metadata: authors: 0: author: Alonso,Juan Diego
1: author: Coupe,Tom
2: author: Olefir,Anna
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docna: 0: docna: Is optimization an opportunity ? an
            assessment of the impact of class size and school size on
            the performance of Ukrainian secondary schools
docty: Policy Research Working Paper
subtopic: Secondary Education,Economics of Education,Educational Sciences,Educational Institutions & Facilities,Educational Populations,Education for Development (superceded),Effective Schools and Teachers,Education For All
teratopic: Education
abstracts: cdata!: Using a rich data set of almost the
            entire population of Ukrainian secondary schools, the
            authors estimate the effect of school size and class size on
            the performance of secondary schools on Ukraine's
            External Independent Test. They find that larger schools
            tend to have somewhat better performance, both in terms of
            test scores and in terms of test participation. The size of
            this effect is relatively small, however, especially in
            rural areas for which the estimates are likely to be more
            clean estimates. Class size is found to be insignificant in
            most specifications and, if significant, of negligible size.
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            assessment of the impact of class size and school size on
            the performance of Ukrainian secondary schools
display_title: Is optimization an opportunity an
            assessment of the impact of class size and school size on
            the performance of Ukrainian secondary schools
listing_relative_url: /research/2011/11/15471196/optimization-opportunity-assessment-impact-class-size-school-size-performance-ukrainian-secondary-schools
topicv3: Teachers Management m1326119 1523,Quality of Education m1326344 491,Education m1327048 470,Secondary Education m1327058 481,Economics of Education m1327511 1540
publishtoextweb_dt: 2011-11-01T00:00:00Z
historic_topic: Education
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model_extractions: WPS5879 Policy Research Working Paper 5879 Is Optimization an Opportunity?

An Assessment of the Impact of Class Size and School Size on the Performance of Ukrainian Secondary Schools _Tom Coupé Anna Olefir Juan Diego Alonso_ The World Bank Europe and Central Asia Region Human Development Sector Unit November 2011
Policy Research Working Paper 5879

# **Abstract**

Using a rich data set of almost the entire population of Ukrainian secondary schools, the authors estimate the effect of school size and class size on the performance of secondary schools on Ukraine’s External Independent Test. They find that larger schools tend to have somewhat better performance, both in terms of test scores and in terms of test participation. The size of this effect is relatively small, however, especially in rural areas for which the estimates are likely to be more clean estimates. Class size is found to be insignificant in most specifications and, if significant, of negligible size.

This paper is a product of the Human Development Sector Unit, Europe and Central Asia Region. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at aolefir@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Is Optimization an Opportunity? An Assessment of the Impact of Class Size and School Size on the Performance of Ukrainian Secondary Schools**

**_Tom Coupé Anna Olefir Juan Diego Alonso_**<sup>**_1_**</sup>

Human Development Sector Unit Europe and Central Asia Regions JEL classification: I28, I29 Key words: Secondary Education, Inputs, Performance, Optimization, Class Size, School Size, Quality of Education

> 1 Tom Coupé, Associate Professor, Kyiv School of Economics (KSE); Senior Economist, Kyiv Economics Institute (KEI), World Bank Consultant; Anna Olefir, Economist, World Bank Consultant, ECA Human Development Sector Unit, Juan Diego Alonso, Education Economist ECA Human Development Sector Unit.
# **I. Introduction**

The substantial positive returns to education for both individuals (e.g. Psacharopoulos and Patrinos, 2004) and countries (e.g. Barro and Lee, 2010) are a fairly established fact in the literature of the economics of education. It comes as no surprise, then, that policy makers and academicians are so interested in understanding the factors that can influence the quantity and quality of education.

While the academic literature on these factors is vast, most of it focuses on developed countries, and while there is some literature on developing countries, only recently have studies using data from countries in Eastern Europe and the Former Soviet Union (henceforth, _transition countries_ ) started to appear. The recent surge in this literature can be explained by the fact that performance measures for these countries have become available, both through the participation of these countries in international assessments of student learning like the Organisation for Economic Cooperation and Development (OECD)‟s Programme for International Assessment (PISA), the Trends in International Mathematics and Science Survey (TIMSS) and Progress in International Reading Literacy Survey (PIRLS), and through the introduction of centralized nation-wide assessments in several transition countries.

In terms of the development of their educational systems, transition countries may be considered to lie somewhere between developed and developing ones. Transition countries typically have had mandatory basic education and enjoy very high levels of school attendance. As a result, so the issue is not how to get children to attend school, as it is in a big part of the developing world. Instead, transition countries face the challenge of how to modernize and reform their educational system so as to provide quality education at an affordable price.

One possible opportunity to realize such quality enhancing reforms might come from taking advantage of the so-called “demographic dividend”, i.e. the sizeable demographic changes that took place in most of the transition countries, especially in the last 20 years. In fact, after the fall of the Soviet Union, transition countries have faced an unprecedented demographic shock, with increasing mortality and emigration, but also with a serious drop in fertility. This negative shock to fertility has translated in an increasingly smaller number of school-aged children, considerably reducing school size and class size over time (Berryman, 2000). In addition, given that this drop 2
in children of school age did not go together with a decline of the number of schools, teachers or classes, student-teacher ratios and the size of schools and classes has decreased substantially. As a consequence, transition countries are now in the situation where they have a disproportionately large number of schools, teachers and classes. And this oversized system does not appear to have led to an improvement in the quality of education.

Many transition governments are now facing the question of what to do with these oversized systems, often characterized by a multitude of very small schools and very small classes within schools. From a budgetary point of view, many governments would like to merge small schools, as the budgetary burden of one big school with many students is typically smaller than the budgetary burden of having a network of many small schools with few students each. Similarly, consolidating classes within schools appears as an attractive option to generate some savings that could then, at least partially, be reinvested in increasing the skills and performance of the remaining schools, classes and teachers, presumably leading to quality improvements in the educational system.

In several transition countries, this consolidation movement is already ongoing<sup>2</sup> . Kuddo (2009) describes the process in Armenia, Kallai and Manui (2004) in Romania, Herrmann (2005) in Hungary, the World Bank (2010) in Bulgaria, McGuinness et al (2001) in Estonia, Hazans (2010) in Latvia, and Berdashkevich and Vlasov (2010) in Russia.

The Government of Ukraine is progressively coming to the understanding that school network optimization should be a key issue on any education reform agenda in the coming years in Ukraine<sup>3</sup> . Optimization of the school network is also among the key steps for reforms in the

> 2 Throughout this document, the terms “optimization”, “consolidation” and “rationalization” are used interchangeably. In all cases, they refer to the territorial reorganization of the school network in a way that could better use the available resources in the system maximizing the installed capacity of current institutions. Since the system is overly underutilized, the optimization/consolidation/rationalization of the school network would entail the closing of classes and schools and the merging/reallocation of students in those classes and schools to the best available option within the nearby institution. This may also require some degree of transportation of students.

> 3 The dialogue on the optimization of the school network in the framework of Bank-supported „Equal Access to Quality Education‟ lending project started to materialize in 2007 when the line Ministry defined the pilot oblasts (Order No571 of August 16, 2007). Since then the project lead to several successful school closures in selected six pilot rural districts - seven schools were closed and eight schools stopped functioning without obtaining official status of closed institutions. Of course, optimization activities were limited to a few pilots, thus its impact in the overall education system is negligible. Nevertheless, close to its end the project supported a number of important activities that created basic conditions for further consolidation in pilots in the near future through necessary investments like school buses, school labs and textbooks for hub schools, training of school directors and teachers

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education sector according to the Presidential Economic Reforms Program for 2010-2014 „Prosperous society, competitive economy, effective government‟<sup>4</sup> . Also the „launch of optimization‟ of the school network is envisaged by the Ukraine‟s Budget Declaration for 2011 which was approved on April 19, 2010. Schools are planned to be closed if they:

- have less than 10 students and only offer grades 1-4 (level I schools);

- have less than 40 students and only offer grades 1-9 (level I-II schools);

- have less than 100 students and offer all grades (1-11/12, level I-III schools)<sup>5</sup> .

School size is thus used as the key decision criterion to close schools. Given that pupils of closed schools will be reallocated to other schools, the remaining schools will see an increase in size and most likely will have the size of their classes increase. Also the Budget Declaration 2011 set to revise the school norms that influence the amount and type of staff to be hired.

In this paper, we attempt to study what the impact of school size and class size are on the performance of schools in Ukraine, using data on educational performance from Ukraine‟s Independent External Test and data on educational inputs from the Ukrainian Ministry of Education, Youth, Sports and Science. The paper is intended as a key input in the discussions around the optimization or consolidation of the network of schools in Ukraine that has been ongoing for some time now.

In Section II, we first review the academic literature on the determinants of educational performance with a particular emphasis on the evidence that links class size and school size to educational outcomes. Section III portrays a picture of Ukraine‟s educational system, again with an emphasis on size of schools and classes. Section IV provides a detailed description of the data used in this study and how the database was assembled. It is the core of the paper and presents our estimates of class size and school size effects within the „educational production functions‟ of Ukraine. Section V, finally, summarizes the main messages and policy conclusions from this empirical study.

> and stimulated optimization discussions and work in non-pilots. While such activities created conditions for modernization of the education, the larger, more comprehensive reform and completion of the consolidation exercise remains to be implemented.

> 4 However, there are still signs of a push-back from the Government‟s original initiative due to fierce local opposition to school closures.

> 5 The system was undergoing transformation to 12-years of schooling (with experiment already in place in some schools) but in mid-2010 the decision was taken to return to the system of 11-years of full secondary education.

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# **II. Literature Review**

In this section, we start by providing a short overview of the findings of the literature on school size and class size effects for both developed and developing countries. Then we zoom in on _transition countries_ , first reviewing those cross-country studies that include transition countries, and after that focusing on studies that use data for specific transition countries.

II.1 The evidence from developed and developing countries There are several reviews of the literature on the determinants of educational performance, both internationally (Hanushek & Woessman, 2010) and focusing on developing countries (Glewwe (2002) and Glewwe & Kremer (2005))<sup>6</sup> . Some of these reviews have focused specifically on the effects of school size and class size. Ahn and Brewer (2009, p.426) for example summarize the channels through which **class size** can matter as follows:

- teachers report less stress and dissatisfaction with working conditions

- teachers may have more time for individual attention

- student motivation may increase leading to better learning

- behavioral and class management issues are less frequent

- achievement scores in grades K-3 improves for students exposed to classes of 17 or less

- achievement gains increase with longer exposure to small classes in grades K-3

- achievement gains are seen for historically underserved and disadvantaged student populations in grades K-3

Reviewing studies for OECD countries, Vignoles et al (2000) conclude that:

1. The impact of class size is mostly insignificant, and where it is significant, the effect is too small to justify expenditures for class size reduction.

2. Interaction effects of class size with other factors (students‟ abilities, school type, teachers‟ actions) have been found to be significant suggesting that class size can affect specific groups of students.

> 6 Two general messages emerge clearly from these reviews. The first one is that methodologically, it is very hard to obtain pure unbiased estimates of the impact of specific determinants on education quality; most studies, including ours, are plagued by issues like selection effects and endogeneity, and experimental studies are rare. The second is that the vast amount of studies on inputs gives a mixed picture, with many studies showing an impact but also many studies finding insignificant effects.

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In line with this, Lazear (1999) shows that smaller classes substitute for better discipline – more specific, students of Catholic schools have better school achievements in larger classes. Babcock and Betts (2009) demonstrate that low-effort students lose more from class size increases as they require more attention of their teachers. Wößmann and West (2002), using a sample of 18 developed countries, find that for most countries class size has an insignificant impact on student performance. However, in Iceland and Greece reduced class size does seem to positively influence TiMSS scores, which they explain by the lower quality of teachers in these countries – teachers there have relatively lower salaries and qualifications.

The arguments in favor of **school size** are similar to those in favor of small classes – smaller schools are more „personalized‟, can have more „adaptive‟ pedagogy and will involve parents more. On the other hand, bigger schools could exploit economies of scale and hence provide better quality for a given level of inputs.

Garrett et al (2004) provide an extensive review of school size literature based on the United States (US) and the United Kingdom (UK) data. Their review suggests an inverted-U relation between school size and student exam scores, though larger schools are typically found to be more cost-efficient. They also point out that teacher and student perceptions of school climate decline<sup>7</sup> and some kinds of violent behavior<sup>8</sup> may increase with school size.

More recently, focusing on the US and Canada, Leithwood and Jantzi (2009) conclude that smaller schools mostly benefit younger students and those with a disadvantaged social and economic background. They state that “elementary schools with large proportions of such students should be limited in size to not more than about 300 students; those serving economically and socially heterogeneous or relatively advantaged students should be limited in size to about 500 students. Secondary schools serving exclusively or largely diverse and/or disadvantaged students should be limited in size to about 600 students or fewer, while those secondary schools serving economically and socially heterogeneous or relatively advantaged students should be limited in size to about 1,000 students (p.1).”

> 7 E.g. parental involvement into school matters decline with school size – Walsh (2010).

> 8 For example, Leung and Ferris (2008) use Canadian data to show that that a student attending a school with more than 2000 students is 22 percent more likely to engage in an act of serious violence.

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Consistent with this, Berry and West (2005), using US data, find a negative effect on future earnings of both a higher school size and a higher pupil-teacher ratio.

The abovementioned studies focus on the estimation of educational production functions where educational performance is the variable to be explained. Other studies estimate **educational cost functions** , in which educational performance is used as an explanatory variable. Studies that use this approach tend to find that _existing schools are smaller than optimal_ (Kenny 1982, Smet 2001, Stiefel _et al._ 2009). But also among these studies there is no clear consensus on the optimal school size. For example, a review of US-based studies by Andrews _et al._ (2002) suggests that 500-600 students may be an optimal size, although there is no consistent evidence of either increasing or decreasing returns to scale. As far as **developing countries** are concerned, Hanusek (1995) summarizes the literature on the effect of class size in developing countries as follows: “The evidence provides no support for policies to reduce class size. Of the thirty studies investigating teacher-pupil ratios, only eight find statistically significant results supporting smaller classes; an equal number are significant but have the opposite sign; and almost half are statistically insignificant. These findings qualitatively duplicate those in the U.S. studies, but are particularly interesting here. Class sizes in the developing-country studies are considerably more varied than those in the U.S. studies and thus pertain to a wider set of environments, providing even stronger evidence that the enthusiasm for policies to reduce class size is misplaced (p.231)”. More recent studies confirm the mixed evidence: Urquiola (2006) finds a negative effect of class size on student performance in Bolivia, while Niaz Asadullah (2005) finds the opposite for Bangladesh. And in a recent review, Hanusek and Woessman (2007, p.66) conclude that “The lack of substantial resource effects in general, and class-size effects in particular, has been found across the developing world, including Africa (...), Latin America (...) and East Asia (...)”. There are only few studies that focus on school size in developing countries. Duflo et al (2009) included school size as one of the explanatory variables into an educational production function for Kenyan schools, and find in some specifications a small negative effect. Liu et al (2009) estimate the effect of a primary school merger policy conducted in rural China. Within this policy about 25,000 rural primary schools a year were closed between 2001 and 2005. They conclude that mergers were beneficial for the school performance of older students (4<sup>th</sup> grade) and worsened the results of younger (1<sup>st</sup> grade) students.

