978) and Mortensen (1977) assume

homogeneous workers facing an exogenous non-degenerate wage offer distribution

that is known to searchers. Since the early literature on search theory further

progress has been made. From a technical point of view, an important improve-

ment is to consider a set-up in continuous time. In discrete time multiple offers

per period of time are possible rendering the models unduly complicated because

of the necessity to handle multiple-offer distributions. The advantage of modern

theories is that the multiple-offer distribution converts to a one-offer distribution

which simplifies the analysis considerably.3

In order to use a search-theoretical framework for analyzing the decision between

active labor market behavior and non-participation, the standard approach has

to be extended. The basic ideas can be outlined as follows: In a dynamic opti-

mization framework the individual determines the value of active labor market

participation including search costs, the loss of leisure time and the possibility

3For new developments in search theory see Mortensen and Pissarides (1999).

3

of being unemployed. This value has to be compared with the value of staying

out of the labor market and receiving alternative income as, for instance, social

assistance. The value of labor market participation is determined by assuming

optimal search behavior. Like in the urn model the worker receives offers being

drawn randomly from a job offer distribution. Each job offer is characterized by

a specific wage. He or she has to decide whether to accept the offer or continue

searching. The solution to the model gives the optimal reservation wage, i.e. the

rational worker should accept the offer if it exceeds this critical wage level and

continue searching if not. For a given distribution of wage offers and other para-

meters, the value of active versus passive labor market behavior can then easily

be determined for an individual and hence the theory is able to predict whether

this individual will participate in the labor market or not.

It can be shown that the reservation wage not only depends on institutional pa-

rameters and indicators of the labor market but also on individual characteristics

including alternative income and the esteem of leisure. Therefore, analyzing par-

ticipation in the aggregate (for a region, say) requires introducing heterogeneity

across workers. Albrecht and Axell (1984) assume that individuals can be divided

into two groups according to different values they attach to leisure. Then even

under identical institutional and labor market conditions, the reservation wages of

the two groups differ. Eckstein and Wolpin (1999) extend the model of Albrecht

and Axell (1984) to allow for more than two types of workers. Other examples of

search models using the esteem of leisure time to introduce heterogeneity among

workers are Burdett and Mortensen (1998) and Van den Berg and Ridder (1998).

2.2 Sketch of a search-theoretical approach for modeling

participation behavior

In the following we outline a search-theoretical model.4 Consider a situation

where risk-neutral workers apply to available vacancies being randomly offered

4In a companion paper (Möller and Aldashev (2005)) we give a more detailed description of

the model.

4

to them by firms. It is assumed that the characteristics of the wage distribution

can be observed at no costs. However, an applicant does not know the wage

offered for a specific job before getting an offer. There are no differences in the

characteristics of jobs apart from the wage. All probability distributions are time

invariant. No recall is allowed for.

Each wage offer is drawn independently from a wage offer distribution F (w).

The exogenous job offer arrival rate is denoted by λ. The number of job offers

received per time period follows a Poisson process. For simplicity assume that

workers live forever and are wealth maximizers. The value of being employed at

wage w is denoted by W (w), the value of search by Ω, the value of a unit of leisure

time by b and the lump-sum costs of participation per unit of time by c.5 Hence

bu := b−c gives the value of a unit of leisure time for an unemployed person, while

b > bu is the corresponding value for a non-participating person. Furthermore,

let δ be the discount rate and σ the exogenous separation rate for labor contracts.

In continuous time, the Bellman equation for the value of employment can then

be written as

W (w) =1

δ + σ(w + σΩ) . (1)

The optimal search strategy is to accept any wage w > r, where the reservation

wage r is defined by W (r) = Ω. It can be shown that the solution for r is given

by the implicit function

Φ (r; ·) = bu +λ

δ + σK(r)− r = 0, (2)

where

K (r) := w − r +

r∫0

F (w) dw > 0. (3)

The partial derivative of Φ with respect to the reservation wage is6

Φr = − λ

δ + σ[1− F (r)]− 1 < 0. (4)

Let x be any parameter in the model. It then follows from the implicit function

5The variable c includes the costs of being available to the labor market.6Throughout the paper we use subscripts to denote partial derivatives.

