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Competition, Student Sorting and Performance Gains in Local Education Markets: The Dutch Secondary Sector

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Title: Competition, Student Sorting and Performance Gains in Local Education Markets: The Dutch Secondary Sector
Language: English
Authors: Cabus, Sofie, Cornelisz, Ilja
Source: European Journal of Education. Sep 2017 52(3):365-386.
Availability: Wiley-Blackwell. 350 Main Street, Malden, MA 02148. Tel: 800-835-6770; Tel: 781-388-8598; Fax: 781-388-8232; e-mail: cs-journals@wiley.com; Web site: http://www.wiley.com/WileyCDA
Peer Reviewed: Y
Page Count: 22
Publication Date: 2017
Document Type: Journal Articles
Reports - Research
Education Level: Secondary Education
Descriptors: Competition, Secondary School Students, Academic Achievement, Achievement Gains, Foreign Countries, Measurement Techniques, Student Characteristics, Family Characteristics, High Achievement, Enrollment Trends
Geographic Terms: Netherlands
DOI: 10.1111/ejed.12221
ISSN: 0141-8211
Abstract: This article empirically examines the implications of competition among Dutch secondary schools: (1) regarding the sorting of students by performance levels in schools at the beginning of secondary education; and (2) regarding performance gains in the secondary school career, controlling for the aforementioned sorting patterns. We used data from about 13,000 students enrolled at 102 school locations in The Netherlands. Using differences in the distribution of competition intensity across local education markets, we applied Kernel estimation techniques to match students from relatively high- to low-competitive markets on the basis of student and household characteristics. Our results indicate that, with increasing competition, relatively more schools target the group of high-achieving students. As a result, schools will arguably have to enrol more "students at the margin" to ensure sufficient enrolment rates. To conclude, we observed that, accounting for sorting patterns, competition was related to small negligible improvements in academic achievement at the bottom of the distribution of student performance within the first three years of secondary education. Furthermore, a negative result for competition was found for categorical academic classrooms settings.
Abstractor: As Provided
Entry Date: 2017
Accession Number: EJ1150468
Database: ERIC
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  Value: <anid>AN0124455297;eje01sep.17;2018Aug13.14:56;v2.2.500</anid> <title id="AN0124455297-1">Competition, student sorting and performance gains in local education markets: The Dutch secondary sector. </title> <p>This article empirically examines the implications of competition among Dutch secondary schools: (<reflink idref="bib1" id="ref1">1</reflink>) regarding the sorting of students by performance levels in schools at the begiining of secondary education; and (<reflink idref="bib2" id="ref2">2</reflink>) regarding performance gains in the secondary school career, controlling for the aforementioned sorting patterns. We used data from about 13,000 students enrolled at 102 school locations in The Netherlands. Using differences in the distribution of competition intensity across local education markets, we applied Kernel estimation techniques to match students from relatively high ‐ to low ‐ competitive markets on the basis of student and household characteristics. Our results indicate that, with increasing competition, relatively more schools target the group of high ‐ achieving students. As a result, schools will arguably have to enrol more ‘students at the margin’ to ensure sufficient enrolment rates. To conclude, we observed that, accounting for sorting patterns, competition was related to small negligible improvements in academic achievement at the bottom of the distribution of student performance within the first three years of secondary education. Furthermore, a negative result for competition was found for categorical academic classrooms settings.</p> <p>In the wake of the global economic crisis, countries face the challenge of making public finances sustainable, whilst also building the foundations for continued long ‐ run economic growth. There is a widespread consensus that a well ‐ educated labour force is vital for any economy and that increasing student performance is crucial in fostering a nation's competitiveness in a globalising world (Barro, [<reflink idref="bib2" id="ref3">2</reflink>] ; Barro & Lee, [<reflink idref="bib3" id="ref4">3</reflink>] ; Benhabib & Spiegel, [<reflink idref="bib6" id="ref5">6</reflink>] ; European Commission, [<reflink idref="bib21" id="ref6">21</reflink>] ,[<reflink idref="bib22" id="ref7">22</reflink>] ; Hanushek & Wössmann, [<reflink idref="bib29" id="ref8">29</reflink>] ; Krueger & Lindahl, [<reflink idref="bib47" id="ref9">47</reflink>] ,[<reflink idref="bib48" id="ref10">48</reflink>] ; Lukas, [<reflink idref="bib54" id="ref11">54</reflink>] ; Mankin, Romer, & Weil, [<reflink idref="bib57" id="ref12">57</reflink>] ; Romer, [<reflink idref="bib67" id="ref13">67</reflink>] ). However, there is much less consensus on how to fund and organise educational provision so that resources are translated into educational outcomes. Hence, school choice and school ‐ level competition policies have increasingly received attention from policy makers. These policies can commonly be described along two important dimensions. On the demand side of schooling, choice programmes are designed for parents to have more freedom in choosing a school for their children. On the supply side, school choice policies foster competition between schools for students and revenues (Plank & Sykes, [<reflink idref="bib65" id="ref14">65</reflink>] ). This article focuses on the supply side by exploring the relationship between school ‐ level competition and performance gains in compulsory education.</p> <p>The literature on school ‐ level competition and performance gains, or productive efficiency, indicates at least four reasons why competition between schools can raise student performance. First, it forces all schools to increase productive efficiency to avoid going out of business (Hoxby, [<reflink idref="bib41" id="ref15">41</reflink>] ). Second, private entities are potentially more efficient in allocating resources to provide services to particular groups than the government (Shleifer, [<reflink idref="bib72" id="ref16">72</reflink>] ). Third, school choice and competition between schools may, under certain conditions, improve parental involvement, which, in turn, leads to higher levels of student performance (Chubb & Moe, [<reflink idref="bib11" id="ref17">11</reflink>] ; Cullen, Jacob, & Levitt, [<reflink idref="bib12" id="ref18">12</reflink>] ; Godwin & Kemerer, [<reflink idref="bib27" id="ref19">27</reflink>] ; Henderson, [<reflink idref="bib32" id="ref20">32</reflink>] ; Hirschman, [<reflink idref="bib38" id="ref21">38</reflink>] ; Hoxby, [<reflink idref="bib40" id="ref22">40</reflink>] ). A fourth reason, student sorting and results from a more efficient matching of students across different schools will receive our particular attention throughout this article (see also Cullen et al., [<reflink idref="bib12" id="ref23">12</reflink>] ; Hoxby, [<reflink idref="bib41" id="ref24">41</reflink>] ; Ladd, [<reflink idref="bib50" id="ref25">50</reflink>] ; Levin, [<reflink idref="bib51" id="ref26">51</reflink>] ).</p> <p>Schools compete for ‘favourable students’ by academic or non ‐ academic features in order to produce achievement gains in an efficient way. These students are those whose academic profile matches the niche for which the school wishes to compete. If such matching is improved, competition between schools may induce an efficient provision with greater school choice (Chubb & Moe, [<reflink idref="bib11" id="ref27">11</reflink>] ; Gibbons, Machin, & Silvia, [<reflink idref="bib25" id="ref28">25</reflink>] ; Levin, [<reflink idref="bib51" id="ref29">51</reflink>] ). If households’ preferences for student performance and other school attributes are heterogeneous, then competition between schools will lead to substantial product differentiation so as to match a school's appeal for particular educational preferences of households for which the schools wish to compete (Belfield & Levin, [<reflink idref="bib5" id="ref30">5</reflink>] ; Levin, [<reflink idref="bib52" id="ref31">52</reflink>] ).</p> <p>In this article, we first constructed a measure that reflected school ‐ level competition intensity in Dutch secondary education. As highlighted by Gibbons and Silva ([<reflink idref="bib26" id="ref32">26</reflink>] ) and Gibbons et al. ([<reflink idref="bib25" id="ref33">25</reflink>] ), this measure ideally: (<reflink idref="bib1" id="ref34">1</reflink>) shows enough variation to be empirically meaningful, and (<reflink idref="bib2" id="ref35">2</reflink>) is not driven by general urban density and school size effects. Therefore, for each school and using geographical information, we constructed a ‘school concentration’ index that measures the number of secondary schools within a pre ‐ defined radius (10km) and takes into account student density. Second, we explored the mechanism whereby the sorting of students could lead to differences in school ‐ level performances between competitive and non ‐ competitive education markets. We present an intuitive mechanism that builds on the differences in the distribution of performance levels within schools and between education markets. And third, we provide indirect evidence on how schools in a competitive and selective education market might compete for ‘favourable’ students by supply ‐ driven product differentiation (Levin, [<reflink idref="bib52" id="ref36">52</reflink>] ).</p> <p>The Netherlands is a particularly interesting case study with respect to school ‐ level competition in local education markets. The compulsory schooling system has been providing universal choice since 1848, with private and public schools under equal government treatment and funding since 1917. The right to establish government ‐ funded schools that provide teaching based on religious, ideological or educational beliefs has resulted in a plurality of private educational choices (Education Inspectorate, [<reflink idref="bib18" id="ref37">18</reflink>] ). By 2010, the secondary sector included 940,200 students in 646 institutions, with 72% of the enrolment concentrated in private government ‐ funded schools (OCW, [<reflink idref="bib64" id="ref38">64</reflink>] ). The Dutch education market for compulsory schooling fits the definition of a quasi ‐ market (Belfield & Levin, [<reflink idref="bib5" id="ref39">5</reflink>] ) in that: (<reflink idref="bib1" id="ref40">1</reflink>) suppliers compete with each other; (<reflink idref="bib2" id="ref41">2</reflink>) entry into and exit from the schooling market are regulated; (<reflink idref="bib3" id="ref42">3</reflink>) household demands are expressed through a voucher ‐ type system of funding; and (<reflink idref="bib4" id="ref43">4</reflink>) the government maintains an important role in accountability and standards. Government ‐ funded schools, regardless of whether they are privately run, cannot charge tuition or have for ‐ profit motives. Schools cannot select by ability, although private schools can select students by criteria that are related to their religious denomination or ideological character (Eurydice, [<reflink idref="bib23" id="ref44">23</reflink>] ). To summarise, the Dutch secondary education context is relevant to examine the potential relationships between school ‐ level competition and performance sorting and gains, acknowledging that the following three assumptions hold: (<reflink idref="bib1" id="ref45">1</reflink>) differences in average student performance exist between schools, (<reflink idref="bib2" id="ref46">2</reflink>) parents have access to information about such differences, and (<reflink idref="bib3" id="ref47">3</reflink>) parents choose (at least partially) on the basis of school performance. Results for Dutch compulsory education confirm that perceived quality, as indicated by observable differences in average performance, is an important choice determinant for parents (Denessen, Driessena, & Sleegers, [<reflink idref="bib15" id="ref48">15</reflink>] ; Dronkers, [<reflink idref="bib17" id="ref49">17</reflink>] ; Herweijer & Vogels, [<reflink idref="bib34" id="ref50">34</reflink>] ; Karsten, Roeleveld, Ledoux, Felix, & Elshof, [<reflink idref="bib45" id="ref51">45</reflink>] ; Koning & Van der Wiel, [<reflink idref="bib46" id="ref52">46</reflink>] ).</p> <p>Students sit for a standardised test at the end of primary education.