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One study studies the effect of school size on student performance using TiMMS data for both developed and developing countries: Schütz (2006) finds significant size effects for 11 out of 51 countries, 8 out of these 11 are developing countries. Most of these significant effects are positive, suggesting that, if there is a relationship between size and performance, bigger schools appear to be typically better.

# II.2 _The evidence from transition countries_<sup>_9_</sup>

The literature on schools in transition countries is much less developed than the literature on either schools in developed countries or schools in developing countries. This paper is indeed the first that tries to summarize the existing literature on schools in transition countries. We divide what follows into two parts: we first focus on the cross-country studies that include transition countries. Next, we focus on single-country studies.

# _a. Cross-country studies_

There is a number of studies that do include data from transition countries, even though they do not focus on transition countries or have specific conclusions based on the estimations they obtain for transition countries.

Hanushek and Luque (2002) and Hanushek (2003), reviewing a hundred production function estimates covering 37 developed and developing countries<sup>10</sup> , state that there is no consistent evidence that more school resources and better teacher quality lead to better test results, since in the majority of studies these variables are found to be insignificant. Despite this, studies for developing countries find some positive relationship in a greater share of cases<sup>11</sup> (possibly because the initial level of education spending matters). Class size is most often found to be insignificant, but for transition countries, if significant typically positive. These authors

> 9 Table A1 and A2 in the appendix summarize the empirical findings of education-relevant factors in transition countries, and in developed and developing countries.

> 10 Among them eight transition economies: Hungary, Latvia, Lithuania, Poland, Slovak Republic, Czech Republic, Romania and the Russian Federation.

> 11 In another review article, Heyneman and Loxley (1983) suggest that school and teacher quality matters more for lower-income countries than for high-income ones. At the same time, family background matters for these countries less.

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recommend that rather than focusing on inputs, the focus should shift to other policies, including giving right incentives for teachers, and increasing school competition.

The importance of incentives is confirmed by a study of Woessman (2003) who estimated an education production function based on student-level data for 260 000 students from 39 developed and developing countries<sup>12</sup> . He finds that school autonomy (teacher incentives) and centrally controlled examinations (student incentives) do positively and significantly influence educational performance. He does not consider the school size variable, however, while _higher class size has a positive effect on education outcomes._ There is one cross country study that focuses on transition countries. Ammermuller et al (2003) estimate an education production function for seven Eastern European countries (excluding Russia) using the TiMMS 2003 wave. Their study finds that _class size has a positive influence on test scores, only if one does not control for selection effects_ . Once selection effects are controlled for the coefficient of class size becomes insignificant. Other included school characteristics, such as shortage of materials and measures of teacher and school autonomy were also found to be insignificant in most cases.

# _b. Single-country studies_<sup>_13_</sup>

Single transition countries studies so far focus on the Central European countries with, as far as we could find, no evidence being available about countries which belong to the Commonwealth of Independent States (CIS).

Three studies use Polish data to study the determinants of educational performance. Herczynski and Herbst (2005) find _a small positive effect of class size_ . They also find that increased school choice improves achievement but only up to a certain threshold, after which the opposite effect takes place. Bukowska and Siwińska-Gorzelak (2011) find _a significantly positive effect of school size_ in almost all their specifications. They also find a positive influence of school competition (and accordingly a negative effect of the Herfindahl index) on students‟ test scores.

> 12 This country included the same eight transition countries as the previous ones – the countries for which TIMSS data were available.

> 13 The few studies on Ukraine are covered in the next section which focuses on the educational system in Ukraine

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Finally, Jakubovsky and Sakowski (2006) find a small positive effect of school size and an inverse u-shaped effect of class size.

Kallai and Maniu (2004) estimate educational production functions for Romania. They found a _positive effect of school size but no effect of class size on students’ test scores_ . Porta (2011) using PISA data for Romania also finds that the _smallest schools (first quintile) perform less well than bigger schools_ , but that the size of this effect is small and significant only for reading scores. A similar study for Serbia (MacDonald et al, 2009) found similar _small but significant effects for reading, math and science scores_ . Hermann (2004b) finds a negative effect of primary school size on the likelihood to entering a better secondary school in Hungary.

Summarizing, the large literature on the effects of class size and school size suggest that while class and school size might have an effect, these effects are unlikely to be large. For transition countries, school size, however, appears to be more significant than class size as a determinant of educational performance and, increasing school size appears to be, if any, beneficial for educational performance. At the same time, the literature also suggests that effects vary from one country to another, pointing to the need for more country-specific studies.

# **III. The Educational System of Ukraine - Some Background**

In Ukraine the state is the main provider of education services, at all levels including general secondary education<sup>14</sup> (GSE). Public schools constitute 99 percent of general secondary institutions educating more than 99.5 percent of students. According to the data of the State Statistics Service of Ukraine the school network in the 2009/2010 school year consisted of 20.368 institutions: 2.177 level I schools (grades 1-4); 5.397 level I-II schools (grades 1-9); 12.312 level I-III schools (grades 1-12)<sup>15</sup> ; 82 level II-III schools; 389 special schools for children with disabilities (boarding schools) and 11 schools of social rehabilitation. Schools for „talented‟ students include 588 gymnasiums 386 lyceums 46 collegiums as well as the so called „specialized‟ schools with more in-depth training in particular subjects.

> 14 In Ukraine general secondary education encompasses primary and secondary education.

> 15 Including gymnasiums, lyceums and collegiums.

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Consolidating the network of general secondary education (GSE) schools has become an ever urging issue in Ukraine considering the demographic and financial situation in the country. Due to the demographic crisis the number of students in Ukrainian schools fell by 40 percent since independence while the number of schools only fell by 7 percent and the number of teachers by only 4 percent<sup>16</sup> . As a consequence, Ukraine is maintaining a large network of small schools that have become smaller and smaller because of the severe drop in birth rates: 30 percent of level I schools have less than 10 students 21 percent of level I-II schools - less than 40 students; 17 percent of level I-III schools - less than 100 students<sup>17</sup> . Overall 19.2 percent of schools are small as defined above and its overwhelming majority is located in rural areas. As a result budget resources while increasing over time mainly support the large network of institutions rather than being directed towards quality-enhancing inputs<sup>18</sup> .

**_Figure 1: Trends in number of students teachers and schools in GSE in Ukraine 1990-2010_**

<!-- Start of picture text --> 120<br>110<br>100<br>90<br>80<br>70<br>60<br>50<br>schools teachers students<br>Index, 1990 = 100<br>1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010<br><!-- End of picture text --> 16 Around 510 thousand teachers work in the sector with 4.2 million students (compared to 537 thousand teachers and 7.1 million students in 1990/1991 school year).

17 World Bank calculations based on a school-level database compiled on the basis of information provided by each of the oblasts and related jurisdictions for the 2009/2010 school year.

18 See for details the Ukraine Public Finance Review (phase II) in FY 2007-08. Currently education sector expenditures account for almost a quarter of consolidated budget (24.8 percent in 2010) and 7.1 percent of GDP. In 2010, expenditures from the consolidated budget for education reached UAH 77.9 billion - a ten-time increase over the 2000 level. This increase exceeded the growth rate of the nominal amount of expenditures of the consolidated budget for these years which multiplied 6.5 times. The bulk of the consolidated budget is earmarked for salaries and utilities which are mainly intended to maintain budgetary institutions and thus crowd out other expenditures. At the same time wages in education remain lower than in many other sectors of the economy including manufacturing, transport, communications, financial services, retailing, etc. In Bulgaria, for example, resources saved thanks to consolidation of schools allowed to increase wages in the education sector by 46 percent between 2006 and 2008. Efficiency gains allowed also allocation of more resources for capital investment within the sector (http://www.worldbank.bg/WBSITE/EXTERNAL/COUNTRIES/ECAEXT/BULGARIAEXTN/0,,contentMDK:226 <u>99182~menuPK:305444~pagePK:2865066~piPK:2865079~theSitePK:305439,00.html).</u> 11
As a result of demographic decline the average school size dropped by one-third from 326.8 students per school back in 1990/1991 to 211.8 in 2010/2011 school year. Interestingly, the slump was most dramatic in urban areas where school size almost halved over the last two decades compared to a 27 percent decline in rural schools. While in 1990/1991 urban schools were about 5 times larger than rural schools, this ratio has decreased to about 4.

Class-size has also been steadily decreasing and reached 18.1 students per class (23.2 – in urban areas and 12.5 – in rural areas)<sup>19</sup> .

In this paper, we investigate school-size and class-size effects on school performance in Ukraine using schools‟ graduates in Ukraine‟s External Independent Test (EIT)<sup>20</sup> . It is important to note that this test only covers part of the graduates of secondary schools.

- The EIT exams are only taken by upper secondary education graduates (grades 11-12), so we miss around 40 percent of lower secondary school graduates in urban areas and almost 50 percent in rural areas (see table 1). Most of them leave for vocational schools as an ultimate goal or as the transit route to the higher education institutions and thus omit the EIT exams. The share of students leaving after the 9<sup>th</sup> grade significantly increased over the last three years which is likely to be the combination of EIT effect and expected enforcement of the three year study in the upper secondary school that was envisaged until mid-2010. Thus, parents and students tried to avoid an extra year in the secondary school and to profit from the opportunity to get into the HEIs through the vocational schools (in some cases – with direct admission to the second or third year of study).

**_Table 1: Number of students that continue study in upper secondary daily schools_**

|**Beginning of**<br>**the school**<br>**year**|9<sup>th</sup>grade<br>graduates|**Total **<br>of them<br>- 10-<br>graders|percent of<br>students<br>continuing<br>study in<br>USS|9<sup>th</sup>grade<br>graduates|**Urban area**<br>of them<br>- 10-<br>graders|**s**<br>percent of<br>students<br>continuing<br>study in<br>USS|9<sup>th</sup>grade<br>graduates|**Rural area**<br>of them<br>- 10-<br>graders|**s**<br>percent of<br>students<br>continuing<br>study in<br>USS|
|---|---|---|---|---|---|---|---|---|---|
|2008/2009|538,689|352,473|65.4|358,120|246,176|68.7|180,569|105,297|58.9|
|2009/2010|311,247|195,319|62.8|167,379|115,096|68.8|143,868|80,223|55.8|

19 The Law of Ukraine on General Secondary Education (Article 14) limits the class size to a maximum of 30 students and when there are less than 5 students in the schools in rural areas the individual training should apply to ensure quality. Classes may be split into groups for teaching particular subjects. Number of students in special schools (boarding schools) is defined by the Ministry of education and science, youth and sports of Ukraine by agreement with the Ministry of Health of Ukraine and the Ministry of Finance.

20 This test became the key basis for entrance to higher education institutions in the country since 2008.

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|2010/2011|559,477|31,7099|56.7|37,1977|22,2072|59.7|187,500|95,027|50.7|
|---|---|---|---|---|---|---|---|---|---|
|Average for<br>three-year<br>period|-|-|61.4|-|-|65.0|-|-|54.8|

Source: State Statistics Service of Ukraine statistics bulletins on general secondary institutions in the relevant years.

- The EIT exams are only taken by those students who are interested in pursuing studies at the university level. For example, in 2009 84 percent of graduates participated in EIT in Ukrainian language and literature and in 2010 – 78 percent. A smaller number of students participate in the EIT in Ukrainian history, math and English (table 2).

**_Table 2: Participation of Ukrainian schools graduates in EIT in 2009-2010_**

|**School**<br>**Years**|**Upper**<br>**secondary**<br>**education**<br>**graduates**<br>**(grades**<br>**11-12)**|**Participants**<br>**of EIT**<br>**(Ukrainian**<br>**language**<br>**and**<br>**literature)**|**Share,**<br>**% of**<br>**graduates**|**Participants**<br>**of EIT in**<br>**(history of**<br>**Ukraine)**|**Share,**<br>**%**|**Participants**<br>**of EIT in**<br>**(Math)**|**Share,**<br>**%**|**Participants**<br>**of EIT in**<br>**(English)**|**Share,**<br>**%**|
|---|---|---|---|---|---|---|---|---|---|
|2009|391,257|329,839|84.0|215,080|55.0|175,493|44.9|70,315|18.0|
|2010|363,751|284,550|78.0|133,549|34.1|183,682|46.9|46,678|11.9|

Source: based on State Statistics Service of Ukraine statistics bulletins on general secondary institutions in the relevant years and official EITs reports of the Ukrainian Centre for Education Quality Monitoring.

- EIT is the main but not the only way for entering the higher education system. According to the Ministry of Education and Science of Ukraine in 2008 overall 91.2% of students were admitted to the higher education institutions of ІІІ-ІV level of accreditation on the basis of the EIT certificates<sup>21</sup> .

So far there has been little analysis of the EIT data. Besides the simple descriptive statistics in the annual EIT report, there are three studies that use EIT data. Kovtunets et al (undated) provide some analysis of whether the EIT exam results predict performance during the first year at university. Muravyev and Talavera (2010) use the EIT to see how an announced (but not implemented) language policy change has affected the subject choice and performance of students at minority language schools. The closest to the current paper is Coupé et al (2010) who use a sample of 300 schools to link EIT scores to a wide set of input variables. They find a

> 21 Analytical note on results of the admission campaign in 2008 and major tasks for the organization of the admission process in 2009 (Annex to the decision of the board of the Ministry of Education and Science of Ukraine of 31.10.2008 No 12/2-4). Some of the tests were not developed in 2008 therefore the exams were conducted. For example, tests in foreign languages – English, German, French and Spanish languages – were introduced in 2009. Other changes encompassed, for example, wider choice for participants (up to 5 subjects instead of only up to 3 in 2008) with reduced number of available subjects for testing (8 disciplines instead of 11).

13
positive effect of school size and no effect of class size. The current paper extends that analysis by drawing on a much bigger sample of thousands of Ukrainian schools. The size of the current dataset not only provides for more precise estimates but also allows for the analysis of more precise questions, like an analysis by gender or by type of settlement. In addition, the current dataset allows us to analyze the Ukrainian plan to close schools with less than 100 students.

# **IV. Data and Analysis**

In this paper, we use several datasets which were matched and combined into one comprehensive dataset. From the Ministry of Education, we obtained data, for all Ukrainian schools, on the total number of students, the number of students by grade, the number of classes by grade and the total number of teachers and staff.

Data about performance on the EIT were obtained from the yearly public data files, posted on the EIT site, which provide, for each school, the distribution of students‟ scores over 10 intervals. In addition, from the Ukrainian Centre for Education Quality Monitoring we obtained mean and median scores data and information about the gender and the language choice of students<sup>22</sup> .

