This paper examines the significance of spatial externalities for youths’ school-to-training transitions in Germany. For this purpose, it is necessary to address the methodological question of how an individual’s spatial context has to be operationalized with respect to both its extent and the problem of spatial autocorrelation. Our analyses show that the “zone of influence” comprises of the whole of Germany, not only close-by districts, and that these effects differ between structurally weak and strong regions. Consequently, assuming that only close proximity affects individual outcomes may disregard relevant contextual influences, and for spatial models that require an a priori definition of the weights for spatial units, it may be erroneous to make a decision based on this assumption. Concerning spatial autocorrelation, we found that neglecting local spatial autocorrelation at the context level causes considerable bias to the estimates, especially for districts that are close to the home district.
There is little doubt that social action and, thus, labor market processes are not just structured in terms of time [
This proposition is unrealistic, to be sure. Opportunity structures are not just point-located; rather, they are distributed in space. In other words, they are spread across the landscape instead of being restricted to a regional container. From this perspective, the impact of local labor market conditions on individual labor market outcomes may be mitigated or reinforced by surrounding areas, which also have an impact on individual outcomes [
When analyzing the impact of such spatial externalities [
The concepts “spatial externalities” or “spillover effects” are of particular importance in the theoretical framework of the new economic geography [
Bearing in mind that labor markets comprise social relations, the picture of a regional labor market that makes up an individual’s opportunity structure accordingly falls short―social relations do not simply stop at the boundaries of a regional “container”. In contrast, thinking of individuals’ opportunity structures in terms of social relations leads to an understanding of individuals’ opportunity structures as a wider social system with rather unmarked boundaries. This argument especially holds if the areal units used for data analysis represent (administrative) artificial regions, such as municipalities, districts, or employment agency districts. This is usually the case in the literature: research on the significance of labor market contexts is only rarely based on empirically defined areal units [
There are two processes relevant for conceptualizing individuals’ opportunity structures as a spatial social system. The first process gives promise to individual spatial mobility and the second process concerns spatial pulling effects. The search behavior of youths is not necessarily a geographically static process [
From an action theoretical perspective, spatial mobility results from youths’ subjective assessments of their situation [
The probability of success, in turn, depends on a) the raw supply of training spots available and b) the supply of training spots in a given area relative to the respective supply in the home district. If, for example, the home district offers very few training positions compared to surrounding districts, the initial search will most likely be unsuccessful until the search radius is widened, and finding a training position is more likely if other regions offer better opportunities in terms of quantity and/or quality, compared to the local regional situation [
If only individual utility maximization processes were considered, as we have done thus far, we would only have to take training positions in districts within reasonable proximity to the place of residence into account. Youths would most likely terminate their search once commuting costs become unacceptable. But on the contextual level of local labor markets, we may additionally assume pulling effects, which result from processes of labor exchange in a long line of (adjacent) districts. For example, take a district with a very high supply of training spots. It will attract youths living in adjacent districts, who will leave training positions in their home district unoccupied. These, in turn, will attract youth living in the next districts and so on. Although training places are strongly concentrated in (urban) centers [
To sum up, we expect that the probability of finding a training spot will increase given an increasing raw or relative supply of positions. Because of individual spatial mobility and indirect pulling effects on the macro level (district), we not only expect training spots in the home district to have this effect, but training spots in all German districts. However, the effect should decrease with increasing spatial distance.
On a theoretical level, thinking about spatial interrelations between observations leads to an understanding of an individual’s opportunity structure as a spatial social system that has to be operationalized as such. At the same time, however, spatial interrelations pose statistical problems on a methodological level because spatial dependencies lead to processes of homogenization and, hence, to spatial autocorrelation of the dependent and/or independent variables. Neglecting them, then, may produce biased estimates of regression coefficients and/or standard errors [
When analyzing spatial effects on individual outcomes, researchers are generally faced with several kinds of spatial dependencies at the individual and/or contextual level. Such dependencies may arise, for example, due to common exposure or social exchange [
However, when mapping an individual’s spatial opportunity structure by considering the availability of non-local training positions as well, the spatial interrelation may also concern the indicators at the context level. Spatial interrelation at the context level generally produces homogenizations of the conditions of local labor markets; therefore, using such spatially correlated context data may result in inappropriate inferences about the effect of spatial opportunity structure on individuals’ labor market outcomes. In case of high local spatial autocorrelation, the contextual effect of non-local training positions may even go undetected. Following Tobler’s first law of geography, which states that “everything is related to everything else, but near things are more related than distant things”, this especially holds true for areas that are in close proximity to one another [
Thus, in order to investigate an individual’s zone of influence, effects of non- local training positions have to be adjusted for spatial autocorrelation. For that purpose, we have to think about the social process underlying the spatial autocorrelation of the crucial predictor variable, which in our case are comprised of local and non-local training positions. Though training spots are geographically related, the underlying process is not only guided by proximity and distance, but rather by social exchange at the labor market that depends, to a great extent, on infrastructure [
We use retrospectively collected life course data on the starting cohort 6―adults from Germany’s National Educational Panel Study [
In our analyses, we only utilize time-to-event data about youths’ transitions from school to training. The outcome variable of interest is individuals’ duration of finding a firm-based training position that we measure monthly. We limit ourselves to this particular transition since (in contrast to school-based training, another educational path in the German vocational training system) firm-based training is expected to strongly depend on the labor market situation. The data contains information about the district participants graduated in, but no reliable information on the place of work during apprenticeship. Therefore, we model the probability of a youth finding a training spot somewhere in Germany, conditional on the training market conditions in her home district as well as in all German districts.