[<reflink idref="bib1" id="ref53">1</reflink>] Based on this test score and their teacher's assessment, the school advises them to attend a particular school type in secondary education. More than 80% choose a school that is in line with this advice (Zijsling, Kuyper, Lubbers, & van der Werf, [<reflink idref="bib49" id="ref54">49</reflink>] ; Zijsling & van der Werf, [<reflink idref="bib77" id="ref55">77</reflink>] ). Students can enrol in pre ‐ vocational secondary education (vmbo), senior general secondary education (havo) or pre ‐ university education (vwo). Depending on whether a school offers all tracks and on school ‐ level policies, students either enrol directly in tracked classes (categorical classes) in their first year or attend comprehensive classes (combined tracks) for the first one or two years.</p> <p>In the empirical analyses on student sorting by performance, we used CITO test scores measured at the start of secondary education (grade 7) for about 13,000 students enrolled in 102 Dutch secondary schools in the school year 1999–00. The data also included background variables on the students, their parents, and the schools. When estimating the effect of competition on educational outcomes, endogeneity is a serious reason for concern (Gibbons & Silva, [<reflink idref="bib26" id="ref56">26</reflink>] ; Gibbons et al., [<reflink idref="bib25" id="ref57">25</reflink>] ). Often, competition measures are also associated with urban density and the composition of the student population. In order to deal with this empirically challenging issue, and in the absence of experimental variation in competition, we propose to: (<reflink idref="bib1" id="ref58">1</reflink>) control for urban density in the competition measure; and (<reflink idref="bib2" id="ref59">2</reflink>) only compare similar students in different local education markets, based on observed characteristics. Kernel matching estimation techniques are then used to match students in highly ‐ competitive education markets (HCM, or the treatment group) to low ‐ or non ‐ competitive education markets (NCM, or the control group), based on student and household characteristics and the distribution of our competition measure. We also used one additional follow ‐ up exam (grade 9) to further investigate whether, depending on the enrolment decision at the beginning of secondary education, competition intensity was associated with differences in productive efficiency across schools.</p> <p>Applying the matching approach to the Dutch data set enabled us to account for a wide array of background characteristics of the student populations. Another reason to focus on data for The Netherlands was that it has one of highest population densities and has been providing universal choice to households since 1848. One could therefore argue that residential decision ‐ making is relatively unbundled with the school choice decision (Nechyba, [<reflink idref="bib62" id="ref60">62</reflink>] ). Some empirical evidence for this is provided by administrative data[<reflink idref="bib2" id="ref61">2</reflink>] in which it can be observed that, in 2008–2009, over 96% of households did not move out of their municipality when their child transitioned from primary to secondary school, a figure that is identical when such a transition does not take place (i.e. from the first to second year in secondary education). As another check, our preferred estimates were compared to those derived from model specifications in which we controlled for a variety of observed differences in household school choice determinants.</p> <p>Our findings highlight three aspects. First, we observed that the configuration of a local education market, in terms of how demand (i.e. choice determinants) and supply (i.e. school features) were matched, was related to the level of competition between schools. Second, the results were in line with a context in which, depending on individual background characteristics, school choice determinants, and school supply characteristics, schools resorted to supply ‐ driven product differentiation to compete for their target population of students. We observed that, if competition intensity increased, schools offering higher (academic) tracks converged in terms of average performance to the lower (vocational) track schools as a result of enrolling more ‘students at the margin’. To conclude, we found a negative relationship between competition intensity and performance gains in the first three years of secondary education, in particular for the higher ability tracks. For students in the relatively lower ‐ ability tracks, there were some improvements in academic achievement in the first three years of secondary education. However, they were so small that they were negligible.</p> <hd id="AN0124455297-2">COMPETITION AND STUDENT SORTING</hd> <p>There are several mechanisms whereby competition may affect the sorting of students by performance levels in the Dutch context, namely: peer effects; (non ‐ ) academic features; and school reputation.</p> <hd id="AN0124455297-3">Untitled</hd> <p>The international literature on the effects of (increased) competition between schools on the sorting of students by performance levels, both across and within education markets, highlights the role of peer effects (Brunner & Imazeki, [<reflink idref="bib9" id="ref62">9</reflink>] ; Kang, [<reflink idref="bib43" id="ref63">43</reflink>] ). These are generally defined as the extent to which students’ learning outcomes depend on their classmates’ characteristics. Rothstein's ([<reflink idref="bib68" id="ref64">68</reflink>] ) model argues that households, in the presence of peer effects and school choice, may prefer less effective schools with desirable peer groups to better, more effective, schools. Schools, in this case, face incentives to enrol high ‐ quality peers rather than offer effective instruction (Burgess, McConnell, Propper, & Wilson, [<reflink idref="bib10" id="ref65">10</reflink>] ). If (private) schools are allowed to enter the market (e.g. through vouchers), assuming peer effects and allowing schools to charge tuition and provide tuition subsidies, the equilibrium outcome is stratified by (income and) ability across schools (Epple & Romano, [<reflink idref="bib19" id="ref66">19</reflink>] ,[<reflink idref="bib20" id="ref67">20</reflink>] ). High ‐ competition education markets will then be stratified by ability (Rothstein, [<reflink idref="bib68" id="ref68">68</reflink>] ). In addition, the variation of peer ability within schools can be an important determinant of school quality. In their attempt to improve quality, schools facing intense competition could resort to curriculum targeting to improve productive efficiency, leading to more homogeneous student populations within schools (Nechyba, [<reflink idref="bib61" id="ref69">61</reflink>] ).</p> <hd id="AN0124455297-4">Untitled</hd> <p>Disregarding potential peer effects, school competition can still affect student sorting in several ways. When facing competition, schools seem to use their position in the local hierarchy of their education market to obtain control over their enrolment (Rincke, [<reflink idref="bib66" id="ref70">66</reflink>] ). If explicit ability selection is not allowed, schools can adopt enrolment schemes that could well be less ability ‐ neutral than they might appear at first (Waslander, Pater, & van der Weide, [<reflink idref="bib74" id="ref71">74</reflink>] ). Alternatively, they can use the curriculum or other (non ‐ academic) features to target certain preferred households. Highlighting the importance of enrolling sufficient numbers of students, McMillan ([<reflink idref="bib58" id="ref72">58</reflink>] ) suggests that some schools will show rent ‐ seeking behaviour and go ‘down ‐ market’ in targeting certain households as a way to ensure sufficient enrolment patterns. School choice advocates and opponents disagree on the effects of competition on schools’ curricula and academic standards (Hoxby, [<reflink idref="bib39" id="ref73">39</reflink>] ,[<reflink idref="bib40" id="ref74">40</reflink>] ).</p> <hd id="AN0124455297-5">Untitled</hd> <p>MacLeod and Urquiola ([<reflink idref="bib55" id="ref75">55</reflink>] ) point to school reputation as another factor affecting the sorting of students. In their model, socioeconomic and ability stratification across schools occur through admission selection processes, regardless of any potential peer effects. Excluding unfavourable students can occur both explicitly and implicitly. One strategy could be to diversify course offerings with respect to, for example, sports, arts or international components, knowing that some courses attract some students more than others. Waslander et al. ([<reflink idref="bib74" id="ref76">74</reflink>] , p. 50) conclude that under the influence of competition: ‘Implicitly or explicitly schools seek the most “desirable” students: first, students who are academically able followed by students who possess other favourable characteristics such as specific socio ‐ economic and ethnic backgrounds’. De Fraja and Landeras ([<reflink idref="bib14" id="ref77">14</reflink>] ) add that, depending on incentive schemes (e.g. policy measures changing the way schools operate or teachers teach), school reputation can lead to the sorting of students by performance levels. Based on these observations, competition between schools can foster or maintain a clear hierarchy in local education markets. In general, it seems to induce product differentiation in which schools match their appeal to educational preferences of households rather than offer a standardised educational product (Levin, [<reflink idref="bib52" id="ref78">52</reflink>] ).</p> <hd id="AN0124455297-6">Untitled</hd> <p>In primary education, freedom of choice is universal, whereas secondary education is organised in tracks according to students’ abilities. The right to establish government ‐ funded schools has resulted in a plurality of private educational choices (Merry & Karsten, [<reflink idref="bib59" id="ref79">59</reflink>] ). Empirical results confirm that parents heterogeneously take into account peers, curriculum and non ‐ academic features and school reputation; thereby realising the potential for significant sorting of students as measured by performance levels (Denessen, et al., [<reflink idref="bib15" id="ref80">15</reflink>] ; Dronkers, [<reflink idref="bib17" id="ref81">17</reflink>] ; Herweijer & Vogels, [<reflink idref="bib34" id="ref82">34</reflink>] ; Karsten et al., [<reflink idref="bib45" id="ref83">45</reflink>] ; Koning & Van der Wiel, [<reflink idref="bib46" id="ref84">46</reflink>] ).</p> <hd id="AN0124455297-7">OUR FRAMEWORK</hd> <hd id="AN0124455297-8">Untitled</hd> <p>Several theoretical models exist with respect to the implications of competition between schools, school choice, and the sorting by socioeconomic status, ability or performance. The observed sorting patterns depend on: (<reflink idref="bib1" id="ref85">1</reflink>) choice constraints (Hirsch, [<reflink idref="bib36" id="ref86">36</reflink>] ; Levin, [<reflink idref="bib53" id="ref87">53</reflink>] ; Nechyba, [<reflink idref="bib60" id="ref88">60</reflink>] ; Teske & Schneider, [<reflink idref="bib73" id="ref89">73</reflink>] ); (<reflink idref="bib2" id="ref90">2</reflink>) heterogeneous preferences (Hastings, Kane, & Staiger, [<reflink idref="bib30" id="ref91">30</reflink>] ); (<reflink idref="bib3" id="ref92">3</reflink>) peer effects (Epple & Romano, [<reflink idref="bib19" id="ref93">19</reflink>] ,[<reflink idref="bib20" id="ref94">20</reflink>] ); (<reflink idref="bib4" id="ref95">4</reflink>) and/or school reputation (Cullen & Rivkin, [<reflink idref="bib13" id="ref96">13</reflink>] ; MacLeod & Urquiola, [<reflink idref="bib55" id="ref97">55</reflink>] ; Rothstein, [<reflink idref="bib68" id="ref98">68</reflink>] ). Empirical results suggest that sorting by performance and socioeconomic status is relatively high, particularly in the tracked secondary sector (Herweijer, [<reflink idref="bib33" id="ref99">33</reflink>] ). To make the implications of such sorting patterns clear, we distinguished between two types of local education markets. First, schools are considered to operate either in a non ‐ or low ‐ competitive education market (NCM) if competition intensity to which the school is exposed is in the lower half of the distribution, or in a high ‐ competitive education market (HCM) if their competition intensity measure is in the upper half. Based on the aforementioned literature of heterogeneous preferences, one can expect schools in NCMs to be relatively similar in terms of academic performance and schools in HCMs to be more academically diverse (i.e. stratified by performance). In conclusion, competition can lead to differences in the distribution of performance levels across schools within a market, regardless of whether or not mean ‐ level differences between local education markets are observed.