A more detailed description of these sources and the matching process can be found in the appendix A1.

## _a. Descriptive Statistics for 2010_<sup>_23_</sup>

For 11683 Ukrainian schools we have information on both 2010 EIT test scores (from the EIT database) and information on input variables (from the Ministry of Education).

Given that our main variables of interest, school size and class size, but also other input variables are very different depending on whether or not the school is located in an urban or rural area, we provide the descriptive statistics for rural and urban schools separately.

> 22 The correspondence between those two sources of data was high but not perfect. For a few schools, we had no mean scores and for somewhat more schools the total number of students according to the two databases was not equal, though such deviations were typically very small. One possible explanation for these differences is that the database of the Ministry‟s EIT Center is updated, f.e. correcting mistakes or including the results of appeals. 23 The descriptive statistics for 2008 and 2009 give a qualitatively similar picture. Note that in this section we will only look at differences in means between groups, delaying the question of significance to the regression analysis.

14
For the descriptive statistics, we also focus on the most common type of schools, the 10361 „ordinary‟ schools<sup>24</sup> , to avoid mixing the effect of size and school type.

We further restrict our sample to those ordinary schools for which we have a complete set of „credible‟ information, that is, they have scores on the Ukrainian exam, do have teachers and students, have a student-teacher ratio less than 50 and a class size less than 35<sup>25</sup> .

To illustrate the effect of school size and class size we divide the samples of rural and urban schools, into four intervals, each interval having approximately about a quarter of the observations. School size is measured by the total number of students at the school, class size is measured by the number of students in the final grade divided by the number of final grade classes (for a vast majority of schools this is the 11<sup>th</sup> grade, for some it is the 12<sup>th</sup> grade).

We use several indicators of school performance

- the mean score

- the median score

- the percentage of students scoring above 173

- the percentage of students scoring above 150

- the percentage of students score below 135.5

- we also compute a „student participation ratio‟, that is, for those schools which have students that take the exam on a specific subject, we compute the ratio of students who take the exam divided by the total number of students in the highest grade<sup>26</sup> .

We also provide summary statistics for the explanatory variables we will use. We have two more measures of school inputs.

- Student-teacher ratio – the total number of students in the school divided by the total number of teachers in the school (these numbers are based on headcounts, not full time equivalents).

> 24 We do exclude „ordinary‟ evening schools. For the regression analysis below, however, we do include all types of schools, controlling for differences through type-specific dummies. 25  We lose about 5 % of the schools by doing this, mainly rural schools.

> 26 We have this indicator for those schools that we were able to match to the MoE database.  For some schools, we clearly have unrealistic participation ratios. We keep them in the sample here but will exclude these schools in further analysis – see below for details.

15
- Student-staff ratio - the total number of students in the school divided by the total number of teachers and non-teaching staff in the school (these numbers are based on headcounts, not full time equivalents).

We also have two measures of the group composition of the exam takers of each school.

- Language – the percentage of EIT exams (other than the Ukrainian exam) taken in Ukrainian. Note that this reflects the language choice of the students taking the test and hence can differ from the language choice of the whole class.

- Gender Composition – the share of boys among those taking the EIT exam. As not all students take the exam, this can differ from the share of boys in the class.

And we have two measures of the economic situation in the area (rayon) where the school is located.

- The unemployment rate at the end of 2009.

- The average wage at the end of 2009.

Finally, we have one measure at the level of the village where the school is located, that control for the possibility that bigger villages can have both bigger schools (because they have a bigger population) and better schools (because better teachers or „better‟ parents might move to bigger villages with more amenities).

- The population in the village where the school is located based on the 2001 population survey. For the big cities, we typically have population data for the district where the school is located.

Descriptive statistics are provided in Tables 3a (rural schools) and 3b (urban schools).

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**_Table 3a. Descriptive statistics for rural schools, by school size quartiles_**

|Rural Schools|F|irst Quartil|e|Se|cond Quart|ile|T|hird Quarti|le|F|ourth Quart|ile|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
||#|Mean|Median|#|Mean|Median|#|Mean|Median|#|Mean|Median|
|Mean Score|1529|148.83|148.80|1495|148.28|148.40|1514|148.65|148.50|1498|147.68|147.80|
|Median Score|1529|146.98|147.00|1495|147.12|147.00|1514|147.77|148.00|1498|147.36|148.00|
|Percentage >173|1529|8.97|0.00|1495|9.08|0.00|1514|10.02|7.14|1498|10.12|7.69|
|Percentage >150|1529|48.41|50.00|1495|46.71|46.15|1514|48.23|50.00|1498|45.69|46.15|
|Percentage<135.5|1529|23.60|20.00|1495|25.36|23.81|1514|24.92|23.08|1498|27.79|25.93|
|Participation Ratio|1529|69.85|70.00|1495|73.91|75.00|1514|73.30|75.00|1498|74.57|74.46|
|Exams Per Student|1529|3.21|3.17|1495|3.22|3.18|1514|3.26|3.22|1498|3.31|3.29|
|Nr of Subjects|1529|5.21|5.00|1495|5.70|6.00|1514|6.12|6.00|1498|6.99|7.00|
|# Students|1529|77.22|80.00|1495|120.06|119.00|1514|171.27|169.00|1498|326.27|288.00|
|# Teachers|1529|17.01|17.00|1495|20.31|20.00|1514|23.13|22.00|1498|36.02|34.00|
|# Non-TeachingStaff|1529|10.77|10.00|1495|12.79|12.00|1514|14.57|14.00|1498|19.66|18.00|
|Students/Teacher|1529|4.59|4.57|1495|6.07|6.00|1514|7.61|7.48|1498|9.17|9.00|
|Students/Staff|1529|2.82|2.81|1495|3.71|3.67|1514|4.66|4.60|1498|5.88|5.78|
|Class Size|1529|8.70|8.00|1495|11.62|11.00|1514|14.76|14.00|1498|18.85|18.50|
|Share Ukrainian|1529|0.93|1.00|1495|0.92|1.00|1514|0.89|1.00|1498|0.85|1.00|
|Share of Males|1529|43.60|44.44|1495|43.66|42.86|1514|43.57|43.75|1498|41.77|41.67|
|Unemployment Rate in Rayon|1529|3.45|3.20|1495|3.24|2.90|1514|2.79|2.50|1498|2.34|2.00|
|Average Wage in Rayon|1529|1389.90|1330.00|1495|1390.30|1323.00|1514|1417.64|1338.00|1498|1457.92|1353.39|
|Population in 2001|1529|754.39|704.00|1495|1030.68|960.00|1514|1523.92|1350.00|1498|2718.11|2343.00|

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# **_Table 3b. Descriptive statistics for urban schools, by school size quartiles_**

|Urban Schools||FirstQuarti|le||SecondQuar|tile||ThirdQuart|ile|F|ourthQuar|tile|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
||#|Mean|Median|#|Mean|Median|#|Mean|Median|#|Mean|Median|
|Mean Score|994|147.50|147.00|976|150.32|150.10|983|152.28|152.10|980|154.75|154.50|
|Median Score|994|146.75|146.00|976|150.00|149.50|983|152.35|152.00|980|155.18|155.00|
|Percentage >173|994|11.05|7.14|976|13.29|10.53|983|15.59|13.51|980|18.89|16.42|
|Percentage >150|994|44.75|43.48|976|50.47|50.00|983|54.68|54.29|980|60.06|60.00|
|Percentage<135.5|994|28.77|26.67|976|23.82|21.74|983|20.48|19.05|980|17.43|16.28|
|Participation Ratio|994|83.27|82.35|976|87.95|88.89|983|92.06|91.43|980|96.64|93.17|
|Exams Per Student|994|3.29|3.25|976|3.36|3.33|983|3.42|3.39|980|3.47|3.46|
|Nr of Subjects|994|6.62|7.00|976|7.48|8.00|983|7.85|8.00|980|8.04|8.00|
|# Students|994|213.67|222.00|976|378.99|380.00|983|544.26|542.00|980|855.35|802.00|
|# Teachers|994|25.47|24.00|976|36.90|36.00|983|48.30|47.00|980|69.40|66.00|
|# Non-TeachingStaff|994|16.74|15.00|976|19.92|19.00|983|22.63|22.00|980|28.99|27.00|
|Students/Teacher|994|8.66|8.81|976|10.64|10.56|983|11.64|11.53|980|12.59|12.55|
|Students/Staff|994|5.29|5.40|976|6.91|6.86|983|7.88|7.79|980|8.86|8.75|
|Class Size|994|17.07|17.00|976|21.04|20.50|983|22.34|22.00|980|24.00|24.00|
|Share Ukrainian|994|0.68|0.97|976|0.69|0.97|983|0.72|0.98|980|0.74|0.98|
|Share of Males|994|43.23|43.61|976|43.16|43.75|983|43.76|43.90|980|43.79|44.19|
|Unemployment Rate in Rayon|994|1.99|1.65|976|2.11|1.70|983|1.99|1.70|980|1.72|1.50|
|Average Wage in Rayon|994|1733.38|1707.00|976|1755.53|1679.00|983|1771.25|1732.60|980|1851.47|1795.00|
|Population in 2001|994|63189.65|32737.00|976|75172.65|49938.00|983|80115.54|52265.00|980|112160|103244|

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Based on tables 3a and 3b, we find that

- The size distribution of urban and rural schools overlaps little. For rural areas, the school size quartile thresholds are at 100 students, 141 students and 209 students while for the urban schools, the thresholds are at 305 students, 458 students and 646 students. Hence, the lowest size quartile for urban schools has an upper limit that is higher than the lower limit of the highest size quartile of rural schools.

- In rural areas, the relation between size and Ukrainian exam scores is limited. Bigger schools have a slightly higher percentage of students among the top students, but also a somewhat higher percentage of low scoring students. The participation ratio, however, is somewhat lower in the lowest quartile.

- While performance does not change much as size increases in rural areas, input variables do change a lot: the schools in the top quartile have, on average, a class size that is about the double of the class size in schools in the lowest quartile. The same is true of the studentteacher ratio.

- In the cities, the relation between size and test scores is much clearer: bigger size goes together with substantially better mean and median test scores, a higher percentage of high scoring students and a lower percentage of low scoring students. For example,  while the lowest urban size quartile has an average mean score of 147.5 and 44.75 percent students scoring „above average‟, the top quartile has an average mean score of 154.75 and 60 percent students scoring „above average‟. In addition, schools in the upper quartiles have substantially higher participation rates than schools in the lower quartiles.

- Besides performance increasing with the size of the school in urban areas, also the class size and the student-teacher ratio increase with the size of the school.

Given that bigger schools in urban areas perform better, on average, than smaller schools in urban areas, and that, on average, schools in rural areas are smaller than schools in urban areas, it is no surprise that schools in rural areas perform worse, on average, than schools in urban areas. The participation ratio is also substantially smaller in rural areas<sup>27</sup> .

> 27 More general, if we compare rural schools to urban schools, we find that the median rural school has 9 students taking the EIT tests against 34 students in urban schools, reflecting the big differences in size between rural and urban schools. Rural Schools have lower mean and median scores (about 148 versus about 153). They have a

19
Note that if we would focus on performance in Mathematics or Ukrainian history, rather than on the Ukrainian test, we get similar results.

As explained in the introduction, Ukraine plans to close schools with less than 100 students<sup>28</sup> . About a quarter of rural areas fall in this category, indeed, the upper bound of the bottom quartile of school size in our sample happens to be 100. The above results suggest that students at these smaller schools are not underperforming in test scores (nor are they over-performing), though they do require substantially more inputs and have somewhat smaller participation rates.

Very few schools in urban areas have less than 100 students (about 1 percent of the urban sample). The descriptive statistics above, however, do suggest that in urban areas increasing school size can increase both quality and save on inputs. This is unlike the descriptive statistics for the rural areas, which suggest that inputs can be saved (at a bigger rate than in urban areas) by having bigger schools but also, that quality would not change much.

In table 4a and 4b, we do a similar exercise as before but using class size quartiles.

- For rural schools, we see little differences among quartiles, though participation is lower in the highest class size quartile.

- For urban schools, participation is lower in the highest class size quartile but the lowest class size quartile has a lower average score and more failing students.

- Classes in urban areas are substantially bigger than classes in rural areas. Quartile thresholds are at 17.5, 21 and 25 students per class for urban areas and 9, 13 and 17 students per class in rural areas.

considerably lower percentage of students who get top grades (median of 4.76 % vs 14.28 %) or who get above average grades (median of 48% vs 57%) but a considerably higher percentage of students who get low scores (median of 23.5% vs 17.5%). Finally, 73 % of the median rural school‟s students participate in the EIT, against 91% at the median urban school. Not surprisingly, the population in communities where rural schools are located is much smaller (median slightly 1000 people) than the urban communities (median around 70000). Not surprisingly, rural schools are substantially smaller than urban schools (median total number of students of 142 versus 466), have somewhat less teachers and non-teaching staff leading to a student-teacher ratio (median 6.6 versus 10.7), a student staff ratio (median 4 versus 7.2) and class size (median of 13 versus 21.5) which are substantially lower in rural areas. At the other side, students of urban schools are more likely to choose other languages than Ukrainian to do the EIT and are located in areas with less unemployment and higher wages. Both in rural and urban areas, the share of boys is around 43 percent, suggesting there is quite a gap in the decision to continue to study.

> 28 Given our performance measure is based on a test taken by school graduates, we do not have schools of level I  or level I-II in our sample.