5

theorem ∂r/∂x = −Φx/Φr that

sign(

∂r

∂x

)= sign (Φx) . (5)

Using (5) it is straightforward to derive the following results from (2): The op-

timal reservation wage responds negatively to an increase in search costs c, the

separation rate, σ, and the discount factor, δ. It increases with the mean of the

wage offer distribution, w, and the value of leisure and unemployment benefits

net of the costs of being available to the labor market.

We are also interested in the response of the reservation wage to an increase in

the dispersion of offered wages. Our measure of dispersion is a mean preserving

spread. To see the implications, introduce a dispersion parameter s in the cumu-

lative density function of the wage offer distribution F (w; s). The parameter s

describes a mean preserving spread iff

∂

∂s

∞∫0

w dF (w, s) = 0 (6)

and

∂

∂s

r∫0

F (w, s) dw > 0 for F (r, s) < 1. (7)

We then obtain the following result:

sign(

∂r

∂s

)= sign (Ks) = sign

∂

∂s

r∫0

F (w, s) dw

> 0 (8)

for F (r, s) < 1. Note that the reservation wage in case of a non-degenerate wage

offer distribution is always below the maximum wage if search costs are positive

which is assumed here. Hence we can conclude that the reservation wage increases

with the mean preserving spread.

The intuition behind this result is that a mean preserving spread in wages raises

the benefits of continuing the search. Since this makes agents pickier, their reser-

vation wage rises. The incentive of continuing the search after having already

obtained a job offer with wage w is simply the possibility that you might be of-

fered a wage above w. Greater wage dispersion increases this chance. Of course,

6

a higher spread also rises the probability of getting a worse offer. However, a

searcher is not obliged to accept it. Hence greater wage dispersion increases the

option value of search.

2.3 Participation behavior in a model with heterogeneous

individuals

For a model of participation behavior in the aggregate, heterogeneity of individu-

als is required, otherwise either all or none will participate. In order to introduce

the source of heterogeneity, let us be more precise in determining the value of

leisure. Unemployed individuals have a money equivalent to the value of pure

leisure, `, plus transfers in form of unemployment benefits, tu, minus the fixed

costs of participation, c. Non-participating individuals enjoy pure leisure of value

` and receive an alternative income ts (social assistance, for example). In the

following it will be assumed that individuals are heterogeneous with respect to

the value attached to pure leisure, only. Thus for an individual i the value of not

working will be bui = `i + tu − c in case of unemployment and bn

i = `i + tn in case

of non-participation. Define ν := bni − bu

i = tn − tu + c. Moreover let tu − c = 0

and hence bui = `i for the ease of exposition. The condition for participation is

δΩi = ri (bui ) > bn

i . (9)

It will be assumed that the participation rate is strictly positive but less than

one. This implies that an agent with the lowest (highest) esteem of leisure in the

population prefers participating (non-participating, respectively). Then there

must be some critical value for leisure, ˜> 0, such that a person with `i = ˜ will

be indifferent between participating or not. If `i > ˜ holds, he or she will stay

out the labor market. The participation indifference condition can be stated as

r := r(bu)

= bn = bu + ν, (10)

where bn = ˜+ tn and bu = ˜. Let g(`) and G(`) be the density and cumulative

density, respectively, of the value of leisure distribution in the population. The

7

probability that a randomly chosen person participates in the labor market is

given by G(˜). This yields for the aggregate participation rate:

π := G(

˜)

= G(bu)

with∂π

∂ ˜=

∂π

∂bu> 0. (11)

It follows that participation behavior can be analyzed by investigating the de-

terminants of the critical value of leisure ˜. By replacing the reservation wage,

r, in (2) by bn and the wealth in case of unemployment, bu, by bu we obtain an

implicit function that determines ˜:

Θ(

˜, .)