</p> <hd id="AN0124455297-9">Untitled</hd> <p>There is as yet no consensus on the magnitude of the effect of competition on performance gains (Belfield & Levin, [<reflink idref="bib4" id="ref100">4</reflink>] ; Gibbons et al., [<reflink idref="bib25" id="ref101">25</reflink>] ; Hsieh & Urquiola, [<reflink idref="bib42" id="ref102">42</reflink>] ). With respect to these gains, important potential caveats follow from the literature discussed in Section 2. It is expected that competition will induce (certain) schools to focus on enrolling high ‐ quality peers (Rothstein, [<reflink idref="bib68" id="ref103">68</reflink>] ; Waslander et al., [<reflink idref="bib74" id="ref104">74</reflink>] ), thereby increasing the importance of school reputation (MacLeod & Urquiola, [<reflink idref="bib55" id="ref105">55</reflink>] ) and the existence of product differentiation (Levin, [<reflink idref="bib52" id="ref106">52</reflink>] ). These high ‐ performing schools, through the effort, time and resources spent on the above activities, as well as the costs associated with delivering quality education, could well have lower levels of academic performance. For example, Dijkgraaf, Geest, and van der Gradus ([<reflink idref="bib16" id="ref107">16</reflink>] ) find that competition in Dutch secondary education is negatively related to educational outcomes. Acknowledging the above literature on school reputation and differentiation, the time and resources spent on targeting, attracting, and accommodating high ‐ performing students, we expect this aspect to negatively impact achievement and even offset the potential positive mechanisms attributed to competition (e.g. matching, pressure to perform).</p> <p>The above highlights two important observations. First, competition is likely to affect several dimensions of educational provision, thereby limiting the potential for achievement gains. In addition, the academic offering of schools could also be affected by competition. Waslander et al. ([<reflink idref="bib74" id="ref108">74</reflink>] ) argue that households value a school's reputation and that schools respond either explicitly or implicitly by improving their reputation through both student intake policies (e.g. selection by ability) and educational offerings (e.g. tracking and non ‐ academic services). Hence, the potential for competition to induce academic achievement gains is constrained by this notion that different schools appeal to different households and that schools also compete on other dimensions than merely delivering gains in performance. Therefore we empirically dealt with the notion of ‘segmented competition’ by comparing achievement gains between HCM ‐ and NCM ‐ schools only for students with similar background characteristics who are enrolled in schools that offer similar academic and/or vocational tracks. And second, based on the different emphasis on (preference for) academic and non ‐ academic features of education, competition between schools is expected to heterogeneously impact the academic performance of students who are enrolled in different school types.</p> <p>To conclude, combining insights from the literature on product differentiation and existing empirical results for The Netherlands, we expect positive school ‐ level competition effects for schools that offer the lowest performance tracks, little or no effects for schools that offer the intermediate performance tracks, and negative effects for schools that offer the highest (academic) tracks.</p> <hd id="AN0124455297-10">EMPIRICAL STRATEGY</hd> <hd id="AN0124455297-11">Untitled</hd> <p>In this first step, we focused on the implicit variation of competition in education markets. In the absence of catchment areas, there are no strict boundaries (e.g. school districts, municipality borders) defining the education market of a school. Using the municipality border is arguably inadequate to correctly define the relevant education market of a school. For example, Herweijer ([<reflink idref="bib33" id="ref109">33</reflink>] ) describes such a situation in Dutch secondary education. In some cities, already 25% of all households send their child beyond the municipality border. This is also why Noailly, Vujic, and Aouragh ([<reflink idref="bib63" id="ref110">63</reflink>] ) define school competition markets in Dutch primary education as the number of alternative schools within a fixed radius around a school. Dijkgraaf et al. ([<reflink idref="bib16" id="ref111">16</reflink>] ) use a similar approach for secondary education and base their performance effect of competition on a Herfindahl Index ‐ measure. In sum, we acknowledge this ‘spatial dependency’ of schools in education markets. We therefore developed a measure of competition between schools in geographically ‐ defined education markets and subsequently accounted for differences in the student population within these markets.</p> <p>First, using geographic information systems,[<reflink idref="bib3" id="ref112">3</reflink>] we calculated the number of competing secondary schools within a meaningful radius around a school. Next, to account for the association between urban ‐ and school density, we calculated this number of surrounding schools within 10 kms per 100 cohort members living in that area. We then may write:</p> <olist> <item> Competitionj=total surrounding schools within 10kmtotal of cohort members within 10km,</item> </olist> <p>where (Competitionj) is the competition intensity index for a given school location j. This index has a mean of close to 1, follows a normal distribution, and is presented in Figure [NaN] .</p> <p>Inspired by the work of Figlio and Hart ([<reflink idref="bib24" id="ref113">24</reflink>] ) and Agasisti ([<reflink idref="bib1" id="ref114">1</reflink>] ), we refer to the measure of Equation as a ‘school concentration index’. It allows for competition to come from different nearby school locations, regardless of their municipality. By calculating the number of surrounding schools on a ‘per 100 cohort members'basis, this reduces the association with general urban density effects and focuses on school concentration driven by competition.[<reflink idref="bib4" id="ref115">4</reflink>] In Table [NaN] , we present pairwise correlations between three measures for competition and urban density (bottom row). These are: (<reflink idref="bib1" id="ref116">1</reflink>) distance to closest school; (<reflink idref="bib2" id="ref117">2</reflink>) density of schools within a radius of 10kms; and (<reflink idref="bib3" id="ref118">3</reflink>) our chosen school concentration index (Equation). Furthermore, we present correlational estimates of competition and several micro ‐ level and macro ‐ level variables. We observed that the school concentration index did a better job on some variables (micro ‐ level socio ‐ economic status, school type, and school choice), but not on all (e.g. denomination and macro ‐ level socio ‐ economic status and housing prices).</p> <p>Pairwise correlations between urban trends and the competition measures</p> <p> <ephtml> <table><tr><th align="left">Variables</th><th align="left"><p>Distancepair ‐ wise corr. (p ‐ value)</p></th><th align="left"><p>Densitypair ‐ wise corr. (p ‐ value)</p></th><th align="left"><p>Concentrationpair ‐ wise corr. (p ‐ value)</p></th></tr><tr><td align="left">Micro ‐ level</td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left">SES</td><td align="left">0.051</td><td align="left">0.039</td><td align="left">0.0165</td></tr><tr><td align="left">(scale)</td><td align="left">(0.0000)</td><td align="left">(0.0000)</td><td align="left">(0.0522)</td></tr><tr><td align="left">Ethnicity</td><td align="left">−0.0544</td><td align="left">−0.1612</td><td align="left">−0.0549</td></tr><tr><td align="left">(Dutch=1)</td><td align="left">(0.0000)</td><td align="left">(0.0000)</td><td align="left">(0.0000)</td></tr><tr><td align="left">Household status</td><td align="left">−0.017</td><td align="left">−0.0879</td><td align="left">−0.0344</td></tr><tr><td align="left">(married=1)</td><td align="left">(0.0462)</td><td align="left">(0.0000)</td><td align="left">(0.0001)</td></tr><tr><td align="left">School type</td><td align="left">−0.0701</td><td align="left">−0.1203</td><td align="left">−0.0155</td></tr><tr><td align="left" /><td align="left">(0.0000)</td><td align="left">(0.0000)</td><td align="left">(0.0681)</td></tr><tr><td align="left">School choice</td><td align="left">−0.0258</td><td align="left">−0.1423</td><td align="left">−0.0243</td></tr><tr><td align="left" /><td align="left">(0.0024)</td><td align="left">(0.0000)</td><td align="left">(0.0043)</td></tr><tr><td align="left">denomination</td><td align="left">0.1477</td><td align="left">0.3969</td><td align="left">0.2342</td></tr><tr><td align="left" /><td align="left">(0.0000)</td><td align="left">(0.0000)</td><td align="left">(0.0000)</td></tr><tr><td align="left">Neighbourhood ‐ level</td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left">house price</td><td align="left">−0.0575</td><td align="left">−0.2114</td><td align="left">−0.2146</td></tr><tr><td align="left">(average)</td><td align="left">(0.4300)</td><td align="left">(0.0000)</td><td align="left">(0.0000)</td></tr><tr><td align="left">SES</td><td align="left">−0.0185</td><td align="left">−0.3179</td><td align="left">−0.234</td></tr><tr><td align="left">(index)</td><td align="left">(0.8000)</td><td align="left">(0.0000)</td><td align="left">(0.0000)</td></tr><tr><td align="left">Urbanicity</td><td align="left">0.5168</td><td align="left">0.7967</td><td align="left">0.1926</td></tr><tr><td align="left">(index)</td><td align="left">(0.0000)</td><td align="left">(0.0000)</td><td align="left">(0.0100)</td></tr></table> </ephtml> </p> <hd id="AN0124455297-12">Untitled</hd> <p>Step 2 explains the composite measure of standardised test scores measuring student performance. We focused on the effect of secondary school ‐ level competition on the sorting of students by analysing student performance in standardised exams at the beginning of secondary education (cf. the CITO end ‐ of ‐ primary test on maths and language skills). All students switch schools when making the transition from the primary to the secondary sector. We considered this individual achievement indicator that is relevant for the track(s) in secondary education for which a student is eligible to be an important source of information on Dutch secondary schools. We wrote the functional form of student on standardised exams at the beginning of secondary education as:</p> <p>2 yi∼f(αi;Xki;υi),</p> <p>where yi represents an individual's outcome measure ‘performance’ i∈{1,2,3…,N} on the standardised exam. This measure captures students’ innate ability αi, a vector of exogenous student characteristics that influence the performance level Xki, and the value ‐ added by the primary school υi. As such, yi measures student performance: (<reflink idref="bib1" id="ref119">1</reflink>) after finishing primary education; (<reflink idref="bib2" id="ref120">2</reflink>) after the student sorting process in secondary education; but (<reflink idref="bib3" id="ref121">3</reflink>) before schooling in secondary education. The latter is particularly important, as we initially wanted to exclude the potential value ‐ added by the secondary school, thereby addressing the critique of not being able to distinguish between potential effects of competition on both productive efficiency and student sorting (Gibbons et al., [<reflink idref="bib25" id="ref122">25</reflink>] ).</p> <hd id="AN0124455297-13">Untitled</hd> <p>Our approach allowed for a quasi ‐ experimental estimate of the ‘impact’ of competition between schools on student sorting by performance. We did so by matching students going to school in highly ‐ competitive areas (treatment group (HCM)) with those going to school in non ‐ or low ‐ competitive areas (control group (NCM)). We defined HCM and NCM, respectively, right and left of the median of the distribution of the competition measure. We accounted for a 5% error bound around the median student, so that the competition measure was corrected for potential computational errors.[<reflink idref="bib5" id="ref123">5</reflink>] In order to isolate the role of competition in sorting by performance in Dutch secondary education from potential competition effects on performance gains whilst in secondary school, the analyses here focus on maths and language performance measured at the beginning of secondary education. Hence, any differences observed between HCM and NCM in these measures can be associated with sorting patterns.