Since some of the relevant regional data is only available from 1999 onwards, we are restricted to focus on groups graduating from school between 1999 and 2006. From the entire sample we are able to extract relevant transition data for about 410 individuals and, on the level of our analyses, 2799 person-time units. The large amount of missing cases mainly arises from the restricted observation period and further sample selection procedures: From the valid information about 14,832 school graduates from 1957 onwards, 1683 individuals finish school between 1999 and 2006, of which 803 individuals begin firm-based vocational training. Further missing cases result either from missing information about the place of residence, which is necessary for merging individual data with regional data, or from missing information on relevant control variables.
When investigating life course data, exact operationalization is of high importance, for individual life courses are not necessarily standardized. For example, individuals may attend more than one school during their lives or they may have temporal gaps between school episodes and complete their schooling later; they may begin an apprenticeship somewhere, abandon it, and start another one elsewhere. In our analyses, we treat the end of the first uninterrupted school career as the starting point of the search time needed to find a training position; uninterrupted school episodes are defined as those in which temporal gaps amount to no more than four months (or six months in case of previous primary school attendance). This way, we ensure that individuals are actually searching for a training position rather than continuing their school career. The search time ends when an individual engages in fully qualifying firm-based vocational training for at least three months. Since we are only interested in events that are directly driven by the spatial opportunity structure of labor markets, we excluded people who begin other forms of training, such as school-based vocational training or university education, as well as right-censored cases.
In order to map an individual’s spatial opportunity structure, we make use of a dataset consisting of several N × N matrices that represent the varied pairwise connectivity between administrative regional units at the district level (Landkreise and kreisfreieStädte, NUTS 3 regions) in Germany. Since Germany is currently divided into 402 of these areal units, all spatial connectivity matrices comprise 402 × 402 districts. In general, merging these matrices with individual data results in a multiple membership dataset, in which each individual or, more precisely, each person-time unit is nested within all of the 402 districts. The structure of the dataset is illustrated in
The zone of influence can be modeled by bringing distances between the spatial units into the equation. To this end, we use geographical data about the administrative areas from the Federal Agency for Cartography and Geodesy (GeoBasis-DE 2015), which enables us to calculate Euclidean distances between the geometric centers of the districts. For this purpose, we use the projected coordinate system Universal Transverse Mercator (UTM) as geographic coordinate systems generally tend to produce biased distance calculations. The calculated distances between the districts allow us to qualify the spatial relation of each district to all other districts, as illustrated in
In addition, we use data on commuting flows of apprentices between home and workplace from the Institute for Employment Research [
the pairwise connection between the districts by the proportion of commuters from districti to district j compared with all commuters from district i. In contrast to the spatial connectivity matrix based on Euclidean distances, this matrix corresponds to a directed spatial network, that is, for each district it represents the importance of all possible destination districts as a training location for non- local youths. We use this measure in order to adjust the effects of the availability of non-local training places for spatial autocorrelation at the context level that mainly arises due to commuting. Likewise, we use discrete measures of the commuting flows from home to the workplace, but define the thresholds according to analytical criteria, as the distribution of the measure is strongly positively skewed.
Beside the category that refers to the connection of one district with itself (where commuting equals zero), we distinguish between the categories “no commuting flows”, “commuting flows up to 0.05%”, “commuting flows from more than 0.05% to 0.1%”, “commuting flows from more than 0.1% to 0.2%”, “commuting flows from more than 0.2% to 0.5%”, “commuting flows from more than 0.5% to 1%”, and “commuting flows of more than 1%”.
Finally, we use a set of control variables at the individual and at the macro level as adjustment factors in our regression models. At the individual level, we control for individuals’ gender, ethnicity, and educational level as well as a time- varying variable that indicates whether vocational preparation was completed or not. At the macro level, we control for the school graduate cohort as a measure of the overall economic situation in Germany at the time of entering the labor market.
Moreover, we differentiate our analyses between structurally weak and strong areas: Several studies [
Structurally weak states are the East German states, Schleswig-Holstein and Lower Saxony in the Northwest, and Rhineland-Palatinate in the far West. All other West German states and the two city-states, Berlin and Hamburg, are considered to be structurally strong.2 Additionally, in our analyses we control for the state to capture possible variations of mobility levels due to unobserved variables.