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# **_Table 4a. Descriptive statistics for rural schools, by class size quartiles_**

|Rural Schools||First Quar<br>|tile<br>|S<br>|econd Qua<br>|rtile<br>|<br>|Third Quar<br>|tile<br>|F<br>|ourth Qua<br>|rtile<br>|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
||#|Mean|Median|#|Mean|Median|#|Mean|Median|#|Mean|Median|
|Mean Score|1839|148.69|148.80|1487|148.45|148.50|1248|148.24|148.30|1462|147.96|148.10|
|Median Score|1839|146.62|147.00|1487|147.48|148.00|1248|147.77|148.00|1462|147.60|148.00|
|Percentage >173|1839|9.11|0.00|1487|9.34|0.00|1248|9.62|7.69|1462|10.25|7.69|
|Percentage >150|1839|47.81|50.00|1487|47.75|50.00|1248|47.15|46.67|1462|46.21|46.29|
|Percentage<135.5|1839|24.26|20.00|1487|24.56|22.22|1248|25.81|25.00|1462|27.37|25.00|
|Participation ratio|1839|74.38|75.00|1487|73.85|75.00|1248|73.25|75.00|1462|69.74|71.75|
|Exams Per Student|1839|3.20|3.17|1487|3.24|3.20|1248|3.28|3.25|1462|3.29|3.26|
|Nr of Subjects|1839|5.04|5.00|1487|5.87|6.00|1248|6.47|7.00|1462|6.94|7.00|
|# Students|1839|106.92|96.00|1487|136.87|125.00|1248|196.17|170.50|1462|274.06|234.00|
|# Teachers|1839|18.98|18.00|1487|21.26|20.00|1248|25.67|23.00|1462|31.99|29.00|
|# Non-Teaching Staff|1839|12.01|11.00|1487|13.35|13.00|1248|15.67|14.50|1462|17.51|16.00|
|Students/Teacher|1839|5.53|5.21|1487|6.39|6.16|1248|7.51|7.37|1462|8.43|8.26|
|Students/Staff|1839|3.39|3.21|1487|3.91|3.78|1248|4.64|4.50|1462|5.39|5.24|
|Class Size|1839|7.04|7.00|1487|11.43|11.00|1248|15.49|15.50|1462|21.88|21.00|
|Share Ukrainian|1839|0.91|1.00|1487|0.90|1.00|1248|0.87|1.00|1462|0.89|1.00|
|Share of Males|1839|43.72|42.86|1487|43.46|44.44|1248|43.21|42.86|1462|42.08|42.31|
|Unemployment Rate in Rayon|1839|3.24|2.90|1487|3.03|2.70|1248|2.80|2.50|1462|2.66|2.30|
|Average Wage in Rayon|1839|1405.11|1336.00|1487|1404.92|1328.00|1248|1417.27|1338.00|1462|1430.95|1338.63|

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**_Table 4b. Descriptive statistics for urban schools, by class size quartiles_**

|Urban Schools||First Quar|tile||Second Qu|artile||Third Qu|artile||Fourth Q|uartile|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
|Mean Score|1022|149.93|149.95|957|151.56|151.20|996|151.87|152.20|958|151.51|151.20|
|Median Score|1022|149.35|149.50|957|151.45|151.50|996|152.00|152.00|958|151.50|151.50|
|Percentage >173|1022|13.42|10.00|957|15.09|12.20|996|15.47|13.64|958|14.84|12.75|
|Percentage >150|1022|50.00|50.00|957|52.94|53.33|996|53.96|54.55|958|53.06|53.44|
|Percentage<135.5|1022|24.93|21.95|957|22.18|20.00|996|21.48|19.62|958|21.88|20.00|
|Participationratio|1022|96.95|88.12|957|86.38|90.00|996|87.87|91.11|958|88.25|91.05|
|Exams Per Student|1022|3.31|3.30|957|3.38|3.38|996|3.41|3.41|958|3.43|3.41|
|Nr of Subjects|1022|6.84|7.00|957|7.58|8.00|996|7.79|8.00|958|7.80|8.00|
|# Students|1022|325.10|293.00|957|474.63|446.00|996|571.38|554.50|958|626.28|573.50|
|# Teachers|1022|34.59|31.00|957|44.01|41.00|996|49.67|47.00|958|52.06|48.00|
|# Non-Teaching Staff|1022|19.23|17.00|957|21.99|20.00|996|23.21|22.00|958|23.93|22.00|
|Students/Teacher|1022|9.21|9.40|957|10.82|10.72|996|11.54|11.54|958|12.02|12.10|
|Students/Staff|1022|5.91|5.99|957|7.14|7.16|996|7.80|7.75|958|8.13|8.08|
|Class Size|1022|13.69|15.00|957|19.54|19.50|996|23.21|23.00|958|28.38|28.00|
|Share Ukrainian|1022|0.71|1.00|957|0.73|1.00|996|0.72|0.96|958|0.68|0.88|
|Share of Males|1022|42.96|43.48|957|43.74|44.44|996|43.49|43.75|958|43.79|44.00|
|Unemployment Rate in Rayon|1022|2.19|1.80|957|2.04|1.70|996|1.91|1.60|958|1.65|1.35|
|Average Wage in Rayon|1022|1676.80|1542.10|957|1758.29|1688.90|996|1807.38|1763.00|958|1874.15|1877.00|
|Population in 2001|1022|51378|17516.00|957|76705|51552.00|996|90898|72611.00|958|113152|105654.00|

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Of course, none of the above results controls for other explanatory variables that can influence the school‟s performance measures. The regression analysis presented below will analyze whether these preliminary findings are confirmed once one controls for such confounding factors.

# _b. Are there selection effects?_

Before we can study the determinants of the test scores, we need to discuss a number of sample selection issues as sample selection has the potential to bias our regression estimates.

We have data on 12,075 schools participating in the 2010 EIT<sup>29</sup> . In the MOE database, however, we only have 11,950 schools which have students in the 11<sup>th</sup> and/or 12<sup>th</sup> grade in 2010. For 11683 schools we have information in both databases, implying we have data for at least 94.5 percent of the Ukrainian schools with graduating students (11,683/(11,683+(12,07511,683)+(11,950-11,683))). Another implication is that almost all schools which have students in the last year of secondary education have students who participate in the EIT. Hence, the „selection‟ introduced by the fact that we use EIT results, which is only taken by students aiming to go to the university, rather than some general test which would be taken by all graduating students , is likely to be minor. Of course, there is also the issue of selection among the students, an issue we will discuss next.

Only those students interested in continuing their studies at a university within Ukraine have an interest in taking the Independent External Test, hence the school average we have are based on a selected group of students rather than all students graduating in a given year. Moreover, while the students take the decision to participate or not themselves, schools do have a possibility to try to influence this choice. For example, if a school would like to get a good average score on the EIT, it can try to persuade weaker students not to take the test.

> 29 We have 12267 schools in the EIT 2009 data and 13678 in the EIT 2008 data. The 2008 EIT database includes vocational schools, which is not the case in 2009 and 2010. In this section, we focus on the descriptive data for the 2010 EIT. The descriptive statistics for 2008 and 2009 give a qualitatively similar picture

23
To study the degree to which there is selection, we use the „student participation ratio‟, that is, for those schools which have students that take the exam on a specific subject, we compute the ratio of students who take the exam divided by the total number of students in the highest grade (for a vast majority of schools this is the 11<sup>th</sup> grade, for some it is the 12<sup>th</sup> grade). Given that all students that participate in the EIT take the Ukrainian exam, a school‟s ratio of the number of students that take the Ukrainian exam on the number of students in the highest year is a good proxy for the extent of selection. If this ratio is 1, it means all students participate, if it is 0 it means nobody participates.

In about 7 % of the cases, the participation ratio indicator is bigger than one, i.e. there are more students taking the test than there are in the 11<sup>th</sup> /12<sup>th</sup> grade. One explanation for this is that the MoE data were recorded at a different time than the EIT exams, and that some students might have changed schools between the recording of the MoE data and the EIT exams. A second possible explanation is that some graduates of previous years were allocated to the school were they graduated in the past. A third explanation is simply that there are mistakes in the database. In the regression analysis presented below, we include in the sample only schools with a participation ratio that is less than 101 percent.

Table 5 gives the 2010 participation ratio statistics by region – we see a substantial variation among oblasts with especially low rates of participation in the Western regions of Zakarpatia and Chernivtsi (between 60 and 70 percent) and high rates of participation in Sevastopol and especially Kyiv (over 90 percent).

Table 6 tries to explain the differences between schools in terms of the 2010 participation ratio. We first run a simple OLS regression (1) of the participation ratio on our main variables of interest and a set of dummies reflecting the settlement status (urban versus rural), the oblast in which the school is located and the type of the school. Then (2) we add a set of additional explanatory variables including the gender composition of the school‟s EIT participant, their language choice, the school‟s location population in 2001, and the average wage and the unemployment rate in the rayon where the school is located in 2009. Next (3) we allow for nonlinear effects in our main input variables, adding squared terms of the total number of students, the student-teacher ratio at the school and the class size of the graduating class. Finally, we use tobit regression (4) to control for the fact that the participation ratio is constrained to be between 24
zero and one. We run these four regressions first on the total sample and then we run separate regressions for urban and rural schools.

25
# **_Table 5 – Participation Ratio by Oblast_**

|Region|#|Mean|Median|St. Dev.|Min|Max|
|---|---|---|---|---|---|---|
|Zakarpatska Oblast|843|60.7|60.0|24.6|3.3|100.0|
|Chernivetska Oblast|754|67.9|69.6|22.2|6.7|100.0|
|Volynska Oblast|1027|74.5|77.3|20.3|1.9|100.0|
|Khersonsksa Oblast|982|74.2|78.0|21.7|4.7|100.6|
|Ivano-Frankivska Oblast|975|76.1|79.5|19.7|9.1|101.0|
|Rivnenska Oblast|1012|76.6|80.0|20.6|12.5|101.0|
|Chernihivska Oblast|1116|77.2|82.4|21.0|3.8|100.0|
|Odeska Oblast|1638|77.9|84.6|21.4|1.6|101.0|
|Khmelnytska Oblast|1280|78.5|84.6|21.3|1.9|100.0|
|Cherkaska Oblast|1339|80.4|85.4|19.2|2.0|100.0|
|Zaporizka Oblast|1309|79.3|85.7|21.4|2.4|100.0|
|Kirovogradska Oblast|1053|79.2|85.7|20.8|9.1|100.9|
|Vinnytska Oblast|1389|81.2|86.7|18.6|4.0|101.0|
|Mykolaivska Oblast|1049|80.3|86.7|21.5|2.9|100.9|
|Autonomous Republic of Crimea|1189|80.9|87.2|19.5|0.9|100.0|
|Zhytomyrska Oblast|944|80.9|87.5|20.1|4.3|100.0|
|Lvivska Oblast|1678|82.0|87.7|18.4|2.0|100.9|
|Poltavska Oblast|1229|83.0|88.2|18.0|7.4|100.0|
|Ternopilska Oblast|813|83.0|88.4|18.4|1.6|100.0|
|Donetska Oblast|2363|82.4|89.5|20.2|0.4|100.7|
|Sumska Oblast|997|82.8|89.5|18.9|1.8|100.8|
|Dnipropetrovska Oblast|2098|84.1|90.0|17.6|1.0|101.0|
|Kyivska Oblast|1420|83.7|90.0|18.5|2.6|100.9|
|Luhanska Oblast|1258|84.6|90.5|17.3|7.2|100.9|
|Kharkivska Oblast|1870|85.5|91.7|17.1|12.5|100.0|
|Cityof Sevastopol|170|85.5|91.8|16.6|20.8|100.0|
|Cityof Kyiv|1033|92.4|96.4|13.5|0.4|100.9|

26
# **_Table 6: Ukrainian Language, Participation Ratio_**

||||Total||||Urban||||Rural||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
||(1)|(2)|(3)|(4)|(1)|(2)|(3)|(4)|(1)|(2)|(3)|(4)|
|# students|0.014***|0.013***|0.031***|0.031***|0.014**<br>~~*~~|0.014***|0.038***|0.038***|0.010**<br>~~*~~|0.008**|0.048***|0.053***|
||16.05|15.35|11.22|8.66|16.61|16.3|12.55|11.87|2.66|1.97|4.34|4.51|
|(# students)<sup>2</sup>|||-0.000***|-0.000***|||-0.000***|-0.000***|||-0.000***|-0.000***|
||||-7.8|-5.49|||-9.57|-8.33|||-3.64|-4.07|
|Student/Teacher|0.173*|0.204**|0.626**|0.737***|0.108|0.115|0.455|0.502*|0.565**<br>~~*~~|0.571***|1.348**|1.478**|
||1.83|2.15|2.4|2.83|1.09|1.15|1.44|1.8|2.68|2.72|2.03|2.41|
|(Stud./Teacher)<sup>2</sup>|||-0.031***|-0.034***|||-0.022**|-0.023**|||-0.082**|-0.088***|
||||-2.94|-3.28|||-2.13|-2.35|||-2.2|-2.69|
|Class Size|0.017|0.016|0.057|-0.247*|0.147**<br>~~*~~|0.156***|-0.169|-0.444**|-0.048|-0.059|0.727***|0.398*|
||0.49|0.45|0.39|-1.79|3.32|3.38|-0.59|-2.23|-0.85|-1.04|3.27|1.78|
|(Class Size)<sup>2</sup>|||-0.003|0.003|||0.006|0.012**|||-0.028***|-0.021***|
||||-0.92|0.85|||0.91|2.54|||-4.29|-3.16|
|urban==1|8.773***|8.529***|7.295***|8.164***|||||||||
||17.39|16.81|13.33|13.41|||||||||
|Gender Comp.||0.089***|0.089***|0.093***||0.041*|0.042*|0.039**||0.102***|0.102***|0.108***|
|||6.54|6.62|8.91||1.76|1.82|2.46||6.24|6.32|7.81|
|Unemployment rate<br>~~2009~~||0.544***|0.561***|0.602***||0.384**|0.285|0.308||0.555***|0.628***|0.688***|
|||4.03|4.16|4.2||2.15|1.6|1.58||3.02|3.44|3.4|
|Average Wage 2009||0.002***|0.002***|0.002***||0|0|0||0.003***|0.003***|0.004***|
|||3.34|3.54|2.66||0.02|0.24|0.09||3.85|3.88|2.99|
|Population||0.003|0.008**|0.010**||0.001|0.004|0.005||0.310*|0.334**|0.348***|
|||1.14|2.54|2.26||0.45|1.13|1.43||1.95|2.29|3.48|
|Share Ukrainian||0.016*|0.017**|0.021**||0.014|0.014|0.019*||0.016|0.018|0.017|
|||1.87|1.99|2.3||1.26|1.27|1.93||1.15|1.25|1.19|
|_cons|75.101**<br>~~*~~|67.172***|63.185***|68.108***|82.443*<br>~~**~~|79.378***|76.311***|81.290***|70.735*<br>~~**~~|59.646**<br>~~*~~|47.878***|50.930***|
||63.76|43.18|31.22|30.41|52.81|37.89|22.19|28.73|23.71|18.3|12.1|9.75|
|sigma||||18.866***||||14.110***||||21.698***|

27
|||||134.82||||90.1||||100.17|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
|R Adj sq.|0.309|0.316|0.32||0.447|0.448|0.459||0.083|0.098|0.107||
|N|10906|10906|10906|10906|4922|4922|4922|4922|5984|5984|5984|5984|

The regression also includes oblast dummies, dummies for different types of schools and evening schools. The full table can be found in excel tables which can be made available upon request. *** means significant at the 1% level, ** at the 5 % level and * at the 10 percent level.T statistics are based on robust standard errors for the OLS specifications.

28
# We find that

- School size is positively correlated with the participation-ratio in both rural and urban areas, though the effect is somewhat smaller in the rural areas. When allowing for a nonlinear effect of school size (specification 3), we find, based on the complete sample, that the maximum participation ratio is reached at 1156 students, which is close to the 98<sup>th</sup> percentile of school sizes in our sample. A school at this level has a participation ratio that is roughly 7 percentage points higher than a school of 455 students (75<sup>th</sup> percentile), 11 percentage point more than a school at the median (227) and 14 percentage point more than a school of 128 students ( the 25<sup>th</sup> percentile). Note that we get these effects after correcting for a wide range of other factors that can affect a school‟s participation ratio. When restricting the sample to urban schools, we get the maximum at 1060 student (95<sup>th</sup> percentile). A school at this level can expect a participation ratio that is 3, 6 and 10 percentage point higher than a school with 666, 465 and 305 students respectively. When restricting the sample to rural schools, we get the maximum at 470 students (between 95<sup>th</sup> and 99<sup>th</sup> percentile). A School at this level can expect a participation ratio that is 3.5, 5.7 and 7 percentage point higher than a school with 208, 141 respectively 100 students.