</p> <p>For causal inference with respect to the role of competition, around the mean ‐ level, αi, Xki, and υi should not differ statistically between HCM and NCM. One can argue that students in HCM are different from those in NCM, violating overall comparability with respect to αi and Xki (see also Gibbons et al., [<reflink idref="bib25" id="ref124">25</reflink>] ). In this respect, we propose Kernel matching estimation techniques to account for differences in the HCM and NCM student population (following Rubin, [<reflink idref="bib69" id="ref125">69</reflink>] ,[<reflink idref="bib70" id="ref126">70</reflink>] ).[<reflink idref="bib6" id="ref127">6</reflink>] We exploited the benefits of Kernel matching with a bandwidth by Epanechnikov approximation. Kernel matching assigns non ‐ zero weights to each individual within a given sub ‐ group. The weights are assigned to the individuals according to the distance within each sub ‐ group of individuals. The distance between individuals in the sub ‐ group is calculated by a propensity score (i.e. the probability that two individuals are similar, based on a set of observed exogenous student ‐ level characteristics). To estimate the score we used a discrete choice Probit model. Kernel matching relies on overlapping characteristics between individuals within a given sub ‐ group (i.e. common support). Each sub ‐ group is specified by a chosen bandwidth. A bandwidth by normal approximation does not trim individuals at the tail of the distribution, as is the case with the default bandwidth by Epanechnikov approximation. A Kernel function k[.] estimates the counterfactual outcome for a treated student as the weighted average treatment effect of untreated students (UTET) (Rubin, [<reflink idref="bib70" id="ref128">70</reflink>] ).</p> <p>Controlling for differences in the student population through Kernel matching gave us the first, basic, model specification that estimates the effects of competition on student sorting by performance levels:</p> <p>3 yi(t=0)=α0+θCompetitionj+∑k=1KγkXki+Ui .</p> <p>Here, the estimate of interest is θ, which is the association of competition with student sorting by performance levels. Note that α0 denotes a constant, & Ui the residual</p> <p>Kernel matching does not account for differences between NCM & HCM in the value added of primary education υi. Thus, in a second model specification, we also controlled for differences between NCM & HCM with respect to the mean level of υi. Here, we proposed to ‘correct’ the performance level of the student by controlling the competition estimate for the mean performance level of the school y¯j.[<reflink idref="bib7" id="ref129">7</reflink>] We also considered the mean performance level of the school as a covariate, as it may capture potential peer effects (see Hastings & Weinstein, [<reflink idref="bib31" id="ref130">31</reflink>] ).</p> <p>4 yi(t=0)=α0+βy¯j+θCompetitionj+∑k=1KγkXki+Ui .</p> <p>In the third model specification, we added a correction for observed differences in the student population with respect to school choice determinants.</p> <p>5 yi(t=0)=α0+βy¯j+θCompetitionj+∑k=1KγkXki+∑c=1CδcDci+Ui,</p> <p>where Dci denotes a vector of c school choice determinants.</p> <p>And, finally, Model 4 considers our most restricted conceptualisation of competition in which we also controlled for supply ‐ driven factors (i.e. school type & denomination). Following the aforementioned literature on product differentiation & local hierarchies, we allowed competition to have a differential relationship with student sorting by school type (i.e. level of vocational/academic track offered). This was done by estimating Model 4 separately for each school type. We then may write for Model 4:</p> <p>6 yi(t=0)=α0+βy¯j+ θtypeCompetitionj+∑k=1KγkXki+∑c=1CδcDci+∑p=1PρpSpj++Ui,</p> <p>where Spj denotes a vector of p school supply covariates (including denomination of the school); & θ<subs>type</subs> the association of competition with student sorting by performance levels for a particular school type (e.g. vocational or academic).</p> <hd id="AN0124455297-14">Untitled</hd> <p>This section estimates performance gains associated with school ‐ level competition, using the first model specification as proposed in Equation & replacing the outcome student performance in grade 7 yi(t=0) measure by student performance in grade 9 yi(t=3). We chose the basic model specification to estimate achievement gains, as it takes a relatively comprehensive approach to competition intensity, allowing for different (demand & supply) mechanisms, whereas the other models estimate the effect of a more restricted concept of competition. We did, however, add results for productive efficiency where prior achievement (grade 7 or yi(t=0)) was added to the basic specification. These results are interpreted as a relationship between competition & achievement in secondary education, net of the differences in both innate capacity & exposure to school quality in primary education across local education markets. In doing so, we aimed to add to the previous literature on controlling for differences in previous value ‐ added by teachers (Sass, Hannaway, Xu, Figlio, & Feng, [<reflink idref="bib71" id="ref131">71</reflink>] ). We then may rewrite Equation as:</p> <p>7 yi(t=3)=α0+α1yi(t=0)+θCompetitionj+∑k=1KγkXki+Ui,</p> <p>To conclude, we also estimated Equation by each school type separately so as to gain insight into how school ‐ level competition related to performance in a context of potential product differentiation (i.e. by academic offering).</p> <hd id="AN0124455297-15">DATA</hd> <p>We used longitudinal data called VOCL99 (Voortgezet Onderwijs Cohort Leerlingen 1999) from students who enrolled in secondary education in grade 7 in the school year 1999–00 in The Netherlands (for an extensive data description, see Kuyper et al., [<reflink idref="bib49" id="ref132">49</reflink>] ). The data consisted of variables such as information on standardised test scores (CITO) for maths & language separately in grade 7 & grade 9; gender; religion/ideology; household information on socioeconomic status & composition; & students’ & parents’ responses to follow ‐ up questionnaires. From a total of 1,144 secondary schools, Statistics Netherlands (CBS) composed a random sample of 246. In total, 126 schools representing 19,391 students participated in VOCL99. The data are only limitedly subject to non ‐ response on our dependent & covariates. Failing to append the data with information on the competition intensity measure, for instance due to school mergers, another 22 schools representing about 5,000 students were dropped from the analysis. Furthermore, controlling for a 5% error bound around the median, another 1,000 students were dropped. The total sample size for evaluating the impact of competition between schools on the sorting of students by performance was therefore equal to (N   =   13,226 students). Of these, about 8,000 in grade 9 evaluated the effects of competition on the productive efficiency.</p> <hd id="AN0124455297-16">Untitled</hd> <p>To match students, we split the distribution of our school concentration index into two samples: control group students at a school in NCM & treatment students at a school in HCM. We used the median of the distribution of the competition measure to specify competitive education markets (HCM) or low ‐ competitive education markets (NCM). A total of 6,524 students attend school in NCM, the control group, & 6,702 HCM, the treatment group. Table [NaN] summarises the descriptive statistics of the dependent variables, test scores in maths & language with respect to grade 7 (N   =   13,226) & grade 9 (N   =   8,375) by control group & treatment group. The standardised tests for maths & language at the beginning of secondary education (CITO) both have a minimum score of 0 & a maximum score of 20. Cronbach's alpha is equal to 0.83, indicating a high reliability of the CITO test. Control students obtained on average 13.33 in maths & in language. Treatment students obtained on average 13.15 in maths & 13.27 in language. Only in the maths results did we observe a difference between control & treatment students of about −0.18 points.</p> <p>T ‐ test of the mean difference between the control group and the treatment group with respect to the outcome variables</p> <p> <ephtml> <table><tr><th align="left">Variable</th><th align="left" /><th align="left">Untreated (1)</th><th align="left">Treated (2)</th><th align="left"><p>Diff (2) ‐ (1)</p></th><th align="left">T ‐ value</th><th align="left">Min</th><th align="left">Max</th></tr><tr><td align="left">Grade 7</td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left">Maths performance</td><td align="left">13,226</td><td align="left">13.33</td><td align="left">13.15</td><td align="left">−0.18</td><td align="left">−2.5649</td><td align="left">0</td><td align="left">20</td></tr><tr><td align="left">Language performance</td><td align="left">13,226</td><td align="left">13.33</td><td align="left">13.27</td><td align="left">−0.06</td><td align="left">−1.0601</td><td align="left">0</td><td align="left">20</td></tr><tr><td align="left">Grade 9</td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left">Maths performance</td><td align="left">8,375</td><td align="left">54.0</td><td align="left">54.9</td><td align="left">0.88</td><td align="left">3.83</td><td align="left">0</td><td align="left">125</td></tr><tr><td align="left">Language performance</td><td align="left">8,534</td><td align="left">53.3</td><td align="left">54.3</td><td align="left">1.01</td><td align="left">4.71</td><td align="left">0</td><td align="left">125</td></tr></table> </ephtml> </p> <p>Greater differences between control & treatment students were found with respect to the test results in grade 9 developed by CITO to measure performance in maths & language. We therefore considered it highly comparable to the CITO exam in grade 7. This test in grade 9 is also valid with a Cronbach's alpha of 0.78. There was a significant correlation between the tests of grade 7 & grade 9. The correlation coefficients with respect to maths were about (ρ   =   0.60; P ‐ value   =   0.0000), & with respect to language about (ρ   =   0.50; P ‐ value   =   0.0000).</p> <p>Table [NaN] presents the descriptive statistics of the student characteristics (before matching) & a list of school & school choice variables by control group (T   =   0) & treatment group (T   =   1) for the total sample of 13,226 students. We observed that both groups were quite similar with respect to their characteristics. There was a male ‐ female ratio close to 1, more than 80% of students were native Dutch, almost 90% had parents who were married & students had on average 2 siblings. 30% reported to be atheist & another 30% to be Catholic. The indicator for socioeconomic status was constructed by GION (Kuyper et al., [<reflink idref="bib49" id="ref133">49</reflink>] ), based on (one of) the parents’ highest education attainment. Six levels follow the International Standard Classification of Education,[<reflink idref="bib8" id="ref134">8</reflink>] namely: (<reflink idref="bib1" id="ref135">1</reflink>) ISCED level 1 primary education; (<reflink idref="bib2" id="ref136">2</reflink>) ISCED level 2 lower secondary education; (<reflink idref="bib3" id="ref137">3</reflink>) ISCED level 3–4 upper secondary education and post ‐ secondary non ‐ tertiary education; (<reflink idref="bib4" id="ref138">4</reflink>) ISCED level 5–6 short ‐ cycle tertiary education or bachelor education; (<reflink idref="bib5" id="ref139">5</reflink>) ISCED level 7 master education; and (<reflink idref="bib6" id="ref140">6</reflink>) ISCED level 8 doctoral degree or equivalent. About 40% of treated/untreated students are assigned to the third category and only a few to the lowest or highest category. We also have indicators for language (see language parent 1/2 ‐ child variables) and cultural differences (see culture parent 1/2 ‐ child variables) between the parents and the child. About 2 per cent of the children had language and cultural differences with their parents.