=λ

δ + σK(˜+ ν)− ν = 0. (12)

From (12) one can calculate the comparative static results for the critical level of

the value of leisure that divides the population into the participating and non-

participating part. Applying the implicit function theorem we obtain the result

that participation increases with the average wage offer, w and the job offer arrival

rate, λ. It decreases with a higher separation rate, σ, higher search costs, c, and

the impatience of agents as measured by the discount rate, δ. Participation also

falls with a lower ν, i.e. if being unemployed becomes less attractive compared to

non-participating. With respect to the dispersion of the wage offer distribution we

can conclude that a higher mean-preserving spread in the wage offer distribution

leads to higher labor market participation.

2.4 Path dependency and band-wagon effects

So far we have considered the participation decision in an intertemporal opti-

mization model of wealth-maximizing individuals. According to the model, par-

ticipation behavior can be described given the wage offer distribution, a set of

parameters and the value-of-leisure distribution in the population. What then

can explain large intertemporal and interregional variations in participation rates

in observationally equivalent situations? As already extensively (and critically)

discussed by Clark and Summers (1982) there might be an impact of expected

future wages and prices on current labor supply resulting from inter-temporal

substitution and income effects. The relevance of inter-temporal substitution of

8

labor supply depends on a set of strong assumptions, some of which are not likely

to be fulfilled in reality. For example, instead of being completely free in choosing

their hours of work, individuals are typically rather restricted in this respect due

to requirements of the employer (Euwals and van Soest (1999)).

In the intertemporal optimization approach there is little or no room for per-

sistence, path-dependency or band-wagon effects. According to the arguments

in Clark and Summers (1982) tradition, however, it is likely that, for instance,

previous employment experience affects the current participation decision. De-

spite the unfavorable actual labor market conditions, female workers in East

Germany would resist to lower their participation rates. Several explanations for

such phenomena are discussed in the literature. First, there might be hysteresis

in individual behavior. The past experience of employment could have caused

lock-in effects. Hence at least to some extent, habit formation through past work

experience might determine the current situation. Already Clark and Summers

(1982) list several arguments that can rationalize path-dependency of participa-

tion. An important one is related to human capital aspects. “Those who are

employed tend to accumulate more human capital, which raises the return to

work in the future relative to leisure. Those out of the labor force may also de-

velop household-specific capital or commitments (i.e. children) which reduce the

return to working relative to remaining outside the labor force.”

A further line of argument is that individual behavior are affected by peer group

effects. Thereby the decisions of others might have an influence on own decisions.

If, for instance, active participation attitude of females is frequently observed in

the neighborhood, than it might influence the attitude of other persons. This can

be seen as a mechanism for establishing a social norm. In the aggregate, such a

mechanism would lead to a self-reinforcing process after some critical values are

reached. As Vendrik (1993) puts it: “... band-wagon effects occur if a woman’s

(non-)participation preferences are reinforced by the (non )participation behavior

displayed by other women in her social reference group...[By contrast] (individual)

habit formation refers to the situation in which a woman’s (non)participation

preferences are reinforced by her own (non) participation experience.” Empirical

9

studies for different countries reported by this author support the relevance of

these effects. In several papers (cf. Vendrik (1993) and Vendrik (1998)) he

develops a dynamic model which he applies to the labor force participation rate

of Dutch married women. His findings suggest that band-wagon effects can offer

a more convincing explanation of the observed empirical patterns. The author

also extends the notion of habit formation in the sense that non-participating

experience could also be a “habit”, but which forms a barrier to entry. If band-

wagon effects are relevant, one would expect neighboring effects to matter. In

the context of econometric estimation this implies the existence of some forms of

spatial autocorrelation.

Possible further extensions in the analysis of participation behavior could be the

inclusion of “life-style” and other cultural factors.7. This would mean that the

type of the region is a relevant factor for the explanation of participation behavior.