- The impact of class size varies from one specification to another, both in terms of significance and in terms of sign. In any case, even if significant, the size of the effect is very small.

# We also find that:

- The student-teacher ratio has a positive effect in all specifications, indicating that schools with a higher number of students per teacher have higher participation ratios. However, this effect is small in general and even insignificant for the urban schools. In rural schools, we find some evidence of a non-linear effect, with the optimal student-teacher ratio being around the 75<sup>th</sup> percentile at 8 students per teacher. But again, deviating from that optimum barely reduces the participation ratio

- As far as other variables are concerned we find that evening schools have low participation ratios (70 percentage points less than the average school) and that urban schools have substantially higher participation rates ( about 8 percentage points). Also the type of school matters: lycea, colegiums and gymnasiums have significantly higher participation ratios (5 to 10 percentage points higher than ordinary schools). Schools located in rayons with higher registered unemployment have somewhat higher

29
participation ratios as do schools located in rayons with higher wages and as do rural schools located in bigger villages.

 Interesting to note is the finding that schools that have a high percentage of males among the EIT participants are also schools that have a somewhat higher participation ratio. Note that this gender effect is much stronger than the language effect – having a higher percentage of students choosing Ukrainian as test language participate in the EIT goes together with only slightly more students participating and this effect is not statistically significant. This suggests that the Ukrainian language test does not scare off those more comfortable speaking Russian. At the same time, the fact that these gender and language ratios are computed based on the test takers rather than on all the students of the graduating class, is likely to introduce a bias in our estimates. Assume for example the extreme situation where all Russian speakers would prefer not to participate rather than taking the Russian language option, then our test based measure would indicate wrongly that the school is all Ukrainian speaking. A simple simulation indicated however, that this (non-random) error-in-variable bias tends to inflate the absolute value of the effect but in most cases only slightly so (less than 10 percent when we take a simulation set up that is similar to the data we have), especially when participation rates of the two groups are not too dissimilar (see appendix).

So far we have discussed the selection of schools into our sample and the selection of students into the test. One additional selection issue is related to the selection of students into schools. Indeed, it is possible that better students prefer to study at the bigger (or smaller) schools or that better students are put into smaller (bigger) classes. In other words, correlation does not necessarily mean causality. Like Urquiola (2006) noticed for Bolivia, also in rural Ukraine there is very often only one school with one class per grade, which reduces the possibility of students to select into schools, and of schools to select students into classes. Hence, our estimates for rural areas should provide „cleaner‟ estimates of the effect of school size and class size on performance. In addition, class size is governed by maximum class size laws which also contribute to the exogeneity of class size. Still, one should be careful when interpreting our results in a causal way.

# _c. Estimating Educational Production Functions_

We next run regressions using the same set of explanatory variables but with the mean test score of the school as a dependent variable. Since our dependent variable has no observations at the limit, there is no need for a Tobit regression, instead we add the participation ratio in 30
specification (4) to control for possible selection effects. We focus first on the score on the Ukrainian exam, and then on the score on the mathematics and the history exam, two exams in which almost all schools participate<sup>30</sup> .

We find that (table 7)

- School size has a significantly positive effect on the school‟s mean Ukrainian exam score in all specifications, though the effect is clearly stronger for urban schools. Using the non-linear OLS specification, an urban school at the 25<sup>th</sup> percentile of the school size distribution has an expected mean score that is 2 points less than a school at the 50<sup>th</sup> percentile, and 4 points less than a school at the 75<sup>th</sup> percentile. For rural schools, the difference between the 25<sup>th</sup> and the 75<sup>th</sup> percentile is only 1 point.

- Class size has a negative effect in all but one specification and this effect is statistically significant. However, the size of these effects is small, moving from the 25<sup>th</sup> to 75<sup>th</sup> percentile does not change the mean by more than 0.5 points, both in rural and urban areas.

We also find that

- Student-teacher ratio has a consistently negative effect but when disaggregating the sample into urban and rural schools, this effect is not significant.

- Evening schools perform substantially less well (10 or more points less), urban schools do better than rural schools (about 2 points more) and there are substantial oblast specific effects. While introducing extra explanatory variables does reduce the importance of oblast specific dummies, some sizeable effects do remain. For example, the average score in urban schools in Lviv is expected to be 7 points more than the average score of schools located in Crimea. For rural schools this difference is 3 points.

- Gymnasia and Lycea score 5 to 10 points higher than other school types.

- The gender composition matters with more boys among the test takers reducing the average school score. Going from the 25<sup>th</sup> percentile to the 75<sup>th</sup> percentile in terms of share of boys will decrease the average score by 1.5 to 2.5 points.

- The unemployment rate is never significant but a higher average wage goes together with a slight decrease in points. Schools in bigger (more populated) communities have slightly higher mean scores.

> 30 In fact, given that on these topics a lower number of students participate, a lower number of schools have a participation ratio above 1 for these subjects resulting in samples that are slightly bigger than when looking at the Ukrainian test scores.

31
- The language of choice has a substantial effect – moving from a school where about 40% of the exams are taken in a language other than Ukrainian (25<sup>th</sup> percentile) to a school where all students take all exams in Ukrainian (75<sup>th</sup> percentile) increases the average score on the Ukrainian exam by about 4 points.

- Controlling for selection by including the participation ratio does not change the results much, even though the participation ratio has a positive and significant effect on the average score, especially for urban areas but also for rural areas. This suggests that better schools have higher grades and higher participation.

- Our explanatory variables explain about 40 percent of the variation in mean scores for rural schools, but substantially less (15 percent) for rural schools.

32
# **_Table 7 – Ukrainian Language, Mean Score_**

|||To<br>2|tal|||Urb<br>2|an|||Ru<br>2|ral||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
||(1)|()<br>Extended|(3)|(4)|(1)|()<br>Extended|(3)|(4)|(1)|()<br>Extended|(3)|(4)|
|# students|0.009***|0.009***|0.011***|0.009***|0.009***|0.009***|0.016***|0.009***|0.002|0.001|0.013***|0.012***|
||19.21|18.5|7.9|6.46|16.83|17.05|9.41|5.6|1.18|0.86|2.98|2.7|
|(# students)<sup>2</sup>|||-0.000**|0|||-0.000***|-0.000*|||-0.000***|-0.000**|
||||-2|-0.96|||-4.72|-1.76|||-2.76|-2.56|
|Student/Teacher|-0.183***|-0.178***|-0.318***|-0.364***|-0.05|-0.087|-0.216|-0.298*|-0.056|-0.047|-0.274|-0.317|
||-3.76|-3.84|-2.74|-3.16|-0.78|-1.43|-1.21|-1.72|-0.66|-0.59|-1.2|-1.4|
|(Stud./Teacher)<sup>2</sup>|||0.007*|0.009**|||0.004|0.008|||0.006|0.009|
||||1.66|2.21|||0.73|1.47|||0.56|0.8|
|Class Size|-0.081***|-0.068***|-0.347***|-0.351***|-0.003|0.015|-0.443***|-0.413***|-0.052**|-0.057**|-0.16|-0.183*|
||-4.6|-3.95|-5.08|-5.17|-0.11|0.55|-3.18|-3.06|-2.08|-2.36|-1.64|-1.88|
|(Class Size)<sup>2</sup>|||0.008***|0.008***|||0.011***|0.010***|||0.003|0.004|
||||4.58|4.78|||3.48|3.26|||1.02|1.34|
|Urban|1.714***|2.047***|2.059***|1.525***|||||||||
||6.55|7.99|7.57|5.68|||||||||
|Gender Comp.||-0.109***|-0.109***|-0.116***||-0.114***|-0.115***|-0.122***||-0.109***|-0.109***|-0.112***|
|||-19.75|-19.8|-21.11||-10.69|-10.82|-12||-16.86|-16.86|-17.35|
|Unemployment rate<br>~~2009~~||0.029|0.023|-0.018||0.031|0.015|-0.036||-0.032|-0.024|-0.044|
|||0.47|0.37|-0.29||0.3|0.14|-0.36||-0.41|-0.31|-0.56|
|Average Wage 2009||-0.001***|-0.001***|-0.001***||-0.001***|-0.001***|-0.002***||0|0|0|
|||-3.15|-3.4|-3.95||-3.64|-3.71|-3.94||0.15|0.07|-0.19|
|Population||0.009***|0.007***|0.007***||0.007***|0.007***|0.006***||0.122***|0.115***|0.105***|
|||4.83|4.2|4.01||3.54|3.5|3.36||8.35|7.88|7.07|
|Share Ukrainian||0.072***|0.072***|0.071***||0.063***|0.064***|0.061***||0.070***|0.070***|0.069***|
|||17.2|17.23|17.35||10.47|10.56|10.49||11.48|11.55|11.6|
|Participation Ratio||||0.073***||||0.179***||||0.031***|
|||||12.85||||15.15||||4.82|
|_cons|154.054**<br>~~*~~|158.393***|160.926**<br>~~*~~|156.307**<br>~~*~~|153.541**<br>~~*~~|159.317***|163.011**<br>~~*~~|149.337**<br>~~*~~|148.706**<br>~~*~~|152.515***|152.942**<br>~~*~~|151.437**<br>~~*~~|

33
||233.99|198.02|161.95|146.12|158.55|126.84|84.79|69.49|87.01|86.29|77.44|76.05|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
|R Adj sq.|0.262|0.321|0.323|0.339|0.391|0.431|0.434|0.483|0.079|0.159|0.16|0.164|
|N|10906|10906|10906|10906|4922|4922|4922|4922|5984|5984|5984|5984|

The regression also includes oblast dummies, dummies for different types of schools and evening schools. The full table can be found in excel tables which can be made available upon request. *** means significant at the 1% level, ** at the 5 % level and * at the 10 percent level.T statistics are based on robust standard errors for the OLS specifications.

34
Next we compare the Ukrainian exam scores to the mathematics and the history scores (table 8a and 8b).

- By and large, the results for the mathematics and history tests are similar to the results for the Ukrainian test. Bigger schools do get better average scores while schools with higher student-teacher ratios and higher class sizes get lower scores, though the latter effect is small and often not significant.

- Gender is much less important for math and history than for Ukrainian (for math even insignificant in urban areas). The fact that there is an effect of language choice on Ukrainian history and to a lesser extent on math outcomes suggest that those schools where students choose to take the exams in a language other than Ukrainian are somewhat weaker in general. Hence, the language effect we found in the Ukrainian language exam is likely to be an upper bound.

- The size of the community has a positive effect on the mean score. For urban schools, the average wage has a negative effect and for the math score unemployment has a positive effect.

- Controlling for selection does not change the general results, and has a small positive effect for urban schools and a small negative effect for rural schools.

- Given the smaller number of students on which the school means are based, it is not surprising that the part of the variation in scores that is explained by our explanatory variables is smaller than in the case of Ukrainian language. For the same reason, it is not surprising that we can explain more in the urban than in the rural regressions.

35
# **_Table 8a – Mathematics, Mean Score_**

|||To|tal|||Ur|ban|||R|ural||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
||(1)|(2)|(3)|(4)|(1)|(2)|(3)|(4)|(1)|(2)|(3)|(4)|
|# students|0.010***|0.009***|0.011***|0.012***|0.010***|0.009***|0.016***|0.014***|0.003|0.002|0.014***|0.015***|
||19.11|17.56|7.36|7.39|17.78|16.89|9.18|8.24|1.48|0.97|2.69|2.82|
|(# students)<sup>2</sup>|||-0.000*|-0.000*|||-0.000***|-0.000***|||-0.000***|-0.000***|
||||-1.84|-1.87|||-4.46|-3.77|||-2.62|-2.72|
|Student/Teacher|-0.219***|-0.194***|-0.419***|-0.417***|-0.136**|-0.129**|-0.503**|-0.550***|-0.057|-0.039|-0.048|0.002|
||-4.23|-3.78|-2.9|-2.88|-2.09|-2|-2.4|-2.65|-0.59|-0.4|-0.18|0.01|
|(Stud./Teacher)<sup>2</sup>|||0.010*|0.010*|||0.014*|0.015**|||-0.008|-0.01|
||||1.85|1.84|||1.8|2.07|||-0.62|-0.81|
|Class Size|-0.031|-0.036*|-0.216***|-0.220***|0.052*|0.038|-0.193|-0.145|-0.034|-0.039|-0.08|-0.117|
||-1.56|-1.83|-2.71|-2.75|1.93|1.35|-1.32|-0.99|-1.13|-1.32|-0.68|-0.99|
|(Class Size)<sup>2</sup>|||0.005***|0.005***|||0.005*|0.004|||0.001|0.001|
||||2.59|2.62|||1.68|1.34|||0.22|0.38|
|Urban|2.170***|1.841***|1.826***|1.841***|||||||||
||7.81|6.48|6.04|6.07|||||||||
|Gender Comp.||-0.022***|-0.022***|-0.022***||-0.009|-0.009|-0.009||-0.026***|-0.027***|-0.027***|
|||-4.36|-4.35|-4.36||-0.98|-1.02|-0.94||-4.41|-4.42|-4.48|
|Unemployment<br>rate 2009||0.140*|0.136*|0.136*||0.220**|0.197*|0.180*||0.048|0.06|0.064|
|||1.93|1.87|1.88||2.04|1.82|1.66||0.5|0.63|0.67|
|Average Wage<br>2009||-0.001**|-0.001**|-0.001**||-0.001*|-0.001*|-0.001**||0|0|0|
|||-2.1|-2.26|-2.19||-1.78|-1.82|-2.5||-0.71|-0.76|-0.27|
|Population||0.013***|0.012***|0.012***||0.011***|0.011***|0.011***||0.136***|0.131***|0.149***|
|||6.63|6.21|6.21||5.54|5.57|5.61||7.28|7.06|7.92|
|Share Ukrainian||0.017***|0.018***|0.018***||0.01|0.011*|0.012*||0.014*|0.014**|0.014*|
|||3.75|3.82|3.81||1.63|1.76|1.86||1.96|2.02|1.94|
|Participation<br>Ratio||||-0.004||||0.064***||||-0.044***|

36
|||||-0.64||||7.23||||-5.91|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
|_cons|156.080***|157.799***|159.920***|160.072***|156.375***|157.339***|160.144***|157.525***|149.958***|151.608***|150.735***|152.247***|
||212.26|169.96|135.99|131.1|145.86|115.15|75.85|72.14|72.02|67.68|60.41|60.94|
|R Adj sq.|0.196|0.202|0.203|0.203|0.303|0.307|0.309|0.319|0.026|0.032|0.033|0.039|
|N|10961|10961|10961|10961|5143|5143|5143|5143|5818|5818|5818|5818|

The regression also includes oblast dummies, dummies for different types of schools and evening schools. The full table can be found in excel tables which can be made available upon request. *** means significant at the 1% level, ** at the 5 % level and * at the 10 percent level.T statistics are based on robust standard errors for the OLS specifications.

