Spatial Mobility and Competition for Jobs:
Some Theory and Evidence for Western Germany
Ren´e Fahr∗
University of Cologne, and IZA, Bonn
Uwe Sunde IZA, University of Bonn Revised Version: 22. February, 2006
Abstract
This paper sheds new light on the role of regional labor market conditions for re- gional mobility. We study competition for vacant jobs along two dimensions - between employed and unemployed job searchers, and between resident and non-resident job searchers - within a simple matching framework. Evidence from estimating regional matching functions with data on job searchers disaggregated by previous employment status and regional provenance indicates that competition for jobs along both dimen- sions affects hiring. Tests of the theoretical predictions suggest that labor market conditions do determine regional mobility, but the countervailing effects of competi- tion between employed and unemployed dilute mobility effects.
JEL-classification: J61, J64, J21, R12
Keywords: Internal Migration, On-the-Job Search, Job Competition, Regional Un- employment
∗Corresponding author. Address: Department of Business Administration, University of Cologne, Herbert-Lewin-Str. 2, 50931 Cologne, Tel. +49-0221-470-6312, email: rene.fahr@uni-koeln.de. We are grateful to the editor Konrad Stahl and two anonymous referees as well as participants at the meetings of RES 2003 in Warwick, EEA 2003 in Stockholm, EALE 2003 in Sevilla, VfS 2003 in Zurich, EALE-SOLE World Congress 2005, San Francisco, and seminar particpants at IZA for helpful comments.
1 Introduction
One of the central questions in the literature investigating regional labor mobility is whether and to what extent local labor market conditions influence individuals’ job search behavior and mobility. Economic theory suggests that regional migration is triggered by higher job finding probabilities elsewhere, and hence serves to equilibrate inter-regional differences in unemployment rates and labor market conditions. There is ample evidence that regional labor migration is micro-efficient, in the sense that individual search outside the home region and regional mobility behavior, measured by the probability of a person to migrate between regions, is encouraged by personal unemployment. Examples are studies by Pissarides and Wadsworth (1989) for the UK, by Antolin and Bover (1997) for Spain, and by Faini et al. (1997) for Italy. Greenwood (1997) provides an extensive overview over empirical findings on this issue. However, in particular for Europe, there is very little evidence that regional labor migration is macro-efficient, i.e. that migration rates respond to unemployment rates implying a tendency of regional unemployment disparities to dis- appear. An exception is the study by Jackman and Savouri (1992), which provides some evidence for the macro efficiency of migration. However, they investigate the dependence of total migration flows on labor market conditions, which allows to draw conclusions on search behavior and labor mobility only under very strong assumptions.1
Recently, several studies have used a matching function approach to model the influence of regional differences in labor market conditions on the formation of new employment relations. Conceptually, this framework provides a simple way to introduce frictions and therefore to generate unemployment in models of the labor market.2 Geographical distance
1When studying total migration flows measured by registered doctor patients, as is done by Jackman and Savouri, a work-related move of one person implies the measurement of mobility of all persons in the household, thereby inflating the observed labor mobility and making causal interpretations difficult.
2See Petrongolo and Pissarides (2001) and the references therein for microfoundations of the matching
can be interpreted as a natural friction to search and therefore in the job creation process.
The matching function is a shorthand embodying these frictions, and acts like a production function for hires where the stock of unemployed searchers and the vacancies registered with employment agencies serve as inputs to explain newly created job matches between searchers and firms.3 Due to the modest data requirements, the matching approach offers itself to analyze the job creation process with spatially decomposed data. The studies by Gorter and Van Ours (1994) and Coles and Smith (1996) are among the first to estimate matching functions with regional data, but treat local labor markets as isolated market places and therefore do not account for endogenous mobility patterns at all.4 Burda and Profit (1996) and Burgess and Profit (2001) take interactions among neighboring regions in the job creation process explicitly into account. Using data from the Czech Republic for the years 1990-1994, Burda and Profit (1996) challenge the assumption of a uniform matching function across space by estimating matching functions with data on the exits from unemployment as dependent variable on the stocks of unemployed and vacancies as explanatory variables. Burgess and Profit (2001) use data for travel-to-work areas in the UK to test for spatial correlation in the cross-section regression residuals of two specifications of the matching function, using filled vacancies and outflow from unemployment as the respective dependent variables. Both studies find evidence for an influence of neighboring labor market conditions on local unemployment outflows, and interpret this as the result of competition for jobs across space.5 However, the data on which these studies are based do not allow to link labor migration to regional disparities
function.
3In the following the terms hires and matches are used interchangeably to denote newly formed em- ployment relations.
4Compare Petrongolo and Pissarides (2001) for an extensive survey of studies estimating the matching function with regional data.
5Burgess and Profit (2001) find evidence for spatial dependencies also when using the flow of filled vacancies as the dependent variable.
in labor market conditions. In particular, by only using unemployment outflows or filled vacancies within a given region, the studies cannot disentangle how large labor migration flows are, how these flows react to changes in the labor market environment, and how strong the competition and crowding out between local and non-local job searchers is.
Previous studies based on a matching approach have therefore been limited in shedding light on the puzzle of micro and macro efficiency of migration.
This paper tries to fill this gap and contributes to the literature in several respects.