3 Data and definitions

3.1 Data

We use the INKAR database (Bundesanstalt für Bauwesen und Raumordnung,

BBR) for data on gender-specific unemployment and employment, active and

non-active population and the share of in- and outgoing commuters at the county

level (NUTS 3). The data on wages and wage dispersion were calculated from

IAB-REG (Institut für Arbeitsmarkt- und Berufsforschung, IAB). IAB-REG is a

1% random sample from the employment register of the Federal Labor Office with

regional information. The data set includes all workers, salaried employees and

trainees being obliged to pay social security contributions and covers more than

80% of all employment. Excluded are public servants, minor employment and

family workers. Because of legal sanctions for misreporting, the earnings infor-

mation in the data is highly reliable. Among others, IAB-REG contains variables

7Also ethnic background variables were used to explain differences in participation rates, see

Antecol (2000)

10

on individual earnings and skills. The regional information is based on the em-

ployer. The analysis here is confined to full-time workers of the intermediate

skill group (apprenticeship completed without a university-type of education).

All male and female workers were selected that were employed at the 30th of

June, 1997. For all regions we then calculated the gender-specific median and

the second and eighth decile of daily earnings.

In IAB-REG a total of 328 West German and 112 East German counties is

available with Berlin being represented by two separate regions (West and East

Berlin). In the INKAR data set, however, separate figures for East and West

Berlin are partly unavailable. Therefore we decided to exclude Berlin from the

data set. This leaves us with a total of 438 regions (i.e. 327 and 111 for West

Germany and East Germany, respectively).

3.2 Definitions of variables

The employment-to-population ratio at the regional level will be calculated as

qr =Nr − Ir + Or

Pr

, (13)

where Nr is the total number of persons being employed in region r, Ir and Or

are the number of incoming (outgoing, respectively) commuters and Pr is the

regional population at working-age. Hence total employment of region r citizens

is measured as

Er = Nr − Ir + Or, (14)

The regional population at working age is split into inactive on the one hand

and the labor force on the other. Let the fraction of the working-age population

entering the labor force be described by πr and hence the labor force is:

Lr = πr(·)Pr, (15)

For the link between employment and the labor force we have

Er = (1− ur)Lr, (16)

11

where ur is the unemployment rate. Combining the identities from above yields

πr =qr

1− ur

, (17)

Because of limited data availability at a highly disaggregated regional level, the

self-employed are not included in our measure of πr. Hence the participation

figures used in the empirical study here are somewhat lower than in other sources.

3.3 Descriptive evidence

Figure 1 depicts gender-specific participation and unemployment rates for East

and West Germany. It is evident that regions situated in East Germany suffer

from much higher unemployment than their counterparts in West Germany. Par-

ticipation of male workers in the East are not markedly different from those in the

West (the so-called old laender). The regression line is downward sloping in all

cases indicating a negative correlation between unemployment and participation.

Figure 1 also indicates that there is considerable variation of unemployment and

participation across regions even within the two parts of the country.

In figure 2 participation rates are plotted against the median nominal wage for

male and female workers. Since the regression line is upward sloping in all cases.

Hence first evidence corroborates the view that higher wage levels foster partic-

ipation. For both genders participation rates at given wages are higher in East

Germany (or the new laender).

4 Econometric analysis

4.1 Spatial econometric issues

Regions are not isolated areas but interact with its neighbors. Workers looking

for employment might consider taking a job not in the region of residence but

in another region that lies within an acceptable commuting distance. Local re-

gional interactions might lead to spatial autocorrelation which can be modeled by

12

two alternative models, the spatial lag and the spatial error model [e.g. Anselin

(2001)]. Formally, the spatial lag model can be described as

y = ρWy + Xβ + ε, (18)

where y is a (N × 1) vector of the dependent variable, X is a (N × k) matrix of

explanatory variables and β the corresponding coefficient vector. W denotes the

(N ×N) spatial weight matrix, ρ a spatial lag parameter to be estimated and ε

a vector of disturbances.8 Let εi andεj be two elements of ε, it is assumed that

cov (εi, εj) = 0 for i 6= j and εi ∼ N(0, σ2

ε

). (19)

