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/lp/springer-journals/spatial-matching-on-the-urban-labor-market-estimates-with-unique-micro-JM0ioph8vi
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- Springer Journals
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- Copyright © The Author(s) 2021
- ISSN
- 1614-3485
- eISSN
- 2510-5027
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- 10.1186/s12651-021-00293-1
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Abstract
In the paper, we investigate spatial relationship on the labor market of Poznań agglomeration (Poland) with unique data on job vacancies. We have developed spatial panel models to assess the search and matching process with a particular focus on spatial spillovers. In general, spatial models may provide different findings than regular panel mod- els regarding returns to scale in matching technology. Moreover, we have identified global spillover effects as well as other factors that impact the job-worker matching. We underline the role of data on job vacancies: the data retrieved from commercial job portals produced much more reliable estimates than underestimated registered data. Keywords: Spatial matching function, Spatial correlation, Urban labor market JEL classification: J23, J64, R12, E24 administrative unit to divide the territory of the Euro- 1 Introduction pean Union. It includes municipalities, agglomerations or Labor markets are spatial in their nature. In metropoli- communes (Eurostat). tan areas, people commute to achieve a better-paid or The Poznań agglomeration is one of the largest metro - more satisfactory job. Large cities are surrounded by politan areas in Poland and lies in the east–west line in minor counties the function of which is often to provide central west Poland. It is also a workhorse of a regional shelter and basic services to people who work in the city economy with the dominant industries of construc- and spend there most of their daytime. However, these tion, services, trade, and logistics. The Poznań agglom - surrounding counties are not homogenous, and may eration is also a highly international place with the strongly differ in their socio-economic development Amazon distribution warehouse, Volkswagen Factory, and functions. They formed more or less self-sufficient Carlsberg, Bertelsmann, among many others. Poznań enclaves that are somehow dependent on its large metro- has a record-breaking low-level of the unemployment politan neighbor. rate that dropped to 1.1% in December 2019. As a result, The aim of this paper is to investigate spatial relation - one of the major problems of local employers was worker ships on the urban labor market with two concepts: spa- shortages (Manpower Group 2020). The distance from tial panel matching function models and in-depth spatial the central city to the boundaries of the agglomeration correlation analysis. In the research we employed unique does not exceed 25 km. The metropolitan area is con - data on job vacancies derived directly from the most nected with the surrounding counties through an exten- substantial Polish internet job portals. We focus on the sive railway and bus network. This situation is beneficial Poznań agglomeration (Poland)—one of the largest met- to commuters which can travel relatively easy to their ropolitan areas in Poland that consists of 18 counties workplaces (Bul 2014). It is also worth noting that despite (LAU level 2). LAU2 (formerly NUTS5) is the smallest the undoubtful economic domination of the core unit, some small but strong local economic centers can also be *Correspondence: woz@amu.edu.pl pointed out. This is because many large enterprises are Faculty of Human Geography and Planning, Adam Mickiewicz University, located outside the metropolitan area (e.g. in Tarnowo Poznan, Poland © The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/. 11 Page 2 of 17 M. Wozniak Fig. 1 Poznań agglomeration (the city of Poznań and 17 neighboring counties) (Source: own elaborations on a basis of OpenStreetMap) Podgórne, Suchy Las, Kostrzyn, Swarzędz, Czerwonak, case of a Cobb–Douglas matching function with constant Komorniki). Figure 1 presents the geographical loca- returns to scale. The authors underline the universality of tion of Poznań and the surrounding counties (Poznań the approach and briefly discuss the applications of the agglomeration). mechanism. The general theoretical foundations of equilibrium Some of the more specific works on labor market models of spatial labor market matching were laid by matching center on Germany and consider various lev- Rouwedall (1998) who exceeded the standard sequen- els of spatial aggregation. Among the most influen - tial job search model (Mortensen 1986) by commuting tial research is the paper by Kosfeld (2007). The author behavior patterns between residential and employment focused on German regions and proved that match- locations. In the model, an urbanized region with several ing function coefficients estimations are not stable over employment centers was developed. The author proved space. In that case, the larger coefficient of a spatial lag in that spatial relationships affect the behavior of job seek - a given region is connected with higher mobility. Among ers in terms of excess commuting. later studies, the paper by Lottmann (2012) needs to Among the most recent papers some general but wide be mentioned. The author applies the spatial matching insight into spatial labor market matching was done by function to the German labor market, makes use of data Brancaccio et al. (2019) or Wong (2015) in a more mod- from 176 labor offices, and provides evidence for spatial est version. The authors provide some general guidelines dependencies that affect the matching process on Ger - to estimating matching functions in several spatial con- man labor markets. The results suggest significant spatial texts excluding the labor market (e.g. taxis, bike-sharing spillovers. This means that regional policy activities have schemes or shipping). They focus on theoretical assump - consequences on a wider scale. Other comprehensive tions, parametrization and estimation procedures in the study of the German labor markets was done by Haller Spatial matching on the urban labor market: estimates with unique micro data Page 3 of 17 11 and Heuermann (2016). They estimate a regional match - worth mentioning that numerous studies investigate the ing function on NUTS3 geographical units and prove problem of spatial correlation and the matching process positive and significant effects of vacancies on matching. on the labor market. However, the first papers focused Other similar works that investigate the spatial process mainly on NUTS2 and NUTS4 areas within the EU coun- on the labor market are those by Fahr and Sunde (2006) tries. As the repercussion of this research, the general for West Germany or Hujer et al. (2009) for the estima- relevance of spatial interaction was confirmed for several tion of the effects of labor market programs. countries, e.g. Spain (López-Tamayo et al. 2000), Finland Among other countries of focus, one of the most inter- (Ahtonen 2005), UK, Japan (Kano and Ohta 2005) or esting research is that of Manning and Petrolongo (2017). USA (Brueckner and Zenou 2003 among many others). They provide a framework for job search behavior across The contribution of the paper is therefore twofold. the markets with a very large number of segments. In Firstly, we provide a supplementary insight into the fact, the authors used census data on unemployment and research on urban labor markets at the low level of spa- vacancies to estimate the matching function across over tial aggregation (LAU2). Such studies are ultimately rare 8000 wards of UK and Wales. They found that the cost (excluding the paper by Manning and Petrolongo (2017), connected with the distance of vacancy was relatively we did not find any contributions). Secondly, we used a high. They also observed that workers were discouraged unique microdata set extracted with the developed Web from applying for a job if they expected strong competi- Application Programming Interface (API) script from tion. Moreover, local policies stimulate the outflow from popular internet job portals and Public Employment unemployment but, due to overlapping effects these pro - Service statistics (PES). The approach is in contrast to grams seem ineffective. the majority of studies that utilize only PES that is highly It is worth mentioning some papers that focus on cen- underestimated in terms of vacancies (e.g. Feng and Hu tral and eastern Europe and investigate spatial matching 2013, Gałecka-Burdziak 2017). Therefore, our data pro - on labor markets. The first is Burda and Profit (1996) vide a reliable insight into the supply and demand of the who estimate the matching function with a spatial com- local labor market in each of its spatial units and consti- ponent. Their major finding is that the matching process tute the basis for the analysis. As a result, we extend the in a given spatial unit is affected by neighborhoods. The knowledge in these fields by adding the in-depth analysis closer the neighborhood the more significant the impact. of the urban labor market. Among later papers, Dmitrijeva (2008) estimates three specifications of the matching function: a stock-stock 2 Public data bias matching function, a stock-flow matching function and The analysis of supply and demand on the labor mar - a spatially augmented stock-flow matching function. The ket is one of the main research fields in labor econom - author uses a data on Latvian, Slovenian and Estonian ics. Although the recent theories of the labor market regions to study the search and match process on labor accept the heterogeneity of jobs and workers, they also markets. Spatial spillovers exist and are statistically sig- pay attention to very different details of job/employee nificant in the case of Latvia and Slovenia (estimations for matching processes. Search theory of labor markets and Estonia were not possible due to the structure of available a derivative matching function concept underline a com- data. plex and time-consuming seeking procedure between As for Poland, the only paper is Antczak et al. (2018). employers and unemployed persons. (e.g. Rogerson et al. The study provides the comprehensive analysis of labor 2005). The crucial from the point of the matching func - markets at the LAU-1 (NUTS4) level. The authors devel - tion estimation is the quality of data. In all reported stud- oped models of spatial econometrics based on three dif- ies data are obtained from public employment services ferent specifications of a matching function to investigate databases. However, public statistics methodology often how spatial interactions affect the process of matching. assume that companies report the number of job vacan- They found the evidence of heterogeneity as well as clus - cies voluntarily. As a result, the most frequent bias in tering and polarization processes. The authors argue that registered data is connected with its underestimation the role of spatial dependencies in creating an outflow to (e.g. Paull 2002, Feng and Hu 2013, Gałecka-Burdziak employment is significant and underline the role of pol - icy measures at regional level. A type of network-based interface that uses Web architecture and protocols To our best knowledge, the paper presented is the first (in particular the HTTP protocol) to directly communicate between applica- that deals with the spatial matching function estimation tions located on separate devices on the network. In that case we use API to using internet data on vacancies. In addition, we did not download data from internet job portals databases to one independent server. find studies on spatial correlation at the low level of spa - In Poland but also in the majority of European countries there is no obli- tial aggregation (LAU2) within the EU countries. It is gation to report job vacancies to public employment services. 11 Page 4 of 17 M. Wozniak 2016—for the Polish case). Additionally, for such reasons share) according to the Gemius/PBI survey (2019). as saving time, money or just too much effort, data are Additionally, we also received support from one of the usually reported with a frequency of a month, a quarter smaller players—http:// www. jobs. pl (no data on the or even a year (Scott and Varian 2014). Other common market share). As we want to compare commercial data problems result from a delay in obtaining the data. We with Public Employment Service statistics, we also got get job vacancies statistics every month but in fact, we do API access to the local database of the PES in Poznań. not know what is happening between these time points. We started developing the API interface and tests in The situation in Poland is unfavorable as Public Employ - the late 2017, however it reached its full functional- ment Service presents only stock data at the end of each ity in 2018. In Fig. 2 we present the comparison of the month. Some of these job offers were reported a long inflow of vacancies since the beginning of the API ser - time ago but because of high turnover or other issues vice operation. they are available in registry for months. Such statistics As an example, we plotted registered vacancies may be perceived as obsolete and not well suited to the (PES) against those downloaded directly from the reality of a highly dynamic labor market. The last but not databases of job portals. It is easy to notice that the least is a bias associated with a specific type of job vacan - difference is enormous and the number of job offers cies that are registered in labor offices. The jobs are often is on average 20 times larger for commercial job por- addressed to low-skilled workers and the wage offer is tals. In general, massive fluctuations of vacancies usually equal or slightly higher than the minimum wage are observed with peaks during spring/summer and in Poland (Roszkowska et al. 2017). Sztandar-Sztanderska drops in autumn/winter. A decrease in the number (2017) on the