We apply and modify the conventional matching function approach to investigate whether regional mobility patterns can be explained by regional disparities in employment con- ditions. In order to disentangle the interacted effects of competition for jobs between individuals with different employment status and across space, we propose a simple the- oretical model, which allows us to analyze how labor market conditions determine search behavior. The model makes predictions about the determinants of competition between job searchers of different regional provenance, of different employment status, as well as about the interactions between competition in both dimensions. To highlight the impor- tance of disentangling job competition in different dimensions, and the contribution to the existing literature, we first estimate different specifications of the matching function that are augmented to account for regional dependencies. We then present an empirical implementation of the model in order to test its predictions.
In contrast to previous studies, our data allow us to distinguish migration flows in terms of hires involving workers of different regional origin, and moreover to distinguish hires of previously unemployed from job-to-job movements. With our data, we are able to address the puzzling differences with regard to labor market driven mobility on the individual level and the apparent lack of evidence for unemployment driven migration on the macro level, and we can account for the possibility that search and mobility behavior might differ between employed and unemployed, as indicated by several micro-studies
surveyed in Greenwood (1997).
Our empirical starting point is the framework proposed by Burda and Profit (1996) and Burgess and Profit (2001), which we extend by investigating matches from different regional provenance as the dependent variable. Some of our estimation results are puzzling in the light of the conventional matching approach: We find that higher unemployment in the regions neighboring to a particular region exhibits a significantnegative effect on hires involving searchers from these neighboring regions. This contradicts both the assumption that larger stocks increase the number of respective hires underlying the matching function, and the intuition that, everything else equal, higher unemployment should lead to more out-migration. A possible explanation is competition not only across the spatial dimension, but also job competition among unemployed and employed job searchers. We therefore disaggregate the dependent variable by the previous job status of the newly hired persons.
When regressing the matching functions separately for previously employed and previously unemployed, we find the aforementioned negative effect of the stock of unemployment in neighboring regions for job-to-job movements from these neighboring regions. In contrast, the stock of unemployed in neighboring regions increases the successful hires of unemployed from these regions. These findings are in line with macro-efficient migration behavior that affects matches involving unemployed searchers from neighboring regions, but they are also in line with job competition between employed and unemployed.
According to our simple model, both dimensions, i.e. competition between unemployed and employed searchers as well as between local and non-local searchers, are important when evaluating the effect of local labor market conditions on migration patterns. If both effects work in opposite directions and cancel each other out, interactions between com- petition for jobs across regions and between individuals with different employment status can explain the puzzling observation of micro-efficient migration behavior of unemployed searchers along with missing evidence for macro-efficient migration behavior caused by
regional unemployment differentials. When testing the theoretical predictions empirically with our data for West Germany, we find evidence that both job competition and endoge- nous mobility behavior determine search and labor mobility. The empirical results indicate that job competition is empirically more important. The crowding out of unemployed job seekers by job-to-job movers in our data for Germany can explain the missing evidence for labor market determined regional mobility of unemployed job seekers despite the evidence pointing at the micro-efficient labor migration that has been found in earlier studies for European countries.
The paper proceeds as follows. In section 2 we develop a simple model of mobility and on-the-job search to organize thoughts and generate testable predictions. Section 3 describes the data used throughout the analysis. Section 4 extends the spatial matching framework by disentangling matches by regional provenance, and investigates search com- petition across space in a reduced form representation. In section 5, we test the predictions of the model. Section 6 concludes.
2 A Simple Model of Mobility and On-the-Job-Search
Estimates of empirical matching functions incorporating components of regional job com- petition have provided hints that competition across regions and different employment status cannot not be ignored in the investigation of the regional job creation process, see e.g. Burda and Profit (1996) and Burgess and Profit (2001). In section 4, we provide sim- ilar evidence. Many findings are difficult to explain within the standard matching model, however, because it leaves open how search decisions are affected by competition effects, and how job competition along several dimensions shapes the composition of hiring flows.
In this section, we develop a simple model of labor market determined regional mobility and a simple model of on-the-job search. A blend of both models provides predictions
how hiring flows are composed along both dimensions, regional origin and job status of searchers.
2.1 Endogenous Mobility
In an economy consisting of several regions, a fraction of the population of a given region is unemployed at a given point in time and searches for employment. Suppose that indi- viduals only differ with respect to their current region of origin and consider the regional migration decision of a given job seeker. For simplicity, we assume that job seekers always search within their home region. However, they also have the opportunity to search in other regions, and the decision to do so is endogenous and depends on the job prospects in other regions.6 An individual will decide to search elsewhere and migrate in case of finding new employment, if the expected net gains from searching elsewhere are positive.
We assume that the intensity of search depends, everything else equal, positively on the total number of hires in other regions, because intensive hiring activities suggest that it is relatively easy to find new employment, thus implying high expected net gains from search.