The appropriate framework for investigating individual processes is event history (or survival) analysis. We conduct our analyses of youths’ transition from school into firm-based training with the aid of a discrete-time event history model [
The model we apply corresponds to a binary logistic regression model. The dependent variable is the transition probability from state 0 (completion of school) to state 1 (taking a firm-based training position). The transition probability is defined as the log-odds for the conditional probability of taking a firm- based training position at time ti. Since the transition probability is dependent
Percent/mean (SD) | |||
---|---|---|---|
Structurally weak regions | Structurally strong regions | Total sample | |
Search time (ref. 0 - 4 months) | 41.1 | 34.8 | 36.8 |
5 - 16 months | 39.6 | 38.5 | 38.8 |
17 - 28 months | 11.0 | 15.0 | 13.8 |
>28 months | 8.3 | 11.7 | 10.6 |
Female | 36.7 | 41.5 | 40.0 |
Native language not German | 7.6 | 26.4 | 20.4 |
Educational level (ref. basic secondary educationa) | 35.8 | 31.5 | 32.9 |
Secondary educationb | 44.9 | 44.6 | 44.7 |
Higher secondary educationc | 19.2 | 23.9 | 32.9 |
Vocational preparation completed | 14.4 | 8.9 | 10.7 |
Cohort (ref. 1999) | 17.1 | 11.6 | 13.3 |
2000 | 18.1 | 20.7 | 19.9 |
2001 | 19.0 | 14.3 | 15.8 |
2002 | 21.7 | 14.3 | 16.7 |
2003 | 8.4 | 17.4 | 14.6 |
2004 | 6.4 | 11.2 | 9.7 |
2005 | 6.0 | 6.8 | 6.5 |
2006 | 3.4 | 3.7 | 3.6 |
Raw supply of training places | 98.4 (5.4) | 97.8 (5.4) | 98.0 (5.4) |
Relative supply of training places | 0.98 (0.07) | 1.00 (0.08) | 0.99 (0.07) |
Distance (ref. home district + 75 km) | 3.9 | 6.2 | 5.5 |
>75 - 150 km | 9.0 | 13.2 | 11.9 |
>150 - 225 km | 13.4 | 17.8 | 16.4 |
>225 - 300 km | 16.3 | 18.0 | 17.4 |
>300 - 375 km | 18.5 | 15.6 | 16.5 |
>375 - 450 km | 16.8 | 12.8 | 14.1 |
>450 - 525 km | 11.2 | 10.0 | 10.3 |
>525 km | 10.8 | 6.6 | 7.9 |
Commuting flows (ref.: >1%, incl. home district) | 2.6 | 2.8 | 2.7 |
≤1%, >0.5% | 1.1 | 1.2 | 1.1 |
≤0.5%, >0.2% | 3.3 | 3.2 | 3.2 |
≤0.2%, >0.1% | 5.9 | 4.9 | 5.2 |
≤0.1%, >0.05% | 8.1 | 6.1 | 6.8 |
≤0.05%, >0% | 5.2 | 5.5 | 5.4 |
0% | 73.9 | 76.4 | 75.6 |
N (person-months units) | 890 | 1909 | 2799 |
on individual search time, we follow a piecewise-constant modeling strategy, where the transition probability is assumed to be constant only within particular time intervals [
In order to take the hierarchical structure of our data into account, we make use of a Huber-White sandwich estimator of variances in order to obtain cluster- robust standard errors. In contrast to hierarchical models [
In order to investigate the influence of non-local training positions on youths’ probability of finding a spot, we look at both the raw supply of local and non-local training spot offers and the ratio between local and non-local training positions. Both kinds of measures are introduced as interactions with spatial distance. In accordance with our hypotheses, we expect the interaction effects between the raw and the relative supply of training positions, irrespective of their distance to the home district, to increase the probability of finding a spot. However, to reveal the impact of the availability of non-local training positions, the regression coefficients have to be adjusted for spatial autocorrelation. To demonstrate the relevance of spatial autocorrelation, we compare two regression models, as shown in
As expected, the main effect for the raw supply of training positions shows that the probability of finding a spot increases with an increasing supply of training places in the first zone―the home district plus 75 kilometers. This applies to both structurally weak and strong regions and to both models a and b. However, the expected positive effects of the supply of training positions in districts that are too far away from home to be reached by commuting―in other words, the pulling effects on the district level―are not apparent in model 1. In structurally weak regions, we find unexpected negative interaction effects for both the raw and relative supply of training positions, meaning that a strong
Structurally weak regions | Structurally strong regions | |||
---|---|---|---|---|
Model 1a: | Model 1b: | Model 2a: | Model 2b: | |
Not controlling for commuting flows | Controlling for commuting flows | Not controlling for commuting flows | Controlling for commuting flows | |
β | β | β | β | |
Raw supply of training places | 0.363*** | 0.333*** | 0.065*** | 0.098*** |
Relative supply of training places | 0.405*** | 0.376*** | 0.021 | 0.124*** |
Raw supply× distance (ref.: home district + 75 km) | ||||
>75 - 150 km | ?0.047 | ?0.128** | ?0.000 | 0.058* |
>150 - 225 km | ?0.085* | ?0.187*** | 0.034 | 0.101*** |
>225 - 300 km | ?0.107** | ?0.224*** | 0.001 | 0.072** |
>300 - 375 km | ?0.163*** | ?0.281*** | 0.049** | 0.121*** |
>375 - 450 km | ?0.112** | ?0.229*** | 0.063*** | 0.136*** |
>450 - 525 km | ?0.111** | ?0.238*** | 0.083*** | 0.156*** |
>525 km | ?0.113** | ?0.249*** | 0.108*** | 0.179*** |
Relative supply × distance (ref.: home district + 75 km) | ||||
>75 - 150 km | 0.092 | 0.011 | ?0.026 | 0.067* |
>150 - 225 km | 0.017 | ?0.092 | 0.021 | 0.124*** |