The spatial error dependence model is given as

y = Xβ + ε and ε = µWε + ε∗ (20)

where

ε∗ = (I− µW) ε (21)

is i.i.d. with variance σ2ε∗.9

4.2 Tests

The OLS model with no spatial dependence is nested both in the spatial lag and

the spatial error dependence model. A likelihood-ratio test can be used to test

whether the restrictions of the OLS model hold against the more general alter-

natives. Building on earlier work of Davidson and MacKinnon (1993), Baltagi

and Li (2001) have proposed a double-length artificial regression to test the null

hypothesis in both variants of the model. The first step of this approach is to

run a regression on the restricted version of the model (i.e. under the assumption

% = 0 or µ = 0, respectively). Denote the residual vector of this regression as

8Note that (18) can be written as y = (I− ρWy)−1 Xβ + (I− ρWy)−1ε = Xβ + ε ,

where X and ε are spatially filtered variables: X := (I− ρWy)X and ε := (I− ρWy) ε.

9If the spatially filtered dependent and independent variables are defined as y∗ = (I− µW)y

and X∗ = (I− µW)X (20) can be stated as y∗ = X∗ β + ε∗.

13

ε and the corresponding variance as σ2ε . For the spatial lag model, the artificial

regression is given by For the spatial lag model, the artificial regression is given

by ε

σε

ιR

=

1

σX

1

σWy

ε

σ2

0 ω −ιRσ

b + residual (22)

where is the vector of eigenvalues of the spatial weight matrix W, ιR is a (R×1)-

vector of ones and b is a vector of coefficients which has no further interpretation.

Let SSR be the sum of squared residuals of the artificial regression. The test

statistic can be calculated as

2R− SSR ∼ χ2(1) (23)

For the spatial error dependence model the artificial double length regression has

to be slightly modified: ε

σε

ιR

=

1

σX

1

σWε

ε

σ2

0 ω −ιRσ

b + residual (24)

Compared to (22) the vector of dependent variables y is replaced by the vector

of OLS-residuals ε.

4.3 Choosing the weight matrix

The spatial weight matrix should reflect the intensity of interactions among re-

gions. A common approach is to use geographically derived weights (measures

of distance, for instance). However, sheer distance gives only a very limited and

in many cases even distorted picture of spatial dependence. Consider two small

towns, A and B, in the periphery of a metropolitan city C. Assume equal dis-

tance between A, B and C. Typically economic conditions in A and B in such a

situation are heavily influenced by strong relationships toward the center C. In

contrast to this, the relationships between A and B, might be more or less negli-

gible. Hence measures like distance or traveling time for constructing the spatial

weight matrix do not capture the intensity of spatial dependence and, therefore,

14

might be misleading. An alternative could be a mass to distance (or square dis-

tance) ratio in analogy to what is known in physics as the law of gravity. This

approach seems to be more plausible than using a mere distance factor. However,

with gravity being symmetric, the impact of region A on C, for instance, is forced

to be the same as the impact of C on A. As the example shows, symmetry might

not be adequate in modeling spatial interactions.

A suitable variable that quantitatively reflects the economic relationships among

regions is given by commuter streams. Using data from the employment statis-

tics of the German Federal Labor Office, we constructed a matrix depicting the

commuting process among the 438 NUTS3 regions in our data set. With in- and

outgoing commuter streams being different, the matrix is not symmetric.

A further problem concerns the normalization of the spatial weight matrix. Typ-

ically, the elements on the main diagonal are set to zero because a region cannot

be a neighbor to itself [see, for example, Anselin (2001)]. Moreover, the sum

of each row is normalized to one. The latter procedure, however, destroys the

information across the rows of the matrix which, under the circumstances here,

might also be considered problematic. A feasible alternative would be to nor-

malize the spatial weight matrix by restricting the sum of rows and columns to

unity while conserving the structure of interregional dependence as far as pos-

sible. This can be done by the so-called RAS method which is widely used in

regional input/output analysis, among others. According to the iterative RAS

algorithm the rows and columns of the matrix are alternately adjusted to fulfill

the restrictions until convergence is achieved. The method yields a compromise in

the trade-off between preserving the structure within columns and within rows.