On the other hand, the search intensity for jobs in other regions depends negatively on the unemployment rates in these regions. The reason is that high local unemployment means fiercer competition for vacancies. In the following, we take the perspective of a destination region of migration flows and model (im-)migration in terms of the hires that involve non-residents as a fraction of the total number of hires in that region. From the perspective of the destination region, the intensity of job search of non-residents in that region, φ, is therefore positively related to the number of matchesm in the region within
6Since migration from non-neighboring regions is only measured with error in our data we restrict our interest to migration between neighboring regions in the empirical analysis.
a period, and depends negatively on the regional unemployment level,uh:7 φ=φ(m, uh) with ∂φ
∂m >0, and ∂φ
∂uh <0. (1)
All matches realized within a region during a period of time are composed of matches involving resident job searchers, mh, and matches involving searchers from other regions, mn: m=mh+mn. The total number of persons actively searching for employment in the region,J, consists of resident unemployed job seekers,uh, and the fraction of non-residents who decide to search in that region, φun: J = uh+φun. To see how this endogenous behavior affects the composition of successful matches consider the share of hires accessed by non-resident job seekers:
β= mn
m . (2)
Assume, there is no discrimination, that is, every job seeker has the same probability of encountering a new job,θ, regardless of his regional origin. Hence, the number of matches achieved by non-residents can be expressed asmn=θφun. Substitution and some calculus delivers the following set of results:8
εβm = ∂β
∂m m
β =εφm µ
1− φun u+φun
¶
>0, (3)
εβuh = εφuh µ
1− φun uh+φun
¶
− uh
uh+φun <0, (4) εβun = 1− φun
uh+φun >0. (5)
In words, this implies that the share of non-resident job accessions increases in the total number of matches, decreases in the level of resident unemployment, and increases in the level of non-resident unemployment.
7These assumptions are in line with evidence from survey data, see Fainiet al. (1997).
8The results are derived in Appendix A.1.
2.2 Endogenous On-the-Job Search
Alternatively, we can construct a similar model for job-to-job transitions, disregarding regional heterogeneity for a moment. Consider an economy in which individuals only differ by their employment status. Individuals can either be employed or unemployed.
Unemployed individuals always search for a new job inelastically. The number of employed searchers, on the other hand, is endogenous and depends on the labor market conditions, similar as before the decision to search for employment elsewhere.9 Let the search intensity of employed, ψ, depend positively on the number of total hires, and negatively on the number of unemployed job seekers, who compete for the same jobs:
ψ=ψ(m, u) with ∂ψ
∂m >0 and ∂ψ
∂u <0. (6)
Analogous to the mobility model, all hires are composed by matches involving unemployed job searchers, mu, and matches involving employed workers (job-to-job transitions), me: m=mu+me. The total number of job seekers is the sum of unemployed (u) and employed (ψe) searchers. As before, we are interested in the composition of matches, which is now measured as the share of hires of unemployed job seekers:
γ = mu
m . (7)
This allows to derive the second set of results:
εγm = −εψm ψe
ψe+u <0, (8)
εγu = ψe
ψe+u(1−εψu)>0. (9) The share of hires accessed by unemployed can therefore be expected to depend negatively on the overall level of hiring as a consequence of job competition and crowding out. On the
9This setting follows closely the framework suggested by Anderson and Burgess (2000). Results are obtained by similar manipulations as in the previous model.
other hand, and consistent with the standard matching view, the relative number of job accessions by unemployed searchers is positively related to the number of unemployed job seekers.10 Extending this model to allow for a third state, inactivity, is straightforward.
Inactive individuals out of the labor force, who decide endogenously whether to re-enter the labor market and search for a job, would behave similarly to employed job searchers in the current context. The composition of hiring flows would be affected in an analogous way. In particular, individuals out of the labor force would search more intensively if labor market conditions are promising, i.e. ifmis higher, and search less intensively if the number of (active) unemployedu is higher. This extension would reinforce the effects of m and uon γ as displayed in conditions (8) and (9).11
2.3 Putting Things Together
These separate results on the composition of hiring flows with respect to regional prove- nance and employment status can be combined to get predictions for an economy in which individuals searching for a new job are heterogeneous with respect to both dimen- sions: geographic origin and employment status. Endogenous inter-regional mobility and job competition between unemployed and employed searchers simultaneously affect job creation patterns in similar ways as when considered in separate models. Consider the fraction of hires made up by employed individuals immigrating from another region:
η = men
m . (10)
10It can be shown thatεγu= 0 if there is ranking of applicants by employers and if employed job seekers are preferred by firms, see also Anderson and Burgess (2000).
11In the empirical application we do not pursue this extension, because our data do not allow us to determine the regional provenance of inflows from out of the labor force. Likewise, modelling the compe- tition between employed searchers and those out of the labor force would require additional assumptions that cannot be tested due to data restrictions, and is therefore beyond the scope of this paper.
Given the previous results, one would expect this ratio to increase in the number of matches and to decrease in the number of unemployed in the destination region. However, the model delivers no clear prediction for the influence of the number of unemployed in neighboring regions onη, which depends on the relative size of the two opposing effects:
εηm > 0 asεβm>0 andεγm <0, (11) εηuh < 0 asεβuh <0 andεγu>0, (12) εηun ≷ 0 asεβun >0 and εγu>0. (13) To show these results, note that the share of matches of employed job seekers moves inversely to the share of unemployed job seekersγ.