</p> <p>T ‐ test of the mean difference between the control group and the treatment group with respect to the student characteristics</p> <p> <ephtml> <table><tr><th align="left">Variable</th><th align="left">Untreated(1)</th><th align="left">Treated(2)</th><th align="left"><p>Diff</p><p>(2) ‐ (1)</p></th><th align="left">T ‐ value</th><th align="left">Min</th><th align="left">Max</th></tr><tr><td align="left">Gender (male=1)</td><td align="left">0.4697</td><td align="left">0.49</td><td align="left">0.0204</td><td align="left">2.34</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Age</td><td align="left">12.47</td><td align="left">12.46</td><td align="left">−0.01</td><td align="left">−1.52</td><td align="left">10</td><td align="left">14</td></tr><tr><td align="left">Country of origin</td></tr><tr><td align="left">Netherlands</td><td align="left">0.885</td><td align="left">0.8657</td><td align="left">−0.0193</td><td align="left">−3.36</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Morocco</td><td align="left">0.0078</td><td align="left">0.0093</td><td align="left">0.0014</td><td align="left">0.9</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Sur/Ant/Aruba</td><td align="left">0.0156</td><td align="left">0.0275</td><td align="left">0.0118</td><td align="left">4.68</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Turkey</td><td align="left">0.0103</td><td align="left">0.0134</td><td align="left">0.0032</td><td align="left">1.68</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Other</td><td align="left">0.0812</td><td align="left">0.0842</td><td align="left">0.0029</td><td align="left">0.61</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Marital Status</td></tr><tr><td align="left">Married</td><td align="left">0.8981</td><td align="left">0.8868</td><td align="left">−0.0113</td><td align="left">−2.1</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Living together</td><td align="left">0.0282</td><td align="left">0.0331</td><td align="left">0.0049</td><td align="left">1.64</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Never married</td><td align="left">0.0061</td><td align="left">0.0127</td><td align="left">0.0066</td><td align="left">3.9</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Widow</td><td align="left">0.0106</td><td align="left">0.0109</td><td align="left">0.0003</td><td align="left">0.18</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Divorced</td><td align="left">0.057</td><td align="left">0.0566</td><td align="left">−0.0005</td><td align="left">−0.12</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Children in household</td><td align="left">2.5162</td><td align="left">2.6826</td><td align="left">0.1664</td><td align="left">8.45</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Language parent1 ‐ child</td><td align="left">0.0185</td><td align="left">0.0176</td><td align="left">−0.0009</td><td align="left">−0.41</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Language parent2 ‐ child</td><td align="left">0.0184</td><td align="left">0.0182</td><td align="left">−0.0002</td><td align="left">−0.08</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Religion/Ideology</td></tr><tr><td align="left">None</td><td align="left">0.3397</td><td align="left">0.2753</td><td align="left">−0.0644</td><td align="left">−8.04</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Catholic</td><td align="left">0.3225</td><td align="left">0.2062</td><td align="left">−0.1163</td><td align="left">−15.31</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Protestant</td><td align="left">0.1426</td><td align="left">0.1119</td><td align="left">−0.0306</td><td align="left">−5.3</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Reformation</td><td align="left">0.0679</td><td align="left">0.248</td><td align="left">0.1801</td><td align="left">29.2</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Islam</td><td align="left">0.0288</td><td align="left">0.0322</td><td align="left">0.0034</td><td align="left">1.14</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Other</td><td align="left">0.0986</td><td align="left">0.1264</td><td align="left">0.0278</td><td align="left">5.06</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Culture parent1 ‐ child</td><td align="left">0.0222</td><td align="left">0.017</td><td align="left">−0.0052</td><td align="left">−2.16</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Culture parent2 ‐ child</td><td align="left">0.0202</td><td align="left">0.0181</td><td align="left">−0.0022</td><td align="left">−0.91</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Socioeconomic status</td></tr><tr><td align="left">Status 1</td><td align="left">0.0599</td><td align="left">0.0637</td><td align="left">0.0038</td><td align="left">0.9</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Status 2</td><td align="left">0.1275</td><td align="left">0.1247</td><td align="left">−0.0028</td><td align="left">−0.48</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Status 3</td><td align="left">0.4413</td><td align="left">0.4166</td><td align="left">−0.0247</td><td align="left">−2.87</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Status 4</td><td align="left">0.2561</td><td align="left">0.2532</td><td align="left">−0.0029</td><td align="left">−0.39</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Status 5</td><td align="left">0.0967</td><td align="left">0.1227</td><td align="left">0.0259</td><td align="left">4.77</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Status 6</td><td align="left">0.0184</td><td align="left">0.0191</td><td align="left">0.0007</td><td align="left">0.3</td><td align="left">0</td><td align="left">1</td></tr></table> </ephtml> </p> <p>1 Note. Culture (language) parent1/2 ‐ child denotes potential cultural (language) differences between the parent(s) and the child. Socio ‐ economic Status 1 to 6 denotes socioeconomic status ranging from lowest (Socion1) to highest (Socion6).</p> <p>Table [NaN] adds further descriptive statistics on school type and denomination. Here, we found important differences in the composition of the control group and the treatment group. For untreated (treated) students, about 28% (22%) were enrolled in schools offering pre ‐ vocational (vmbo), a further 10% (8%) in pre ‐ university (vwo) and 1% (6%) in general secondary (havo) education. We refer to these types of schools as categorical classes. Most schools in The Netherlands, however, offer a combination of educational tracks in their first year(s) of secondary education, called comprehensive classes. These can be all school ‐ types taken together (vwo ‐ havo ‐ vmbo), pre ‐ university and general secondary education taken together (vwo ‐ havo), or general secondary and pre ‐ vocational education taken together (havo ‐ vmbo). We observed that the ‘vwo ‐ havo'comprehensive school types (40% ‐ 35% of treated ‐ untreated students) and ‘havo ‐ vmbo’ (19% ‐ 21% of treated ‐ untreated students) accommodated many students. Furthermore, a relatively high share of students in HCM was attending Catholic (33%) and Reformation schools (30%). Only a few attended Public (10%) and Protestant schools (15%). In areas with a relatively low school concentration index, Public (37%), Catholic (28%) and Protestant schools (21%) attracted most of the student population.</p> <p>T ‐ test of the mean difference between the control group and the treatment group with respect to the school characteristics</p> <p> <ephtml> <table><tr><th align="left">Variable</th><th align="left">Untreated(1)</th><th align="left">Treated(2)</th><th align="left">Diff (2) ‐ (1)</th><th align="left">T ‐ value</th><th align="left">Min</th><th align="left">Max</th></tr><tr><td align="left">School type</td></tr><tr><td align="left">Vwo</td><td align="left">0.0987</td><td align="left">0.0759</td><td align="left">−0.0228</td><td align="left">−4.64</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">vwohavovmbo</td><td align="left">0.0578</td><td align="left">0.0592</td><td align="left">0.0014</td><td align="left">0.36</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">vwohavo</td><td align="left">0.3466</td><td align="left">0.4009</td><td align="left">0.0544</td><td align="left">6.47</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Havo</td><td align="left">0.0103</td><td align="left">0.06</td><td align="left">0.0497</td><td align="left">15.6</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Havovmbo</td><td align="left">0.2082</td><td align="left">0.1887</td><td align="left">−0.0194</td><td align="left">−2.8</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Vmbo</td><td align="left">0.2785</td><td align="left">0.2152</td><td align="left">−0.0634</td><td align="left">−8.48</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Denomination</td></tr><tr><td align="left">Public</td><td align="left">0.3671</td><td align="left">0.1047</td><td align="left">−0.2624</td><td align="left">−37.5</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Catholic</td><td align="left">0.2761</td><td align="left">0.3261</td><td align="left">0.05</td><td align="left">6.27</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Protestant</td><td align="left">0.2062</td><td align="left">0.1498</td><td align="left">−0.0565</td><td align="left">−8.51</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Reformation</td><td align="left">0.0819</td><td align="left">0.2977</td><td align="left">0.2159</td><td align="left">32.8</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Other</td><td align="left">0.0687</td><td align="left">0.1217</td><td align="left">0.053</td><td align="left">10.4</td><td align="left">0</td><td align="left">1</td></tr></table> </ephtml> </p> <p>2 Notes. Abbrevations used in the table: Pre ‐ university education (vwo), General secondary education (havo), and pre ‐ vocational secondary education (vmbo). In the first two years of secondary education, schools can either place students directly in categorical classrooms (i.e., ‘vmbo’, ‘havo’ or ‘vwo’) or in heterogeneous classroom settings (i.e., ‘vwohavovmbo’, ‘vwohavo’ or ‘havovmbo’). Denomination denotes the denomination of the school. Note that public schools and state schools are synonyms throughout this article.</p> <p>To conclude, Table [NaN] captures some descriptive statistics on household preferences with respect to school choice. In the follow ‐ up questionnaires, parents had to fill in a question about their main reason for chosing their child's secondary school. In both the control group and the treatment group, more than 30% had chosen the secondary school according to their child's wishes. There were major differences between parents of low and high competitive education markets when it came to the denomination of the school. In the treatment group, 27% of the parents answered that it was the main reason for their choice. It was only 11% for those in the control group. In this group, the main reason next to the ‘child's wishes’ seemed to be spread out over the different possible answers.</p> <p>T ‐ test of the mean difference between the control group and the treatment group with respect to the household preferences of school choice</p> <p> <ephtml> <table><tr><th align="left">Variable</th><th align="left">Untreated(1)</th><th align="left">Treated(2)</th><th align="left">Diff (2) ‐ (1)</th><th align="left">T ‐ value</th><th align="left">Min</th><th align="left">Max</th></tr><tr><td align="left">Results of school</td><td align="left">0.1004</td><td align="left">0.0816</td><td align="left">−0.0188</td><td align="left">−3.7585</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Distance to school</td><td align="left">0.0612</td><td align="left">0.0376</td><td align="left">−0.0236</td><td align="left">−6.27</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Denomination of school</td><td align="left">0.1093</td><td align="left">0.2731</td><td align="left">0.1638</td><td align="left">24.42</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Educational choices</td><td align="left">0.1058</td><td align="left">0.073</td><td align="left">−0.0328</td><td align="left">−6.63</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Atmosphere at school</td><td align="left">0.0687</td><td align="left">0.0563</td><td align="left">−0.0124</td><td align="left">−2.95</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Guidance of students</td><td align="left">0.0848</td><td align="left">0.0907</td><td align="left">0.006</td><td align="left">1.21</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Type of first class</td><td align="left">0.049</td><td align="left">0.0254</td><td align="left">−0.0237</td><td align="left">−7.22</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Other sibling in school</td><td align="left">0.0185</td><td align="left">0.0221</td><td align="left">0.0035</td><td align="left">1.44</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Wishes of child</td><td align="left">0.3768</td><td align="left">0.3244</td><td align="left">−0.0524</td><td align="left">−6.32</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Other</td><td align="left">0.0256</td><td align="left">0.016</td><td align="left">−0.0096</td><td align="left">−3.89</td><td align="left">0</td><td align="left">1</td></tr></table> </ephtml> </p> <hd id="AN0124455297-17">Untitled</hd> <p>First, the propensity score values show the likelihood of assignment to HCM (T   =   1) depending on student ‐ level and household ‐ level characteristics, such as gender, age, country of origin, marital status and socioeconomic status of the household.[<reflink idref="bib9" id="ref141">9</reflink>] Second, we were able to check for the assumption of common support using the propensity score values. Figure [NaN] plots a fair overlap in the propensity score values between the control and the treatment group (N   =   13,130). As such, we lose information on about 100 students due to a lack of common support.