>225 - 300 km | ?0.011 | ?0.141* | 0.030 | 0.136*** |
>300 - 375 km | ?0.094* | ?0.227*** | 0.071*** | 0.181*** |
>375 - 450 km | ?0.074 | ?0.206*** | 0.113*** | 0.222*** |
>450 - 525 km | ?0.110* | ?0.244*** | 0.115*** | 0.223*** |
>525 km | ?0.118* | ?0.259*** | 0.172*** | 0.278*** |
Notes: *p < 0.05, **p < 0.01, ***p < 0.001 (two-tailed tests), cluster-robust S.E., controls: main effect of distance, main effect of commuting (ref.: home district + strong commuting flows), interaction effects between commuting and the raw supply of training places as well as the relative supply of training places respectively, school-leaving cohort, state (Bundesland), individual search duration, sex, ethnic origin, school-leaving qualification, completion of vocational preparation.
supply in non-local districts diminishes the individual probability of finding a spot. In structurally strong areas, the interaction effects are positive, as expected, but contrary to our expectations they increase with distance, and are only statistically significant for districts that are more than 300 kilometers away from home.
In models 1b and 2b, spatial autocorrelation is taken into account by controlling for commuting flows between home and workplace. The results show that the estimates in models 1a and 2a are considerably biased due to spatial autocorrelation, which arises due to commuting. In models 1b and 2b, the raw and relative supply of training positions in all zones has statistically significant effects, with the exception of the raw supply in districts located in structurally weak regions that are not more than 225 kilometers from home. Also, the coefficients rise considerably, compared to models 1a and 2a. Two results are unexpected, though: For structurally weak regions, the interaction effects are still negative in model 2b, and for both regions the effects roughly increase with distance, a result that does not lend itself to a substantial interpretation. We will discuss these problems in the last section in detail.
All in all, our results show that both the raw and relative supply of training positions throughout Germany have an effect on the probability of finding a spot. To be able to verify these effects, it is necessary to control for spatial autocorrelation; neglecting to do so produces a significant underestimation of the effects of the supply of training spots in all non-local districts, and to false conclusions, specifically for areas relatively close to home.
The relevance of our methodical results can best be shown by means of probabilities instead of logit coefficients.
secondary education, no vocational preparation; states: Hamburg (structurally strong areas) and Schleswig-Holstein (structurally weak areas). We distinguish two scenarios: the probability of finding a training spot when a relevant district offers a high/low supply of training positions. A high supply is represented by a raw supply of 120, i.e., a ratio of 1.2 between successfully concluded training contracts (plus vacant positions) and unsuccessful applicants (plus vacant positions), and a relative supply of 1.2, i.e., the ratio between the supply of training places in the home district i and a given district j. For districts with a low supply, the values are 80 and 0.8, respectively.
A comparison between figures a and b shows that neglecting spatial autocorrelation leads to biased estimates. In structurally weak regions, the predicted probabilities of finding a training position are underestimated in case of zero autocorrelation between a favorable home district and the respective non-local district. If autocorrelation is at its maximum, they are overestimated. For example, in
For structurally strong regions, the directions of over- and underestimation are exactly the reverse. For favorable districts, we find an overestimation in case of zero autocorrelation and an underestimation when autocorrelation is at its maximum (see
Because we measured spatial autocorrelation by means of commuting flows in our analyses, our results can be interpreted with respect to the integration of districts into the (trainee) labor market as well. The findings presented here show that not controlling for spatial autocorrelation leads to an underestimation of spatial effects for a) isolated districts in structurally weak regions and b) well- integrated districts in structurally strong regions. In other words, if extreme conditions are obtained in a district, i.e., a combination of regional structural weakness and isolation or regional structural strength and pronounced connection to other districts, contextual effects are underestimated if spatial autocorrelation is not controlled for. For “mixed” districts―those located in structurally weak but well-connected areas, and isolated districts located in structurally strong areas―contextual effects are overestimated. All this refers to favorable districts that offer a high raw and relative supply of training positions. For unfavorable districts, we find under- and overestimation to be mirror-inverted― i.e., an underestimation in “mixed” districts and an overestimation in “extreme” districts―but the bias is small enough to be negligible.