Similarly, a blend of the previous models can help predicting the behavior of the fraction of hires of resident unemployed:
ζ = muh
m . (14)
The models then imply:12
εζm<0,εζuh>0, andεζun ≷0. (15) Also the fraction of hires of unemployed immigrating from another region:
ξ= mun
m , (16)
can be investigated, implying the following predictions:
εξm ≷0,εξuh ≷0, andεξun >0. (17) Finally, if the fraction of hires of resident employed,
χ= meh
m , (18)
12The results in this and in the following equations are derived by the same arguments as mentioned in equations (11) to (13).
is concerned, the following behavior can be predicted when using again the reasoning as in equations (11) to (13):
εχm≷0,εχuh ≷0, andεχun <0. (19) Note, that the effect of the number of matchesm and the number of unemployedu in the destination region on the respective hiring shares in equations (15) and (19) depends on the relative size of the opposing job competition and the endogenous mobility effects.13 Which of the effects prevails is primarily an empirical question. Before turning to the empirical implementation, we introduce the data used in the application below.
3 Data
In order to estimate empirical matching functions and to implement the simple framework discussed before, we require data on hiring flows, and stocks of unemployed and vacancies.
We use yearly data on unemployment, vacancies and hires for the years 1980 through 1997 for 117 regions in Western Germany. The data on the stocks of unemployed and vacancies are taken from official labor statistics and available on the level of so called Employment Office Districts. The matching flows are computed from individual level data and stem from an anonymized representative 1% sample of German social security records provided by the German Federal Institute for Employment Research (IAB). The database is sup- plemented by data on unemployment benefits recipients and by establishment information (see Bender, Haas, and Klose (2000) for details). The data allow to identify the precise date of a hire, as well as the employment history and the geographical location (including
13Allowing for endogenous search behavior of individuals out of the labor force would modify the results slightly. In particular, additional matches of persons entering from out of the labor force would imply lower elasticitiesεηm,εζm,εξm andεχm. The intuition behind this conjecture is that matches of (local) searchers entering from out of the labor force crowd out both employed as well as unemployed searchers, thereby decreasing the scale effectsεβmas well asεγm in absolute terms.
changes in the location) of the respective individual. In particular, a change in the em- ployment status of an individual indicates a transition from unemployment to employment and vice versa. No change in the employment status, but a change in the firm identifier indicates a job-to-job transition. Hiring flows are the cumulative flows between October 1st of a year tand September 30th of the following year t+ 1 in a respective cell defined by region and previous employment status. The hiring flows are merged with a snapshot of the stocks of unemployed and vacancies taken at September 30th of the year before the flows are constructed (i.e. t). Regions are identified by locations of employers, thus changes in (plant of) employer identifiers imply changes in region identifier, and thereby regional mobility. We aggregate matches into year-region cells, where regions correspond to labor market districts. The definition is provided by the Federal Office of Building and Regional Planning, and accounts for a scientific analysis of commuting flows as well as some political constraints. In particular, the used definition of labor market districts is designed to capture commuting areas and minimize commuting flows across districts. We merge the hires data and the stock data to the respective coarser region definition, which is in most of the cases the one from official labor statistics defining regions as Employ- ment Office Districts. We are confident that the regional definition used in the analysis is close to the correct level of aggregation for the purpose of the present analysis. The level of regional disaggregation provides a maximum of regional variation with a minimum of spurious spatial interactions e.g. moves of employment location without implying also a movement of domicile. In our data, any regional mobility most likely implies mobility of workers reallocating their households rather than more commuting. A list with the labor market regions used in the empirical analysis, as well as a map indicating their location, are contained in the Appendix.
The central concept to incorporate the spatial pattern of search and matching behav- ior on the labor market is that of regional contiguity between two regions. We define two
regions to be contiguous when these regions share a common border. The corresponding spatial weights matrixW, which we use extensively in our analysis, is therefore a symmet- ric 117×117 matrix with entries 0 and 1, where 1 indicates contiguity.14 As a first test for spatial dependencies we test whether the variables of primary interest in the context of empirical labor market matching exhibit spatial autocorrelation. For example, if matches are positively spatially autocorrelated, a high job creation activity in a certain region is associated with high job creation in nearby regions. The null of global autocorrelation of hires can be rejected, but we find substantial heterogeneity across regions, with some regions exhibiting significant positive local spatial autocorrelation, and others with sig- nificant negative local spatial autocorrelation, which indicates spatial dependencies in the matching process.15
4 Estimates of Spatially Augmented Matching Functions
Given the evidence for the importance of spatial dependencies in matching outcomes pre- sented in earlier contributions, and given our findings of spatial autocorrelation of relevant variables in our data set, it is questionable whether the results obtained by conventional matching functions neglecting the spatial dimension can produce unbiased estimates. To investigate this issue, we exploit the fact that our data set allows us to decompose hir- ing flows with respect to regional provenance and former job market status of the hired workers. Table 1 contains the sample averages of these different concepts of matches over all years and regions in order to give some information about the quantitative relevance of the different measures. As before, we denote non-decomposed hires by m, hires of in-
14The entries on the main diagonal ofW are zeros, since a region cannot be contiguous to itself.
15We test the null hypothesis of no global or local spatial autocorrelation, using the respective Moran’s I-test statistics, see Anselin and Bera (1999) for details. We also find evidence for strong positive spatial autocorrelation in the stocks of unemployed and vacancies, see Fahr and Sunde (2002) for detailed results.
dividuals from within the region by mh, hires of individuals who have been employed in a neighboring region or in a other non-neighboring region previous to the current hiring by mn or mf, respectively. Hirings from unemployment are denoted by mu and hires of employed byme.