basis of qualitative research claims that of vacancies is particularly observed in two periods PES in Poland is marked with institutional and organi- of the year: the beginning of May (short spring holi- zational instability, limited human resources, insufficient days in Poland) and Christmas/New Year time. Peaks spending on labor market programs. This state of affairs are mainly observed during spring (March) and early discourages employers from contacting labor offices and summer (June). When we look into extracted trends register the vacancies through the complicated, time- from public and commercial data, one can observe consuming procedure. Because of that, the number of some similar patterns in the inflow of vacancies, i.e., registered unemployed persons that find the job within a the rise and fall in certain periods of the years. How- given month often exceeds the number of vacancies reg- ever, in general, drops are more severe and peaks are istered during this time (Tyrowicz 2014; Nagel 2016). not so dynamic in public data. As a result, access to reliable data on the inflow of vacancies was the major problem for us as several sources confirmed the poor quality of registered data 2.1 Microdata—a closer look on vacancies in Poland. In fact, the only plausible quan- The API interface was fully operating in the late 2018, titative data could be accessed through internet job however we managed to extract data starting from the portals and there was no common database that could beginning of the year. Then, we disaggregated the data be accessed. The solution is API interface that could by counties of origin by the field named “location” that extract and aggregate the data on job vacancies from indicates the geolocation of each job offer. As a result, the largest job portals in Poland. The other argument vacancies were sorted according to the data source that supports the approach is that the role of the Inter- (public vs commercial) and its geographical loca- net in the job-seeking procedure is incontestable all tion. We downloaded data from 01 January 2018 to 31 over the world (Suvankulov et al. 2012; Smith and Page December 2019 on a daily basis. Every 24 h the API 2015, Eurostat, 2018). Nowadays, the internet traffic is interface connected to the three selected web services still rising and there is strong evidence that the larg- and downloaded the data on job vacancies to the SQL est flows of job vacancies can be accessed through the database. In addition, also PES data were downloaded network. Such job offers appear on the web portals that every day, however, the daily dynamics of PES data on aim at pairing job seekers with employers. the inflow of vacancies at county level was very low. In Three of the largest Polish internet job offering por - fact, some days with the NULL inflow appeared. The tals agreed to share their databases with us and pro- monthly inflow rate of new vacancies is presented in duced unique Application Programing Interfaces Fig. 3. (API) for our purposes. We started collaboration with In turn, the data on unemployment were extracted the largest Polish job offering portal—http:// www. olx. from the Public Employment Service (local labor pl (61% of the total market share) as well as the third office). The unemployment rate is published by PES largest http:// www. infop raca. pl (5% of the total market monthly for the agglomeration in total. However, we Spatial matching on the urban labor market: estimates with unique micro data Page 5 of 17 11 Fig. 2 Total daily inflow of vacant jobs in the Poznań agglomeration between 1 October 2017 and 31 December 2019 (a) and weekly trend (b)*.*commercial job portals are compared with Pubic Employment Service data. The trend for PES data on (B) is shown on the right axis (Source: own elaboration based on the data collected with the API interface from commercial job portals and public employment service. Monthly trends were extracted with classical seasonal decomposition by moving averages (Kendall and Stuart 1983); yearly frequency of time series was set to 12) can easily estimate monthly unemployment rate data the registered data on unemployment that are reported for each of 18 counties having the number of the unem- monthly. Luckily, in Poland unemployment data are ployed for each month and the working-age popula- much more reliable, because every person that loses a job tion for counties derived from Census data. As one can has to register in the employment office to get free health easily observe (Fig. 4), the unemployment rate is diver- insurance. Therefore, in practice a vast majority of unem - sified although ultimately low (even below 1% in two ployed persons register in the labor office to get access to counties in December 2019). There are some areas with medical services. a slightly higher unemployment rate (southwestern part Unemployment rate and job vacancies rate dropped of the agglomeration) and slightly lower (central and during 2018–2019. On average, in January 2018 one can northeastern counties). observe higher rates than in December 2019. The last For further analysis, we aggregated (summed) the daily month of the 2019 had a record-low unemployment rate vacancies inflow data to monthly frequency to match (1.1%) together with 1% vacancies ratio. In turn, in Janu- ary 2018 the unemployment rate was about 2% accom- panied with a similar level of the job vacancy rate. The phenomena led to serious problems related to finding Unemployment rate for each LAU2 was computed according to formula: the workers and caused, inter alia, a significant rise in wages number of unemployed persons/labor force. and a massive inflow of migrants from Eastern Europe. The number of unemployed persons is published monthly by local PES The core metropolitan unit (Poznań) is in the above- service at: https:// poznan. praca. gov. pl/ average group in terms of vacancies and below-average in The Census data on population and labor force are available at: https:// terms of unemployment. In general, counties with higher bdl. stat. gov. pl/ BDL/ start 11 Page 6 of 17 M. Wozniak Fig. 3 Monthly rates of vacancies* for 18 counties of the Poznań agglomeration in January 2018–December 2019. *vacancies rates (vr) were computed according to the formula: vr = , where v is the number of vacancies and e is the number of employed persons. The number of the v+e employed was extracted from the Local Data Bank of CSO at: https:// bdl. stat. gov. pl/ BDL/ start (Source: own elaboration) unemployment are located in the peripheries of the are highly correlated (0.79) which means that pub- agglomeration and counties with lower unemployment lic and commercial data share some common trend are located in the central part of the area. also regarding a given spatial unit. If unemployment What is interesting is the case of the Kleszczewo is higher, people tend to find jobs more often and the county (a small east-central unit), characterized by con- inflow to unemployment also rises (Table 1 ). stant and the highest job vacancy rate (above 