Our results show that the differing patterns of probabilities in structurally weak and strong regions are remarkable. In structurally weak regions―the five eastern states, Lower Saxony, and Schleswig-Holstein―finding a training position depends far more on local conditions than it does in structurally strong regions. We find the biggest difference between favorable and unfavorable districts for the home district (plus a 75-kilometer radius); with distance this gap closes (see
With regard to our hypotheses, we were able to verify the assumed positive influence of the raw and relative supply of training positions in the home district and in all other German districts, but only for structurally strong regions. Contrary to our second assumption, however, those benefits gained from non-local districts do not decrease with increasing distance. Our findings for structurally weak regions contradicted the expectations in several aspects. We found effects of non-local districts on the probability of finding a training position; however, not all non-local districts have this effect. The relative supply of training places only has an effect for districts that are more than 225 kilometers away from home (relatedly, in structurally weak regions, the relative supply has an overall weaker effect than the raw supply, while in structurally strong regions the opposite is true). Additionally, the probability of finding a training spot decreases with an increasing supply in non-local districts. We will discuss all open questions in detail in the following section.
In this paper we have examined the significance of the spatial opportunity structure for individual labor market outcomes by utilizing the example of youths’ transitions from school to firm-based vocational training. When investigating opportunity structures, two methodological issues have to be addressed: the extent of such structures as well as the presence of spatial autocorrelation. Regarding the extent of opportunity structures, we must ask whether it is sufficient to only consider the local context. In our case, we have two reasons to assume that non-local conditions additionally affect the outcome. The first is that generally youths searching for a training position are spatially mobile: they are likely to accept offers that require commuting or even moving house. Second, local conditions themselves are a function of individual actions in adjacent areas, which in turn are affected by other areas, and so on. Such pulling effects on the contextual level point to the necessity of acknowledging that labor market opportunity structures are not only point-located. An individual opportunity structure does not end at the boundaries of an isolated regional container but, rather, extends across the landscape. From this perspective, opportunity structures correspond to a wider social system with unmarked boundaries. While our first argument, spatial mobility, is topic-specific and may not be applicable to other research, we believe that our second point is universally valid.
Our findings show that in the case of youths’ transitions from school to firm-based vocational training, non-local labor market conditions matter. The probability of finding a training spot is affected not only by the supply of positions offered in the home district and its vicinity, but additionally by those presented in districts up to more than 500 kilometers from home. These effects, though, differ markedly depending on the structural strength of the wider region in which the home place is situated. In structurally strong regions―in our case, regions with a positive net trainee balance―the probability of finding an apprenticeship increases with an increasing supply of training spots in non-local districts, as expected. In structurally weak regions, we assumed that these effects would be weaker, but instead an increasing supply of positions in non-local districts is associated with a decreasing probability. The reason for this unexpected result has to be determined by future research. If we consider Windzio’s findings [
Turning to our second methodological issue, our findings demonstrate that ignoring spatial autocorrelation leads to severely biased estimates. In the sample we analyzed, spatial autocorrelation does not occur at the individual level. We have no clustering of individual observations within districts or in adjacent or nearby districts, as is often the case with countrywide surveys. But at the context level of administrative districts, spatial interrelations lead to spatial autocorrelation, i.e., to a homogenization of the value of the contextual predictor variables of strongly tied areal units. In order to map the actual extent of an individual’s spatial opportunity structure, our regression results had to be adjusted for local spatial autocorrelation between the home district and all other districts, respectively. For this purpose, we used data on commuting flows between home and workplace and introduced into our models interaction terms between these commuting flows and our main predictor variables, i.e., the raw and relative supply of training spots.
Our comparison showed that neglecting local spatial autocorrelation leads to considerably biased estimates especially for districts with a distance of up to 300 kilometers to the home district. For youth living in unfavorable districts with a small raw and relative supply of training position offers, the probability of finding a spot is already so small that the bias is negligible. For favorable districts, however, not controlling for spatial autocorrelation is associated with over- or underestimation, depending on the wider region’s structural strength and the level of connectedness between the home district and other districts. If either regional structural weakness and isolation or regional structural strength and pronounced connection to other districts are combined, contextual effects are underestimated; for “mixed” districts, i.e., well-connected districts located in structurally weak areas, and isolated districts located in structurally strong areas, contextual effects are overestimated.