<INSERT TABLE 1 ABOUT HERE>
We can only determine the regional origin of 58 percent of all matches in our sample without error. The reason is that we cannot trace down the regional origin of hires involving searchers who have not been registered as unemployed or who have not been previously employed. While we do denote the remaining hires as coming from other regions, one has to keep in mind that a considerable share of them is coming from the local and neighboring labor market. The model outlined in section 2 and empirically implemented in section 5 therefore concentrates on flows into matches from neighboring regions. The way we deal with hires of unknown regional origin leads to downward biased numbers of hires from neighboring regions. Significant effects for flows from neighboring regions therefore provide a conservative estimate of the true effects.16 While a quarter of all hires of unemployed involve the hiring of a non-resident, Table 1 shows that about half of all job-to-job movements imply also movements across labor market districts. Moreover, in all dimensions of regional decomposition of hires, hires of previously employed workers (i.e. job-to-job movements) make up a larger share than hires of unemployed job searchers.
This observation should be kept in mind, as it indicates that regional mobility and job status of job seekers might be closely intertwined.
16The variability in hires from different regional origin is not affected by these measurement issues.
Moreover, the region and time fixed effects should absorb measurement error from allocating hires with unknown regional origin to hires from non-neighboring regions appropriately as long as the distribution of these hires over the true regional origin is stable.
To examine the role of spatial externalities in the matching process, we begin by estimating conventional matching functions of the Cobb-Douglas specification
lnmit=A+α1lnUit+α2lnVit+εit, (20) where mit denotes the matches created in region i within a period of time, i. e. the sum of all hires observed between t and t+ 1, Uit is the stock of unemployed job seekers in regioni at the beginning of the period for which the matches are measured. Likewise,Vit denotes the stock of vacancies in i at time t. Moreover, α1 and α2 are parameters and ε denotes a vector of normally distributed, homoskedastic and uncorrelated errors. The term A reflects variables that potentially affect the efficiency or speed of the matching process. Apart from a constant,Aincludes a set of year-dummies to control for non-linear time effects.17 Our data allow us to estimate this specification for different concepts of regionally decomposed flows. The relevant stock of vacancies for all these definitions of the regionally decomposed hires is obviously vacancies registered by local firms with the local employment agencies. Contrary to that, the relevant stock of searchers is different for each specification. The results for the model estimated with data pooled across regions is presented in Table 2.
<INSERT TABLE 2 ABOUT HERE>
The first column in Table 2 shows the estimates of a standard matching function pooling over regions and years and provides a comparison of estimates with our data to the results in the literature. The stock of unemployed exhibits a highly positive coefficient with a value of 0.41 and the stock of vacancies with a value of 0.51. The result is comparable to estimates of matching functions on the occupational level for the same time span in
17The time dummies account also for the effect of the reunification of East and West Germany in 1990.
In fact, for many specifications the coefficients for the time dummies differ for pre- and post-reunification periods. However, a detailed discussion of these effects is beyond the scope of this paper.
Germany as in Fahr and Sunde (2004). Interestingly, the coefficients for the stock of unemployed and vacancies differ only by 0.1. This is in contrast to Burgess and Profit (2001) who report coefficients of 0.75 and 0.21 for the stock of unemployed and the stock of vacancies, respectively, for a comparable specification when taking the unemployment outflows as the dependent variable. They find the reverse relation for the coefficient estimates of the stock of unemployed and vacancies when filled vacancies are taken as the dependent variable. We interpret this difference as a result of the choice of the hiring measure as the dependent variable in our specification. The other columns in Table 2 show estimates with pooled data when using a regionally decomposed hiring flow measure with the relevant stocks on the right hand side. The results obtained from using regionally decomposed hires as dependent variable reveal that the stock of local vacancies seems to be increasingly important with the distance of job searcher involved in the hires. This points at the mobility enhancing role of labor market conditions.
<INSERT TABLE 3 ABOUT HERE>
So far, we have not taken advantage of the panel structure of our data. Burgess and Profit (2001) have shown that coefficient estimates of matching functions with regionally decomposed cross-sectional data may exhibit pure scale effects due to the size of travel-to- work areas. To account for this possibility, the columns denoted “relevant stocks model”
in Table 3 provide estimates with region and time fixed effects of the specifications as in Table 2. In fact, the results differ substantially from those in Table 2 and suggest that the findings there are driven to a large extent by different sizes of the regional labor markets.
The coefficient estimated for the stock of searchers in Table 3 becomes negative and small in the specification with all matches as the dependent variable and insignificant for the specification with regionally decomposed hiring flows. For the stock of vacancies we find a significant coefficient between 0.04 and 0.09 depending on the definition of the dependent
variable. This considerable difference in the estimates of a matching function with re- gionally disaggregated data between a pooled specification and a fixed effects specification is in line with the literature. For a comparable specification, Burgess and Profit (2001) find large positive coefficients for the stock of unemployed when unemployment outflows are taken as the dependent variable. They find similarly strong results for the stock of vacancies when filled vacancies are the dependent variable. Their coefficient estimates are comparable to those reported in Table 3 for the respective stock which is related to the flow variable in a less direct way (i.e. stock of unemployed in the filled vacancies model and stock of vacancies in the unemployment outflow model). Burgess and Profit (2001) report a significant small negative coefficient (-0.042) for the stock of unemployed when the flow of filled vacancies is the dependent variable and a significant positive coefficient of 0.071 for the stock of vacancies when the outflow of unemployment is the dependent variable.