2.5%) and The summary of the data used in further computa - rather permanent unemployment (1.2%). Kleszczewo is tions is presented in Table 2. All the data relate to LAU2 a rural county with the lowest number of employees in (NUTS5 in former Eurostat nomenclature) administra- the agglomeration (989 people in 2018). The agricultural tive regions. It is worth noting that the data are divided nature of the commune and the above-average inflow of into “rates” and “raw data”. In the case of raw data, the new vacancies (due to the localization of the large dis- range is huge, because the series for central metropoli- tribution center) seem to be the best explanation for the tan area has skewed distribution to the right. In turn, presented indicator level. the rates are normally-distributed with close match When we compute the cross-correlation coeffi - between the median and the mean. Time series were cient for the data, we obtain some puzzling results. tested against stationarity. Test statistics is based on the The inflow of vacancies is positively correlated with estimation of augmented Dickey-Fuller (ADF) regres- the unemployment inflow. It means that if the inflow sions for each variable as presented by Maddala and towards unemployment is higher, employers are more Wu (1999). All series except for the number of unem- likely to create new jobs and post vacancies. In turn, if ployed persons contain a unit root. the unemployment inflow is lower, employers are less likely to post new vacancies. This can be explained by 2.2 Correlation at the low level spatial labor market the greater willingness of employers to hire workers The interaction between spatial units in the labor mar - during higher supply of labor. Both inflows of vacancies kets were confirmed in several empirical research (e.g. Spatial matching on the urban labor market: estimates with unique micro data Page 7 of 17 11 Fig. 4 Evolution of the unemployment rate and job vacancy rate in 18 counties of the Poznań agglomeration in 2018–2019*. *unemployment rates were computed on the basis of data reported by PES; job vacancy rates were computed on the basis of data collected from commercial job portals (Source: own elaboration) Patacchini and Zenou 2007; Netrdová and Nosek 2020). commutes long distances every day. Such markets are not Spatial correlation can be particularly observed in independent and function in a network of interconnec- local labor markets where a significant share of people tions determined by the flow of workers and job vacancies. 11 Page 8 of 17 M. Wozniak Table 1 Cross-correlation matrix u vp vj inf out ur pvr jvr u NA – – – – – – – vp 0.98 NA – – – – – – vj 0.97 0.96 NA – – – – – inf 0.98 0.97 0.98 NA – – – – out 0.97 0.97 0.98 0.99 NA – – – ur − 0.142 − 0.14 − 0.15 − 0.17 − 0.18 NA – – pvr − 0.04 0.015 − 0.02 − 0.04 − 0.04 0.014 NA – jvr − 0.02 0.017 0.01 − 0.02 − 0.02 0.02 0.79 NA u is the number of the unemployed, vp is the number of new vacancies in public statistics; vj is the number of new vacancies gathered via the API interface from commercial job portals; inf is the number of newly unemployed persons; out is new hires; ur is the rate of unemployment; pvr and jvr are vacancy inflow rates from public statistics and commercial job portals respectively Table 2 Descriptive statistics of data Min Max Mean Median Std Unit root Raw_data u 37 7296 404 161 1027 0.36 vp 0 218 12 3 38 0.00 vj 3 4464 270 50 829 0.00 inf 3 1218 67 23 180 0.00 out 2 547 35 12 94 0.00 Rates ur 0.0079 0.026 0.0144 0.014 0.003 0.00 pvr 0 0.014 0.0008 0.0004 0.0015 0.00 jvr 0.0004 0.116 0.015 0.011s 0.019 0.00 u is the number of the unemployed, vp is the number of new vacancies in public statistics; vj is the number of new vacancies gathered via the API interface from commercial job portals; inf is the number of new unemployed persons; out is new hires; ur is the rate of unemployment; pvr and jvr are vacancy inflow rates from public statistics and commercial job portals respectively Consequently, spatial weights matrix W for 18 coun- spatial weight matrix is also one of the most criticized ties of the Poznań metropolitan area is one of the key elements of econometric models because it is pre-defined elements of the spatial models. The matrix defines the and the estimation procedure does not influence the type of interactions among counties and it is necessary to matrix weights (Arbia and Fingleton 2008). However, compute the strength of correlation between neighboring there is no ideal way to account for a spatial spillover in areas. We can distinguish three general types of spatial the model. matrices which can be included in the model specifica - The spatial weights matrix W is a N × N positive matrix tion. They are based on the construction of checker and that summarizes spatial relations between units. Data figure moves; thus we have the Rooks matrix, Bishops appear both in rows and columns. Hence, the non-zero matrix, and Queens matrix (Chen 2012). In the case of elements of the matrix indicate whether two locations are the Rooks matrix, interaction with horizontal and verti- neighbors. As a consequence, element w indicates the ij cal neighbors is considered; the Bishops matrix includes intensity of the relationship between cross sectional units neighbors lying in diagonal fields, and the Queens matrix i and j. By convention w = 0 for the diagonal elements ij captures interactions with all neighboring regions. of W. Each element of the matrix is defined as: There are many more types of spatial weight matrices: w w ··· w 11 12 1n geographical (distance or based on travel time), socio- w w . . . w 21 22 2n economic (based on relative trade, commuting flows, W = . . (1) . . . . : . or similar measures), based on the order of neighbors w w ··· w n1 n2 nn or simply across borders (Vega and Elhorst 2015). The Spatial matching on the urban labor market: estimates with unique micro data Page 9 of 17 11 Fig. 5 Spatial weights matrices used in computations (Source: own elaboration) Table 3 The Moran and Geary tests for spatial correlation Matrix ur jvr pvr Moran I Geary C Moran I Geary C Moran I Geary C Contiguity 0.16 0.87 − 0.04 0.79 − 0.005 0.77 (0.04) (0.21) (0.3) (0.15) (0.12) (0.1) Distance-based 0.06 0.83 0.04 0.82 0.03 0.78 (0.09) (0.07) (0.04) (0.11) (0.04) (0.12) Graph-based 0.07 0.86 − 0.04 0.86 − 0.01 0.82 (0.21) (0.06) (0.33) (0.12) (0.15) (0.08) ur is the rate of unemployment; pvr and jvr are vacancy rates from public statistics and commercial job portals respectively N(i) is the vector of neighbors of location j, which is (time, money, etc.) which however may be compen- determined by the matrix construction (Rooks, Bishops sated by e.g. a higher salary. In turn, the second type or Queens). The intensities of spatial relations are defined has lower costs which may be preferable in the case of by some preset rules that are usually based on contigu- having a low-paid job or other obligations (e.g. chil- ity or distance (Anselin 2001; Getis and Aldstadt 2010). dren, family, etc.). The choice of the matrix used in