Since the implications of the RAS method in the context of modeling spatial

dependence are not well studied yet, we compare the results of the two variants,

RAS and row normalization.

15

4.4 The empirical model

Based on the theoretical considerations in section 2, the regression approach

outlined below captures the main influences on participation behavior at the

regional level. Using cross-section regional (macro) data, our approach stands

in the tradition of the famous study of Clark and Summers (1982) on female

participation behavior in the U.S., although our theoretical motivation differs.

As a framework for the empirical analysis, an eclectic specification is chosen.

From the search-theoretical model we have derived that participation rate should

depend positively on the mean and spread of the wage offer distribution. Note,

however, that information on this notional distribution is not directly available.

For the present purpose we assume that the mean and the dispersion of the

observed wage distribution are correlated with the corresponding moments of

the unknown wage offer distribution. In the specification for the econometric

estimation we use the median wage of the intermediate skill group instead of the

mean because of the top-coding in the wage data. As a measure of dispersion we

use decile ratios.

In the theoretical model an overall measure of dispersion was considered for the

sake of simplification. For the empirical specification, however, we introduced

two indicators that aim to capture differences in the matching process below

and above the median. More specifically, we decided to introduce the D5 to

D2 ratio as a measure of dispersion in the left tail of the wage distribution and

correspondingly the D8 to D5 ratio for the right tail.

Moreover, the search-theoretical model implies that participation is related to

the discount rate, δ, and the instability of labor contracts as described by the

separation rate, σ. In the following it is assumed that the discount rate of agents

does not vary systematically across regions. Because of differences in the regional

industry structure, we consider the separation rate to be region-specific. As a

suitable proxy for σr we can use the regional unemployment rate ur. The upshot

of the specification motivated by the search-theoretical model is to regress the

labor-force-to-population ratio in region r on the median wage, the unemployment

16

rate and the two decile ratios introduced above.

As described in subsection 2.4, there are also socio-economic and cultural influ-

ences on participation behavior. We try to capture these aspects by introducing

dummy variables for the type of the region.10

A further aspect concerns the differences between West and East Germany. Four

decades of a ‘real existing socialism’ likely gave rise to different patterns of partic-

ipation behavior. According to habit formation considerations it seems plausible

that history still influences participation today. Hence a study of participation

behavior using data for the old and new laender has to deal with these intra-

country differences adequately. We therefore allow the parameters of the model

to vary between both parts of the country.

The band-wagon effects described by Vendrik (1998) are likely to generate some

form of spatial autocorrelation. This gives further ground for spatial econometric

methods to be employed in estimating the model. The equation to be estimated

is

πr =

(a0 + a1ur + a2 ln wr +

8∑i=1

a3iRTir + a4 ln DLr + a5 ln DHr

)×WEST

+

(b0 + b1ur + b2 ln wr +

8∑i=1

b3iRTir + b4 ln DLr + b5 ln DHr

)× EAST + εr,

(25)

where index r stands for the region, RTi (i = 1, · · · , 8) are (0,1) dummy variables

for region types. DL := D5/D2 and DH := D8/D5 are proxies for wage disper-

sion in the lower and upper tail of the wage distribution, respectively, ur is the

regional unemployment rate and wr is the median of regional wages.11 WEST

and EAST are (0,1) dummy variables for the old and new laender, respectively.

10For this purpose the classification scheme proposed by BBR is used that comprises nine

different types of regions, ranging from a metropolitan to rural areas11All wage variables are taken with respect to the intermediate skill group (appreticeship

completed). This group represents the great majority of workers. Moreover, all explanatory

variables except dummies are taken as deviations from the mean, where this normalization is

done separately for the West and the East.