**_Table 8b –Ukrainian History, Mean Score_**

|||To<br>|tal<br>|||Ur<br>|ban<br>|||Ru<br>|ral<br>||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
||(1)|(2)|(3)|(4)|(1)|(2)|(3)|(4)|(1)|(2)|(3)|(4)|
|# students|0.006***|0.005***|0.006***|0.006***|0.005***|0.005***|0.008***|0.007***|0.001|0.001|0.012***|0.013***|
||12.67|11.97|4.28|4.3|10.76|10.59|5.02|4.53|0.95|0.79|2.73|2.9|
|(# students)<sup>2</sup>|||0|0|||-0.000*|0|||-0.000***|-0.000***|
||||-0.43|-0.46|||-1.86|-1.48|||-2.82|-2.95|
|Student/Teacher|-0.224***|-0.208***|-0.288**|-0.287**|-0.130**|-0.145**|-0.333*|-0.340*|-0.09|-0.082|-0.178|-0.16|
||-4.83|-4.54|-2.3|-2.29|-2.24|-2.54|-1.9|-1.93|-1.05|-0.97|-0.76|-0.68|
|(Stud./Teacher)<sup>2</sup>|||0.005|0.005|||0.008|0.009|||0|-0.001|
||||1.14|1.13|||1.31|1.35|||0.02|-0.1|
|Class Size|-0.095***|-0.082***|-0.410***|-0.410***|-0.031|-0.016|-0.452***|-0.446***|-0.083***|-0.086***|-0.332***|-0.333***|
||-5.34|-4.6|-5.51|-5.5|-1.29|-0.64|-3.18|-3.15|-3.07|-3.19|-3.08|-3.08|
|(Class Size)<sup>2</sup>|||0.009***|0.009***|||0.011***|0.010***|||0.007**|0.007**|
||||5.16|5.16|||3.4|3.37|||2.47|2.44|
|Urban|1.641***|1.847***|1.983***|1.994***|||||||||
||6.65|7.35|7.4|7.37|||||||||
|Gender Comp.||-0.017***|-0.017***|-0.017***||-0.029***|-0.030***|-0.032***||-0.014**|-0.014**|-0.012*|
|||-3.09|-3.12|-3.06||-3.01|-3.09|-3.29||-2.02|-2.02|-1.82|
|Unemployment rate<br>2009||0.034|0.028|0.029||-0.031|-0.026|-0.027||0.011|0.013|0.024|

37
|||0.49|0.42|0.43||-0.31|-0.26|-0.27||0.12|0.14|0.27|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
|Average Wage 2009||-0.001***|-0.001***|-0.001***||-0.001***|-0.002***|-0.001***||-0.001|-0.001|-0.001|
|||-3.72|-4.01|-4.01||-4.04|-4.19|-4.06||-1.06|-1.14|-1.09|
|Population||0.007***|0.005***|0.005***||0.005***|0.005***|0.004**||0.091***|0.079***|0.081***|
|||4.03|3.04|3.06||2.95|2.65|2.49||5.38|4.48|4.74|
|Share Ukrainian||0.052***|0.052***|0.052***||0.046***|0.046***|0.046***||0.047***|0.047***|0.047***|
|||12.41|12.39|12.39||8.34|8.35|8.33||7.01|7.06|7.1|
|Participation Ratio||||-0.002||||0.022**||||-0.015**|
|||||-0.33||||2.52||||-2.07|
|_cons|154.661**<br>*|155.621**<br>*|158.498**<br>*|158.593**<br>*|155.297**<br>*|157.593**<br>*|162.157**<br>*|160.874**<br>*|149.420**<br>*|150.028**<br>*|151.062**<br>*|151.739**<br>*|
||246.41|197.65|154.34|144.47|173.78|140.19|87.32|81.47|101.52|93.1|81.19|79.35|
|R Adj sq.|0.153|0.169|0.171|0.171|0.295|0.311|0.314|0.316|0.046|0.055|0.056|0.057|
|N|11086|11086|11086|11086|5137|5137|5137|5137|5949|5949|5949|5949|

The regression also includes oblast dummies, dummies for different types of schools and evening schools. The full table can be found in excel tables which can be made available upon request. *** means significant at the 1% level, ** at the 5 % level and * at the 10 percent level.T statistics are based on robust standard errors for the OLS specifications.

38
From the EIT center, we also obtained school averages disaggregated by gender. Note that, based on descriptive statistics, girls do better than boys, on average, on all subjects, except for Geography, with the gender gap to be most substantial on the Ukrainian exam.

When running regressions by gender, we use the average score of the female students, respectively male students, of a school and regress it on the same set of explanatory variables, with the exception that our language variable is now the percentage of exams (other than the Ukrainian exam) taken in Ukrainian by the female students of a school rather than by all students.

We find that for the Ukrainian exam (table 9a and 9b)

- Like for the total sample, school size has a positive effect on the school‟s mean Ukrainian exam score for both males and female students. Again, the effect is clearly stronger for urban schools.

- Class size has a negative effect for male and female students and this effect is statistically significant for male students and almost significant for female students. The size of these effects is bigger for males than for females but in both cases moving from the 25<sup>th</sup> to 75<sup>th</sup> percentile does not change the mean by more than 1 point.

We also find that

- Student-teacher ratio has a consistently negative effect but like for the whole sample, for females when dis-aggregating the sample into urban and rural schools, this effect is not significant. For boys there is a significant negative non-linear effect, but the size of this effect is very small.

- Evening schools perform substantially less well (more so for girls than for boys), urban schools do better than rural schools and there are substantial oblast specific effects.

- Gymnasia and Lycea score 5 to 10 points higher than other school types.

- The gender composition matters little for girls but is significant for boys: more boys among the test takers reduces the average school scores of boys somewhat: going from the 25<sup>th</sup> percentile to the 75<sup>th</sup> percentile in terms of share of boys will decrease the average score by 0.3 to 0.6 points. The fact that we found a negative effect of the share of

39
boys on the school score when using the total school average (girls and boys combined) is thus mainly due to the fact that girls on average score better, but not (or only marginally so) because mixed gender classes have a negative effect on class performance.

- The unemployment rate is never significant but a higher average wage goes together with a slight decrease in points. Schools in bigger (more populated) communities have slightly higher mean scores. This was true for the total school average but also for the male and female average.

- Both for female and male students, the language of choice has a substantial effect on the average grade, with the more students take exams in Ukrainian the better the average Ukrainian score

- Like before, both for males and females the participation ratio has a positive and significant effect on the average score in urban areas. For rural areas, the effect is smaller and only significant for females. This suggests that better schools have higher grades and higher participation, except for male students in rural schools.

- Our explanatory variables explain more of the variation in mean scores for urban schools, and less for rural schools, and more for girls than for boys.

Results for the mathematics and the Ukrainian history exam are broadly similar to what we found so far. It is worth to note however that for males, there is no effect of language choice on math achievement however.

40
# **_Table 9a – Female Students, Ukrainian_**

|||To|tal|||Urb|an|||R|ural||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
||(1)|(2)|(3)|(4)|(1)|(2)|(3)|(4)|(1)|(2)|(3)|(4)|
|# students|0.009***|0.009***|0.012***|0.009***|0.009***|0.009***|0.015***|0.009***|0.003|0.003|0.020***|0.017***|
||16.8|16.11|7.17|5.6|14.96|15.03|8.09|4.77|1.54|1.41|3.67|3.29|
|(# students)<sup>2</sup>|||-0.000**|0|||-0.000***|0|||-0.000***|-0.000***|
||||-2.3|-1.21|||-4.11|-1.63|||-3.38|-3.12|
|Student/Teacher|-0.190***|-0.171***|-0.122|-0.187|-0.082|-0.107|0.007|-0.079|-0.036|-0.033|-0.3|-0.382|
||-3.44|-3.15|-0.83|-1.28|-1.15|-1.53|0.03|-0.37|-0.36|-0.33|-1|-1.32|
|(Stud./Teacher)<sup>2</sup>|||-0.003|0.001|||-0.006|-0.002|||0.006|0.011|
||||-0.44|0.1|||-0.77|-0.26|||0.37|0.72|
|Class Size|-0.073***|-0.053***|-0.325***|-0.279***|0.003|0.033|-0.292*|-0.211|-0.049|-0.052*|-0.191|-0.188|
||-3.61|-2.64|-3.84|-3.32|0.11|1.12|-1.7|-1.25|-1.64|-1.75|-1.57|-1.56|
|(Class Size)<sup>2</sup>|||0.007***|0.006***|||0.007*|0.005|||0.004|0.004|
||||3.52|3.14|||1.94|1.42|||1.09|1.23|
|Urban|1.724***|2.018***|1.926***|1.232***|||||||||
||5.8|6.82|6.07|3.9|||||||||
|Gender Comp.||0.003|0.004|-0.013*||-0.007|-0.007|-0.023*||0.004|0.005|-0.007|
|||0.35|0.58|-1.83||-0.56|-0.5|-1.84||0.52|0.57|-0.82|
|Unemployment<br>rate 2009||0.122|0.12|0.074||0.049|0.031|-0.018||0.093|0.106|0.077|
|||1.62|1.59|1||0.43|0.27|-0.16||0.94|1.06|0.79|
|Average Wage<br>2009||-0.001***|-0.001***|-0.001***||-0.002***|-0.002***|-0.002***||0|0|0|
|||-3.48|-3.62|-4.18||-4.38|-4.38|-4.6||0.24|0.15|-0.2|
|Population||0.008***|0.007***|0.007***||0.007***|0.007***|0.006***||0.114***|0.105***|0.089***|
|||4.04|3.7|3.5||3.06|3.19|3.05||6.69|6.25|5.16|
|Share Ukrainian||7.291***|7.302***|7.158***||7.507***|7.500***|7.330***||6.057***|6.112***|6.015***|
|||15.1|15.11|15.12||11.57|11.63|11.7||8.11|8.19|8.15|

41
|Participation<br>Ratio||||0.091***||||0.174***||||0.055***|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
|||||13.05||||11.98||||6.82|
|_cons|157.635***|157.246***|158.781***|152.888***|157.263***|158.611***|159.879***|146.369***|154.198***|152.828***|153.189***|150.478***|
||217.36|173.75|136.42|121.88|144.11|115.96|71.21|57.63|85.21|80.1|69.16|67.23|
|R Adj sq.|0.218|0.239|0.24|0.258|0.355|0.38|0.382|0.422|0.075|0.088|0.089|0.098|
|N|10730|10723|10723|10723|4890|4886|4886|4886|5840|5837|5837|5837|

The regression also includes oblast dummies, dummies for different types of schools and evening schools. The full table can be found in excel tables which can be made available upon request. *** means significant at the 1% level, ** at the 5 % level and * at the 10 percent level.T statistics are based on robust standard errors for the OLS specifications.

# **_Table 9b – Male Students, Ukrainian_**

|||To<br>|tal<br>|||Ur<br>|ban<br>|||Ru<br>|ral<br>||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
||(1)|(2)|(3)|(4)|(1)|(2)|(3)|(4)|(1)|(2)|(3)|(4)|
|# students|0.010***|0.009***|0.010***|0.009***|0.009***|0.009***|0.016***|0.009***|0|0|0.009*|0.010*|
||17.25|16.22|6.09|5.38|15.34|14.99|7.9|4.88|0.04|-0.02|1.65|1.73|
|(# students)<sup>2</sup>|||0|0|||-0.000***|0|||-0.000*|-0.000*|
||||-0.78|-0.27|||-3.63|-1.3|||-1.77|-1.83|
|Student/Teacher|-0.201***|-0.206***|-0.479***|-0.503***|-0.048|-0.076|-0.381*|-0.469**|-0.036|-0.071|-0.178|-0.164|
||-3.42|-3.53|-3.18|-3.34|-0.66|-1.04|-1.78|-2.24|-0.34|-0.68|-0.57|-0.53|
|(Stud./Teacher)<sup>2</sup>|||0.014***|0.016***|||0.012*|0.016**|||0.001|0|
||||2.6|2.8|||1.69|2.3|||0.07|0.01|
|Class Size|-0.100***|-0.101***|-0.487***|-0.460***|0.005|0.004|-0.602***|-0.552***|-0.084**|-0.097***|-0.247*|-0.250*|
||-4.55|-4.52|-5.53|-5.22|0.16|0.11|-3.54|-3.3|-2.57|-2.98|-1.92|-1.94|
|(Class Size)<sup>2</sup>|||0.011***|0.010***|||0.014***|0.013***|||0.004|0.004|
||||5.03|4.81|||3.86|3.57|||1.18|1.17|
|Urban|2.099***|2.256***|2.424***|2.087***|||||||||
||6.64|7.02|7.11|6.1|||||||||
|Gender Comp.||-0.024***|-0.028***|-0.025***||-0.038***|-0.041***|-0.040***||-0.021**|-0.021**|-0.022**|
|||-3.04|-3.57|-3.26||-2.95|-3.15|-3.12||-2.17|-2.24|-2.32|
|Unemployment<br>rate 2009||-0.054|-0.064|-0.084||0.023|0.018|-0.028||-0.163|-0.159|-0.153|

42
|||-0.67|-0.79|-1.04||0.18|0.14|-0.23||-1.57|-1.52|-1.47|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
|Average Wage<br>2009||-0.001**|-0.001**|-0.001***||-0.001*|-0.001**|-0.001**||0|0|0|
|||-2.08|-2.36|-2.63||-1.87|-1.97|-2.15||-0.5|-0.55|-0.47|
|Population||0.009***|0.006***|0.006***||0.006**|0.005**|0.005**||0.126***|0.119***|0.123***|
|||3.56|2.76|2.66||2.25|2.1|1.98||6.78|6.3|6.35|
|Share Ukrainian||6.568***|6.579***|6.518***||4.626***|4.722***|4.614***||7.418***|7.448***|7.465***|
|||12.88|12.88|12.85||6.83|6.97|6.9||9.49|9.51|9.52|
|Participation<br>Ratio||||0.046***||||0.180***||||-0.012|
|||||6.25||||12.71||||-1.39|
|_cons|148.970***|150.224***|154.541***|151.036***|148.271***|150.637***|156.805***|142.434***|141.009***|141.960***|142.554***|143.334***|
||183.11|139.74|113.34|101.81|131.2|98.1|65.05|53.01|63.84|59.46|52.72|51.8|
|R Adj sq.|0.195|0.211|0.214|0.218|0.321|0.333|0.337|0.376|0.038|0.056|0.056|0.057|
|N|10503|10485|10485|10485|4876|4873|4873|4873|5627|5612|5612|5612|

The regression also includes oblast dummies, dummies for different types of schools and evening schools. The full table can be found in excel tables which can be made available upon request. *** means significant at the 1% level, ** at the 5 % level and * at the 10 percent level. T statistics are based on robust standard errors for the OLS specifications.