While the specifications so far have taken account of the regional heterogeneity of the hires and highlighted the importance of including region fixed effects, we have not modelled the process of spatial externalities in the search process. Burda and Profit (1996) have developed a model of non-sequential endogenous search across space to account for such externalities. However, the augmented matching function implied by this model cannot be estimated directly. Therefore, Burda and Profit (1996) and Burgess and Profit (2001) estimate an approximation of this matching function by augmenting the conventional matching function with spatially lagged stocks of unemployed and vacancies as additional regressors. We follow their approach and augment the standard matching function in order to incorporate regional search competition. Consider the following spatial competition model,
lnmit=A+α1lnUit+α2lnVit+α3lnW Uit+α4lnW Uit+εit, (21)
whereW U denotes the stock of unemployed in neighboring regions and W U the stock of unemployed in all other regions but in the resident and neighboring regions. In contrast to the linear approximation of a matching function as estimated in Burda and Profit (1996) and Burgess and Profit (2001), we do not include spatially lagged stocks of vacancies. In- cluding spatially lagged stocks of vacancies would imply a mis-specification in our context.
The reason is that, by definition of our data, a new match in a certain region implies a filled vacancy in that region, because regions are determined by the location of the employer.
We estimate these specifications also for the regionally decomposed dependent variable.
The results are contained in Table 3 in columns called “spatial competition model”. For the specifications with total matches or matches from resident searchers as the dependent variable we find no change in the observed effects when including the stock of unemployed from neighboring and non-neighboring regions. Neither the coefficients for the resident nor for the non-resident unemployment stock are significant. When regressing matching flows that involve hires from neighboring regions, we obtain a substantially larger and sig- nificantly negative coefficient for the unemployment stock in neighboring regions. In light of the conventional empirical matching framework, this effect is puzzling and counterin- tuitive, because the relevant stock of job seekersdecreases the number of matches. At the same time, we estimate a small but significantly positive coefficient for the stock of unem- ployed from non-neighboring regions. This effect is not directly interpretable, because the stock of non-neighboring unemployment is not the relevant pool for the dependent flow variable under consideration. Nevertheless, the positive coefficient suggests substantial regional search competition. The spatial competition model estimated for matches from non-neighboring regions reveals similar results as the relevant stocks model. However we find a significant negative effect of local unemployment, which could indicate competition for jobs across space. The fact that we do not observe a significant effect of the relevant stock of unemployed, W U, could be due to the measurement problem in the flow of hires
from non-neighboring regions.
All these effects are difficult to interpret within the conventional representation of the matching process with regional job competition. A priori, one could rationalize a positive as well as a negative influence from the resident stock of unemployed on matches from non-neighboring regions.18 However, considering the prevalence of the comparatively large mobility exhibited by job-to-job movements in Table 1, one possible explanation for the puzzling negative effect ofW U in the specification for matches from neighboring regions mnis competition between employed and unemployed for the available vacancies provided that the search behavior differs systematically between these groups. To shed some light on this issue, we estimate equation (21) with regionally decomposed data separately for hires from unemployment and employment. The results are displayed in Table 4 and show that the stock of local unemployed exerts a significant negative influence on total matches of employed workers and resident employed workers. The opposite is found for total matches involving unemployed searchers and those matches involving only resident unemployed. This finding is a clear indication for the existence of job competition between employed and unemployed searchers. When regressing hires that involve searchers from neighboring regions, unemployment in the destination region exerts no significant effect, implying that it is of no relevance for the migration decision. This is true both for employed and unemployed searchers. In contrast, we find significant negative effects for the stock of unemployed in neighboring regions on matches, regardless whether these matches involve employed workers from the same or different regions. Similarly, we find significant positive effects of unemployment in neighboring regions on hires involving unemployed searchers.
The effects of unemployment in non-neighboring regions are positive regarding me, men
18A high number of unemployed could deter job seekers from distant regions and lead to less immigration.
If the high unemployment numbers represent an overall recession we might observe a more intensive search across boarders and therefore more immigration from non-neighboring regions.
and mun.
<INSERT TABLE 4 ABOUT HERE>
Summing up, we find a negative impact of local and non-local unemployment on job- to-job moves, indicating job competition; we find positive effects of unemployment in neighboring regions on the hires of these people in a given region, which is in line with the positive effect of the stock of job searchers on matches underlying the matching function;
we find a positive effect of local unemployment on matches involving hires of unemployed locals, but a negative effect of local unemployment on matches involving unemployed non- locals. All these results suggest that competition for available vacancies between employed and unemployed, as well as across regions is potentially important for the composition of new matches. However, the conventional matching approach cannot go beyond providing suggestive evidence as the one presented. To disentangle the different effects, the next step is therefore to implement the simple framework presented in section 2, which allows us to identify effects of labor market conditions on endogenous search behavior and mobility patterns.