17

5 Results

5.1 Spatial correlation

Given the spatial matrix constructed from data on commuter streams and hav-

ing it normalized by the two alternative methods described above, the question

is whether the spatial lag or the spatial error dependence model is more adequate

than OLS in describing the data. Hence we first present the results of the spec-

ification tests described in section 4.2. Table 1 shows that spatial correlation is

significant for the analysis of participation of male and female workers in most

cases. Concerning the choice of model, the spatial lag model is accepted in all

cases (although the significance is only weak if the RAS normalization is used.).

Irrespective of the normalization method, the spatial autocorrelation coefficient

in the error model is highly significant for male, but not for female workers.

The estimate of the spatial correlation parameter in the spatial lag model, ρ,

is negative for male and female workers, while the estimated parameter for the

error dependence model, µ, is about 0.4 for male and close to zero for female

workers. The results for the test statistics show that the Likelihood Ratio (LR)

and the Double-Length-Artificial Regression Tests produce qualitatively equiva-

lent results. The LR-test seems to be slightly less conservative especially in the

case of the spatial error model. All in all, we find clear evidence for the existence

of spatial autocorrelation patterns.

5.2 Analysis of participation behavior

Table 2 gives the regression results for male workers for OLS and the spatial lag

and spatial error model using the two alternative normalization methods. The

table shows that the estimates are qualitatively the same in all variants. There

are, however, certain differences in magnitude. The constant term is markedly

higher in the spatial lag model, while the wage coefficients are generally higher

in the spatial error model.

18

The signs of the estimated coefficients of unemployment and the wage level are

in line with the predictions of the theoretical model. The negative effect of the

unemployment rate on regional participation is highly significant in all cases.

The magnitude of the estimated coefficients is similar for East and West regions.

According to our results a one percentage point rise in unemployment decreases

participation by about 0.4 percentage points. This indicates that participation is

less attractive if employment becomes more unstable or labor market conditions

deteriorate in general.12 The magnitude of the wage effect for male workers differs

between East and West. For the old laender the coefficient of log wages is between

0.6 and 0.8 for the old and about 0.2 for the new laender, where the t-statistics

in the latter case are in some cases slightly below the 5%-significance level.

While the sign of the coefficients for the log wage and the unemployment rates

are in line with the predictions of the search model, the results for the measures

of dispersions are at least partly at odds with theory. In all variants we find that

wage dispersion in the lower tail of the distribution exhibits a negative impact

on participation, while the coefficients for the dispersion measure in the right

tail are positive, but insignificant in all cases but one. For West Germany the

negative impact of dispersion below the median is highly significant and robust

with respect to the different estimation approaches used here, while it is not

statistically significant for the new laender.

All in all we have to conclude that the influence of economic variables in the new

laender is only weak, while there are strong and highly significant effects in the

West. The same is true for the regional type dummies. The corresponding effects

are not statistically significant for East German regions. Hence for this part

of the country we do not observe that participation of male workers differs with

respect to population density and centrality. By contrast, a clear pattern emerges

for West Germany: Regional types RT2 to RT4 and RT6, i.e. the periphery

regions of metropolitan and intermediate core cities (RT1 and RT5), show lower

participation ceteris paribus. Our results imply that participation behavior of

12In terms of traditional labor market analysis, this could also be described as a “discouraged

worker effect”.

19

male workers in core cities on the one hand and low-density regions on the other

(RT7, RT8 and the reference type RT9) is fairly similar, if other influences are

controlled for.

The results for female workers are contained in table 3. Again, we find that

unemployment has a strong negative effect on regional participation behavior.

For the sub-sample of West German regions the estimated coefficient is about

0.5 irrespective of the method used for estimation. Hence in the old laender the

depressing effect of unemployment on participation of females is stronger than

that of males. For female workers in the East the coefficient is slightly above 0.3

and thereby somewhat lower than the corresponding figure for males.