</p> <p>Table [NaN] summarises the t ‐ test statistics of the difference between the weighted untreated students and treated students with respect to their characteristics after the Kernel matching procedure had been applied. Overall, we observed a good match and that comparability had improved considerably, but still included these observed covariates in the analyses for further robustness.</p> <p>T ‐ test of the mean difference between the treatment group and matched untreated group with respect to the student characteristics</p> <p> <ephtml> <table><tr><th align="left" /><th align="left">Diff.</th><th align="left">T ‐ value</th><th align="left">Min</th><th align="left">Max</th></tr><tr><td align="left">Gender (male=1)</td><td align="left">0.007</td><td align="left">0.8</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Age</td><td align="left">−0.01</td><td align="left">−1.33</td><td align="left">10</td><td align="left">14</td></tr><tr><td align="left">Country of origin</td></tr><tr><td align="left">Netherlands</td><td align="left">−0.0097</td><td align="left">−1.67</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Morocco</td><td align="left">−0.0001</td><td align="left">−0.05</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Sur/Ant/Aruba</td><td align="left">0.0036</td><td align="left">1.29</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Turkey</td><td align="left">0.0004</td><td align="left">0.18</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Other</td><td align="left">0.0059</td><td align="left">1.25</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Marital Status</td></tr><tr><td align="left">Married</td><td align="left">−0.009</td><td align="left">−1.67</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Living together</td><td align="left">0.004</td><td align="left">1.34</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Never married</td><td align="left">0.0016</td><td align="left">0.87</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Widow</td><td align="left">0.0015</td><td align="left">0.89</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Divorced</td><td align="left">0.0019</td><td align="left">0.47</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Children in household</td><td align="left">0.0503</td><td align="left">2.46</td><td align="left">1</td><td align="left">5</td></tr><tr><td align="left">Language parent1 ‐ child</td><td align="left">0.0025</td><td align="left">1.11</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Language parent2 ‐ child</td><td align="left">0.0019</td><td align="left">0.85</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Religion/Ideology</td></tr><tr><td align="left">None</td><td align="left">−0.0055</td><td align="left">−0.71</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Catholic</td><td align="left">0.0024</td><td align="left">0.34</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Protestant</td><td align="left">−0.0004</td><td align="left">−0.08</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Reformation</td><td align="left">−0.0008</td><td align="left">−0.1</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Islam</td><td align="left">0.0018</td><td align="left">0.58</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Other</td><td align="left">0.0025</td><td align="left">0.43</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Culture parent1 ‐ child</td><td align="left">0.0007</td><td align="left">0.3</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Culture parent2 ‐ child</td><td align="left">−0.0006</td><td align="left">−0.25</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Socioeconomic status</td></tr><tr><td align="left">Status 1</td><td align="left">0</td><td align="left">−0.01</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Status 2</td><td align="left">−0.0067</td><td align="left">−1.14</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Status 3</td><td align="left">−0.0144</td><td align="left">−1.67</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Status 4</td><td align="left">−0.0025</td><td align="left">−0.34</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Status 5</td><td align="left">0.0211</td><td align="left">3.88</td><td align="left">0</td><td align="left">1</td></tr><tr><td align="left">Status 6</td><td align="left">0.0025</td><td align="left">1.13</td><td align="left">0</td><td align="left">1</td></tr></table> </ephtml> </p> <p>3 Notes. The T ‐ test presents output from Kernel matching estimation with a bandwidth by Epanechnikov approximation. The total sample counts (N   =   13,130) students.</p> <hd id="AN0124455297-18">ESTIMATION RESULTS</hd> <hd id="AN0124455297-19">Untitled</hd> <p>We estimated four models to evaluate how competition related to the sorting of students by performance. We gradually extended the list of covariates in the four subsequent models. In the first, we controlled for the background variables used in the matching process (e.g. gender, ethnicity, and socioeconomic status of the household). Model 2 added the mean performance level of the school. We included household determinants with respect to school choice (i.e. demand ‐ driven effects) in Model 3. In Model 4, supply ‐ driven factors (i.e. denomination and offering of categorical classrooms) were added and reported the relationship between competition and sorting by performance level by school type.</p> <p>First, we related competition to the sorting of students by performance in maths in Table [NaN] . We reported the standardised estimation coefficients for ease of interpretation of the effect. The standardised estimate of θ̂ in Model 1 is equal to 0.0043 of one standard deviation and is statistically insignificant. We observed that in Model 2 and in Model 3, the standardised estimate of θ̂ remained close to zero and was not significant. Only in Model 4 did we observe medium, negative, and statistically significant results for competition and the sorting of students by performance levels. Overall, when controlling for supply ‐ side factors such as denomination and school type, school concentration was negatively associated with sorting by performance in maths ( ‐ 0.035 s.d.) In the last column of Table [NaN] , we present the standardised sub ‐ estimates of θ̂; each corresponding to the result for competition intensity for a particular school type (vwo, vwo ‐ havo, havo, havo ‐ vmbo, vmbo). We observed that the strongest results for sorting by performance were found in the highest ability school types (up to −0.22 s.d. for havo school type). This indicates that, with higher levels of observed school concentration, school tracks of this type attract students who, on average, perform less well than their counterparts in less competitive areas. This is in line with an explanation whereby competitive pressure leads schools to open up more slots in academic tracks; thereby competing for relatively ‘favourable’ students.</p> <p>Estimates of the relationship between competition intensity and the sorting of students by performance on math upon entry in secondary education, by school type</p> <p> <ephtml> <table><tr><th align="left" /><th align="left">Model 1</th><th align="left">Model 2</th><th align="left">Model 3</th><th align="left">Model 4</th><th align="left">Model 5</th></tr><tr><td align="left">Competition (<p>θ̂</p>)</td><td align="left">0.0043</td><td align="left">−0.0076</td><td align="left">−0.0102</td><td align="left">−0.0349</td><td align="left" /></tr><tr><td align="left" /><td align="left">(0.0100)</td><td align="left">(0.0091)</td><td align="left">(0.0090)</td><td align="left">(0.0083)</td><td align="left" /></tr><tr><td align="left"><p>θ̂</p> by school type:</td></tr><tr><td align="left">Vwo</td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left">−0.0960</td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left">(0.0207)</td></tr><tr><td align="left">vwohavo</td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left">−0.0878</td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left">(0.0112)</td></tr><tr><td align="left">havo</td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left">−0.2180</td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left">(0.1051)</td></tr><tr><td align="left">vwohavovmbo</td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left">0.1260</td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left">(0.1181)</td></tr><tr><td align="left">Havovmbo</td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left">−0.0381</td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left">(0.0200)</td></tr><tr><td align="left">vmbo</td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left">−0.0036</td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left">(0.0184)</td></tr><tr><td align="left">Background Controls</td><td align="left">Yes</td><td align="left">Yes</td><td align="left">Yes</td><td align="left">Yes</td><td align="left">Yes</td></tr><tr><td align="left">School Mean</td><td align="left">No</td><td align="left">Yes</td><td align="left">Yes</td><td align="left">Yes</td><td align="left">Yes</td></tr><tr><td align="left">Demand Factors</td><td align="left">No</td><td align="left">No</td><td align="left">Yes</td><td align="left">Yes</td><td align="left">Yes</td></tr><tr><td align="left">Supply Factors</td><td align="left">No</td><td align="left">No</td><td align="left">No</td><td align="left">Yes</td><td align="left">Yes</td></tr><tr><td align="left">Specification</td><td align="left">Kernel</td><td align="left">Kernel</td><td align="left">Kernel</td><td align="left">Kernel</td><td align="left">Kernel</td></tr><tr><td align="left">Bandwidth</td><td align="left">normal</td><td align="left">normal</td><td align="left">normal</td><td align="left">normal</td><td align="left">normal</td></tr><tr><td align="left">Std.error</td><td align="left">robust S.E.</td><td align="left">robust S.E.</td><td align="left">robust S.E. robust S.E.</td><td align="left">robust S.E.</td></tr><tr><td align="left">Number of obs.</td><td align="left">13,130</td><td align="left">13,130</td><td align="left">13,130</td><td align="left">13,123</td><td align="left" /></tr><tr><td align="left">R ‐ squared</td><td align="left">0.1117</td><td align="left">0.2626</td><td align="left">0.2671</td><td align="left">0.4337</td><td align="left" /></tr></table> </ephtml> </p> <p>4 Notes. Dependent variable in all models is standardised maths performance upon entry in secondary education (grade 7). Robust standard errors between brackets. Star levels denote 1% ‐ significance (***), 5% ‐ significance (**) and 10% ‐ significance (*). The models present output from Kernel matching with bandwidth by Epanechnikov approximation. Abbrevations used: Pre ‐ university education (vwo), General secondary education (havo), and pre ‐ vocational secondary education. In the first two years of secondary education, schools have the discretion to either place students directly in categorical classrooms (i.e. ‘vmbo’, ‘havo’ or ‘vwo’) or in heterogenous classroom settings (i.e. ‘vwohavovmbo’, ‘vwohavo’ or ‘havovmbo’). Model 4 is estimated for all school types together, as well as by school type (5th column). Competion measure is standardised.</p> <p>In what follows, we performed two sensitivity checks. First, we checked whether the estimate of θ̂ was sensitive to the chosen cut ‐ off value of the median student to match students from competitive with non ‐ competitive education markets. We explored the distribution of the estimate of θ̂ (i.e. Model 1) when choosing other cut ‐ off values than the median, for example, the 25 ‐ percentile to the 75 ‐ percentile. We also trimmed 5% around the chosen cut ‐ off value. The estimates are available with the authors upon request. In general, it was observed that taking the cut ‐ off value at 25 per cent yielded somewhat larger estimates, whilst taking it at 75 per cent yielded somewhat smaller estimates. Again, the sign of the estimates was negative for all models except Model 1. We concluded that the estimate of θ̂ was robust to taking other cut ‐ off values. Second, we carried out the same analyses on the effects of competition on student sorting by language performance (Table [NaN] ). The standardised estimate of θ̂ in Model 1, Model 2, and Model 3 was also close to zero, and not significant. Again, in Model 4, we observed medium, negative, and significant results for competition intensity and the sorting of students by language performance levels.[<reflink idref="bib10" id="ref142">10</reflink>] The patterns observed when disaggregating the results by school type were similar to those found for maths in Table [NaN] .