computations is often As usual, the matrices were row-standardized in the quite arbitrary (Vega and Elhorst 2013). To incorporate [0,1] range: the spatial information into the model, we construct dif- ij ferent spatial weights matrices—we developed three w = ij ij common types of spatial matrices that were included in our models. The first was a neighbors-based Queens Standardization ensured that the models with differ - style contiguity matrix, thus interactions with all neigh- ent W could be comparable. Finally, we plotted matri- bors are defined. The second was distance-based matrix ces on maps to highlight the differences between them that included three nearest spatial locations for each (Fig. 5. centroid. The last matrix (a hybrid of distance approach) Having the matrices, we could test for spatial autocor- was graph-based, where the neighbor relationships are relation. We used two common procedures for calculat- defined by the triangulation, which extends outwards ing the strength of spatial dependencies in the Poznań to the convex hull of the points and which is planar (as agglomeration. Moran’s I measure and Geary’s C test. We defined in spdep R package by Bivand (2018)). use the Monte Carlo simulation approach for computing The Queens matrix assumes that workers freely roam both: Moran’s and Geary’s statistics. MC proved statis- the local labor market with no preferences on the local- tics effectiveness (Ren et al. 2014). In that case values are ization of job vacancies. In turn, distance-based and randomly assigned to the polygons, and the measures of graph-based matrices assume that workers prefer jobs spatial correlation are computed. This is repeated several which are closer to where they live. The first type of times to establish the distribution of expected values. The spatial relations may involve higher transactional costs 11 Page 10 of 17 M. Wozniak Fig. 6 LISA clusters for the unemployment rate (mean value for 2019, local Moran statistics) ( Source: own elaboration) observed values (Moran’s I and Geary’s C) are then com- first indicator local Moran statistics was identified for the pared with the simulated distribution to see how likely it significance level = 0.1 and plotted on Fig. 6 is that they do not co-vary. The results of Moran’s I and The strongly colored regions are therefore those that Geary’s C tests for the unemployment rate and vacancies contribute significantly to a positive global spatial auto - ratio are reported in Table 3. correlation outcome, while paler colors contribute sig- Similarly, as Galecka et al. (2017) proved, spatial inter- nificantly to a negative autocorrelation outcome. This actions are stronger for stock than for inflows in the means that pale colors are surrounded by dissimilar val- case of Poland. The dependency is also visible in our ues that occur near one another. The north-eastern clus - dataset (Table 3)—correlations are significant rather for ter shows significant clustering for the unemployment the unemployment rate than the vacancies inflow rate. rate in the agglomeration. On the other hand, the south- According to p-values, Global Moran’s and Geary’s tests western cluster contributes negatively to the autocorre- show weak positive spatial correlation for the unemploy- lation outcome and is surrounded by units of dissimilar ment rate in the Poznań agglomeration. In turn, both job values. The Getis-Ord Gi statistic (Ord and Getis 1995) vacancy rates seem to be randomly distributed in space looks at neighbors within a defined proximity to identify and do not follow spatial patterns. The results, however, where either high or low values cluster spatially (Fig. 5). strongly depend on the kind of spatial matrix used in Extracted clusters are areas with significant z-values. computations (e.g. according to Moran’s I computed with a distance-based matrix there is evidence for weak, posi- 2.3 Spatial panel matching function models tive spatial correlation also in the case of both vacancy To investigate in-depth the spatial relationship between rates). supply and demand on the local labor market we develop As global tests are calculated from local relationships, spatial panel matching function models. We also com- we moved to local indicators of spatial correlation (LISA) pared the spatial models with its non-spatial equivalents. that measure the correlation between the same vari- The general model is based on the labor market matching ables in the two neighboring spatial units (Anselin 1995). function by Mortensen and Pissarides (e.g. Mortensen Two measures are usually employed for clustering: local 1986; Mortensen and Pissarides 1994; Pissarides 2000). Moran and Getis-Ord statistics. Such indicators detect As we noticed in the previous section, the role of spa- clusters of similar values around a particular location or tial interactions in the local labor market is undoubtful. identify areas that do not follow the global trend. As the The number of new vacancies is not evenly distributed in space and force workers to commute. Daily commut- ing is a widely spread phenomenon in almost every city agglomeration (e.g. Wong et al. 2020). It was also inves- We have no data on vacancy stocks so we focused on the unemployment tigated and confirmed for Poznań and surrounding rate that confirmed spatial correlation significance. Spatial matching on the urban labor market: estimates with unique micro data Page 11 of 17 11 Fig. 7 LISA clusters for the unemployment rate (mean value for 2019, Gettis-Ord statistics) (Source: own elaboration) counties by e.g. Bul (2014). Job seekers may search and M = m(U ,u,v). match vacancies in different counties if they find a job that suits them best (a better job or a higher salary). The economic foundation of this approach is provided Parallelly, employers hire workers from different geo - by, e.g. Coles and Petrolongo (2008). A laid-off worker graphical locations as they are interested rather in skill seeks for a new vacancy as quickly as possible. If the match that does not depend on geolocation. These spa - worker is lucky, he or she can quickly exit unemploy- tial aspects of the matching process are reflected in the ment, even during the same month. Also, the approach model that we present in the further elaboration (Fig. 7). that the unemployed trade rather with the inflow than The matching function governs how agents meet with with the stock of vacancies is supported by empirical each other in a spatial environment. The function cap - research—studies suggest that the vast majority of newly tures search frictions that occur during the process and posted vacancies is filled during the first 7 days (e.g. Bur - produces the number of matches having the given argu- dett and Cunningham 1998). Job seekers tend to scroll ments. The number of new matches M on the labor mar- new vacancies; they hardly ever go back to the older job ket is the result of two inputs: unemployment stock U and adds. vacancies stock V ( M = m(U ,V ) ). Further developments The situation corresponds to the conditions