The estimated coefficient of the wage level is slightly lower than 0.1 in the West

and somewhat higher than 0.1 in the East. For West German regions we find a

remarkable difference in the wage coefficient between male and female workers.

Irrespective of the estimation methods our results indicate that male participation

compared to that of females is much more sensitive to wage changes in the West,

while the reverse is true for the East.

Inequality has no significant effect on participation of female workers in the East,

whereas for the West German regions we find that wage dispersion below the

median exhibits a negative effect on participation as it is the case for male workers.

Hence for the sub-sample of West German regions the estimation results in this

respect contradict the implications of the search-theoretical model which predicts

a higher option value of participation if wage dispersion increases.

Remembering that all explanatory variables are taken as deviations from the

mean and this normalization is done separately for the West and the East, the

constant term can be interpreted as the expected participation rate for the region

with average characteristics except for the spatial lag model13. It turns out

that the participation rate in the average region is quite similar between East

and West for male workers. Ranging between 15 and 20 percentage points, the

13In case of the spatial error model it holds that E(y) = E(Xβ), while in case of the spatial

lag model we have E(y) = (I− ρWy)−1 E(Xβ), hence E(y) 6= E(Xβ) if ρ 6= 0.

20

differences are, however, quite substantial for female workers. This indicates a

substantial gap in participation behavior between the old and new laender. A

further remarkable result is that, controlled for other influences, participation

rates of females in the East are not markedly different from that of males.

6 Discussion and conclusions

Using spatial econometric methods we have shown that regional variations in par-

ticipation rates in West German regions can reasonably be explained by economic

factors. For the new laender, the explanatory power of the economic variables

is weaker. The search-theoretical model, chosen as a backbone of our theoretical

considerations, predicts that a higher regional wage level fosters labor-market

participation, while higher job insecurity as measured by the unemployment rate

deters persons from active labor market behavior. The empirical analysis strongly

corroborates these basic implications of the theory.

Higher regional unemployment depresses participation markedly in both parts of

the country. The strongest effect is observed for females in the West. According

to our results a one percentage point rise in the unemployment rate decreases

participation by between 0.3 and 0.5 percentage points. A further finding is that

the regional wage level has a significant positive effect on participation in most

cases. Sensitivity of participation with respect to earnings is highest for male

workers in West Germany, while wages are of minor importance for participation

of East German male workers. Moreover, our estimates indicate certain variation

of active labor market behavior with respect to the type of the regions in West

Germany. Interestingly we find similarities between core cities with high popula-

tion density on the one hand and peripheral rural areas on the other. Both exhibit

relatively high rates of participation if other economic factors are controlled for.

By contrast, the surroundings of core cities typically exhibit lower participation

rates. These spatial patterns of participation are, however, not valid for East

Germany. For the “new laender” we do not observe any systematic variation of

participation with respect to the type of the region.

21

Testing for spatial autocorrelation gives the result that “neighborhood-effects”

are prominent. It is shown that the Likelihood Ratio and the Double-Length

Artificial Regression Test indicate that a spatial autocorrelation model is superior

to OLS. The only exception is found for the spatial error model in case of female

workers. The presence of spatial autocorrelation might suggest possible band-

wagons effects.

Although our empirical findings support major predictions of the search theo-

retical model, we obtain contradictory results concerning the effects of wage dis-

persion on participation. According to our empirical results, a higher spread in

the wage distribution tends to lower participation rates. Differentiating between

wage dispersion in the lower and upper tail of the distribution we find a robust

and statistically significant negative effect of wage inequality below the median

on the participation behavior of male and female workers. This is clearly at odds

with the search-theoretical model presented here and might suggest that the as-

sumptions of the approach like risk-neutrality of agents do not hold in reality. If,

for instance, agents are risk averse, a higher wage dispersion is associated with

higher wage uncertainty. Hence there is a trade-off between the higher option

value of participation and the utility losses of uncertainty. The total effect on

utility is ambiguous and depends on the degree of risk aversion. We have to leave

this aspect for future research.

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