</p> <p>Estimates of the relationship between competition intensity and the sorting of students by performance in language upon entry in secondary education, by school type</p> <p> <ephtml> <table><tr><th align="left" /><th align="left">Model 1</th><th align="left">Model 2</th><th align="left">Model 3</th><th align="left">Model 4</th><th align="left">Model 5</th></tr><tr><td align="left">Competition (<p>θ̂</p>)</td><td align="left">0.0171</td><td align="left">−0.0006</td><td align="left">0.0002</td><td align="left">−0.0266</td><td align="left" /></tr><tr><td align="left" /><td align="left">(0.0100)</td><td align="left">(0.0091)</td><td align="left">(0.0091)</td><td align="left">(0.0089)</td><td align="left" /></tr><tr><td align="left"><p>θ̂</p> by school type:</td></tr><tr><td align="left">vwo</td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left">−0.1301</td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left">(0.0265)</td></tr><tr><td align="left">vwohavo</td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left">−0.0770</td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left">(0.0125)</td></tr><tr><td align="left">havo</td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left">−0.2372</td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left">(0.1128)</td></tr><tr><td align="left">vwohavovmbo</td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left">0.1548</td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left">(0.1233)</td></tr><tr><td align="left">Havovmbo</td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left">−0.0799</td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left">(0.0214)</td></tr><tr><td align="left">vmbo</td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left">−0.0157</td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left">(0.0196)</td></tr><tr><td align="left">Background Controls</td><td align="left">Yes</td><td align="left">Yes</td><td align="left">Yes</td><td align="left">Yes</td><td align="left">Yes</td></tr><tr><td align="left">School Mean</td><td align="left">No</td><td align="left">Yes</td><td align="left">Yes</td><td align="left">Yes</td><td align="left">Yes</td></tr><tr><td align="left">Demand Factors</td><td align="left">No</td><td align="left">No</td><td align="left">Yes</td><td align="left">Yes</td><td align="left">Yes</td></tr><tr><td align="left">Supply Factors</td><td align="left">No</td><td align="left">No</td><td align="left">No</td><td align="left">Yes</td><td align="left">Yes</td></tr><tr><td align="left">Specification</td><td align="left">Kernel</td><td align="left">Kernel</td><td align="left">Kernel</td><td align="left">Kernel</td><td align="left">Kernel</td></tr><tr><td align="left">Bandwidth</td><td align="left">normal</td><td align="left">normal</td><td align="left">normal</td><td align="left">normal</td><td align="left">normal</td></tr><tr><td align="left">Std.error</td><td align="left">robust S.E.</td><td align="left">robust S.E.</td><td align="left">robust S.E.</td><td align="left">robust S.E.</td><td align="left">robust S.E.</td></tr><tr><td align="left">Number of obs.</td><td align="left">13,130</td><td align="left">13,130</td><td align="left">13,130</td><td align="left">13,123</td><td align="left" /></tr><tr><td align="left">R ‐ squared</td><td align="left">0.0903</td><td align="left">0.2210</td><td align="left">0.2280</td><td align="left">0.3612</td><td align="left" /></tr></table> </ephtml> </p> <p>5 Notes. Dependent variable in all models is standardised language performance upon entry in secondary education (grade 7). Robust standard errors between brackets. Star levels denote 1% ‐ significance (***), 5% ‐ significance (**) and 10% ‐ significance (*). The models present output from Kernel matching with bandwidth by Epanechnikov approximation. Abbrevations used: Pre ‐ university education (vwo), General secondary education (havo), and pre ‐ vocational secondary education. In the first two years of secondary education, schools can either place students directly in categorical classrooms (i.e. ‘vmbo’, ‘havo’ or ‘vwo’) or in heterogenous classroom settings (i.e. ‘vwohavovmbo’, ‘vwohavo’ or ‘havovmbo’). Model 4 is estimated for all school types together, as well as by school type (5th column). Competion measure is standardized.</p> <p>From our analyses, we concluded that, in Model 1, the sorting of students across schools gave rise to a zero ‐ effect in terms of overall performance. However, in line with Epple and Romano ([<reflink idref="bib20" id="ref143">20</reflink>] ), we observed that the equilibrium outcome was stratified by (innate) ability across school types (or products). Depending on demand ‐ and supply factors, increasing competition induced schools to compete for their target student population in terms of performance levels in maths and language. We also noted that, with more competition, more schools offered places in the higher ‐ ability academic tracks. These results are in line with a context in which these schools go down ‐ market, or converge in terms of performance level to schools offering lower tracks when facing greater competition. Put differently, they target students ‘at the margin’ to ensure sufficient enrolment patterns (see also McMillan, [<reflink idref="bib58" id="ref144">58</reflink>] ). Hence, depending on individual background characteristics and school choice determinants, schools could well resort to supply ‐ driven product differentiation in order to compete for their target population of students.</p> <hd id="AN0124455297-20">Untitled</hd> <p>The full estimation results of Model 1, including the CITO test scores at the beginning of secondary education, are summarised in Tables [NaN] and [NaN] .</p> <p>Estimates of the relationship between competition intensity and performance gains on maths by third year of secondary education, by school type</p> <p> <ephtml> <table><tr><th align="left" /><th align="left">Model 1</th><th align="left">Model 2</th><th align="left">N</th></tr><tr><td align="left">Competition (<p>θ̂)</p></td><td align="left">0.0462 </td><td align="left">0.02444 </td><td align="left">8373</td></tr><tr><td align="left" /><td align="left">(0.0109)</td><td align="left">(0.0088)</td><td align="left" /></tr><tr><td align="left">vwo:</td></tr><tr><td align="left"><p>θ̂</p></td><td align="left">−0.2789 </td><td align="left">−0.2353 </td><td align="left">780</td></tr><tr><td align="left" /><td align="left">(0.0512)</td><td align="left">(0.0450)</td><td align="left" /></tr><tr><td align="left">vwohavo:</td></tr><tr><td align="left"><p>θ̂</p></td><td align="left">0.3061 </td><td align="left">0.0819 </td><td align="left">551</td></tr><tr><td align="left" /><td align="left">(0.1493)</td><td align="left">(0.0726)</td><td align="left" /></tr><tr><td align="left">havo:</td></tr><tr><td align="left"><p>θ̂</p></td><td align="left">−0.3440 </td><td align="left">−0.2589 </td><td align="left">325</td></tr><tr><td align="left" /><td align="left">(0.0775)</td><td align="left">(0.0730)</td><td align="left" /></tr><tr><td align="left">havovmbo:</td></tr><tr><td align="left"><p>θ̂</p></td><td align="left">0.0062</td><td align="left">0.0098</td><td align="left">1,537</td></tr><tr><td align="left" /><td align="left">(0.0201)</td><td align="left">(0.0192)</td><td align="left" /></tr><tr><td align="left">vwohavovmbo:</td></tr><tr><td align="left"><p>θ̂</p></td><td align="left">−0.0027</td><td align="left">0.0305 </td><td align="left">3,444</td></tr><tr><td align="left" /><td align="left">(0.0159)</td><td align="left">(0.0153)</td><td align="left" /></tr><tr><td align="left">vmbo:</td></tr><tr><td align="left"><p>θ̂</p></td><td align="left">0.0410 </td><td align="left">0.0371 </td><td align="left">1,736</td></tr><tr><td align="left" /><td align="left">(0.0139)</td><td align="left">(0.0128)</td><td align="left" /></tr><tr><td align="left">Background Controls</td><td align="left">Yes</td><td align="left">Yes</td><td align="left" /></tr><tr><td align="left">Pre ‐ test</td><td align="left">No</td><td align="left">Yes</td><td align="left" /></tr></table> </ephtml> </p> <p>6 Notes. Dependent variable in all models is standardised maths performance in year 3 of secondary education (grade 9). Robust standard errors between brackets. Star levels denote 1% ‐ significance (***), 5% ‐ significance (**) and 10% ‐ significance (*). The models present output from Kernel matching with bandwidth by Epanechnikov approximation. Abbrevations used: Pre ‐ university education (vwo), General secondary education (havo), and pre ‐ vocational secondary education. In the first two years of secondary education, schools have the discretion to either place students directly in categorical classrooms (i.e., ‘vmbo’, ‘havo’ or ‘vwo’) or in heterogenous classroom settings (i.e., ‘vwohavovmbo’, ‘vwohavo’ or ‘havovmbo’). Competion measure is standardised.</p> <p>Estimates of the relationship between competition intensity and performance gains on language by third year of secondary education, by school type</p> <p> <ephtml> <table><tr><th align="left" /><th align="left">Model 1</th><th align="left">Model 2</th><th align="left">N</th></tr><tr><td align="left">Competition (<p>θ̂)</p></td><td align="left">0.0509 </td><td align="left">0.0332 </td><td align="left">8530</td></tr><tr><td align="left" /><td align="left">(0.0104)</td><td align="left">(0.0093)</td><td align="left" /></tr><tr><td align="left">vwo:</td><td align="left">−0.0650 </td><td align="left">−0.0199</td><td align="left">734</td></tr><tr><td align="left"><p>θ̂</p></td><td align="left">(0.0358)</td><td align="left">(0.0358)</td><td align="left" /></tr><tr><td align="left">vwohavo:</td><td align="left">0.4013 </td><td align="left">0.1812 </td><td align="left">563</td></tr><tr><td align="left"><p>θ̂</p></td><td align="left">(0.0617)</td><td align="left">(0.0583)</td><td align="left" /></tr><tr><td align="left">havo:</td><td align="left">−0.1444</td><td align="left">−0.0755</td><td align="left">329</td></tr><tr><td align="left"><p>θ̂</p></td><td align="left">(0.1024)</td><td align="left">(0.0903)</td><td align="left" /></tr><tr><td align="left">havovmbo:</td><td align="left">0.0770 </td><td align="left">0.0852 </td><td align="left">1,584</td></tr><tr><td align="left"><p>θ̂</p></td><td align="left">(0.0247)</td><td align="left">(0.0248)</td><td align="left" /></tr><tr><td align="left">vwohavovmbo:</td><td align="left">−0.0573 </td><td align="left">−0.0395 </td><td align="left">3,550</td></tr><tr><td align="left"><p>θ̂</p></td><td align="left">(0.0160)</td><td align="left">(0.0155)</td><td align="left" /></tr><tr><td align="left">vmbo:</td><td align="left">0.0900 </td><td align="left">0.0907 </td><td align="left">1,770</td></tr><tr><td align="left"><p>θ̂</p></td><td align="left">(0.0159)</td><td align="left">(0.0154)</td><td align="left" /></tr><tr><td align="left">Background Controls</td><td align="left">Yes</td><td align="left">Yes</td><td align="left" /></tr><tr><td align="left">Pre ‐ test</td><td align="left">No</td><td align="left">Yes</td><td align="left" /></tr></table> </ephtml> </p> <p>7 Notes. Dependent variable in all models is standardised language performance in year 3 of secondary education (grade 9). Robust standard errors between brackets. Star levels denote 1% ‐ significance (***), 5% ‐ significance (**) and 10% ‐ significance (*). The models present output from Kernel matching with bandwidth by Epanechnikov approximation. Abbrevations: Pre ‐ university education (vwo), General secondary education (havo), and pre ‐ vocational secondary education. In the first two years of secondary education, schools can either place students directly in categorical classrooms (i.e. ‘vmbo’, ‘havo’ or ‘vwo’) or in heterogenous classroom settings (i.e. ‘vwohavovmbo’, ‘vwohavo’ or ‘havovmbo’). Competion measure is standardised.</p> <p>First, when considering the results for competition and associated gains in maths achievement (Table [NaN] ), it is observed that competition intensity is positively related to student performance in maths over the academic years. By grade 9, the standardised estimate of θ̂ is equal to 0.0462 significant at 1% ‐ level. Once controlled for the CITO test scores in maths at the beginning of secondary education, the estimate of θ drops to 0.0244 significant at 1% ‐ level. The same analysis with respect to language performance yields similar results (Table [NaN] ). By grade 9, the standardised estimate of θ is equal to 0.0509 significant at 1% ‐ level. Controlling for CITO test scores in language at the beginning of secondary education, the estimate of θ̂ drops to 0.0332 significant at 1% ‐ level. This drop after including end ‐ of ‐ primary/beginning of secondary school achievement is in line with an interpretation where competition contributes similarly to achievement in primary education and competition intensity is correlated across both education sectors. In addition, adding prior achievement, at least partially, captures differences in innate capacity for students across schools in HCM and NCM.