on the of this basic model consider a so-called flow approach local labor market in Poznań. A record-breaking low in which besides stocks we include flows of unemployed unemployment rate resulted in a persistent unemploy- and vacancies: M = m(U ,V ,u,v) (Blanchard and Dia- ment stock which consists mainly of those who are una- mond 1994). We can also distinguish mixed models that ble or unmotivated to start legal employment. As a result, include values of a single stock or flows: M = m(U ,v) the employers trade rather with the inflow of unem - (Gałecka-Burdziak 2017). These models can be useful ployed persons than with the stock. In that case, a major- in modeling the job search process when we can easily ity of new hires is connected with employee turnover, assume that stock of unemployed trade with the inflow of frictional unemployment or the inflow of workers from new vacancies. other regions or countries (e.g. Ukraine or Belarus). In the paper we present the combination of the stock Consequently, the model can be written as a common 7 α β with flow model. Therefore, new vacancies trade with Cobb-Douglass formula: M = AU v . Note that the both: unemployed persons (U) and the inflow of the stock-flow implies that the total number of unemployed newly registered unemployed (u). Consequently, the gen- U can be decomposed into the stock of unemploy- eral specification of the matching function can be written ment U as well as the inflow of newly registered persons ∂M ∂v as: u. The model assumptions are that > 0, > 0 and U U 2 2 ∂M ∂M < 0, < 0 so the function is increasing in both U v arguments but its increments are decreasing. Further, however a questionable assumption is the one about constant returns to scale of the function. The lat - See Shaphiro and Stiglitz (1984) for more details on a job queuing approach. In turn, Ebrahimy and Shimer (2010) provide a theoretical framework for ter was either falsified or confirmed in several empirical stock-slow matching. 11 Page 12 of 17 M. Wozniak studies (e.g. Shimmer (2005); Guerrazzi (2015)) and it is on the labor market is complex and results from different also a point of our interest regarding the low-level of spa- factors which are sometimes difficult to identify (Vega tial aggregation. Therefore, we can simplify further calcu - and Elhorst 2016). lations and write the model in the logarithmic form of a Having this in mind, the second model is the spatial linear model: Durbin error model (SDEM) which is the extension of the SLX model and can also be useful in detecting local logM = logA + α log(U) + α log(u) + βlog(v) 1 2 (2) spillovers. Additionally, the model assumes the spatial pattern in an error term due to omitted factors. The Further, the model is enhanced with spatial depend- SDEM can overcome both spatial autocorrelation rela- encies according to the distance-based spatial weights tionships of independent variables and spatial errors matrix. We use the matrix because it provided the high- between regions. Formally, SDEM is enhanced SLX and est average estimates for spatial correlation for all vari- contains both spatial exogenous interaction effects as ables (Table 3). well as a spatial error term. Thus, ε in (4) evolves to i,t The spatial dependencies can be included in the model W ε + u , where ε is a specific space effect term that i,j in several ways: by a spatial lag of either a dependent or can be either correlated or not with the regressor, is independent variable. The error component can be also the parameter describing the strength of spatial cor- enhanced by spatial spillovers (Anselin et al. 2008). To relation among errors and u = N(0, σ ) is white noise. keep things clear, we make use of spatial econometric SDEM however fails in the identification of global spill - models’ taxonomy provided by Vega and Elhorst (2013; over effects which can be also significant on the labor 2015). On its basis we develop three different spatial market. matching function models in terms of spillover and direct Consequently, the third specification of a spatial model effect. We take the model with spatial lags of independ - is the spatial autoregressive model (SAR). It includes the ent variables (SLX) as a point of departure as suggested spatial lag of a dependent variable and allows detect- by Vega and Elhorst (2015). SLX allows accounting for ing global spatial effects. In that case, including endog - both direct and spillover effects and is a complement of enous interaction effects means that the number of new the critique of spatial econometrics. In terms of (2), the matches in a given unit may affect other units in the SLX panel model for a cross-section of N observations agglomeration even if the units do not have the common over time t = 1 . . . T may be written as: borders. It could be justified economically as unemployed persons seek for a job in the whole agglomeration and Y = αl + X β + WX θ + ε , ε ∼ 0, σ l , (3) t N t t t t N may commute throughout several counties. Job search and matching is not limited to neighboring units. For- where Y is the vector dependent variable; X is the matrix mally speaking the spatial matching function SAR model of explanatory variables; W is a positive N × N matrix; is: α is the parameter of constant term; β , θ are the vectors of model parameters. Rewriting (3) of the empirical case log M = α + δW log M + β log U i,t i,j i,t 1 i,t presented in this study comes to the SLX matching func- (5) + β log u + β log v +ε , 2 i,t 3 i,t i,t tion panel model: where δ is the spatial coefficient. In turn, the common log M = α + β log U + β log u i,t 1 i,t 2 i,t panel model without a spatial component would turn + β log v 3 i,t into: + θ W log U + θ W log u 1 i,j i,t 2 i,j i,t log(M ) = αlog(A ) + β log U + β log u 1 i,t 2 i,t i.t i,t + θ W log v +ε 3 i,j i,t i,t + β log v + μ + e . (4) 3 i,t i i,t In that case, the direct effects are the coefficient esti - (6) mates of nonspatial variables β and the spillover effects In further computations we used the data described are those associated with the spatially lagged explanatory in the previous section. Thus, we had a balanced panel variables θ ; i, j are spatial indexes and t is the time index. with n = 18, T = 24 and N = 432. Due to the limitations SLX includes spatial interactions of explanatory variables of the API interface, we were able to retrieve 24 months’ so we can assess the impact of spatially lagged exogenous time-series for each panel unit which could be a little too variables on the number of new matches. However, sev- short (e.g. Griffith 2013). We are fully conscious of the eral econometric studies investigate also endogenous limitations of the data, however, some empirical stud- interaction effects or interactions between error terms ies successfully use even smaller datasets. For instance, (e.g. Lee and Yu 2016). The nature of spatial interactions Pereira et al. (2017) developed a spatial regression model Spatial matching on the urban labor market: estimates with unique micro data Page 13 of 17 11 Table 4 Estimation