However, even though we controlled for spatial autocorrelation, our results give rise to the assumption that our estimations are still biased, because contrary to our second hypothesis, contextual effects for structurally strong areas do not decline with spatial distance. Three possible explanations are conceivable: First, in structurally strong regions indirect pulling effects on the macro level do not decrease with distance; second, they are stronger than the individual level effects of spatial mobility (which are still assumed to decrease with distance); and third, our measure for local spatial autocorrelation―apprentices’ commuting flows between the home-district and all other districts respectively―does not entirely capture all spatial interdependencies in the data. There may be indirect pulling effects that result from unobserved processes of labor exchange between all districts in Germany. Such further reaching complex interrelations of districts have to be subject for future research about spatial effects on individual outcomes. Furthermore, the effects of remote districts may especially concern particular group(s) of people, like youths searching for training spots that are only available in a handful of locations in Germany. This may happen if industries or sectors are heavily concentrated, as is the case of biotechnology in southern Germany, North Rhine-Westphalia, and Berlin, or car manufacturing in southern and northern Germany. Lastly, for some occupational fields, the German training system offers only school-based training, so the next question may be whether these transitions are also structured by local and non-local conditions as well.
Our results show that for future analyses of spatial effects certain assumptions may be premature. First, assuming that only close proximity affects individual outcomes may disregard relevant contextual influences of the wider surroundings of the home, workplace, and so on, leading to biased estimates, because the characteristics of the wider surroundings may constitute essential control variables. It is also possible that contextual effects do not decrease with distance. For spatial models that require an a priori definition of the weights for spatial units, for example, the Spatial Durbin Model, it may therefore be erroneous to make a decision based on this assumption.
Wicht, A. and Nonnenmacher, A. (2017) Modeling Spatial Opportunity Structures and Youths’ Transitions from School to Training. Open Journal of Statistics, 7, 1013-1038. https://doi.org/10.4236/ojs.2017.76071
Model 1a: Not controlling for commuting flows | Model 1b: Controlling for commuting flows | |||
---|---|---|---|---|
β | s.e. | β | s.e. | |
Search time (ref. 0 - 4 months) | ||||
5 - 16 months | −1.332*** | 0.001 | −1.327*** | 0.001 |
17 - 28 months | −2.741*** | 0.001 | −2.718*** | 0.002 |
>28 months | −2.917*** | 0.002 | −2.881*** | 0.004 |
Female | 0.133*** | 0.001 | 0.126*** | 0.001 |
Native language not German | 0.243*** | 0.001 | 0.256*** | 0.002 |
Educational level (ref. higher secondary educationa) | ||||
Secondary educationb | −0.142*** | 0.001 | −0.151*** | 0.002 |
Basic secondary educationc | −1.214*** | 0.001 | −1.240*** | 0.003 |
Vocational preparation | 2.254*** | 0.001 | 2.257** | 0.001 |
Cohort (ref. 1999) | ||||
2000 | 0.149*** | 0.001 | 0.141*** | 0.002 |
2001 | −0.175*** | 0.001 | −0.175*** | 0.002 |
2002 | −0.083*** | 0.002 | −0.089*** | 0.003 |
2003 | 0.383*** | 0.003 | 0.391*** | 0.003 |
2004 | −0.071*** | 0.004 | −0.049*** | 0.004 |
2005 | −0.261*** | 0.003 | −0.244*** | 0.004 |
2006 | −0.343*** | 0.003 | −0.335*** | 0.005 |