43
So far we have focused on the mean score. However, we also have data on the percentage of students in different parts of the distribution. We therefor run regressions with the percentage of students scoring above 173 and the percentage of students scoring below 135.5 (table 10a and 10b).

Overall, the results confirm the findings we made so far (even though, as expected, the signs switch for the regression where we use the bottom students). One exception is that the studentteacher ratio now has, for urban schools, a consistently negative effect on the percentage of students above 173. Given the low variation in that ratio, however, going from the 25<sup>th</sup> percentile to the 75<sup>th</sup> percentile, does not change the percentage of top scoring students by more than 1 percentage point.

44
# **_Table 10a – Top Students, Ukrainian_**

||||Total|||U|rban||||Rural||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
||(1)|(2)|(3)|(4)|(1)|(2)|(3)|(4)|(1)|(2)|(3)|(4)|
|# students|0.012***|0.011***|0.011***|0.008***|0.011***|0.011***|0.014***|0.007**|0.007***|0.006***|0.021***|0.019***|
||15.36|14.4|5.15|3.89|12.83|12.42|5.29|2.55|3.44|2.87|3.68|3.31|
|(# students)<sup>2</sup>|||0|0|||0|0|||-0.000***|-0.000**|
||||-0.23|0.59|||-1.33|0.65|||-2.88|-2.57|
|Student/Teacher|-0.303***|-0.290***|-0.317*|-0.375**|-0.241**|-0.276***|-0.683**|-0.771***|-0.048|-0.03|-0.218|-0.288|
||-4.38|-4.26|-1.85|-2.2|-2.52|-2.92|-2.55|-2.9|-0.44|-0.28|-0.75|-0.99|
|(Stud./Teacher)<sup>2</sup>|||0.003|0.006|||0.017**|0.022**|||0.002|0.006|
||||0.53|1|||2.03|2.53|||0.17|0.5|
|Class Size|-0.051*|-0.045*|-0.418***|-0.423***|0.045|0.044|-0.590**|-0.557**|-0.038|-0.045|-0.189|-0.227|
||-1.94|-1.69|-3.92|-3.98|1.03|0.95|-2.2|-2.09|-1.06|-1.28|-1.36|-1.64|
|(Class Size)<sup>2</sup>|||0.011***|0.011***|||0.015***|0.014**|||0.004|0.005|
||||3.96|4.1|||2.64|2.46|||1.02|1.4|
|Urban|3.691***|3.745***|3.884***|3.212***|||||||||
||9.53|9.85|9.61|7.99|||||||||
|Gender Comp.||-0.094***|-0.094***|-0.102***||-0.131***|-0.133***|-0.141***||-0.084***|-0.084***|-0.090***|
|||-11.9|-11.89|-13.16||-8.21|-8.29|-8.91||-9.24|-9.24|-10.04|
|Unemployment<br>rate 2009||0.017|0.011|-0.04||-0.095|-0.09|-0.145||-0.013|-0.003|-0.035|
|||0.19|0.12|-0.45||-0.6|-0.57|-0.93||-0.11|-0.02|-0.31|
|Average Wage<br>2009||-0.001***|-0.001***|-0.002***||-0.001**|-0.001**|-0.001**||-0.001|-0.001|-0.001*|
|||-3.27|-3.48|-3.97||-2.12|-2.26|-2.36||-1.32|-1.38|-1.71|
|Population||0.013***|0.012***|0.011***||0.012***|0.011***|0.010***||0.179***|0.171***|0.154***|
|||4.49|3.96|3.79||3.54|3.34|3.24||7.11|6.39|5|
|Share Ukrainian||0.058***|0.058***|0.056***||0.060***|0.061***|0.058***||0.040***|0.040***|0.039***|
|||11.37|11.37|11.12||7.4|7.51|7.08||5.96|6.04|5.94|
|Participation<br>Ratio||||0.092***||||0.193***||||0.051***|
|||||11.36||||10.89||||5.59|

45
|_cons|20.388***|25.156***|28.127***|22.302***|21.423***|28.104***|35.492***|20.758***|11.662***|15.815***|16.095***|13.631***|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
||19.95|20.3|17.46|13.09|14.22|14.71|9.99|5.5|4.88|6.2|5.65|4.7|
|R Adj sq.|0.251|0.272|0.273|0.285|0.345|0.365|0.367|0.393|0.047|0.069|0.07|0.076|
|N|10906|10906|10906|10906|4922|4922|4922|4922|5984|5984|5984|5984|

The regression also includes oblast dummies, dummies for different types of schools and evening schools. The full table can be found in excel tables which can be made available upon request. *** means significant at the 1% level, ** at the 5 % level and * at the 10 percent level.T statistics are based on robust standard errors for the OLS specifications.

**_Table 10b – Bottom Students, Ukrainian_**

|||To<br>|tal<br>|||Ur<br>|ban<br>|||R<br>|ural<br>||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
||(1)|(2)|(3)|(4)|(1)|(2)|(3)|(4)|(1)|(2)|(3)|(4)|
|# students|-0.013***|-0.013***|-0.018***|-0.015***|-0.013***|-0.013***|-0.028***|-0.018***|0.003|0.003|-0.014|-0.013|
||-16.1|-15.49|-6.83|-5.84|-15.31|-15.69|-9.56|-6.24|0.8|0.96|-1.45|-1.36|
|(# students)<sup>2</sup>|||0.000***|0.000*|||0.000***|0.000***|||0.000*|0.000*|
||||2.58|1.87|||6.02|3.5|||1.85|1.79|
|Student/Teacher|0.231**|0.231***|0.323|0.382|0.022|0.088|-0.203|-0.074|0.001|-0.001|0.427|0.454|
||2.48|2.58|1.33|1.57|0.19|0.81|-0.62|-0.24|0.01|-0.01|0.85|0.9|
|(Stud./Teacher)<sup>2</sup>|||-0.004|-0.007|||0.014|0.008|||-0.016|-0.017|
||||-0.49|-0.8|||1.31|0.77|||-0.63|-0.7|
|Class Size|0.155***|0.125***|0.673***|0.678***|0.008|-0.035|0.910***|0.862***|0.127**|0.130**|0.267|0.282|
||4.43|3.62|4.55|4.61|0.17|-0.75|3.25|3.2|2.36|2.5|1.22|1.29|
|(Class Size)<sup>2</sup>|||-0.015***|-0.015***|||-0.021***|-0.020***|||-0.004|-0.004|
||||-4.19|-4.31|||-3.5|-3.37|||-0.61|-0.7|
|Urban|-1.132**|-1.933***|-1.845***|-1.166**|||||||||
||-2.27|-3.93|-3.48|-2.18|||||||||
|Gender Comp.||0.190***|0.190***|0.199***||0.178***|0.177***|0.189***||0.197***|0.197***|0.199***|
|||14.56|14.6|15.17||7.42|7.49|8.37||12.71|12.71|12.68|
|Unemployment rate 2009||0.005|0.013|0.065||-0.095|-0.062|0.019||0.134|0.122|0.135|
|||0.04|0.1|0.5||-0.51|-0.33|0.1||0.78|0.71|0.78|
|Average Wage 2009||0.001*|0.001*|0.001**||0.002***|0.002***|0.002***||-0.001|-0.001|-0.001|
|||1.74|1.96|2.28||3|3|3.19||-0.73|-0.67|-0.6|

46
|Population||-0.010***|-0.008***|-0.008**||-0.006*|-0.007**|-0.006*||-0.146***|-0.138***|-0.131***|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
|||-3.3|-2.69|-2.52||-1.94|-2.02|-1.81||-4.15|-3.8|-3.65|
|Share Ukrainian||-0.138***|-0.138***|-0.137***||-0.113***|-0.113***|-0.109***||-0.151***|-0.151***|-0.151***|
|||-14.6|-14.62|-14.66||-9.34|-9.38|-9.38||-9.93|-9.97|-9.98|
|Participation Ratio||||-0.093***||||-0.283***||||-0.02|
|||||-6.98||||-11.7||||-1.24|
|_cons|19.660***|13.176***|9.094***|14.973***|22.591***|14.405***|9.827***|31.458***|24.955***|18.951***|18.027***|18.971***|
||16.05|8.4|4.56|6.58|12.64|6.16|2.77|7.42|7.38|5.37|4.49|4.58|
|R Adj sq.|0.135|0.192|0.193|0.201|0.276|0.319|0.325|0.374|0.048|0.111|0.111|0.112|
|N|10906|10906|10906|10906|4922|4922|4922|4922|5984|5984|5984|5984|

The regression also includes oblast dummies, dummies for different types of schools and evening schools. The full table can be found in excel tables which can be made available upon request. *** means significant at the 1% level, ** at the 5 % level and * at the 10 percent level.T statistics are based on robust standard errors for the OLS specifications.

47
# _d. How good are annual data for measuring educational performance?_

So far we have been using the data from the 2010 EIT. We also have data for the 2008 and 2009 EIT. Given that we have 3 years of data for both inputs and outputs one could argue we can use panel data techniques to estimate the determinants of educational performance in Ukraine. However, yearly test score data can be quite crude measures of educational performance. To illustrate this, we follow Kane and Staiger (2002) who suggest several ways to check to what extent test scores can be used as school level indicators of performance.

First, one can check to what extent scores are correlated over time – that is, to what extent do schools that score well in one year also score well in subsequent years. The idea behind this measure is that one reasonably can expect school quality to be, to a large extent, stable over time. If our school performance measure varies a lot from one year to another year, with changes in one year reverting the next year, our school performance measure is likely to be a noisy indicator of the underlying real school quality. We use the Ukrainian exam as this exam is compulsory for everybody who is interested in further studies, and we use the mean score by school as score indicator.

**_Figure 2: Correlation in Test Scores_**

<!-- Start of picture text --> Correlation in Test Scores over Time<br>90<br>80<br>70<br>60<br>50<br>40 Ukraine<br>US<br>30<br>20<br>10<br>0<br>0 1 2 3<br>Number of Years Apart<br>Correlation<br><!-- End of picture text --> 48
As can be seen from the above figure, the correlation between scores in 2 subsequent years is substantial and positive (about 0.61 in Ukraine) and this correlation decreases over time. Note that the correlation in the US (where fourth grade math scores are used) is substantially higher, but also decreases over time. One explanation for this difference is that secondary schools in the US are substantially bigger – if we restrict the sample to the schools that have more than the median of graduates taking the Ukrainian test, we get correlations close to 0.8.

Next, one can look to what extent changes in scores are correlated. In case changes are purely random, one would expect increases in one year to be followed by decreases in the next year and the correlation would be -0.5. Kaine and Staiger (2002) find a correlation of -0.37 for the US data. In our sample of Ukrainian schools, we find -0.465. This suggests that 93% (0.465/0.5) of the changes from one year to another are transitory rather than permanent<sup>31</sup> . The latter implies that by averaging out yearly variations and taking averages over longer periods one will get closer to the stable underlying school quality variable.

We come to the same conclusion if we use as a performance indicator the percentage of students scoring 150 or above (reflecting to what extent a school‟s students score (approximately) above the national average, correlations of 0.5, 0.46 and -0.454), the percentage of students scoring below 135.5 (roughly the bottom 20 percent of students, correlations of 0.41, 0.37 and -0.469) or the percentage of students scoring above 173 (roughly the top 10% students, correlations of 0.548, 0.513 and -0.485<sup>32</sup> ).

The discussion above argues against using panel data techniques: panel estimation techniques focus on the variation over time while the variation in educational quality over time is expected to be small relative to the variation across schools. In addition, given that changes in inputs over time are also relatively small (compared to the cross-sectional variation and compared to the kind of policy changes we are analyzing here) the effect of errors in variables is likely to be substantial in a panel data set-up.

> 31 A similar sized correlation is obtained when restricting the sample to the bigger schools (above median number of students taking the Ukrainian test)

> 32 It is impossible to aggregate the categories in such a way that the top and the bottom group would be approximately of equal size.

49
We therefore run regressions using weighted averages of the mean score over the three EITs, 2008-2009-2010, using the students participating in each year as weights. We use these weights both for the dependent and the explanatory variables<sup>33</sup> .

# _e. Using Weighted Averages over 3 Years_

Table 11a and 11b present the regression results for the participation ratio and the mean Ukrainian score.

Given that we take out part of the random variation by taking weighted averages, it comes to no surprise that the explanatory power of our regressions increases, adding roughly 10 percentage points to the adjusted R<sup>2</sup> .

In general, the results are similar to what we found above when just using 2010 data, albeit that the sizes of the class and school size effects are slightly smaller.

> 33 An implicit assumption here is that the production functions are stable over time- this is likely to be a harmless assumption, even though there were slight changes in the organizational procedure of the tests ( f.e. some very specific groups of students were not required to participate) from  year to year.