results for spatial panel and panel models Table 5 Estimation results for spatial panel and panel models with commercial job portals data on vacancies* with public employment service data on vacancies* Spatial panel models** Non-spatial panel Spatial panel models** Non-spatial panel models models Variable SAR SLX SDEM Fixed effects Pooled Variable SAR SLX SDEM Fixed effects Pooled A – – – – − 1.49*** A – – – – 1.41*** (0.000) (0.000) Wlog(M) 0.23*** – – – Wlog(M) 0.24*** – – – (0.000) (0.000) Log(u) − 0.18 − 0.37 − 0.37 − 0.20 0.42*** Log(u) -0.10 -0.34 -0.38 -0.10 0.44*** (0.11) (0.11) (0.07) (0.10) (0.000) (0.38) (0.14) (0.1) (0.39) (0.000) log(inf ) 0.169* 0.177* 0.174* 0.19* 0.53*** log(inf ) 0.184** 0.191* 0.178* 0.20** 0.54*** (0.017) (0.02) (0.015) (0.01) (0.000) (0.009) (0.01) (0.014) (0.006) (0.000) log(v) 0.22*** 0.20* 0.21** 0.25*** 0.04* log(v) 0.02 0.02 0.04 0.03 0.04 (0.005) (0.01) (0.003) (0.000) (0.1) (0.41) (0.46) (0.35) (0.26) (0.08) Wlog(U) – 0.14 0.18 – – Wlog(U) – 0.23 0.29 – – (0.57) (0.44) (0.38) (0.23) Wlog(inf ) – 0.13 0.11 – – Wlog(inf ) – 0.18 0.10 – – (0.24) (0.36) (0.12) (0.35) Wlog(v) – 0.12 0.07 – – Wlog(v) – 0.05 0.04 – – (0.24) (0.47) (0.29) (0.35) We – 0.22*** – – /We – 0.23*** – – (0.000) (0.000) R-squared 0.88 0.06 0.87 0.05 0.84 R-squared 0.87 0.03 0.88 0.02 0.84 Spatial Haus- 7.95 119.78 45.4 94.29 – Spatial Hausman 94 67.5 80.31 74.13 – man (0.04) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) LM test for 5.27 0.92 4.70 – – LM test for 6.55 1.22 6.26 – – effects*** (0.000) (0.07) (0.000) effects*** (0.000) (0.1) (0.000) AIC/BIC 378/472 397/498 283/489 395/484 444/460 AIC/BIC 389/483 397/498 392/497 408/497 444/460 *p-values are reported in brackets *p-values are reported in brackets ** Spatial models were estimated with region fixed effects. ** Spatial models were estimated with region fixed effects, ***LM is the Lagrange Multiplier test for individual effects ***LM is the Lagrange Multiplier test for individual effects job portals data on vacancies and other five with PES for 28 Portuguese NUTS3 and 12 time points (N = 336). data on job vacancies. For each of these two groups three The authors argue that small area estimation methods, models were spatial panels (SLX, SDEM and SAR) and "borrow strength" from adjacent regions and therefore two models were regular panels without spatially lagged compensate for the small sample sizes which is often variables (a fixed-effect estimator and a pooled model). observed in these areas. In turn, Acosta and Valejos We used a distance-based matrix in computations as it (2018) provide a simulation of information loss depend- has proven the highest values for spatial correlation (on ing on the n in spatial regression. They show that includ - average). ing 25 units provides the evidence for spatial correlation Spatial models were estimated with two-step Maxi- only slightly weaker than including 50 units. They also mum Likelihood as implemented insplm R package conclude that strong prior information may compensate (Millo and Piras 2012). In turn, the regular panel model for a small sample size. The spatial models were tested and confirmed for indi - vidual effects with the Lagrange Multiplier test for spatial panel models. Time fixed effects proved to be nonsig - nificant in an overall test (Baltagi et al. 2003). The fixed effects estimator was chosen on the basis of a Hausman spatial panel models test extension (Mutl and Pfaffer - The package is available from the Comprehensive R Archive Network at mayr 2011; Bell et al. 2019). The tests results are reported http:// CRAN.R- proje ct. org/ packa ge= splm in Tables 4 and 5. The package contains routines to the estimation of various spatial models. Finally, we have estimated 10 models on the basis of It is based on the maximum likelihood implementation of the specifications formula (4), (5) and (6). Five models were estimated with of models with individual effects that are/are not spatially autocorrelated. 11 Page 14 of 17 M. Wozniak was estimated with a fixed effect estimator; a pooled study area. It indicates that if the number of new matches model was assessed with an OLS approach. In that case (M) changes in one unit, it somehow affects all units in we used plm R packge (Croissant and Millo 2018) that the agglomeration. Wlog(M) is a spatially lagged depend- provides a set of estimators for panel data. The results ent variable the coefficient of which is highly significant are presented in Table 4 (commercial data on job vacan- and positive. It appears that the matching process in one cies) and Table 5 (PES data on job vacancies). region significantly affects the outflow in other areas with Comparison of both R-squared and AIC/BIC crite- positive externalities. The larger the outflow in a given ria leads to the conclusion that spatial models estimated area, the larger in the rest of the units. It may be the with commercial job ads are better fitted with the data result of the great mobility of workers on the urban labor (they produced higher R-squared and lower AIC/BIC market that commute long distances (through several scores). In turn, spatial models estimated with PES data counties) to get to work. Thus, workers in the agglomera - have not confirmed the existence of the matching func - tion (globally) may match with vacancies that appear in a tion. The inflow of new vacancies is not significant in that given county (locally). case; thus, we focus on the analysis of the output of mod- The SLX and SDEM models indicate that local spillo - els estimated with combined data (PES data on unem- ver effects are not significant. Local spillovers mean that ployment + commercial job portals data on vacancies). a given region affects the adjacent units while not having Therefore, the SAR, SLX, SDEM and panel fixed-effects effect on the rest of counties. This finding supports the models identified the spatial matching function which existence of global effects on the local labor market. In exhibits strictly decreasing returns to scale. In turn, the case of SDEM, the additional variable is the spatially the pooled model indicates the constant return to scale lagged error term ( /We) that is positive and significant. matching function. The result corresponds to the papers estimates indicated that the shock in a given region may that estimate the matching function with disaggregated be induced by unobservable effects in adjacent areas. data (e.g. Yashiv (2006) or Kangasharju et al. (2005)). We u Th s, SDEM provides the evidence of spatial autocor - can than support a hypothesis that some studies with relation because of other significant factors that were the exemplary well-known paper by Petrolongo and Pis- omitted in the specification of the matching function. sarides (2001) may overstate the dominance of the CRS This finding, in turn, may partially explain the decreasing matching function. return to scale matching function. Spatial panel models show that matching technology on the market is the result of trade between the inflow 3 Conclusions of new