State (ref. Schleswig-Holstein) | ||||
Lower Saxony | 0.754*** | 0.003 | 0.751*** | 0.003 |
Rhineland-Palatinate | 1.418*** | 0.005 | 1.436*** | 0.005 |
Brandenburg | 1.500*** | 0.006 | 1.543*** | 0.008 |
Mecklenburg-Western Pomerania | 2.431*** | 0.006 | 2.492*** | 0.008 |
Saxony | 0.962*** | 0.006 | 0.973*** | 0.007 |
Saxony-Anhalt | 1.086*** | 0.006 | 1.108*** | 0.006 |
Thuringia | 1.027*** | 0.006 | 1.059*** | 0.006 |
Raw supply of training places | 0.363*** | 0.032 | 0.333*** | 0.038 |
Relative supply of training places | 0.405*** | 0.045 | 0.376*** | 0.059 |
Distance (ref. home district + 75 km) | ||||
>75 - 150 km | 0.006 | 0.030 | 0.021 | 0.036 |
>150 - 225 km | 0.008 | 0.030 | 0.033 | 0.037 |
---|---|---|---|---|
>225 - 300 km | 0.008 | 0.027 | 0.038 | 0.035 |
>300 - 375 km | −0.031 | 0.025 | −0.001 | 0.034 |
>375 - 450 km | −0.019 | 0.027 | 0.004 | 0.035 |
>450 - 525 km | −0.013 | 0.027 | 0.009 | 0.036 |
>525 km | −0.075** | 0.028 | −0.055 | 0.036 |
Raw supply × distance (ref.: home district + 75 km) | ||||
>75 - 150 km | −0.047 | 0.038 | −0.128** | 0.047 |
>150 - 225 km | −0.085* | 0.039 | −0.187*** | 0.048 |
>225 - 300 km | −0.107** | 0.037 | −0.224*** | 0.049 |
>300 - 375 km | −0.163*** | 0.039 | −0.281*** | 0.050 |
>375 - 450 km | −0.112** | 0.039 | −0.229*** | 0.050 |
>450 - 525 km | −0.111** | 0.037 | −0.238*** | 0.048 |
>525 km | −0.113** | 0.038 | −0.249*** | 0.049 |
Relative supply × distance (ref.: home district + 75 km) | ||||
>75 - 150 km | 0.092 | 0.049 | 0.011 | 0.057 |
>150 - 225 km | 0.017 | 0.048 | −0.092 | 0.058 |
>225 - 300 km | −0.011 | 0.048 | −0.141* | 0.058 |
>300 - 375 km | −0.094* | 0.048 | −0.227*** | 0.058 |
>375 - 450 km | −0.074 | 0.048 | −0.206*** | 0.057 |
>450 - 525 km | −0.110* | 0.049 | −0.244*** | 0.057 |
>525 km | −0.118* | 0.047 | −0.259*** | 0.057 |
Commuting flows (ref.: >1%, incl. home district) | ||||
≤1%, >0.5% | − | − | −0.006 | 0.062 |
≤0.5%, >0.2% | − | − | 0.077 | 0.045 |
≤0.2%, >0.1% | − | − | −0.008 | 0.043 |
≤0.1%, 0.05% | − | − | −0.165*** | 0.044 |
≤0.05%, >0% | − | − | 0.102* | 0.044 |
0% | − | − | −0.022 | 0.040 |
Raw supply × commuting (ref.: >1%, incl. home district) | ||||
≤1%, >0.5% | − | − | 0.120 | 0.080 |
≤0.5%, >0.2% | − | − | 0.128* | 0.058 |
≤0.2%, >0.1% | − | − | 0.071 | 0.058 |
≤0.1%, 0.05% | − | − | 0.002 | 0.055 |
≤0.05%, >0% | − | − | −0.080 | 0.056 |
0% | − | − | 0.216*** | 0.051 |
Relative supply × commuting (ref.: >1%, incl. home district) | ||||
---|---|---|---|---|
≤1%, >0.5% | − | − | 0.110 | 0.095 |
≤0.5%, >0.2% | − | − | 0.117 | 0.064 |
≤0.2%, >0.1% | − | − | 0.114 | 0.067 |
≤0.1%, 0.05% | − | − | −0.026 | 0.063 |
≤0.05%, >0% | − | − | 0.032 | 0.064 |
0% | − | − | 0.232*** | 0.060 |
Constant term | −1.687*** | 0.023 | 1.696*** | 0.029 |
Model 2a: Not controlling for commuting flows | Model 2b: Controlling for commuting flows | |||
---|---|---|---|---|
β | s.e. | β | s.e. | |
Search time (ref. 0 - 4 months) | ||||
5 - 16 months | −1.316*** | 0.000 | −1.313*** | 0.001 |
17 - 28 months | −1.599*** | 0.001 | −1.596*** | 0.001 |
>28 months | −2.234*** | 0.002 | −2.229*** | 0.002 |
Female | 0.141*** | 0.000 | 0.139*** | 0.001 |
Native language not German | −0.643*** | 0.001 | −0.638*** | 0.001 |
Educational level (ref. higher secondary educationa) | ||||
Secondary educationb | 0.404*** | 0.001 | 0.403*** | 0.001 |
Basic secondary educationc | −0.486*** | 0.001 | −0.493*** | 0.001 |
Vocational preparation | 1.025*** | 0.001 | 1.029*** | 0.002 |
Cohort (ref. 1999) | ||||
2000 | −0.705*** | 0.001 | −0.706*** | 0.002 |
2001 | −0.548*** | 0.002 | −0.545*** | 0.002 |