50
# **_Table 11a – Ukrainian Language, Participation Ratio_**

|||To|tal|||Ur|ban|||Ru|ral||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
||(1)|(2)|(3)|(1)|(2)|(3)|(1)|(2)|(3)|(1)|(2)|(3)|
|# students|0.011***|0.011***|0.022***|0.022***|0.011***|0.011***|0.028***|0.028***|0.008**|0|0.028***|0.028***|
||14.94|14.76|9.51|8.74|13.48|13.39|10.59|11.88|2.49|-0.13|2.74|3.48|
|(# students)<sup>2</sup>|||-0.000***|-0.000***|||-0.000***|-0.000***|||-0.000**|-0.000***|
||||-5.92|-4.67|||-8.04|-7.96|||-2.52|-3.5|
|Student/Teacher|-0.047|0.017|0.552**|0.577***|-0.004|0.004|0.336|0.35|0.217|0.262|1.789**|1.826***|
||-0.52|0.18|2.32|2.78|-0.04|0.04|1.08|1.48|1.17|1.44|2.14|3.76|
|(Stud./Teacher)<sup>2</sup>|||-0.029***|-0.030***|||-0.017*|-0.017**|||-0.112**|-0.113***|
||||-2.85|-3.51|||-1.68|-2.03|||-2.21|-4.32|
|Class Size|-0.113***|-0.111***|-0.548***|-0.619***|0.108**|0.123***|-0.874***|-1.018***|-0.181***|-0.199***|0.148|0.091|
||-3.16|-3.04|-3.45|-4.29|2.45|2.59|-2.9|-4.07|-3.12|-3.48|0.56|0.39|
|(Class Size)<sup>2</sup>|||0.010**|0.012***|||0.022***|0.025***|||-0.014*|-0.013*|
||||2.48|3.02|||3.24|4.3|||-1.83|-1.89|
|urban==1|7.657***|7.480***|6.874***|6.993***|||||||||
||18.36|18.23|15.66|16.69|||||||||
|Gender Comp.||0.208***|0.209***|0.209***||0.053*|0.054*|0.050**||0.258***|0.260***|0.262***|
|||12.79|12.89|15.59||1.85|1.92|2.53||13.04|13.33|14.83|
|Unemployment rate 2009||0.124|0.146*|0.152*||0.198|0.18|0.203||0.111|0.145|0.147|
|||1.48|1.73|1.89||1.53|1.4|1.62||1.06|1.39|1.41|
|Average Wage 2009||0.001|0.001|0.001||0|0|0||0.001*|0.002**|0.001|
|||1.51|1.41|1.27||-0.08|-0.15|-0.14||1.8|1.97|1.63|
|Population||0|0|0.001||0|0.001|0.001||1.181***|1.126***|1.141***|
|||-0.08|0.37|0.37||0.3|0.6|0.72||4.25|4.13|5.76|
|Share Ukrainian||0.019***|0.019***|0.019***||0.016**|0.016**|0.017**||0.021*|0.022**|0.022**|
|||2.94|2.94|3.27||2.01|2.08|2.54||1.89|2.02|2.28|
|_cons|85.403***|74.391***|74.494***|75.616***|87.765***|84.430***|89.448***|91.395***|82.578***|66.452***|55.629***|56.676***|
||86.91|50.41|38.29|40.65|66.83|36.88|25.6|31.27|27.98|20.16|12.83|13.54|

51
|sigma||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
||||11.718***||||9.146***||||12.966***|
|R Adjsq.|||129.76||||84.7||||98.3|
|N|0.408|0.425|0.428|0.568|0.57|0.578||0.164|0.206|0.216||
||8663|8661|8661<br>8661|3695|3695|3695|3695|4968|4966|4966|4966|

The regression also includes oblast dummies, dummies for different types of schools and evening schools. The full table can be found in excel tables which can be made available upon request. *** means significant at the 1% level, ** at the 5 % level and * at the 10 percent level.T statistics are based on robust standard errors for the OLS specifications.

**_Table 11b – Ukrainian Language, Mean Score_**

|||To|tal|||Ur|ban|||Ru|ral||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
||(1)|(2)|(3)|(4)|(1)|(2)|(3)|(4)|(1)|(2)|(3)|(4)|
|# students|0.009***|0.009***|0.009***|0.007***|0.008***|0.008***|0.016***|0.008***|0|-0.002|0.010***|0.009***|
||18.93|19.08|7.05|5.41|15.76|16.08|9.49|4.94|-0.11|-1.32|2.81|2.61|
|(# students)<sup>2</sup>|||0|0|||-0.000***|-0.000**|||-0.000***|-0.000***|
||||-1.36|-0.3|||-5.28|-1.98|||-3.5|-3.38|
|Student/Teacher|-0.169***|-0.198***|-0.052|-0.114|-0.095|-0.154**|-0.09|-0.186|0.097|0.057|0.175|0.112|
||-3.77|-4.57|-0.42|-0.96|-1.49|-2.5|-0.46|-1.02|1.37|0.84|0.87|0.54|
|(Stud./Teacher)<sup>2</sup>|||-0.005|-0.002|||-0.002|0.003|||-0.015|-0.011|
||||-1.03|-0.37|||-0.36|0.43|||-1.48|-1.04|
|Class Size|-0.102***|-0.083***|-0.556***|-0.495***|0.027|0.068*|-1.062***|-0.811***|-0.083***|-0.089***|-0.087|-0.092|
||-5.04|-4.15|-6.29|-5.72|0.77|1.85|-4.44|-3.79|-3.18|-3.58|-0.72|-0.77|
|(Class Size)<sup>2</sup>|||0.013***|0.012***|||0.026***|0.020***|||-0.001|-0.001|
||||5.57|5.23|||4.89|4.15|||-0.32|-0.18|
|Urban|1.670***|2.099***|2.061***|1.296***|||||||||
||7.08|9.04|8.4|5.54|||||||||
|Gender Comp.||-0.120***|-0.121***|-0.144***||-0.136***|-0.135***|-0.151***||-0.122***|-0.122***|-0.131***|
|||-15.46|-15.53|-18.53||-8.31|-8.27|-10.44||-14.12|-14.09|-14.88|
|Unemployment<br>rate 2009||0.029|0.036|0.02||0.003|0.02|-0.032||0.004|0.016|0.011|
|||0.67|0.84|0.47||0.03|0.24|-0.39||0.09|0.32|0.22|
|Average Wage||0|0|0||-0.001|-0.001|-0.001||0|0|0|

52
|2009|||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
|||-0.95|-1.19|-1.53||-1.27|-1.35|-1.41||0.6|0.61|0.47|
|Population||0.002***|0.001*|0.001*||0.001|0.001|0||0.328***|0.303***|0.264***|
|||2.64|1.65|1.67||1.05|0.76|0.55||3.66|3.43|3.14|
|Share Ukrainian||0.060***|0.060***|0.058***||0.046***|0.046***|0.042***||0.064***|0.065***|0.064***|
|||16.17|16.2|16.55||8.64|8.87|9.34||11.86|11.96|12.05|
|Participation<br>Ratio||||0.111***||||0.287***||||0.035***|
|||||16.81||||20.44||||4.89|
|_cons|155.632***|159.839***|162.916***|154.634***|155.255***|160.703***|170.099***|144.392***|146.993***|151.392***|149.832***|147.877***|
||225.59|187.01|146.63|126.33|143.91|108.96|63.07|52.27|83.11|82.73|72.38|70.85|
|R Adj sq.|0.361|0.404|0.407|0.432|0.476|0.503|0.511|0.593|0.156|0.221|0.224|0.228|
|N|8663|8661|8661|8661|3695|3695|3695|3695|4968|4966|4966|4966|

The regression also includes oblast dummies, dummies for different types of schools and evening schools. The full table can be found in excel tables which can be made available upon request. *** means significant at the 1% level, ** at the 5 % level and * at the 10 percent level.T statistics are based on robust standard errors for the OLS specifications.

53
# **V. Conclusions**

The empirical analysis undertaken in this study points to the fact that the size of schools and classes does not appear to be very important for the educational quality of secondary schools in Ukraine, a finding that is broadly in line with what has been found for other countries and hence there is little evidence for a trade-off between efficiency and quality. In the case of Ukraine, if anything, our findings are suggestive that school size has a small positive effect and that class size has no significant effect on school performance.

Table 12a and 12b summarize the effects of class size and school size across specifications. Our results show that bigger schools tend to have higher participation ratios and tend to have higher mean test scores, more students among the top students and less students among the bottom students. This is especially true for urban schools, where the difference between the 25<sup>th</sup> percentile (about 300 students) and the 75<sup>th</sup> percentile (over 600 students) of the school size distribution is about 4 test score points and about 7 percentage points in terms of participation ratio. For the rural schools, the effect of moving from the 25<sup>th</sup> percentile (about 100 students) and the 75<sup>th</sup> percentile (over 200 students) of the school size distribution is substantially smaller, at roughly half the values found for urban schools. At the same time, the rural area estimates are likely to be less affected by a possible endogeneity bias.

Since increasing the size of schools, _on average,_ will result in an increase in the size of classes, we could wonder what would happen with performance. Indeed, not much. Going from the 25<sup>th</sup> percentile to the 75<sup>th</sup> percentile of the class size distribution does not affect the performance much, relative to going from the 25<sup>th</sup> percentile to the 75<sup>th</sup> percentile of the school size distribution – often the difference is even insignificant and sometimes the difference is even positive.

Our estimates also imply that there seems to be an „optimal‟ size, a point after which further increasing school size goes together with lower mean scores. Our estimates of that point (which varies from about 400 for rural schools to over 1000 for urban schools), however, show that few Ukrainian schools already have reached that point. Our estimated optimal point is also substantially higher than 100 students suggesting that the 100-student cut-off point used by the 54
Ukrainian government in the Budget Declaration 2011 for ordering the optimization of complete schools (levels I-III) may be very conservative, especially for urban schools, almost none of which are below this threshold and for which the estimated optimal point is often over 1000. This suggests there is a lot of room for consolidation.

From a policy point of view, our findings suggest that consolidating the network of schools through a downsizing in the number of small schools and a transfer process of students in those schools to neighboring ones is unlikely to harm school performance on the EIT. If anything it may even increase educational outcomes. Of course, an important caveat here is that this “no harm conclusion” is only likely to hold if the organization of the transfer and of the commuting to the receiving schools is organized efficiently.

While our results are suggestive, they further need to be interpreted with caution as we have not been able to investigate in detail to what extent our findings reflect causal relationships rather than correlation. Nor can we claim that these empirical findings can be extended to schools other than complete schools (level I-III), since the analysis was undertaken with measures of school performance for 12<sup>th</sup> -graders. Both these areas remain avenues for further research as well as the analysis of the student-level EIT data as opposed to the school-level analysis presented here<sup>34</sup> .

The consolidation of the network of schools in Ukraine is an important area of reform for improving the efficiency of educational spending and for achieving fiscal sustainability of the sector. If managed well, a sound optimization strategy can bring tangible results on the access, equity and quality fronts. But rationalizing the network of schools is usually one of the most difficult education reforms since it usually faces with strong resistance in communities, and among parents and teachers. Therefore, a necessary pre-requisite to embark in such reforms is a strong political will and coordinated efforts of Government agencies and local authorities to materialize. A detailed roadmap with a thorough nationwide analysis and realistic investment plans should be clearly defined. And public campaigns need to be incorporated as an essential

> 34 In a first attempt, Thoryk (2011) uses 2007 TIMSS data to estimate the effect of school size on school performance in transition countries. Overall his country specific estimates suggest there is little relation between school size and performance. His results for Ukraine suggest an insignificant effect of size on 4<sup>th</sup> grade science and 8<sup>th</sup> grade mathematics, an inverted U shape for 4th year math and a U-shaped relationship for 8<sup>th</sup> grade science. While the latter two results are significant, the size of the effect is found to be negligible.

55
component so as to ensure wide dissemination of the rationale behind it and a clear explanation of how benefits from optimization will outweigh costs for all key stakeholders.

56
**_Table 12a: Effect of school size, difference in dependent variable, relative to median school size_**

|Dependent Variable|type|FirstQuartile|Median|ThirdQuartile|At Max|Max at|
|---|---|---|---|---|---|---|
|Participation Ratio(Ukrainian)|urban|-3.8|0|3.5|6.3|1060|
|Participation Ratio(Ukrainian)|rural|-1.5|0|2|5.6|470|
|Average Ukrainian Score|urban|-2|0|2|6.4|1600|
|Average Ukrainian Score|rural|-0.4|0|0.5|1.3|427|
|Average Mathematics Score|urban|-2|0|2.1|6.8|1641|
|Average Mathematics Score|rural|-0.4|0|1.3|3.1|443|
|Average Ukrainian HistoryScore|urban|-1|0|1.2|8.5|2159|
|Average Ukrainian HistoryScore|rural|-0.3|0|0.5|1.1|422|
|Average Ukrainian Score - Female Students|urban|-1.8|0|1.9|5.9|1584|
|Average Ukrainian Score - Female Students|rural|-0.6|0|0.8|2|446|
|Average Ukrainian Score - Male Students|urban|-2|0|2.1|7.5|1762|
|Average Ukrainian Score - Male Students|rural|-0.6|0|0.8|2|446|
|% students having> 173 on the Ukrainian Exam|urban|-2|0|2.3|15.6|3065|
|% students having> 173 on the Ukrainian Exam|rural|-0.7|0|1|3.1|538|
|% students having< 135.5 on the Ukrainian Exam|urban|3.2|0|-3.2|-7.5|1291|
|% students having< 135.5 on the Ukrainian Exam|rural|0.36|0|-0.4|-0.7|316|
|Participation Ratio - weighted average variables|urban|-2.9|0|2.7|4.9|1105|
|Participation Ratio - weighted average variables|rural|-0.9|0|1.1|2.5|430|
|Average Ukrainian Score- weighted average variables|urban|-1.8|0|1.8|4.8|1408|
|Average Ukrainian Score- weighted average variables|rural|-0.3|0|0.3|0.5|344|

Differences are percentage points for the participation ratios and points for the test scores For the 2010 regressions, school quartiles are at about 100, 140 and 210 for rural areas and 305,465 and 666 for urban areas. For the weighted average regressions, quartiles are at 110,154 and 225 for rural areas and 322, 484 and 685 for urban areas 57
**_<u>Table 12b: Effect of class size, difference in dependent variable, relative to median class size</u>_**

|Dependent Variable|Type|First|Media|Third|at|Max/Min|Signif.|
|---|---|---|---|---|---|---|---|
|Participation Ratio(Ukrainian)|urban|-0.2|0|0.4|-0.3|14.9|NS|
|Participation Ratio(Ukrainian)|rural|-0.5|0|-0.4|0|13.1|S|
|Average Ukrainian Score|urban|0.1|0|0.2|0|20.8|S|
|Average Ukrainian Score|rural|0.4|0|-0.3|-0.6|28|Almost|
|Average Mathematics Score|urban|-0.1|0|0.2|-0.1|17.9|Almost|
|Average Mathematics Score|rural|0.3|0|-0.3|-1.3|55.2|NS|
|Average Ukrainian HistoryScore|urban|0.1|0|0.2|0|21.5|S|
|Average Ukrainian HistoryScore|rural|0.7|0|-0.5|-0.7|22.4|S|
|Average Ukrainian Score - Female Students|urban|0|0|0.22|0|20.1|S|
|Average Ukrainian Score - Female Students|rural|0.4|0|-0.3|-0.6|25.6|Almost|
|Average Ukrainian Score - Male Students|urban|0.1|0|0.3|0|21|S|
|Average Ukrainian Score - Male Students|rural|0.6|0|-0.6|-1|28.4|Almost|
|% students having> 173 on the Ukrainian Exam|urban|-0.1|0|0.6|-0.1|19.1|S|
|% students having> 173 on the Ukrainian Exam|rural|0.4|0|-0.3|-0.5|23.8|NS|
|% students having< 135.5 on the Ukrainian|urban|-0.2|0|-0.4|0|21.2|S|
|% students having< 135.5 on the Ukrainian|rural|-0.7|0|0.6|1.9|35.3|NS|
|Participation Ratio - weighted average variables|urban|-0.2|0|0.5|-0.2|20.3|S|
|Participation Ratio - weighted average variables|rural|0.9|0|-1.4|1.4|5.2|Almost|
|Average Ukrainian Score- weighted average|urban|-0.2|0|0.6|-0.2|20.3|S|
|Average Ukrainian Score- weighted average|rural|0.4|0|-0.5|3.2|-38|NS|

Differences are percentage points for the participation ratios and points for the test scores For the 2010 regressions, school quartiles are at about 100, 140 and 210 for rural areas and 305,465 and 666 for urban areas. For the weighted average regressions, quartiles are at 110,154 and 225 for rural areas and 322, 484 and 685 for urban areas 58