5 Job Competition and the Composition of Matches
The effects of competition between employed and unemployed, and between resident and non-resident job searchers can only be estimated indirectly, because endogenous on-the- job search is unobservable. However, the model presented in section 2 makes several predictions concerning the composition of hiring flows as well as the determinants of these flows and their composition as stated in conditions (3) to (19). In order to test these predictions, we estimate the following basic specification:
lnyit =α0+α1lnUit+α2lnVit+α3lnW Uit+εit. (22)
As dependent variable yit, we consider the fraction of hires of workers exhibiting a par- ticular characteristic over all hires between period tand t+ 1. These characteristics are regional origin of hired workers (from same region or from another region) and employment status during search (employed or unemployed), and combinations of these. As explana- tory variables embodying the competition aspects, we use Uit, the stock of unemployed in region i at time t, that is at the beginning of the observation period, and W Uit as the spatially lagged level of unemployment of region i at time t, that is, the (weighted) average of unemployment levels in regions neighboring region i;ε is an i.i.d. error term.
Ideally, we would also include the flow of hires as an explanatory variable in an estimation of equation (22), but this is prevented due to the obvious endogeneity of the variable.19 We therefore follow Anderson and Burgess (2000) and instrument the flow of hires by the stock of vacancies Vit to test the implications of the simple model. Since matches and the stock of vacancies are correlated, while the stock of vacancies is uncorrelated with the relative sizes of the hiring flows and therefore orthogonal toε,V is a valid instrument for m. All specifications were estimated with region and time fixed effects.20 Estimates of this specification with various dependent variables allow us to find out to what extent regional mobility is driven by labor market conditions. More importantly we are able to compare the importance of endogenously determined regional job competition with competition between employed and unemployed job searchers and the interplay of both forms of job market competition. This is possible, since our data set allows us to decompose matching flows not only with respect to the regional origin of the searchers involved, but also with respect to the previous job status (employed or unemployed) of the hired workers.
Table 5 contains estimation results for different specifications of the dependent variable.
19If a shock toε affects the flow of hires exhibiting a certain characteristic, by construction it would also affect the total number of hires, and therefore the explanatory variable, violating the exogeneity assumption.
20For expositional brevity we do not indicate the fixed effects in equation (22).
Column (1) tests the predictions of the endogenous mobility model, stated in equations (3) to (5), by using the fraction of hires constituted by individuals stemming from the respective neighboring regions over all hires. As predicted by the model, the number of matches exerts a positive but insignificant effect on the number of hires of non-locals.
A possible reason for this is the neglect of job competition between unemployed and employed.21 The predicted negative effect of local unemployment on matches involving non-local searchers is also found, but is insignificant as well. Unemployment in neighboring regions should exert a positive influence according to the model. We do not find this effect for this specification. The evidence for a model which is only based on endogenous mobility behavior triggered by labor market conditions is therefore rather weak.22
<INSERT TABLE 5 ABOUT HERE>
Column (2) contains estimation results for the fraction of all hires constituted by unemployed applicants. This specification tests the implications of the job competition model between employed and unemployed seekers, as stated in equations (8) and (9). In fact we find that the fraction of hires of unemployed with respect to the total number of hires is significantly positively related to the number of unemployed searchers and significantly negatively related to the total number of matches as instrumented by the stock of vacancies due to job competition and crowding out by employed job seekers.23
21This effect is amplified by the neglect of searchers that re-enter from out of the labor force.
22Robustness checks using alternative specification for β like the matches involving individuals from anywhere else but the region where they are hired or the ratio of hires of unemployed from neighboring regions over all hires of unemployed yield similar results and are available upon request.
23Estimations of a model with the share of matches of individuals from out of the labor force as dependent variable delivers an insignificant negative coefficient for the stock of vacancies. When using the share of all matches involving non-employed, including both unemployed and individuals out of the labor force, as dependent variable, the coefficient for the vacancy stock is -0.013 with a standard error of 0.006, and therefore slightly smaller than for the share of unemployed displayed in the table. These results suggest
The significant positive effect on spatially lagged unemployment indicates that the job competition is not confined to the borders of the local labor market.
Column (2) tests a model which does not explicitly take account of endogenous search behavior across space triggered by labor market conditions. This is done in Columns (3), and (4) which evaluate the predictions of the model combining endogenous mobility and endogenous on-the-job search. The predictions for the fraction of matches of employed non-resident applicants in equation (11) to (13) are tested for newly hired from neighboring regions in Column (3). The coefficients of the number of matches and local unemployment are of the predicted sign but insignificant. The influence of neighboring unemployment on the fraction of non-resident employed matches over all matches is significantly nega- tive. This suggests that the effect of job competition between employed and unemployed searchers in equation (13) is stronger than the spatial competition component. Column (4) regresses successful unemployed resident job seekers as a fraction of all hires. Results here reflect precisely the predictions stated in equation (15). Again, the significant posi- tive effect from the stock of unemployed in neighboring regions suggests that the influence of job competition outweighs the spatial competition effect. Columns (5) and (6) pro- vide evidence for those effects, that can be unambiguously signed in equations (17) and (19).24 Moreover, the negative effect of local unemployment on the fraction of resident job-to-job movers in column (6) again suggests that the competition between employed and unemployed searchers dominates any spatial competition effects.
The empirical implementation of the model shows that local labor market conditions
that individuals out of the labor force indeed react to labor market conditions, but that neglecting them in the analysis does not impose overly strong restrictions on the model that could alter the main results.
A more extensive set of estimation results for robustness checks using alternative specifications for γ is available from the authors upon request.