2002 | −0.305*** | 0.001 | −0.301*** | 0.002 |
2003 | −0.639*** | 0.002 | −0.634*** | 0.003 |
2004 | −0.545*** | 0.003 | −0.542*** | 0.003 |
2005 | −0.701*** | 0.003 | −0.694*** | 0.003 |
2006 | −0.150*** | 0.003 | −0.144*** | 0.003 |
State (ref. Hamburg) | ||||
North Rhine-Westfalia | 1.066*** | 0.003 | 1.070*** | 0.004 |
Hesse | 0.785*** | 0.004 | 0.780*** | 0.005 |
Baden-Wuerttemberg | 0.997*** | 0.004 | 1.000*** | 0.005 |
Bavaria | 0.812*** | 0.004 | 0.820*** | 0.005 |
Saarland | 2.073*** | 0.004 | 2.070*** | 0.005 |
---|---|---|---|---|
Berlin | 0.727*** | 0.006 | 0.779*** | 0.013 |
Raw supply of training places | 0.065*** | 0.013 | 0.098*** | 0.019 |
Relative supply of training places | 0.021 | 0.017 | 0.124*** | 0.030 |
Distance (ref. home district + 75 km) | ||||
>75 - 150 km | 0.035 | 0.020 | 0.113*** | 0.021 |
>150 - 225 km | 0.042* | 0.017 | 0.119*** | 0.022 |
>225 - 300 km | 0.027 | 0.018 | 0.104*** | 0.022 |
>300 - 375 km | 0.065*** | 0.018 | 0.142*** | 0.022 |
>375 - 450 km | 0.065*** | 0.017 | 0.142*** | 0.022 |
>450 - 525 km | 0.051** | 0.016 | 0.129** | 0.021 |
>525 km | 0.109*** | 0.017 | 0.189*** | 0.022 |
Raw supply × distance (ref.: home district + 75 km) | ||||
>75 - 150 km | −0.000 | 0.019 | 0.058* | 0.024 |
>150 - 225 km | 0.034 | 0.018 | 0.101*** | 0.025 |
>225 - 300 km | 0.001 | 0.019 | 0.072** | 0.025 |
>300 - 375 km | 0.049** | 0.017 | 0.121*** | 0.024 |
>375 - 450 km | 0.063*** | 0.017 | 0.136*** | 0.025 |
>450 - 525 km | 0.083*** | 0.016 | 0.156*** | 0.023 |
>525 km | 0.108*** | 0.017 | 0.179*** | 0.024 |
Relative supply × distance (ref.: home district + 75 km) | ||||
>75 - 150 km | −0.026 | 0.024 | 0.067* | 0.028 |
>150 - 225 km | 0.021 | 0.021 | 0.124*** | 0.027 |
>225 - 300 km | 0.030 | 0.022 | 0.136*** | 0.027 |
>300 - 375 km | 0.071*** | 0.020 | 0.181*** | 0.026 |
>375 - 450 km | 0.113*** | 0.020 | 0.222*** | 0.026 |
>450 - 525 km | 0.115*** | 0.021 | 0.223*** | 0.026 |
>525 km | 0.172*** | 0.018 | 0.278*** | 0.025 |
Commuting flows (ref.: >1%, incl. home district) | ||||
≤1%, >0.5% | − | − | −0.113** | 0.038 |
≤0.5%, >0.2% | − | − | −0.095** | 0.033 |
≤0.2%, >0.1% | − | − | −0.142*** | 0.030 |
≤0.1%, 0.05% | − | − | −0.176*** | 0.031 |
≤0.05%, >0% | − | − | −0.351*** | 0.031 |
0% | − | − | −0.166*** | 0.029 |
Raw supply × commuting (ref.: >1%, incl. home district) | ||||
≤1%, >0.5% | − | − | 0.003 | 0.039 |
≤0.5%, >0.2% | − | − | 0.033 | 0.036 |
---|---|---|---|---|
≤0.2%, >0.1% | − | − | −0.027 | 0.033 |
≤0.1%, 0.05% | − | − | −0.103** | 0.035 |
≤0.05%, >0% | − | − | −0.272*** | 0.036 |
0% | − | − | −0.097*** | 0.030 |
Relative supply × commuting (ref.: >1%, incl. home district) | ||||
≤1%, >0.5% | − | − | −0.042 | 0.054 |
≤0.5%, >0.2% | − | − | −0.052 | 0.042 |
≤0.2%, >0.1% | − | − | −0.097** | 0.037 |
≤0.1%, 0.05% | − | − | −0.178*** | 0.037 |
≤0.05%, >0% | − | − | −0.329*** | 0.039 |
0% | − | − | −0.209*** | 0.036 |
Constant term | −1.674*** | 0.015 | −1.588*** | 0.023 |
Notes: *p < 0.05, **p < 0.01, ***p < 0.001 (two-tailed tests), cluster-robust S.E. The values of the raw and relative supply of training places are standardized; the S.E. of individual level effects are not interpretable due to the data structure. aAbitur/Fachabitur, bMittlere Reife/Realschulabschluss, cHauptschulabschluss.
Notes: *p < 0.05, **p < 0.01, ***p < 0.001 (two-tailed tests), cluster-robust S.E. The values of the raw and relative supply of training places are standardized; the S.E. of individual level effects are not interpretable due to the data structure. aAbitur/Fachabitur, bMittlere Reife/Realschulabschluss, cHauptschulabschluss