vacancies and the inflow of unemployed persons The aim of this paper was to investigate spatial processes rather than the stock which appeared insignificant. The on low-level spatial labor markets with a unique set of coefficient of the unemployment inflow was a little lower data. We extracted data on job vacancies from the three than the coefficient of the inflow of vacancies. It means largest commercial job portals in Poland. Unlike other that an increasing inflow of unemployment and vacan - studies that use public statistics, we employed a dedi- cies by 1% would result in an increase in new matches cated API-based service to download and aggregate the by ~ 0.17% and ~ 0.21% respectively. This finding may data across spatial units to obtain more a reliable insight reflect the situation on the local labor market. Ultimately, into demand for workers. Our analysis focused on the the low unemployment rate of 1.1% and a high demand one of the largest urban areas in Poland (Poznań agglom- for workers force the employers to trade with the inflow eration) that consists of 17 small spatial units of the of the newly unemployed rather than with the stock that LAU2 class. We proved the existence of spatial autocor- consists of persons that are not well-motivated or unable relation and identified the clusters that significantly con - to start work. Therefore, new matches result from worker tribute positively and negatively to the unemployment turnover, migrants from other regions and countries, and rate. We therefore extend studies on labor market spatial those entering the labor market from the inactivity zone. correlation by adding the analysis of small spatial units The SAR model generates the strong process of global which have not been the object of studies so far. We also spillovers showing that the effect was observed in the contribute by the analysis of the spatial panel matching function on the urban labor market with a unique dataset combined with the registered data on unemployment and commercial data on job adds. The package is available from the Comprehensive R Archive Network at In the paper, we estimated spatial and non-spatial mod- https:// cran.r- proje ct. org/ web/ packa ges/ plm/ index. html els with public and commercial data on job vacancies. There are several routines that support estimation of different types of panels (inter alia, fixed and random effects, variable coefficient models, the The results clearly show the drawbacks of PES data on general method of a moments estimator, general feasible generalized least vacancies. Although estimations proved the existence of squares models). Spatial matching on the urban labor market: estimates with unique micro data Page 15 of 17 11 spatial dependencies, the PES estimations did not iden- Also, a special point of interest should be solutions for tify the matching function and produced worse fit to foreign workers, especially from Ukraine or Belarus, data. In effect, we were able to produce further conclu - who are already present on the local labor market. The sions on the basis of the models estimated with the data immigrants may help to fill the huge gap in labor sup - on job vacancies extracted from commercial job portals. ply. However, the complicated and time-consuming In addition, if we were only to follow the estimates of the institutional procedures may discourage them from pooled models, we would confirm the common finding looking for a job. The institutional weakness is also of the existence of the CRS matching function also at reflected in the extremely underestimated data on reg - the low level of spatial aggregation (as identified by both istered vacancies. PES is not fulfilling its function in the pooled models). However, the estimated spatial models job-workers matching process. Thus, the other recom - exhibit decreasing returns to scale (DRS) and this finding mendation would be improving job placement services goes along with the hypothesis of exaggerating the role and increasing the cooperation between employers and of the CRS matching function (e.g. Yashiv (2006) or Kan- PES. gasharju et al. (2005)). The present situation connected with the shock of the We believe, DRS in that case are mainly the result of COVID-19 pandemic did not hit particularly severe the the omitted variables (as identified by the SDEM). These local labor market—the registered unemployment rate unidentified factors may be connected with on-the- in December 2020 in the Poznań agglomeration was still job search or the exploitation of other channels in the very low and reached merely 2.1%. As a result, the identi- recruitment procedure and bias the elasticities of the fied issues of the spatial matching process may evolve and matching function ((Fahr and Sunde 2005; Sunde 2007). should be a point of interest also in the near future. These additional factors may be particularly important Acknowledgements because of permanent worker shortages on the local Not applicable. labor market. One should remember that our analysis Authors’ contributions was carried out for the specific urban labor market that MW conceived and designed the analysis, collected the data, developed the was characterized by the record-low unemployment level analysis tools, performed the analysis and wrote the paper. The author read (~ 1.5% on average) and a high demand for workers. In and approved the final manuscript. fact, in 2018–2019, workforce shortage was the largest Funding problem on the local labor market (LMO 2020). Moreo- Not applicable. ver, under an extremely low unemployment rate firms Availability of data and materials are not likely to unthinkingly post new vacancies—a job The datasets and scripts generated and/or analysed during the current study add is an additional cost which might not return. Hence, are available in the GitHub repository, https:// github. com/ wozni ak2/ spati alMF. the positive sign of cross-correlation between these two variables. As a result, creativity counts and various search Declarations behaviors are used in order to find a trading partner. Competing interests Another finding (made on the basis of API-gathered The authors declare that they have no competing interests. data) includes strong positive externalities connected with the matching process among 18 LAU2 units of the Received: 14 September 2020 Accepted: 19 March 2021 urban labor market. The externalities are global in their nature which means the one outflow to employment in one unit affects also others not necessarily the closest References ones. The externality may be connected with job com - Acosta, J., Vallejos, R.: Eec ff tive sample size for spatial regression models. muting—workers may travel through several counties Electron. J. Statist. 12(2), 3147–3180 (2018). https:// doi. org/ 10. 1214/ 18- and an increase in the number of new vacancies in one EJS14 60 Ahtonen, S.M.: Matching across space: Evidence from Finland. 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Journal for Labour Market Research – Springer Journals
Published: Apr 6, 2021