</p> <p>In conclusion, unconditional on demand ‐ and supply ‐ driven factors, competition was positively associated with achievement gains in maths and language for the lowest ability and comprehensive tracks. However, it was negatively related in the categorical academic tracks. We compared our findings with Dijkgraaf et al. ([<reflink idref="bib16" id="ref145">16</reflink>] ), who measured competition in The Netherlands by a Herfindahl ‐ Hirschman ‐ Index (HHI) (Hirschman, [<reflink idref="bib37" id="ref146">37</reflink>] ), based on secondary schools located within a distance of 10kms. They found a negative effect for competition across several school quality measures, estimating an OLS regression, and controlling for a series of school ‐ and neighbourhood ‐ level characteristics. They interpreted these seemingly counterintuitive findings as Dutch schools competing through product differentiation on the basis of ‘secondary’ elements, such as sports and music facilities, leaving less time and money for the primary process of teaching. Excluding the 21 largest cities, the results based on a subset of relatively more monopolistic schools in rural areas yielded even stronger negative results for competition, suggesting either a potential non ‐ linear effect and/or important rural/urban differences. Dijkgraaf et al. ([<reflink idref="bib16" id="ref147">16</reflink>] ) only measured competition for schools offering the highest ability tracks, which means that their results are in line with those presented here.</p> <p>Our findings can also be interpreted alongside the results of Noailly et al. ([<reflink idref="bib63" id="ref148">63</reflink>] ) who provide an example for Dutch primary schools. They analysed the effect of competition on student ‐ level performance in standardised exit exams (CITO ‐ tests) using two competition measures based on a 1.5 km radius around the centre of the 4 ‐ digit postcode in which a school was located (i.e. number of alternative schools and an (inverted) Herfindahl index). Controlling for school and neighbourhood characteristics, they found small positive effects for competition, instrumented by the distance of the school zip ‐ code to the town ‐ centre and on achievement. Excluding the most competitive markets (the 4 largest cities) further reduced the effect of competition on achievement, which could imply that schools in less competitive rural areas competed relatively more on other characteristics, such as denomination. Noailly et al. ([<reflink idref="bib63" id="ref149">63</reflink>] ) interpreted these modest effects as being in line with the concept of product differentiation, and argued that schools competed on other (non ‐ academic) activities and/or facilities.</p> <hd id="AN0124455297-21">CONCLUSION AND DISCUSSION</hd> <p>Early ability tracking in the first year(s) of secondary education is an important feature of the Dutch education system. By its very design, this leads to strong patterns of sorting by ability and performance across schools. Early (strict) tracking policies can be detrimental to schooling and labour market outcomes (Borghans, Diris, Smits, & de Vries, [<reflink idref="bib7" id="ref150">7</reflink>] ). Based on our results, we posit that school ‐ level competition, through product differentiation, could further contribute to sorting by performance levels. This can have important policy implications. For example, Hanushek and Wössmann ([<reflink idref="bib28" id="ref151">28</reflink>] ) and Wössmann ([<reflink idref="bib75" id="ref152">75</reflink>] ) demonstrate that a system of early tracking is likely to increase the socioeconomic achievement gap (e.g. possibly through peer effects). For the Netherlands, Herweijer ([<reflink idref="bib35" id="ref153">35</reflink>] ) adds that migrant students are underrepresented in the highest tracks of secondary education. He concludes that the system of early tracking is disproportionately harmful to non ‐ Western immigrant students, thereby undermining equity.</p> <p>One potential policy response to the above observations could be to eliminate, or defer, ability tracking. However, a proper understanding of whether schools, facing competition, will resort to product differentiation is necessary when making predictions about whether or not such policy measures will reduce disproportionate levels of sorting by performance. The results presented in this article argue that, regardless of ability tracking, sorting by performance could persist because of product differentiation in a market in which schools need to compete for students. These findings suggest that the potential for school ‐ level competition to foster academic excellence for students of all performance levels, at least in the current Dutch secondary education system, seems limited. Policy makers should thus look for ways to ensure that competition between schools will be based on the quality of the education offering and not on attracting relatively high ‐ performing, students. As MacLeod and Urquiola ([<reflink idref="bib56" id="ref154">56</reflink>] ) show, allowing schools to select students on the basis of academic performance leads to school reputation becoming excessively important, thereby reducing ability dispersion in schools and lowering skill acquisition. Such a context of explicit selection, either by ability or on other dimensions, fosters local hierarchies within the education system (Waslander et al., [<reflink idref="bib74" id="ref155">74</reflink>] ), which is found to be true for the current situation in Dutch secondary education (Brink & van Bergen, [<reflink idref="bib8" id="ref156">8</reflink>] ). In particular, schools do (i) market certain profiles, (ii) practise a variety of gatekeeping methods and (iii) compete for particular students (Karsten, Ledoux, Roeleveld, Felix, & Elshof, [<reflink idref="bib44" id="ref157">44</reflink>] ), which are all potential factors mitigating the potential for school ‐ level competition to spur gains in academic performance. Policies aiming to improve such gains should thus focus on the demand ‐ side by informing households on the academic quality of schools, but also on the supply ‐ side by limiting the potential for schools to explicitly select solely on the basis of current academic performance.</p> <ref id="AN0124455297-22"> <title>Footnotes</title> <blist> <bibl id="bib1" idref="ref1" type="bt">1</bibl> <bibtext>In 2005, approximately 85% of all primary schools used the CITO Eindtoets Basisonderwijs source: “Van Citotoets naar brugklas en door naar diploma” (CBS, 2012). </bibtext> </blist> <blist> <bibl id="bib2" idref="ref2" type="bt">2</bibl> <bibtext>“BRON_po08_vo09” data set, obtained from the Ministry of Education, Culture and Science. </bibtext> </blist> <blist> <bibl id="bib3" idref="ref4" type="bt">3</bibl> <bibtext>Source: “BRON_po08_vo09” data set, obtained from Ministry of Education, Culture and Science. </bibtext> </blist> <blist> <bibl id="bib4" idref="ref43" type="bt">4</bibl> <bibtext>We only report the results for this measure of competition in this article. The results for the two other measures (distance to nearest competitor and number of competitors within a fixed radius) gave qualitatively similar results and are available upon request. </bibtext> </blist> <blist> <bibl id="bib5" idref="ref30" type="bt">5</bibl> <bibtext>We consider computation errors in this respect unlikely, as we use the exact address of the schools’. However, when especially close to the median, computational errors with respect to the competition measure could bias the results (i.e., students are wrongly assigned to high ‐ competitive or low ‐ competitive education markets). This is not desirable, and should be anticipated. </bibtext> </blist> <blist> <bibl id="bib6" idref="ref5" type="bt">6</bibl> <bibtext>Kernel matching does not account for omitted variable bias. </bibtext> </blist> <blist> <bibl id="bib7" idref="ref129" type="bt">7</bibl> <bibtext>Looking at sorting based on performance at the start of secondary education does not allow us to include an individual measure for the value added at primary education. </bibtext> </blist> <blist> <bibl id="bib8" idref="ref134" type="bt">8</bibl> <bibtext> <ulink href="http://www.uis.unesco.org/Education/Documents/isced-2011-en.pdf">http://www.uis.unesco.org/Education/Documents/isced-2011-en.pdf</ulink> </bibtext> </blist> <blist> <bibl id="bib9" idref="ref62" type="bt">9</bibl> <bibtext>We estimated the propensity score values using a Probit model. 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Groningen: GION. </bibtext> </blist> <blist> <bibl id="bib77" idref="ref55" type="bt">77</bibl> <bibtext>Zijsling, D. H., & van der Werf, M. P. C. (2007). VOCL99 ‐ schoolverlaters VMBO. Beschrijving van het bestand. [Description of the data VOCL99]. Groningen: GION. </bibtext> </blist> </ref> <p>Graph: Distribution school concentratition measure competition. We also constructed two other, more traditional, competition measures: ‘distance to nearest competitor’ (measured as Euclidian distance to nearest other school ‐ site) and ‘school density (measured as the number of secondary schools within 10kms surrounding a school). Our preferred school concentration index, whilst still related, has the lowest correlation with a measure for the degree of urbanicity</p> <p>Graph: Check of the common support assumption</p> <aug> <p>By Sofie Cabus and Ilja Cornelisz</p> </aug>
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  Data: Competition, Student Sorting and Performance Gains in Local Education Markets: The Dutch Secondary Sector
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  Data: <searchLink fieldCode="AR" term="%22Cabus%2C+Sofie%22">Cabus, Sofie</searchLink><br /><searchLink fieldCode="AR" term="%22Cornelisz%2C+Ilja%22">Cornelisz, Ilja</searchLink>
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  Data: <searchLink fieldCode="SO" term="%22European+Journal+of+Education%22"><i>European Journal of Education</i></searchLink>. Sep 2017 52(3):365-386.
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  Data: Wiley-Blackwell. 350 Main Street, Malden, MA 02148. Tel: 800-835-6770; Tel: 781-388-8598; Fax: 781-388-8232; e-mail: cs-journals@wiley.com; Web site: http://www.wiley.com/WileyCDA
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  Data: <searchLink fieldCode="EL" term="%22Secondary+Education%22">Secondary Education</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22Competition%22">Competition</searchLink><br /><searchLink fieldCode="DE" term="%22Secondary+School+Students%22">Secondary School Students</searchLink><br /><searchLink fieldCode="DE" term="%22Academic+Achievement%22">Academic Achievement</searchLink><br /><searchLink fieldCode="DE" term="%22Achievement+Gains%22">Achievement Gains</searchLink><br /><searchLink fieldCode="DE" term="%22Foreign+Countries%22">Foreign Countries</searchLink><br /><searchLink fieldCode="DE" term="%22Measurement+Techniques%22">Measurement Techniques</searchLink><br /><searchLink fieldCode="DE" term="%22Student+Characteristics%22">Student Characteristics</searchLink><br /><searchLink fieldCode="DE" term="%22Family+Characteristics%22">Family Characteristics</searchLink><br /><searchLink fieldCode="DE" term="%22High+Achievement%22">High Achievement</searchLink><br /><searchLink fieldCode="DE" term="%22Enrollment+Trends%22">Enrollment Trends</searchLink>
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  Data: This article empirically examines the implications of competition among Dutch secondary schools: (1) regarding the sorting of students by performance levels in schools at the beginning of secondary education; and (2) regarding performance gains in the secondary school career, controlling for the aforementioned sorting patterns. We used data from about 13,000 students enrolled at 102 school locations in The Netherlands. Using differences in the distribution of competition intensity across local education markets, we applied Kernel estimation techniques to match students from relatively high- to low-competitive markets on the basis of student and household characteristics. Our results indicate that, with increasing competition, relatively more schools target the group of high-achieving students. As a result, schools will arguably have to enrol more "students at the margin" to ensure sufficient enrolment rates. To conclude, we observed that, accounting for sorting patterns, competition was related to small negligible improvements in academic achievement at the bottom of the distribution of student performance within the first three years of secondary education. Furthermore, a negative result for competition was found for categorical academic classrooms settings.
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