24Insignificant scale effects in columns (1), (5) and (6) can potentially also be affected by competition of searchers from out of the labor force.
trigger endogenous search behavior by non-resident searchers as well as by employed work- ers. The interaction of both competition models explains the variation in the share of hires from the pool of resident unemployed over all hires within a region quite well. The same holds for the share of hires involving unemployed from neighboring regions and hires from the pool of resident employed over all hires. Things are a bit more intricate when trying to explain the fraction of hires of non-local employed searchers over all matches within a region, suggesting that there are more effects at work than we are able to cover in our simple model. The estimation results for those coefficients in columns (4) to (6) where the model does not give a clear prediction of the resulting effect suggests that effects from endogenous on-the-job search dominates any effects from endogenous regional mobility.
This confirms the impression concerning the importance of job competition versus spa- tial competition that is suggested by the simple descriptive statistics of the relative hiring flows in Table 1. Regional job creation patterns are shaped by endogenous job competition between employed and unemployed workers, and endogenous spatial mobility processes, but endogenous job competition seems to be empirically more relevant.
6 Conclusion
This paper sheds new light on the earlier puzzling findings of only weak evidence concern- ing the influence of local labor market conditions for labor mobility (i.e. labor mobility is macro-efficient) despite strong evidence that individual migration decisions are driven by economic factors (i.e. labor migration is micro-efficient). The main conjecture of this paper is that the interacting effects of job competition between employed and unemployed, as well as competition for jobs across regions might provide an explanation for these findings.
We find strong evidence for endogenous mobility decisions determined by labor market conditions. The data also suggest that endogenous behavior is correlated along both di-
mensions, regions and employment status, but that endogenous job competition seems to be the more important phenomenon. While the unemployed do consider local labor mar- ket conditions in their migration decision, they are crowded out by job-to-job movers. Our results show that only analyzing patterns of total migration as in Jackman and Savouri (1992), can be misleading since total migration flows cannot be used to disentangle job- to-job movers from those coming from unemployment, or to disentangle labor motivated mobility from other determinants for migration. On the other hand, the present study demonstrates that data on a sufficiently aggregated level are needed to investigate inter- actions in the mobility behavior of different type of movers. This would be problematic in a framework investigating the individual determinants of migration.
Two other important issues concerning labor mobility have been disregarded on pur- pose in this study. The data used here do not allow to investigate firm mobility. However, high transaction costs are likely to make firms less mobile than labor. In this context, the focus of the present paper is on the more interesting and important aspect of labor mobility. Secondly, regional disparities in labor market conditions have been reduced to regional disparities in hiring flows and stocks of unemployed and vacancies. Given that the data were generated in an economic environment characterized by a highly centralized wage bargaining, and institutions like the “Fl¨achentarifvertrag”, other regional disparities such as regional wage dispersion are probably less of an issue than in other countries.
Moreover, such dispersion in regional characteristics should eventually also be reflected in search behavior, and therefore the flow and stock data on which this study is based.
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A Appendix
A.1 Derivation of Results
In the following we derive the elasticities as stated in equations (3) to (5). The elasticities for the endogenous on-the-job search and the combined model are derived in a similar manner.
A.1.1 Derivation of equation (3)
Recall for the derivation of equation (3) to (5) the definition ofβ:
β = mn
m = θφun θuh+θφun
Using that θ = mJ and denoting the first derivative of φ with respect to m by φ0m resulting in
∂β
∂m = (J1φun+θunφ0m)(θuh+θφun)−θφun(J1uh+J1φun+θφ0mun) (θuh+θφun)2
= θunφ0m
θuh+θφun − θ2φφ0mu2n (θuh+θφun)2
= θ2unuhφ0m (θuh+θφun)2
To find out about the sign of the elasticity we augment this derivative to
∂β
∂m m
β = θ2unuhφ0m
(θuh+θφun)2 ·θuh+θφun
θφun ·(θuh+θφun)
= θuhφ0m
φ =εφm µ
θuh 1 m
¶
= εφm
µ θuh θuh+θφun
¶
=εφm µ
1− φun uh+φun
¶
>0
A.1.2 Derivation of equation (4)
Taking the derivative ofβ with respect touh we get:
∂β
∂uh = φ0uhun(uh+φun)−φun(1 +φ0uhun) (uh+φun)2
= φ0uhun
(uh+φun) − φun
(uh+φun)2 − φφ0uhu2n (uh+φun)2 .
Augmenting this derivative with uβh delivers the elasticity εβuh. Substituting uφun
h+φun
forβ and simplifying delivers:
∂β
∂uh uh
β = φ0uhuh
φ − uh
uh+φun − φ0uhunuh (uh+φun)
= εφuh µ
1− φun (uh+φun)
¶
− uh
(uh+φun) <0. A.1.3 Derivation of equation (5)
Note that the derivative of θ with respect to un yields −(u φm
h+φun)2. This results in the following derivative of β with respect to un
∂β
∂un =
³
θφ−(uφ2unm
h+φun)2
´
·θ(uh+φun)
θ2(uh+φun)2 − θφun
³ −φmuh
(uh+φun)2 −(uφ2mun
h+φun)2 +θφ
´
θ2(uh+φun)2
= φ
(uh+φun)− φ2unm
θ(uh+φun)3 +φ2mun(uh+φun)
θ(uh+φun)4 − φ2un (uh+φun)2
= φ
(uhφun)− φ2un (uh+φun)2
= φuh
(uh+φun)2 .
Augmenting the derivative with uβn we get for the elasticityεβun:
