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# Determinants and Consequences of Language-in-Education Policies

Christelle Garrouste

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Christelle Garrouste. Determinants and Consequences of Language-in-Education Policies. Department of Education, Stockholm University. Studies in comparative and international education, ISSN 0348-9523 (74), 2007, Studies in comparative and international education, ISSN 0348-9523, Stockholm University, 978-91-7155-517-5 (print). hal-05190369

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Public Domain
DETERMINANTS AND CONSEQUENCES
OF LANGUAGE-IN-EDUCATION
POLICIES

Essays in Economics of Education

Christelle Garrouste

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Institute of International Education
Department of Education
Stockholm University
2007
© Christelle Garrouste 2007

Institute of International Education

Department of Education

Stockholm University

SE-10691 Stockholm, Sweden

All rights reserved

ISBN 978-91-7155-517-5

ISSN 0348-95-23

Printed in Sweden by

US-AB Print Center, Stockholm 2007
*To my father*
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ABSTRACT

This thesis consists of three empirical studies in economics of education on the determinants and consequences of language-in-education (LiE) policies. The “Environmental settings – Inputs – Processes – Immediate outcomes – Long-term outcomes” (EIPOL) evaluation model is applied to LiE policies and programs and serves as the overall framework of this research (see Introductory Chapter). Each study then targets at least one stage of the EIPOL framework to test the validity of the “green” vs. “free-market” linguistic theories. Whereas the two first studies derive models tested empirically in the African context, the third is tested on a sample of countries from the International Adult Literacy Survey (IALS).

The first study, *Rationales to Language-in-Education Policies in Postcolonial Africa: Towards a Holistic Approach*, considers two issues. First, it explores the factors affecting the choice of an LiE policy in 35 African countries. The results show that the countries adopting a unilingual education system put different weights on the influential parameters than countries adopting a bilingual education system and that both groups of countries validate somehow both the “green” and the “free-market” approaches. Second, the article investigates how decision makers can ensure the optimal choice of language(s) of instruction by developing a non-cooperative game theoretic model with network externalities. The model shows that it is never optimal for two countries to become bilingual, or for the majority linguistic group to learn the language of the minority group, unless there is minimum cooperation to ensure an equitable redistribution of payoffs. This finding confirms the “free-market” theory.

The second study, *The Role of Language in Learning Achievement: A Namibian Case Study*, investigates the role played by home language and language proficiency on mathematics scores of 5048 Grade-6 learners in 275 Namibian schools, via the second survey data by the Southern and Eastern Africa Consortium for Monitoring Educational Quality (SACMEQ). Hierarchical linear modeling is used to partition the total variance in mathematics achievement into its within- and between-school components. Results of the analysis show that although home language plays a limited role in explaining within- and between-school variations in mathematics achievement, language proficiency, when proxied by reading scores, plays a significant role in the heterogeneity of results. Thus, confirming the role of language skills in learning achievement and so validating the “green” theory.

Finally, the third study, *Language Skills and Economic Returns*, investigates the economic returns to language skills, assuming that language competencies constitute key components of human capital. It presents results from eight countries enrolled in the International Adult Literacy Survey (IALS). The study finds commonalities between countries in terms of the valuing of language skills, independent of the type of language policy applied at the national level. In each of the eight countries compared, skills in a second language are estimated to be a major factor constraining wage opportunities. This study validates the “free-market” theory.

**Descriptors:** Language-in-education policies, decision making analysis, non-cooperative game, language skills, hierarchical linear modeling, human capital theory, rate of return analysis, post-colonial Africa, IALS, SACMEQ

ISBN 978-91-7155-517-5

ISSN 0348-95-23
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# CONTENTS

ABSTRACT..................................................................................................................5

ACKNOWLEDGEMENTS................................................................................................9

INTRODUCTION........................................................................................................11

STUDY I Rationales to Language-in-Education Policies in Postcolonial Africa: Towards a Holistic Approach........................................................................25

STUDY II The Role of Language in Learning Achievement: A Namibian Case Study................................................................................................................63

STUDY III Language Skills and Economic Returns................................................97

ANNEXES ..................................................................................................................127
Table A Current language settings of countries in Study I

Table B Current external settings of countries in Study I (economic and financial dependency)
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ACKNOWLEDGEMENTS

This thesis is the result of a long intellectual and life journey, which started many years
ago when I was still a little girl and was listening to my family's stories about former
French Indochina and Africa. My need to explore my family's history and, beyond that, to
understand the tenants and consequences of that significant piece of World's history that is
colonialism, have motivated me to study fervently international economics and
international relations at university. I was seeking answers to naive questions, such as,
what impact does colonialism still have on former colonies and how can these countries
emerge successfully from that past. During an internship at UNESCO in 2001, I came
across the very specific field of international and comparative education and realized what
powerful tools it could provide me to explore these questions. It became then obvious that
the way national education policies were formulated was not only one of the tenants and
consequences of colonialism, but also one of the keys for former colonies to move forward
from that past.

Consequently, in 2002, I moved to Sweden, Stockholm, and embarked on a long
and exciting PhD journey at the Institute of International Education (IIE). The people met
there have all greatly stimulated me intellectually by their exceptional world culture, field
experience and/or scientific knowledge. The fact that IIE is in the true sense of the word an
international and cross-disciplinary working environment fulfilled all my expectations as a
young and hungry-for-knowledge researcher. The support from Professor Chinapah, who
advised me to apply to IIE, Professor Tuijnman, who was my initial supervisor at IIE, and
Professor Daun, who took over my supervision during the later stages of my thesis, has
enabled me to explore freely all the corners of this topic. Thanks should also be addressed
to Dr. Benson from the Center of Bilingual Studies at Stockholm University and Dr.
Limage from UNESCO for their support and enthusiasm for my topic and feedback on
early drafts of Study I, and Dr. Taylor for proof reading the introduction of this work.

Yet, this work would probably never have been completed without the academic
year spent at Teachers College, Columbia University, in 2004-2005, under the supervision
of Professor Levin. A very special thank goes therefore to Professor Levin and Professor
Steiner-Khamsi for their availability and wise advises, as well as to Professor Garcia and
Professor Rivera-Batiz for fruitful discussions on the whole thesis.
The Department of Economics of Stockholm University has also provided me with econometrics tools that enabled the completion of the empirical studies presented in this thesis. Moreover, the Marie Curie Fellowship obtained at the Department of Economics of Padua University has provided me with the final methodological inputs at the very last stage of this work. Special thanks go to Professor Brunello, Professor Rettore and Professor Battistin for sharing with me their extended research experience via wise and constructive comments and suggestions on Study II.

Furthermore, I would like to address my gratitude to all the Government officers, NEPRU and UNAM researchers, SIDA officers, school headmasters, school inspectors, teachers and students met during my fieldtrips to Namibia in December 2003 and April-May 2004 in preparation of Study II. They have all shown great enthusiasm for this project and provided me with all the support I needed. Thank you all, I will come back!

Special thanks to all my friends in and outside academia all over the world for their magnificent friendship and support throughout this journey. No need to list any names here, you recognize yourselves!

Last but not least, I want to dedicate this work to my loving family who has brought me where I am today, especially my beloved Dad, my Mum and my brother Erik, but also Massimo who knows how to stimulate my soul and brain like no other and who is leading me through my next life journey.

Christelle Garrouste

Stockholm, November 2007
# INTRODUCTION

The dominant monolingual orientation is cultivated in the developed world and consequently two languages are considered a nuisance, three languages uneconomic and many languages absurd. In multilingual countries, many languages are facts of life; any restriction in the choice of language is a nuisance; and one language is not only uneconomic, it is absurd (Pattanyak, 1984; quoted by Skutnabb-Kangas & Garcia, 1995, p. 221).

## 1. General Framework of the Thesis

The present thesis builds upon the paradoxical position endorsed by the education sector as a mediator between two opposite linguistic theoretical approaches. On the one hand, the “green” theory of ecological protection claims that endangered languages should be protected by all means respecting linguistic human rights. On the other hand, the “free-market” theory advocates for a homogenization of the market’s communication tools to facilitate trade in globalized markets (Kibbee, 2003)<fnref n="1" />.

It is in this complex ideological environment that education policies have to define which language(s) should be selected as media of instruction within the classroom. Answering that question is of course not straightforward since the type of language-in-education (LiE) policy adopted by a government reflects its social, cultural and economic ambitions.

The present thesis adopts a holistic approach to the choice of LiE policies by suggesting the consideration of both the rationales and the consequences of an LiE option in the decision making process. Such an approach enables the constructive confrontation of the two theoretical linguistic schools by highlighting their complementarities rather than their oppositions. More concretely, this thesis opts for the “Environmental settings – Inputs – Processes – Immediate outcomes – Long-term outcomes” (EIPOL) grid of evaluation suggested by Bhola (1990). Within this grid, *environmental settings* aim at providing information on the settings to be able to make planning decisions; *inputs* aim at making programming decisions such as alternative project designs and personnel decisions; *process* aims at making decisions related to methodologies and implementation; *immediate*

<footnote n="1">¹ For more details about the tenants of this debate, see Study III.</footnote>
*outcomes* cover learning outcomes and other intermediary outcomes of the program; and
*long-term outcomes* cover the long-term effects of the program on the educational and
socio-economic domains (ibid.).

The environmental settings are here defined according to Lewis' (1980) classification in terms of diffusion variables, setting variables and mobility variables and a distinction is made between private and social outcomes (or benefits) with respect to the principles of the human capital approach.

As Figure 1 displays, this classification enables the inclusion of all the dimensions necessary for the evaluation of an LiE policy, and constitutes therefore an ideal structure for the design of this thesis' overall conceptual framework. The theoretical assumptions grounding this framework are presented in each of the three studies compiled for this thesis: Study I – Rationales to Language-in-Education Policies in Postcolonial Africa: Towards a Holistic Approach; Study II – The Role of Language in Learning Achievement: A Namibian Case Study; and Study III – Language Skills and Economic Returns.

Each of the three studies targets specific levels of analysis of this framework. For instance, Study I targets explicitly the environmental settings, inputs and process levels. In turn, Study II, by addressing the role of languages in the learning achievement of Namibian grade-6 pupils, targets the private immediate outcomes dimension. Finally, Study III targets the social immediate outcomes and long-term private outcomes of the framework.

<figure><img src="image_6.png" /><figcaption>Figure 1 General Framework of the Thesis</figcaption></figure>

Note: a. Social welfare designates civic involvement, democratic empowerment, social cohesion, etc.
## 2. Aims and Objectives of the Research

The overall objective of this thesis is to investigate the determinants and consequences of LiE policies in the frame of the theoretical debate opposing the “green” and the “free-market” theories, to identify which level of evaluation each theory serves best. It is assumed that neither of the two approaches is sufficient to explain all the levels of evaluation identified in Figure 1. Rather, it is believed that either approach can be validated as optimal from a decision-making point of view according to which level of analysis is identified as the priority by the decision maker.

This potential complementary nature of the two theories is tested by each study within this thesis. More specifically, each study aims at answering the following questions:

### Study I:

A. How much do environmental settings affect the nature of LiE policies in postcolonial Africa?

A conceptual and theoretical framework is developed based on sociolinguistics literature and tested empirically on 35 African countries with ordered logistic regression (see Tables A and B in Annexes). The main hypothesis is that in some countries, internal factors (e.g., behavioral, community-type and institutional settings) might have a larger impact on the number of languages retained as media of instruction than external factors (e.g., financial and economic dependency, colonial history and openness to external ideologies). If so, the “green” theory is expected to be validated. In the opposite case of a comparatively stronger position of external factors the “free-market” is expected to be validated.

B. What is the optimal decision for a LiE policy-maker?

A non-cooperative game with network externalities is developed to inform this issue. The assumption is that the most optimal LiE policy ranks the language of the majority group first as the medium of instruction. This implies that the “free-market” theory should be validated unless a cooperative approach is adopted by the players of the game.

### Study II:

A. How much do pupils' linguistic characteristics affect mathematics achievement compared to some other individual and structural parameters?
A hierarchical linear model (HLM) is developed and tested on Grade-6 Namibian learners, controlling for within- and between-school variations. In this model, the assumption is that mathematics achievement is facilitated by language proficiency, which is itself facilitated by mother-tongue instruction. The “green” theory is therefore expected to be validated by this model. The data used are all issued from the Namibian SACMEQ II survey but the modeling process results mainly from non-quantitative observations gathered upon two short field visits to Namibia in December 2003 and April-May 2004².

## Study III:

A. Does proficiency in the official language(s) play a significant role on wages?

B. Are language skills more rewarded in countries applying an official bilingual policy than in countries applying another type of language policy?

An empirical human capital model is developed to elucidate both questions controlling for gender and immigration status. The assumptions are, first, that language skills are expected to have a positive impact on wage opportunities and, second, that the reward of language skills are higher in countries implementing a bilingual LiE policy. These assumptions are tested using the International Adult Literacy Survey (IALS) for eight countries. In this last study, the “green” theory is expected to be validated if wage opportunities are positively affected by language skills in non-international or dominant languages, and if the second assumption is true. Otherwise, the “free-market” theory will be validated.

## 3. Main Findings

Study I's first model shows that of the 35 countries considered, the countries adopting a unilingual education system weigh differently the environmental parameters than countries adopting a bilingual education system. For instance, multilingual policies appear positively influenced by both external settings and community-type settings, and negatively influenced by institutional settings and degree of openness.

These results neither validate or invalidate the hypothesis in favor of the "green" vs. "free-market" theory, which demonstrates that both theoretical approaches may be of equal validity when addressing Bhola's (1990) three first levels of evaluation (i.e. environmental settings, inputs and process).

<footnote n="2">² See acknowledgements in Study II.</footnote>
Study I's second model confirms the hypothesis in favor of the "free-market" theory by demonstrating that it is never optimal for two countries to become bilingual in one another's language, or for the majority linguistic group to learn the language of the minority group, unless there is minimum cooperation to ensure an equitable redistribution of payoffs.

In turn, Study II suggests that although home language plays a limited role in
explaining within- and between-school variations in Namibian pupils' mathematics
achievement, language proficiency (proxied by reading scores) plays a significant role at
both levels of analysis, thus supporting the significant role of language in learning
achievement. This study confirms the hypothesis in favor of the "green" theory.

Finally, Study III reveals commonalities between the eight countries of the sample in terms of language skills valuing, independent of the type of language policy, confirming the hypothesis that the higher the second language skills the higher the wage opportunities. However, this positive effect of language skills on earnings is only observed for skills in an international or dominant language, which confirms the "free-market" theory at the expense of the "green" theory.

**4. Definitions and Delimitations of the Research**

Among the terms recurrently used in this study and grounding its *raison d'être* are
'language-in-education policy', 'bilingual education policy', 'bilingual skills', 'value' of
bilingual skills, and 'literacy'. Although the theoretical background of each concept is
depicted in the following studies, a short definition of each term is presented to avoid any
lexical confusion and to delimitate the scope of the study.

The term ‘language-in-education (LiE) policy’ is, throughout this dissertation, used
to refer to the third element of language planning, named by Cooper (1989) as ‘acquisition
planning’. According to language policy theories, ‘language planning’ corresponds to the
activity – most visibly undertaken by governments because of the massive changes it
involves in a society – that aims at changing the linguistic behavior of a speech
community. On the other hand, ‘language policy’ refers to the “body of ideas, laws,
regulations, rules and practices intended to achieve the planned language change in the
society, group or system” underlying the actual language planning process (Kaplan &
Baldauf, 1997, p. xi)<fnref n="3" />. Language planning consists of three elements: status planning, corpus planning and acquisition planning. The two first derive from Kloss' (1969) addition to Haugen's (1966) *Model of language planning*, and the third was later introduced by Cooper (1989). Kloss (1969) defined corpus planning as concerned with the internal structure of the language, and status planning as the efforts undertaken to change the use and function of a language within a given society. Cooper (1989) later added acquisition planning to cover the efforts to spread and promote the learning of a language. Because most of these efforts are monitored by the education system, 'acquisition planning' is also called 'language-in-education policy' (see Study I for a detailed classification of language policies and LiE policies).

Note that countries are classified in this work in terms of their ‘official’ LiE policy with no effort made to verify whether the policy is actually implemented or not. This delimitation constitutes a limitation, which could have been overcome with a rigorous qualitative investigation in absence of time or budget constraints. This limitation should be taken into consideration in the interpretation of the results.

Further, the definition of bilingual education retained for this dissertation (in Study I and Study III) is the one offered by Fishman (1979), in which, “[i]n very general terms, bilingual education implies some use of two (or more) languages of instruction in connection with teaching other than language per se” (p. 12). Consequently, bilingual education policies are the programs using two or more languages of instruction. A bilingual person is, in turn, defined as one whose linguistic ability in two languages is similar to that of a native speaker (Malmkjær, 1991).

Moreover, the concept of value as applied to language competences refers to the theory of utility-value according to which the value of a good depends on the utility that consumers estimate the good will provide them. Thus, the utility-value theory defines the link between the usage value and the exchange value, which is the market price. In the case of education, the value reflects the objective preferences of the actors for that activity above other activities, and the price is no more than the translation of these preferences in monetary terms in the context of scarcity at a given place and time (Grin, 1999, p. 33).

<footnote n="3">³ “‘Language policy’ may be realized at a number of levels, from very formal language planning documents and pronouncements to informal statement of intend (i.e. the discourse of language, politics and society) which may not at first glance seem like language policies at all. Indeed, ..., policy statements tend to fall into two types – symbolic and substantive, where the first articulates good feelings toward change (or perhaps ends up being so nebulous that it is difficult to understand what language specific concepts may be involved), and the latter articulates specific steps to be taken” (Kaplan & Baldauf, 1997, p. xi).</footnote>
The value of language can be given a market or non-market, private or social equivalent. The private market value of competences in second languages is defined by wage differentials, which fall to the share of individuals in possession of these competences. This study is especially interested in *net* differentials that is, the wage gaps between individuals that are unequal in terms of their level of possession of linguistic competences, but similar in terms of age or professional experience. The estimation methods are presented in Study III. Further, the private non-market value targets the satisfaction directly felt by the practice of activities enabled by certain language proficiency. The social market value is the sum of private market values, moderated by positive or negative externalities. Finally, the social non-market value is the aggregation of private non-market values collected at the individual level. However, despite the obvious worth of non-market and social market values, the complexity of the collection of comparative data on such values compelled this study to limit its analysis solely to market values of second language competences.

Furthermore, the definition of literacy used in this study is the one adopted by the IALS, according to which literacy is a mode of adult behavior (see Study III for the rationale behind this definition). Overall, literacy consists in “[u]sing printed and written information to function in society, to achieve one’s goals, and to develop one’s knowledge and potential” (Statistics Canada, 2002, p. 15).

Beyond the above lexical specifications, it is important to mention that the general complexity embedded in language issues requires from any research on these matters a certain interdisciplinary research method. In the present case, although the research questions adhere to the fundamental positivist economic paradigm, references to sociolinguistic, political, educational and linguistic concepts are judged necessary to capture the manifold dimensions of the topic. Following Grin’s (1999, p. 3) argument, the method adopted here is therefore applied interdisciplinarity (or “interdisciplinarity by articulation” as defined by Coenen-Huther, 1989) rather than methodological interdisciplinarity (as defined by Wallerstein, 1989; 2004, as part of his world-systems analysis<fnref n="4" />).

<footnote n="4">⁴ Against the dissection of social phenomena in separate independent academic disciplines, such as politics, economics, sociology, and culture studies, the world-systems analysis claims the need for a holistic historical social science. Originally, the ambition of this perspective was to broaden the loci of analysis in the following way: “World-systems analysis was an attempt to combine coherently concern with the unit of analysis, concern with social temporalities, and concern with the barriers that had been erected between different social science disciplines” (Wallerstein, 2004, p. 16). This implies the analysis of materials from</footnote>
Finally, due to the relatively recent development of the consideration of languages
in economic terms, and hence, the consequent scarcity of empirical demonstrations of its
impact on education, it should be underlined that this study defines itself more as a
tentative and explorative study than as a demonstration of definite or well established
findings.

5. Significance of the Studies

In view of the above delimitations and limitations, the significance of this work lies mainly
in its effort to address LiE policy issues within a holistic and interdisciplinary frame of
analysis at an international comparative level. In so doing, this study hopes to improve
political decision-making and implementation practices at several levels. First of all,
understanding the construct rationales to LiE policies, their outcome in term of learning
achievement, and the status of languages for the international labor market, can provide
necessary information to help policy makers and international donor agencies evaluate LiE
policies in a more holistic, and hence efficient, perspective.

Such contribution falls well into the demands for interdisciplinarity raised by
several sociologists, linguists and sociolinguists, who recommended integrating linguistic
analysis as part of the peoples' and nation states' economic, political and cultural
development (Goke-Patriola, 1993; and Mackey, 1992). They hoped this would avoid the
emergence of an educational hegemony built on the exclusive cultural, political and
economic positions of the schools (Apple, 1990; Williams, 1976), which had already led to
the rise of elitist systems, such as described by Bourdieu (1991) in occidental countries,
and witnessed by Goke-Patriola (1993) in postcolonial countries.

Secondly, all the studies of this thesis belong to the broad category of quantitative
multilevel analysis. Studies I and III are classic inter-country analyses and Study II is an
inter-pupil and inter-school analysis. As underlined by Bray & Thomas (1995), the
importance of multilevel analysis for certain types of inquiry is an increasingly recognized

multiple disciplines, for example history, economics, political science or sociology, within a single analytical
frame. Therefore, Wallerstein specifies that "The resulting world-systems analysis was not multidisciplinary,
since the analysts were not recognizing the intellectual legitimacy of these disciplines. They were being
unidisciplinary" (p. 19). Hence, this unidisciplinarity can be understood as resulting much more from a
methodological 'interdisciplinary' quest than from 'multidisciplinarity'.
fact<fnref n="5" />. However, they claim that too many studies lack an international dimension or a multilevel dimension within a national framework. A decade later, this weakness persists and the present study hopes to overcome these traditionally observed weakness by attempting to combine different units and levels of analysis in each study. For instance, by comparing the results of the environmental factors analysis among 35 countries, Study I adds an international-level to the initial country-level analysis. In turn, Study II investigates both pupil and school levels within the Namibian framework and Study III lifts up the traditional human capital return analysis to an international dimension.

Finally, the results of this research have the capacity to challenge the attitudes at the microeconomic (individuals and firms) and macroeconomic (public) levels towards language skills. For instance, among the hypotheses<fnref n="6" /> tested in this work, the validation of the hypothesis that “the higher the level of bilingual skills, the higher the wages” tested in Study III has the potential to support private and public efforts to develop competencies in languages, either through bilingual education policies or other vocational education and training options, if the environmental settings necessary for their construction and implementation are gathered. On the other hand, if this hypothesis had been invalidated by this study it could have led to the questioning of the worth of bilingual education policies and promoted unilingual education policies<fnref n="7" /> or even no LiE policy at all. The significance of this study lies therefore also in its capacity to address the interests of the stakeholders involved in this debate, namely decision-makers, entrepreneurs, teaching staff and students.

**6. Limitations of the Studies and Recommendations for Further Research**

Among the three studies of this thesis, two make use of international educational achievement or literacy studies: the second survey from the Southern African Consortium on Monitoring and Evaluation of Education Quality (SACMEQ II survey) is used in Study

<footnote n="5">⁵ See, for instance, Burstein (1980; 1988); Cronbach (1976); Goldstein (1987); Raudenbush & Willms (1991).</footnote>

<footnote n="6">⁶ In this dissertation, the terms hypothesis and assumption are used as synonyms.</footnote>

<footnote n="7">⁷ Policies of promotion of the official language, also called ‘unilingualism’, consist in promoting a single language at all levels of the society, i.e. political, legislative, social, economic, educational, etc. They can promote the dominant language, in which case it is the national language when it has acquired the status of official language, or a colonial language of international diffusion. Although these policies only recognize one language, minority languages can still beneficiate from certain linguistic rights (Leclerc, 2006).</footnote>
II; and the International Adult Literacy Survey (IALS) in Study III. It is important to underscore the limitations of such datasets. As explained by Beaton, Postlethwaite, Ross, Spearritt & Wolf (1999), such international studies have the advantage of compelling participating countries to subject their curricula to close scrutiny. They can alert ministries to differences between their curricula and that of other countries, in terms of emphasis given to different subject areas for instance. However, the weakness of these studies is the misinterpretation that may result from such comparisons. Differences among countries do not necessarily imply any deficiency of curricula, rather the adoption of a particular curriculum may be justified by the state of development of a country's education system.

Furthermore, the nature of the variables derived from such surveys does not allow for in-depth analyses of the tenants of within- and between-countries variations. Hence, any result should be supplemented by further field study analyses before deriving any policy recommendations. Besides, as an outsider to the data collection process, the researcher analyzing these data is subject to 'ecological fallacy' [i.e. conclusions drawn from the erroneous assumption that a relationship established at one level of aggregation (e.g., among countries) holds at any other level of analysis (e.g., among students within countries)]. For the same reason, sampling error bias and endogeneity issues are also common fallacies encountered by empirical works based on such datasets. Rather than resolving them, the present research has put emphasis in attempting to account for these issues.

Beyond the general weaknesses embedded in large international survey data, it is worth emphasizing the limitations suffered by the empirical applications of all three studies due to lack of data on language background and language skills at an international level. This lack of data has resulted in the use of challenging proxies which weaken the impact of the findings. For instance, Study I bases its empirical test solely on data arbitrarily recoded (see Tables A and B in the Annex section of this thesis for a detailed overview of the information grounding the computation of the data used in Study I)<fnref n="8" />; Study II makes use of a seriously questionable dummy variable to define pupils' home language status; and, in absence of informative data, all the studies make the challenging assumption that the official LiE policies of the sampled countries are actually implemented in all schools. Similarly, the lack of longitudinal studies at the international level addressing the issues

<footnote n="8">⁸ These two tables were removed from the version of Study I submitted to the Economics of Education Review (reproduced in this thesis with authorization from Elsevier) to comply with the format imposed by the journal. They are annexed to this thesis for transparency and clarification reasons.</footnote>
raised in this thesis limited the interpretation scope of the results tremendously. These data
pitfalls need to be addressed by further international survey designers and researchers.

Finally, this research did not include any analysis of the social returns to language
skills nor of the impact of language skills on economic development. These two
dimensions would of course need to be accounted for to complete the holistic evaluation
framework presented in this introduction. Such analyses are therefore strongly
recommended for further research.
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STUDY I
<figure><img src="image_7.png" /></figure>
# Rationales to Language-in-Education Policies in Postcolonial Africa: Towards a Holistic Approach*

Christelle Garrouste⁺

Institute of International Education, Department of Education, Stockholm University,
106 91 Stockholm, Sweden

## Abstract

This article considers two issues regarding language-in-education (LiE) policies in the African postcolonial context. First, it explores the factors affecting the choice of a LiE policy. In that effort, the literature from the sociolinguistics is reviewed towards the design of a conceptual and theoretical framework identifying the different influential parameters on LiE policies. That framework is then tested empirically on 35 African countries. The results show that the countries adopting a unilingual education system put different weights on the influential parameters than countries adopting a bilingual education system. Second, the article investigates how the decision makers can ensure an optimal choice of language(s) of instruction by developing a non-cooperative game theoretic model with network externalities. The model shows that it is never optimal for two countries to become bilingual, or for the majority linguistic group to learn the language of the minority group, unless there is minimum cooperation to ensure an equitable redistribution of payoffs.

JEL classification: I21; I28.

Keywords: Educational economics; Efficiency

<footnote>* Submitted to the *Economics of Education Review*, August 7, 2007. Reproduced with permission from Elsevier.</footnote>

<footnote>⁺ Corresponding author: Tel: +46-8163208; Fax: +46-8153133; Email address: garrouste.norelius@interped.su.se (C. Garrouste).</footnote>
# 1. Introduction

The globalization of the debate around language policy options emerged at the end of the Second World War as an indirect consequence of the major economic and social recession that reached as far as the participating countries' economic partners and colonial territories. In the early 1960s, occidental economists – among whom Schultz, Becker, Mincer, Weisbrod and Denison – started to study the elements affecting the capacity of production of human beings and their effect on production. Analyzing the quantitative and qualitative characteristics of a population (e.g., health, migrations, information and education) as production factors implied incorporating their contribution to economic growth into a production function. These works led to the theorization of human capital, which received major echoes in the political occidental world and it became soon commonly admitted that the pursuit of education leads to individual and national economic growth. This new approach aroused the interest of governments to analyze the causes of the human skills deficit characterizing most post-war economies. Consequently, large literacy assessment surveys were developed, especially in North America, and international campaigns for universal literacy<fnref n="1" /> were launched in most developing countries.

These efforts have led to different explanations of human skills deficit, among which one of the most recurrent is the fact that the education of indigenous peoples and minorities in large parts of the world has so far been organized in direct contradiction to our best scientific knowledge of how it should be organized (Skutnabb-Kangas, 2001). More specifically, the assumption that literacy is limited to a single language is particularly pernicious, because of its political, social and educational implications (Kaplan & Baldauf, 1997, 146).

In order to understand what motivates most governments around the world to opt for such language policies, it is important to keep in mind the economic stimuli that lay behind. Language policy and planning<fnref n="2" /> is primarily an outgrowth of the positivist economic and social paradigms which dominated the 1950s and 1960s. As a result, “most of the motivation for language planning, during its early development as a discipline in the

<footnote n="1">¹ In this context, 'literacy' refers to the ability to deal with written text – both to encode and decode it. In other words, literacy consists of the set of skills, required by any given society, of individuals who wish to function above the subsistence level. Unequivocally, the teaching of literacy has passed over time to the professional education sector, whose main function is to ensure the dissemination of an appropriate literacy through the population (Kaplan & Baldauf, 1997: 143-145).</footnote>

<footnote n="2">² Originally designated ‘language engineering’, the discipline emerged as an approach to articulating programs (usually in newly independent ‘developing countries’) for ‘language problems’ solving (Kaplan & Baldauf, 1997, xi).</footnote>
1960s and 1970s, was socio-political and focused on nation building, primarily using the nineteenth century European model of one state, one language, one culture, regardless of how inappropriate such a model might have been for the new emerging multilingual polities” (Kaplan & Baldauf, 1997, 153).

The consequences of this political orientation were dramatic. Nyati-Ramahobo (1999) argues that the recurrent underachievement that characterizes African education systems and continues to exclude many children from economic performance ensues from the use of a foreign language as medium of instruction. In Van Dyken’s (1990) words, “the [African] continent’s limited literacy is related to the degree to which the mother tongue has been ignored in favor of the international colonial languages” (Van Dyken, 1990, 40). Nowadays, it is widely admitted that the adoption and elevation of an African language to “official status” constitutes a positive step for literacy (Bhola, 1981; Kagan, 1982; Ouane, 1990), identity building, cultural reaffirmation and group identity, thereby for democracy; and the existence of a positive relationship between literacy in local languages and economic growth is well recognized. More generally, language is today commonly viewed as a special commodity necessary for national and international development and communication (see, for instance, Jernudd, 1981; Baldauf & Jernudd, 1983; Jernudd & Jo, 1985; Swales, 1985; and Kaplan & Baldauf, 1997).

In view of the spectacular evolution that has taken place in the contextual settings for the decision-making of language planners over the past decades, several African countries have moved from unilingual planning to multilingual approaches. Yet, still today, among the 2011 languages (i.e. 30 percent of the world's languages) counted for the 56 African Nation-States, only 14 have an official status, of which French still dominates in 23 countries, English in 19 countries, Portuguese in 5 countries, and Spanish (including Canary Islands) in 2 countries (Grimes, 2000; Leclerc, 2006). Hence, in view of the remaining dominance of colonial languages with official status, the rationales behind this evolution of choice remain obscure.

This paper aims, therefore, at lifting the shade on the rationales ruling decisions on language-in-education (LiE) policies in post-colonial Africa. In that effort, this paper divides this issue into two sub-issues: (1) What are the most influential factors affecting the decision process of African policy makers? (2) How can a policy maker choose the most privately and socially optimal subset of languages of instruction?
To answer the first question, a conceptual framework is designed building on findings from sociolinguistics (section 2), which is then tested empirically on 35 African countries selected on the basis of the availability, reliability and comparability of their data (section 3). Finally, to answer the second question, a game-theoretical model is developed (section 4). This paper deviates from previous research mainly by its cross-disciplinary theoretical and methodological frameworks.

## 2. Conceptual framework

### 2.1 Conceptualizing language-in-education (LiE) policies

In order to understand what language-in-education policy embeds it is essential to understand the terms ‘language planning’ and ‘language policy’. On the one hand, ‘language planning’ is an activity – most visibly undertaken by governments because of the massive changes it involves in a society – that aims at changing the linguistic behavior of a speech community. On the other hand, ‘language policy’ refers to the “body of ideas, laws, regulations, rules and practices intended to achieve the planned language change in the society, group or system” underlying the actual language planning process (Kaplan & Baldauf, 1997, xi). Hence, “the exercise of language planning leads to, or is directed by, the promulgation of a language policy by government (or other authoritative body or person)” (ibid.).

The term ‘language planning’ includes both structural (‘form’) and contextual (‘function’) aspects of language planning (Haugen, 1966 and 1983) and differentiates between ‘corpus planning’ and ‘status planning’ (Kloss, 1969). Whereas corpus planning is concerned with the internal structure of the language, status planning<fnref n="3" />, in contrast, refers to all efforts undertaken to change the use and function of a language (or language variety) within a given society (Mesthrie, Swann, Deumert & Leap, 2000, 385). More recently, two additional dimensions of language planning have been identified, namely ‘acquisition planning’ (Cooper, 1989) and ‘prestige planning’ (Haarmann, 1990). Whereas acquisition planning covers the efforts to spread and promote the learning of a language mainly through language-in-education planning, prestige planning is directed towards creating the favorable psychological background necessary for a sustainable success of the language

<footnote n="3">³ Usually the term ‘status’ is used to mean ‘rank’, ‘(social) position’ or even ‘prestige’. Kloss, however, uses the term as a synonym of ‘function’ or ‘domain’ (Mesthrie *et al.*, 2000, 418).</footnote>
planning activities (Mesthrie *et al.*, 2000). Interested specifically in the use of language as medium of instruction, i.e. LiE policies, this paper retains ‘acquisition planning’ as the third dimension of language planning (after corpus and status planning) and deliberately ignores Haarmann’s prestige planning.

Even if LiE planning takes place at only one level of the language planning process (i.e. acquisition planning), its efficiency depends on its ability to proceed interdependently with the other two dimensions of the system (i.e. the corpus and status planning). Hence, the legitimacy of a LiE planning requires first the existence of a national language planning and then the adoption of a LiE policy. In return, all decisions taken at the educational level should be reported to the national language planning organ.

## 2.2 Rationales to LiE policies

In 1974, Fishman commented on the necessity to add to the language policy analysis even the most technical aspects of language planning in a social context as “there are always habits and attitudes and values and loyalties and preferences, not only in the target populations, but among the planners themselves” (Fishman, 1974, 19). Fishman’s (1974) argument is supported by many critical linguists, such as Garvin (1974) and Joseph & Taylor (1990), for whom language issues can not be addressed without considering their relationship with power and ideology. Hence, because language planning process is affected by social variables such as attitudes, power and authority relationships, as well as ideologies, a language policy should integrate factors such as the viability, historical presence, geographic importance and demographic and political status of the language(s) involved. Indeed, as Mackey (1992) stresses, the making of a language policy is not a mere academic exercise, but more often a practical response to social, economic and political pressures.

In his analysis of the relationship between hegemony and curriculum, and referring to Williams (1976), Apple (1990) explains that the interrelationship between all these variables is related to the existence of a strong hegemonic power in all educational policies. Schools do not only process people, they process knowledge as well<fnref n="4" />. They act as agents of cultural and ideological hegemony, in Williams’ words, as agents of ‘selective tradition’ and of ‘cultural incorporation’, helping to create people with the meanings and

<footnote n="4">⁴ This idea has been defended by most British sociologists. See, for instance, Young (1971).</footnote>
values required by the economic environment. As a consequence, the socially 'legitimate'
knowledge taught in schools depends on the school's cultural, political and economic
position (Apple, 1990, 6-7). Applied to language-in-education, this hypothesis can be
illustrated by the sustainable relative power of colonial languages in African education in
favor of the promulgation of elite status.

As Goke-Patriola (1993) highlights in the context of post-colonial states in Africa, “one of the things which educational systems do is to define the ‘legitimate language’” and as a consequence “all other varieties of speech are subject to sanctions which are either externally imposed (by the authorities and the reality of the market, for example) or they are self-imposed” (p. 97). This can be explained by what Bourdieu (1991) refers to as ‘the laws of the transmission of linguistic capital’, which have the following consequences:

As a linguistic market strictly subject to the verdicts of the guardians of legitimate culture, the educational market is strictly dominated by the linguistic products of the dominant class and tends to sanction the pre-existing differences in capital. The combined effect of low cultural capital and the associated low propensity to increase it through educational investment condemns the least favored classes to the negative sanctions of the scholastic market, i.e. exclusion or early self-exclusion induced by lack of success... those least inclined and least able to accept and adopt the language of the school are also exposed for the shortest time to this language and to educational monitoring, correction and sanction (Bourdieu, 1991, 62).

In addition to this internal hegemony, Goke-Patriola (1993) highlights the influence
of external hegemony and power in African societies, characterized by economic, cultural
and psychological dependency on foreign culture and powers. This external dependency is
largely favored by the inherited educational systems and their LiE policies.

Alongside this global understanding of the construct of LiE policies, Lewis (1980) explains that the significance of bilingualism and bilingual education<fnref n="5" /> is determined by its relation to the ‘total structure’ of political, economic and religious institutions. Within this total social structure, differences in language can occur, led by, or leading to, a complex system of heterogeneities in the formulation of bilingualism and the implementation of LiE policies. Lewis (1980) identifies the nature of linguistic heterogeneity using the following sets of variables: 1) diffusion variables, 2) setting variables, and 3) mobility variables (see Figure 1).

<footnote n="5">⁵ If we understand bilingual education as the use of two or more languages as media of instruction, then bilingualism and multilingualism become synonymous. This amalgam is used throughout this paper.</footnote>
This classification has the advantage of covering all the factors and dimensions highlighted by the literature reviewed above. By weighting each set of variables for a sample of ten countries applying official bilingual education programs, Lewis' (1980) study was the first of its kind to offer an international comparative picture of the determinants of bilingual education policies. In this paper we adapt this classification to any type of LiE policy.

The combination of all these environmental settings influences the choice of language policy and in turn, of LiE policy, which can range from multilingual education programs to unilingual education programs (see Figure 2 for a classification of language policies and corresponding LiE programs based on the definitions by Leclerc, 2006; Trueba, 1979; and Skutnabb-Kangas & Garcia, 1995). Whereas unilingual education programs consist in the use of one single language as medium of instruction, usually the national language or majority language, multilingual education programs imply the use of two (or more) languages of instruction in connection with teaching other than language per se (Fishman, 1979).

Figure 1 summarizes these contributions into a concept map<fnref n="6" /> serving as a reference framework within which the findings of the present investigation will be examined, quantified and interpreted. The inter-concept relationships are ruled by the sociolinguistic theories presented in this section. Figures 1 and 2 show that the environmental settings defined by Lewis (1980) have an impact on the nature of the language policy which in turn defines the LiE policy. The LiE policy can then be implemented by bilingual or unilingual programs according to the orientation of the language policy. The environmental settings are composed of three sets of variables: (1) diffusion variables; (2) setting variables (composed of behavioral, external, community-type, institutional and historical settings); and (3) mobility variables.

The *first set of variables* is ‘diffusion variables’, which refers to the influence of international practices on the provision of bilingual education in a given country. Although Lewis (1980) defines diffusion variables in terms of increase of inter-nation communication, he does not specify the nature of these diffusion variables. Therefore, in the current study, we choose to define Lewis’ concept of ‘diffusion’ as a synonym of policy borrowing or lending. In her book *The Global Politics of Educational Borrowing*

<footnote n="6">⁶ This concept map was designed using CmapTools, which is a software environment developed by the Institute for Human and Machine Cognition (IHMC).</footnote>
*and Lending*, Steiner-Khamsi (2004) alongside other educationalists analyzes the effects of globalization on education in terms of ‘borrowing’ and ‘lending’ of education policies. She defines the concept of ‘borrowing’ as “what can be learned and imported from elsewhere” and the concept of ‘lending’ as “what can be taught and exported to elsewhere” (ibid, 1-2). In this context, diffusion can be understood in terms of degree of openness to new political inputs. A proxy indicator of such openness is the Index of Economic Freedom which takes into account ten different types of freedoms ranging from trade freedom to investment freedom. If a country presents a high degree of freedom then we assume that its openness for import or export of education policies will be high.

The *second set of variables* identified by Lewis (1980) targets the ‘settings’ of bilingual education policies, i.e. the historical, institutional, behavioral, external, and community-type settings. These ‘settings’ embody “the differences in the immediate context of the provision of bilingual education in different countries or for different ethnic groups within a single country” (ibid., 6). More specifically, *historical settings* can be determined by the study of historical antecedents such as colonization. They help identifying the chances of national acceptability of any kind of bilingual education among succeeding generations. Moreover, *institutional settings* cover the rules and measures developed by political institutions to guarantee the implementation of bilingual education. Here, we adapt this definition to the needs of our study by measuring institutional settings in terms of the relevance of the languages chosen for instruction to the needs of the labor market, where the more common languages between the education sector and the labor market the more positive the expected effect of the institutional settings. Furthermore, *behavioral settings* reflect the way in which systems behave towards target groups of bilingual education, rather than the way in which students, teachers, or parents, behave. For instance, Lewis shows that a comparative study may reveal whether causal relations exist between the demand for bilingual education (emphasizing the vernacular) and levels of economic advance and types of educational philosophy adhered to. He shows that in the case of the United States economic advances are correlated to the homogenization of education systems, including the homogenization of LiE policies. In the African context, however, this type of homogenization has proven to be instead correlated to the colonial era, which is not a sign of economic development. Therefore, we decide instead to understand behavioral settings as the efforts made by the African authorities to implement bilingual programs that incorporate mother-tongue instruction. In turn, *external settings*
have to do with a country's relationship with other states, far and near. For instance, external settings include commercial and financial dependency towards other states. Then, *community-type settings* characterize the type of bilingual community for which bilingual education is thought desirable, with an emphasis on geographical situation (isolated communities, enclaves, bounded communities, and segregated communities). However, in this paper, we define community-type in terms of scope of applicability of the LiE policy (for all vs. for a specific group).

Finally, the *third and last set of variables* identified by Lewis (1980) is 'mobility variables', which depict movements within and across linguistic, ethnic and national boundaries. Movements can be classified into two main types according to their within or across national boundaries nature: nomadism and seasonal migration or commuting, and voluntary vs. involuntary migration. All these types of migrations may have different effects on the nature of languages (i.e. corpus planning) and language needs (i.e. status and acquisition planning). However, Lewis added this category in the context of occidental countries. In the African context, it does not bring in anything specific, since all the countries have been similarly positively influenced by such flows of populations. We, therefore, treat this parameter as a constant and not as an explicative variable.

The objective of this section was to review the contributions of the sociolinguistics to our research question. What emerged from this review is the fact that sociolinguistics provides specifically strong insights into the influence of a combination of pedagogical rationales and powerful contextual social, economic and political forces on decisions about medium of instruction (Tollefson & Tsui, 2004). Nevertheless, sociolinguistics could not provide for deeper analysis of the explicit mechanisms characterizing the identified relationships. The methodological tools necessary for such inquiry (i.e. for the quantification of the above mechanisms) are instead to be found in the positivist economic paradigm.

**3. How much do environmental settings affect the nature of LiE policies in postcolonial Africa?**

This section aims at quantifying the relationships identified in Figure 1. In that effort, 35 African countries have been selected based on the availability, reliability and comparability of their data. These countries are Angola, Benin, Botswana, Burkina Faso,
Burundi, Cameroon, Central Africa (Republic of), Congo-Brazzaville, Congo-Kinshasa, Cote d'Ivoire, Egypt, Gabon, Gambia, Ghana, Guinea-Bissau, Kenya, Lesotho, Libya, Mali, Mauritania, Morocco, Mozambique, Namibia, Niger, Nigeria, Rwanda, Senegal, Sierra Leona, Swaziland, Tanzania, Togo, Tunisia, South Africa, Zambia, and Zimbabwe.

The empirical model estimates an ordered logistic regression, where the independent variable is the type of LiE policy adopted, defined as four categories: 0. unilingual policy; 1. bilingual (excluding mother-tongue instruction); 2. bilingual (including mother-tongue instruction); 3. trilingual. This formulation gives equal weight to all categories. It orders the different types of LiE policies from the weakest to the strongest category of multilingual policies (see Trueba, 1979 and Skutnabb-Kangas & Garcia's, 1995, classifications of multilingual programs presented in Figure 2).

The explanatory variables are defined as follows<fnref n="7" />:

➤ *L* is a count of the number of languages that the schools can officially choose among as media of instruction.

➤ *E* measures the external settings, i.e. a country's relationship with other states, far or near. It is defined as the proportion of linguistic commonalities with the exportation and importation main partners, and the main bilateral donor. Here, we assume all the languages to have the same weight. The linguistic commonality takes values ranging between 1, when all the languages of instruction are common to the languages of the main export partner (or main import partner or main bilateral donor), and 0 if none of the languages of instruction is common to any of the languages of the main partner.

➤ *C* is the community-type settings, i.e. the type of language ideology applied, namely pluralism, vernacularization, assimilation, separatism or internationalization (see previous section). It takes the value of 1 if it is designed to cover the whole school population (e.g., assimilation/integrative approach) and 0 if it only targets a distinctive community or a non-compulsory level of education (e.g., separatism approach, such as Apartheid).

➤ *I* covers the institutional settings, i.e. the rules and measures developed by political institutions to guarantee the implementation of bilingual education. It is defined as the proportion of languages taught in school that are common to the languages spoken on the labor market. This variable is used as a proxy of the capacity of the LiE policy to respond to the linguistic needs of the labor market. The value of *I* ranges between 1, if

<footnote n="7">⁷ See Annexes A and B for a detailed outline of the sources of computation of these variables.</footnote>
all the labor market languages are taught in school, and 0, if none of the languages of the labor market are offered by the education system.

> *H* refers to the historical settings, i.e. the colonial influence on the LiE policies. It is defined as the portion of colonial languages in the total number of languages of instruction defined in the LiE policy.

> *D* measures the diffusion variables, i.e. the influence of external practices on the provision of a type of LiE policy. This parameter is measured by the 2006 Index of Economic Freedom, which measures and ranks 161 countries based on their overall percentage of freedom calculated across 10 specific freedoms equally weighted. These freedoms are business freedom, trade freedom, monetary freedom, freedom from government, fiscal freedom, property rights, investment freedom, freedom from corruption and labor freedom. This index is a good proxy of the degree of openness of a country to new ideas and practices<fnref n="8" />.

From our theoretical framework, we expect a negative sign for the *L*, *I*, *H* and *D* estimates and a positive sign for *E* and *C*. In other words, we expect that the higher the weight of *L*, *I*, *H* and *D* the higher the probability that the country will opt for a unilingual policy; and reciprocally, the higher the weight of *E* and *C* the higher the probability for the implementation of a multilingual policy.

Among the thirty-five countries of our sample, ten are Francophone unilingual<fnref n="9" />, six are English-speaking unilingual<fnref n="10" />, four are Arabic-speaking unilingual<fnref n="11" />, three are Lusophone unilingual<fnref n="12" />, one is solely Francophone and English-speaking<fnref n="13" />, one is solely Francophone and Arabic-speaking<fnref n="14" />, six are bilingual in English and a national language<fnref n="15" />, two are bilingual in French and a national language<fnref n="16" /> and two are trilingual (in at least 1

<footnote n="8">⁸ For more details about the computation of the Index of economic Freedom see http://www.heritage.org/index/</footnote>

<footnote n="9">⁹ The 10 Francophone unilingual countries of the sample are Benin, Burkina Faso, Congo-Brazzaville, Congo-Kinshasa, Cote d'Ivoire, Gabon, Mali, Niger, Senegal and Togo.</footnote>

<footnote n="10">¹⁰ The 6 English-speaking unilingual countries of the sample are Botswana, Gambia, Ghana, Nigeria, Sierra Leona, Zambia.</footnote>

<footnote n="11">¹¹ The 4 Arab-speaking unilingual countries of the sample are Egypt, Libya, Morocco and Tunisia.</footnote>

<footnote n="12">¹² The 3 Lusophone unilingual countries of the sample are Angola, Guinea-Bissau and Mozambique.</footnote>

<footnote n="13">¹³ The only solely Francophone and English-speaking country of the sample is Cameroon.</footnote>

<footnote n="14">¹⁴ The only solely Francophone and Arab-speaking country of the sample is Mauritania.</footnote>

<footnote n="15">¹⁵ The 6 countries bilingual in English and a national language are Kenya, Lesotho, Namibia, South Africa, Swaziland and Tanzania.</footnote>

<footnote n="16">¹⁶ The 2 countries bilingual in French and a national language are Burundi and Central Africa.</footnote>
national language)<fnref n="17" />. The gathered information is coded using the principles for each parameter outlined above and displayed in Table 1. The data sources used to compute Table 1 are the CIA (2006) World Fact Book, Leclerc's (2006) online dataset on language policies across the world, the OECD (2006) statistics on Gross Bilateral ODA, the WTO's statistics on bilateral trade from March 2006 and the 2006 Index of Economic Freedom by the Heritage Foundation & the Wall Street Journal, as well as consultations of official documents in all the sampled countries.

Table 2 presents the sample means and Table 3 shows the results of the estimated ordered logistic model (complete and reduced forms).

In the complete model, which includes all the above defined variables, the variable *H* (historical settings) appeared non-significant. A test for collinearity revealed it to be highly negatively correlated with the community-type settings *C* (r = -.5815). After testing for different specifications of the model, the exclusion of the *H* variable from the regression proved to be the only option to improve the fit of the model as a whole. Therefore, the historical settings *H* are thereafter assumed to be partly embedded in the community-type settings *C*.

In the reduced model (which excludes *H*), all estimates present the expected sign. For instance, for a one unit increase in *E*, the expected ordered log odds increases by 6.07 as we move to the next higher category of LiE policy. For one unit increase in *C*, we expect a 4.42 increase in the expected log odds as we move to the next higher category of LiE policy. Whereas *E* and *C* appear strongly significant statistically (at the .05 and 0.1 levels respectively), there is no statistically significant effect of *L*, *I* and *D* (which is actually not surprising given the extremely small size of our sample).

Nevertheless, the likelihood ratio chi-square of 19.68 with a p-value of .0014 tells us that our model as a whole is statistically significant. Moreover, the tests conducted on the proportional odds assumption, namely the likelihood ratio test and the Brant test, both confirm that our model does not violate the proportional odds assumption; and the robust test applied to test for the presence of heteroskedasticity also confirmed the absence of correlation between the error term and the explanatory variables.

Hence, what comes out from this analysis is that Lewis' framework (or at least, our arbitrary numerical interpretation of it) appears suitable to explain the contextual factors influencing the choice between different types of LiE policy in post-colonial Africa.

<footnote n="17">¹⁷ The 2 trilingual countries are Rwanda and Zimbabwe.</footnote>
According to this model, “unilingual” countries may justify their choice by either a strong inclination for a separatist language ideology (C); low initial linguistic commonalities with their main external economic or financial partner (E), strong degree of influence from external ideologies and practices (D), which corresponds to a high inclination to policy borrowing; perfect institutional settings (I) with the same language being taught at school and used on the labor market; or a too high number of official languages to choose between as media of instruction (L).

The opposite set of explanations applies to “multilingual” countries, who may
justify their choice by either a strong inclination to the vernacularization of languages (C);
high initial linguistic commonalities with their main external economic or financial partner
(E), low degree of influence from external ideologies and practices (D), which corresponds
to a low inclination to policy borrowing; weak institutional settings (I) with the need to
improve the adequacy between the languages being taught at school and the languages
used on the labor market; or a reasonably low number of official languages to choose
between as media of instruction (L).

All the above results can partly be indirectly imputed to the distribution of
countries within each group, with a majority of English-speaking countries among the
bilingual countries, and all Lusophone and Arabic-speaking and most Francophone
countries among unilingual countries. The English-speaking countries are still influenced
by the British colonial education system, which privileged bilingual mother-tongue
instruction. At independence, English-speaking countries opted therefore for a
democratization of the learning of English to the whole population and kept the teaching of
the mother tongues (which also explains the high weight of the community-type settings
C). On the contrary, the French and Portuguese colonial policies privileged unilingual
education systems with instruction exclusively in the colonial language<fnref n="18" />. The remaining
unilingualism of these countries is therefore also an indirect heritage of the colonial era but
with opposite consequences as for former British colonies.

Finally, all the results presented here should be taken with cautiousness because of
the exploratory nature of this empirical application, which implies questionable definitions
of the estimated parameters. The most explicit example is the use of the Index of Economic
Freedom as a poor proxy of degree of openness to new ideas and practices. Because

<footnote n="18">¹⁸ See Gifford & Louis, 1971; Kelly, 2000; and Lin & Martin, 2005, for an extended overview of colonial and postcolonial education in Africa.</footnote>
specification errors in the parameters may increase the risk for collinearity and endogeneity which may bias the results, further research should attempt to improve the definition of these parameters.

Hence, by providing some exploratory insights on the role played by environmental settings on the number of potential languages of instruction and thereby on the type of LiE policy (e.g., unilingualism vs. bilingualism), the model tested in this section answered partially the question of which factors may affect the LiE policies in postcolonial Africa but it did not tell us whether or not the decision taken was rational. It is, therefore, now important to find out which combination of languages, i.e. which LiE policy, would theoretically produce an optimal outcome to the community. This second question is answered in the next section.

**4. What is the optimal decision for a LiE policy-maker?**

This section is concerned with how a LiE policy-maker can select the languages of instruction that will optimize the utility of its community. A non-cooperative game with network externalities is developed as a suggestive option to answer this issue. We rely mainly upon the works by Selten & Pool (1991), Church & King (1993) and Dalmazzone (1999) who explored the concept of network externalities and how it applies to public investments in language knowledge and language learning. More specifically, it relies upon Selten & Pool's (1991) game equilibrium of the distribution of foreign language skills, as well as Church & King's (1993) game-theoretical model of bilingualism and network externalities and Dalmazzone's (1999) discussion of the use and usefulness of network externalities to address second language (i.e. any language additional to the mother-tongue) issues.

**4.1 Network externalities approach**

Dalmazzone (1999) explains that, in the specific context of languages, the network externalities approach builds on the assumption that the ‘user-value’ of belonging to a given linguistic group increases with the size of the group itself. Hence, learning a language means becoming part of a *network*, that is “a community made up of complementary components in which every new entrant, besides gaining access to the
benefits of a set of services, also adds to the potential benefits of all other members (i.e.,
generates an *external effect*)" (Dalmazzone, 1999, 63).

The external effects can be both direct and indirect. The direct external effect is the
communication value associated with a language, when it is used to serve as an interface in
the largest possible number of potential interactions. Indeed, in order to benefit from the
knowledge in a language, one needs to interact with at least one other person who knows
that language. In a community of *n* individuals speaking the same language, there are *n*(*n*-
1) potential binary interactions. Further, an additional (*n*+1)th individual speaking the
same language would yield direct benefits to all others by adding 2*n* potential new
interactions. This means that once a language has acquired an advantage over other
potential alternatives, its comparative advantage tends to become greater and greater (e.g.,
this is the case of English, which is now the most commonly studied foreign language and
the most used language of commerce, communication and information storage<sup>19</sup>).

In addition to this direct effect, an additional member of a linguistic group can also
provide an indirect benefit to other members by increasing the demand for language-
sensitive goods and services (schools, libraries, bookstores, broadcasting, theatre,
productions, etc.) and thereby, if economies of scale are present, improving the supply and
possibly the variety of such services within the community. Although it is generally
assumed that externalities associated to a network are positive, they can become negative
when the exposure of a small country to a larger linguistic community's culture and
ideologies leads to the loss of its indigenous culture and set of beliefs. In this particular
case, not belonging to the linguistic network would be more beneficial since it would
provide that country with a natural protection against cultural colonization and other
unwanted foreign mass cultural products.

An important point highlighted by Dalmazzone (1999) is the fact that the number
of speakers alone is not necessarily the only, nor always the most, fundamental factor in
determining the communication value of a language. Rather, it is important to take into
account factors such as the variety of the potential interactions, the particular purpose or
job for which the language is to be used, the geographic and economic position of a
country, etc.

<footnote n="19">¹⁹ English counts 397 million secondary speakers, and 70 percent of the world's mail and about 80 percent of all information stored in data banks are estimated to be in English (Dalmazzone, 1999).</footnote>
Selten & Pool's (1991) predictive model of some general features of distributions of non-native<fnref n="20" /> language skills demonstrates the role played by the size of a language community in determining the strategic choice to learn a foreign language. Their model defines the learning costs, communicative benefit and payoffs at individual, group and aggregated levels. Finally, they provide a proof of the existence of equilibrium points for every aggregated game. This very theoretical work is a solid input in the research on language acquisition as a network externality game.

Finally, building on Selten & Pool (1991), Church & King (1993) derived a formal proof that the private optimum of foreign language learning and the collective optimum may not coincide<fnref n="21" /> by applying conclusions reached by the literature on network externalities to problems of language. Their result implies that the maximization of collective welfare, in the presence of externalities in a language market, requires collective institutions capable of internalizing the externality (i.e. capable of correcting the inefficiencies in the aggregated result of individual choices) (Dalmazzone, 1999). In other terms, languages are public goods and require LiE policies to maximize their utility.

In his analysis of knowledge as a global public good, Stiglitz (2006) insists on two critical properties of public goods: non-rivalrous consumption and non-exclusivity. Non-rivalrous consumption occurs when the consumption of one individual does not detract from that of another (i.e. the marginal cost of usage is zero), and non-exclusivity means that it is difficult, if not impossible, to exclude an individual from enjoying the good. It is easy to see how the knowledge of languages satisfies both attributes: if I teach you a language, I continue to enjoy (even more) the knowledge of the language at the same time as you; and, by the same token, once the language is accessible for learning in all schools, anyone can enjoy the language, i.e. no one can be excluded, so everyone might want to enjoy it. Hence, the central public policy implication of public goods is that the state must play some role in the provision of such goods to make sure they will not become undersupplied. One way of financing this type of investment is by charging a monopoly price on the language. Carr (1985) was the first to defend this idea that the market of languages is similar to a natural monopoly.

<footnote n="20">²⁰ The terminology “native” versus “non-native” languages is used by Selten & Pool (1991) to designate “mother-tongues” versus “foreign languages”.</footnote>

<footnote n="21">²¹ Whereas the private optimum results from the uncoordinated investments of individuals maximizing their own utility, the collective optimum maximizes total social welfare (see Church & King, 1993, for further details).</footnote>
Dalmazzone (1999) builds upon this monopoly assumption and highlights that the presence of positive effects related to network size can give rise to a “critical mass”, which corresponds to a minimum size for a linguistic group, relative to the whole population, necessary to be sustained in equilibrium. Hence, minority languages of small populations can easily be assimilated if they are not effectively protected, because the return on a human capital investment in these languages is perceived as low, *ceteris paribus* (“all other things being equal”), relative to the yield on other languages. Conversely, once diffusion has reached a given level, further expansion may be self-sustaining.

This theoretical hypothesis seems to fit rather well the context of selection and use of African languages, which appear to have been successful only when the given languages were spoken by large numbers of people. Swahili has been successfully used in Tanzania and Kenya. Similarly, Hausa, which is spoken by more than 8 million people in Nigeria, is serving both the purposes of literacy and national integration at least in the northern parts of Nigeria and in neighboring Niger (Ntiri, 1993, 363). Moreover, the decision to adopt an African language for an educational purpose is often not based on the mother tongue criterion (how large a number of people speak the language as a mother tongue) but on the community language criterion (the function of the language as the dominant means of communication in a certain area of the country), which refers to the network externalities approach. In this context, there are about 159 languages identified as community languages that serve the purposes of general communication over fairly wide areas within countries in Africa (UNESCO/BREDA, 1985, 10). Twenty-three of these are shared community languages, that is, they are spoken in more than two countries. For example, Fulfulde is spoken in 10 countries and Kiswahili and Malinke in six. Monolingualism in an African language is reported for only seven countries, namely: Cape Verde, Comores, Lesotho, the Seychelles, Somalia, Swaziland and Madagascar. All others adopt more than one African language for educational purposes (ibid, 13).

Dalmazzone (1999) summarizes the prerequisites for efficient public intervention in the provision of public goods that embed complex systems, such as culture, traditions and languages, by referring to Arthur's (1988) four generic conditions: (1) large set-up or fixed costs; (2) learning effects; (3) coordination effects; and (4) adaptive expectations.

Whereas *large set-up and fixed costs* such as those associated with the investment necessary to the maintenance and development of a modern language give the advantage of falling unit costs as the size of the speech community expands, *learning effects* improve
the efficiency of investments in language capital, provision of language-related services
and, more generally, activities meant to promote a language diffusion and export.
Moreover, *coordination effects* refer to the advantages associated with undertaking actions
and making choices synergetic to those of the other individuals in the same environment.
These effects result from the application of cooperative games, i.e. “the formation of
coalitions in which participants must work together to maximize a payoff, which will later
be divided among members” (Cornes & Sandler, 1996, 18)<fnref n="22" />. Finally, *adaptive
expectations* account for the fact that the increased prevalence of a language enhances
beliefs of further prevalence.

From Selten & Pool's (1991) and Church & King's (1993)<fnref n="23" /> game-theoretic models
of bilingual education policies we know that if the available policy instruments affect all
members of a language group homogeneously, then policies that effectively subsidize
language acquisition are warranted only for the majority language (i.e. the language with
the largest number of speakers). The analysis run in the previous section verifies this
assumption (see effect of C = 1 on logLiE). Hence, we expect that the belonging to a large
linguistic network will be more prized than the willingness to give equal status to all
languages independently of the size of the linguistic population.

This supports as well what Dalmazzone (1999) explains with regard to the potential
negative nature of network externalities, that is that the belonging to networks has a
negative impact on the survival of endogenous languages in the formulation of national
LiE policies. Again, this is confirmed by the analysis run in previous section where the
languages of instructions are often the same as the languages of the former colonial power,
or trade partner or donor partner. African countries tend to opt for bilingual education
systems mainly to support/facilitate the learning of a colonial language or international
trade language<fnref n="24" />. For instance, among the few bilingual Francophone countries, only one is
bilingual in a national language, namely Burundi. All the others are bilingual in French and
English or French and Arabic, which are all international languages.

<footnote n="22">²² Although pure public goods are often associated with non-cooperative games, it is expected that the repetition of plays of the games might elicit the cooperative strategy as players see that cooperation will augment everyone’s payoffs when compared with non-cooperation (see Prisoners’ Dilemma) (Cornes & Sandler, 1996).</footnote>

<footnote n="23">²³ We strongly recommend the reading of Selten & Pool's (1991) and Church & King's (1993) respective article for an appreciation of the game-theoretic models they have developed and upon which this study relies.</footnote>

<footnote n="24">²⁴ As shown in Table 2A, whenever used, mother-tongue instruction is merely used in pre-primary education and first cycle of primary education before transiting to a colonial or international language.</footnote>
Hence, the high weight put on colonial and trade networks confirms Selten & Pool's (1991), Church & King's (1993) and Dalmazzone's (1999) common hypothesis that the incentive to learn a language increases with the size of the network.

## 4.2 The model

Based on the theoretical principles of the public goods' network externalities approach presented above, this paper proposes to develop a non-cooperative game model describing how an African policy-maker can choose optimally the languages of instruction in schools depending on the strategy adopted by the other policy-makers, e.g., former colonial powers, trade partners, main foreign investors and bilateral donors.

From Selten & Pool's (1991) model, we keep three important assumptions: (1) we impose no limit on the number of languages in existence; (2) we assume that there is a positive number of languages in the world; and (3) we treat as fixed the distribution of native languages, assuming that everyone has one and only one native language<fnref n="25" />. These restrictions allow Selten & Pool to partition the world population into communities, each community consisting of the native speakers of a particular language.

However, whereas Selten & Pool and Church & King assume that a member of language community *i* always learns language *i* and has no choice in this respect (which delimitates their analysis to second language acquisition), our model assumes that the learning of language *i* is conditioned by the individual strategy (hence, it is not obvious). This assumption is necessary to reflect the reality in African countries where individuals are not necessarily taught in their native language (see results from previous section in that matter). Therefore, our model aims at broadening the scope of Selten & Pool's and Church & King's studies.

The game takes place in a world with *m* languages, 1, ..., *m*. Every individual has one and only one of these languages as his native language. He is a native speaker of that language. Every language other than an individual's native language is a foreign language for that individual. Let *M* be the set {1, ..., *m*} of all languages. All languages are perfect substitutes. This assumption was applied by Church & King (1993) to overcome the

<footnote n="25">²⁵ In addition to the three assumptions presented here, Selten & Pool (1991) also identify a fourth assumption, namely they permit languages with native speakers and languages without native speakers to exist. Although this assumption may be justified by attempts to create non-native languages such as "Esperanto" to play the role of international lingua franca, no such language actively belongs today to the languages of the world (see Grimes, 2000). This assumption has therefore no rationality in our model.</footnote>
difficulties raised by the fact that some languages may be more efficient communicative media than others and that some languages might beneficiate from particular intrinsic value. Here, “no one cares if one language disappears, and no one prefers communicating in one language rather than in an other” (ibid, 343)<fnref n="26" />.

The set of all individuals with native language *i* is the community *i*. Each language community *i* is described as a continuum of individuals represented as points in an interval [*i*, *i* + *a*<sub>*i*</sub>], with *a*<sub>*i*</sub> > 0. Each member of the *i*th community is identified with a number *s* such that *i* ≤ *s* ≤ *i* + *a*<sub>*i*</sub>. The measure of all individuals is normalized to 1:

$$ (2.1) \qquad \sum_{i=1}^{m} a_i = 1. $$

We call *a*<sub>*i*</sub> the size of language community *i*. The players of the game are the members of the language communities 1, ..., *m*. Geometrically, the world community can therefore be represented as a set of *m* line segments, where *m* is the number of communities. The *i*th community is represented as a line segment from *i* to *i* + *a*<sub>*i*</sub>. Figure 3 replicates the example given by Selten & Pool (1991) of such a geometric representation for a world of four communities. The sum of the lengths of the four line segments is 1.

Each individual must know at least one language to be able to communicate with others. We assume that all members of the language communities are identical except for their language endowment<fnref n="27" />. Each player can choose between three pure strategies. He/she can learn his/her native language (i.e. mother-tongue) at a learning cost *c*<sub>*i*</sub> and remain unilingual. He/she can learn a non-native language (i.e. foreign language) at a cost *c*<sub>*j*</sub> (where *j* is any other language than *i*) or decide to learn both his/her native language and a non-native language (and thereby become bilingual) at a cost *c*<sub>*i*+*j*</sub>, where *c*<sub>*i*</sub> < *c*<sub>*j*</sub> and *c*<sub>*i*+*j*</sub> = *c*<sub>*i*</sub> + *c*<sub>*j*</sub>. The benefit of language *i* is a function of the size of the community *i*, *a*<sub>*i*</sub> and the cost of learning a language is a function of the degree to which the language learnt is

<footnote n="26">²⁶ For analyses not treating languages as perfect substitutes, see Marschak (1965), Sabourin (1985) and Grin (1992).</footnote>

<footnote n="27">²⁷ Church & King (1993) use this assumption.</footnote>
different from the native language<fnref n="28" />. Hence, the cost of learning the native language (or mother tongue) will be assumed to tend towards null and the cost of learning a foreign language to tend towards 1.

A member $s_i$ obtains utility $v(a_i)$ if he learns only his native language $i$, $v(a_j)$ if he learns only a foreign language $j$ and $v(a_i + a_j)$ if he learns both his native language and a foreign language $j$. It is the fact that we assume that the utility of each member increases with the size of the community, i.e. $v' > 0$, that creates the existence of the network externality underlying this model. Hence, the payoff of $s_i$ associated with learning a language is affected by the learning decisions of all other individuals, including the member of his own community $i$.

To solve the equilibrium of this game let us fix the number of world languages to two, i.e. $m=2$. Hence, a member $s_1$ obtains utility $v(a_1)$ if he learns only language 1 (i.e. his mother tongue), $v(a_2)$ if he learns only language 2 and $v(a_1 + a_2)$ if he learns both languages.

## 4.3 Equilibrium

By assuming that no agent learns unless there is a strictly positive net benefit from doing so, we can formulate the best-response functions as the following decision rules:

$$ (2.2a) \quad \text{any member } s_1 \text{ learns language 1 iff } v(a_1) - v(a_2 + \hat{a}_2) > c_1; $$

$$ (2.2b) \quad \text{any member } s_1 \text{ learns language 2 iff } v(a_2) - v(a_1 + \hat{a}_1) > c_2; $$

$$ (2.2c) \quad \text{any member } s_1 \text{ learns languages 1 and 2} $$

$$ \text{iff } v(a_1 + a_2) - v(a_1 + \hat{a}_1) > c_1 + c_2, $$

and reciprocally,

$$ (2.2a)' \quad \text{any member } s_2 \text{ learns language 1 iff } v(a_2) - v(a_1 + \hat{a}_1) > c_2; $$

<footnote n="28">²⁸ Selten & Pool (1991) opt for a similar assumption, focusing however, on the differences of learning costs between foreign languages, whereas Church & King (1993) opt for identical costs of learning for all languages. Here, we opt for a differentiation of learning costs between native and foreign languages, assuming the learning cost of all foreign languages to be identical.</footnote>
(2.2b)' any member $s_2$ learns language 2 iff $v(a_1)-v(a_2+\hat{a}_2)>c_1$;

(2.2c)' any member $s_2$ learns languages 1 and 2

$$ \text{iff } v(a_1+a_2)-v(a_2+\hat{a}_2)>c_1+c_2; $$

where $\hat{a}_1$ and $\hat{a}_2$ are the number of individuals from the other community that choose to speak language 2 and the number of individuals from the other community that choose to speak language 1, respectively, in equilibrium.

We now assume that the language community 1 is larger than the language community 2 ($a_1 > a_2 \Leftrightarrow v(a_1) > v(a_2)$) and the cost of learning a mother tongue is much less than the cost of learning a foreign language ($c_i < c_j$). For simplification we assume that the learning cost of learning a mother-tongue is equal to zero and the learning cost of learning a foreign language is equal to 1 ($c_i = c_j = 1$). The Nash equilibrium of this game is characterized by proposition 1.

**PROPOSITION 1:**

(i) If $v(a_1+a_2)-v(a_1)<v(a_1+a_2)-v(a_2)<c_j$, then ($\hat{a}_1=0, \hat{a}_2=0$) is the unique pure-strategy Nash equilibrium;

(ii) If $v(a_1+a_2)-v(a_1)<c_j<v(a_1+a_2)-v(a_2)$, then there are two pure-strategy Nash equilibria ($\hat{a}_1=a_1, \hat{a}_2=0$) and ($\hat{a}_1=a_1+a_2, \hat{a}_2=0$);

(iii) If $c_j < v(a_1+a_2)-v(a_1)$, then there exist three pure-strategy Nash equilibria ($\hat{a}_1=a_1+a_2, \hat{a}_2=0$), ($\hat{a}_1=0, \hat{a}_2=a_1+a_2$) and ($\hat{a}_1=a_1+a_2, \hat{a}_2=a_1+a_2$);

**Proof:**

(The proof of Proposition 1 follows the same logic as the first proposition of the model by Church & King, 1993)<fnref n="29" />

According to proposition 1, if the cost of learning a foreign language is too high, then no one learns a foreign language, which means that unilingualism in mother-tongue is optimal. If the cost of bilingualism pays for speakers of language 2 but not for speakers of language 1 (because $a_1 > a_2$), then there are two pure-strategy Nash equilibria. The first

<footnote n="29">²⁹ See Church & King's (1993) appendix p. 344.</footnote>
is that all speakers of language 2 learn language 1 (unilingualism in a foreign language) and speakers of language 1 only learn language 1. The second is that all speakers of language 2 learn both language 1 and 2 (bilingualism) and speakers of language 1 only learn language 1. If the cost is very low, then there are three equilibria. In the first equilibrium, all speakers of language 2 learn languages 1 and 2 and speakers of language 1 only learn language 1. In the second equilibrium, all speakers of language 1 learn languages 1 and 2 and all speakers of language 2 learn language 2. In the third equilibrium, all speakers of languages 1 and 2 learn both languages 1 and 2.

Further, let us assume that the decision of any agent of a language community to learn only his mother tongue, only a foreign language or become bilingual is representative of the decision of all the members of that community<fnref n="30" />. Hence, the efficiency of the strategy adopted by a policy maker who wishes to maximize total surplus depends again on the learning costs $c_i$, $c_j$ and $c_{i+j}$.

Let the total surplus be denoted by $W_{NN}$ if both communities decide to only learn their respective native language (mother-tongue education policy); $W_{BB}$ if both communities decide to become bilingual in languages 1 and 2 (bilingual education policy); $W_{BN}$ if community 1 decides to learn both languages 1 and 2 and community 2 only learns its native language; $W_{NB}$ if community 1 only learns its native language and community 2 decides to become bilingual; $W_{12N}$ if community 1 decides to learn only language 2 and community 2 learns its national language (language 2); $W_{N21}$ if community 2 decides to learn only language 1 (unilingual education policy in foreign language) and community 1 only learns language 1 (mother-tongue education policy); $W_{12B}$ if community 1 learns only language 2 and community 2 decides to become bilingual; and $W_{B21}$ if community 1 decides to become bilingual and community 2 learns only language 1. In this context, $a_1 > a_2$, $c_i = 0$ and $c_j = 1$ yield:

$$ (2.3a) \qquad W_{NN} = a_1v(a_1) + a_2v(a_2); $$

$$ (2.3b) \qquad W_{BB} = W_{12B} = W_{B21} = 2(a_1 + a_2)v(a_1 + a_2) - (a_1c_2 + a_2c_1); $$

$$ (2.3c) \qquad W_{BN} = W_{12N} = a_2v(a_2) + (a_1 + a_2)v(a_1 + a_2) - a_1c_2; $$

<footnote n="30">³⁰ This assumption is applied by Selten & Pool (1991) and Church & King (1993).</footnote>
$$ (2.3d) \qquad W_{NB} = W_{N21} = a_1v(a_1) + (a_1 + a_2)v(a_1 + a_2) - a_2c_1. $$

**PROPOSITION 2:**

$$ (i) \qquad W_{BB} < W_{BN} < W_{NB} $$

$$ (ii) \qquad W_{NN} < W_{NB} \quad \text{iff} \quad c_1 < (a_1/a_2)[v(a_1 + a_2)] + [v(a_1 + a_2) - v(a_2)] $$

**Proof:**

(i) Follows directly from (2.3b), (2.3c) and (2.3d), since $a_1 > a_2$.

(ii) From (2.3a) and (2.3d), $W_{NB} - W_{NN} = (a_1 + a_2)v(a_1 + a_2) - a_2c_1 - a_2v(a_2)$ which is positive iff proposition (ii) holds. $\square$

According to proposition 2, when taking into consideration the benefits of communication and the cost of learning a foreign language (assuming the cost of learning a mother-tongue equal to zero), the optimal policy is the one where the community 1 learns its native language (language 1) and the community two decides to learn both languages, or to learn only the language of community 1 (i.e. the language of the majority). This result confirms the ones from Church & King (1993) and Selten & Pool (1991). The reason why it is never optimal for all individuals to become bilingual is because the sufficient condition for all individuals to be able to communicate with each other is that one community becomes bilingual. If more than one community learns both languages, no further gains will be generated (Church & King, 1993, 340).

Moreover, the reason why group 2 should become bilingual and not group 1 is because we assume the size of the language community 1 to be larger than the one of community 2. Hence, only the smallest group should become bilingual or at least learn the language of the majority group (size effect).

Finally, when comparing the private optima (proposition 1) with the social optima (proposition 2), it appears that when the cost of learning is very high it is privately and socially optimal to learn only the native language; when the cost is very low, it is privately and socially optimal for members of communities 1 and 2 to learn language 1. Nevertheless, the private and social equilibria do not coincide anymore when the cost of
learning is close to its maximum border (i.e. $(a_1/a_2)[v(a_1+a_2)]+[v(a_1+a_2)-v(a_2)]$. In that case, it is socially optimal for everyone to learn language 1 but it is privately optimal for everyone to only learn the native language. In equilibrium, both groups will therefore learn their native language only. Again this result confirms the findings by Church & King (1993), who explain this divergence between the efficient and Nash equilibrium solutions as a consequence of the existence of network externalities: “when an individual makes the choice whether to learn or not, she does not take into account the benefit that others get from being able to communicate with one additional person” (ibid, 341).

Finally, it is worth noticing that in all cases, it is always more efficient to learn at least the native language (as component of a bilingual education program or as unique language of instruction when the cost of learning a foreign language is too high). However, our model has also shown that the presence of network externalities in cooperative games can cause the extinction of minority languages. As suggested by Dalmazzone (1999), apart from the application of targeted bilingualism to specific linguistic groups, another way to combat this extinction is therefore by applying cooperative games. By forming coalitions, members of minority linguistic groups may work together to maximize a payoff, which could later be divided among members. Both the private and social equilibria could be affected by such cooperation in favor of minority languages. By producing learning effects (through the development of services and media or other diffusion networks in the minority language) the coalitions could even generate sufficient payoff to incite the majority language group to learn the minority language (i.e. $W_{BN} > W_{NB}$, where $W_{BN} = W_{12N}$ and $W_{NB} = W_{N21}$ still hold).

## Acknowledgments

The author would like to thank Henry M. Levin and Gita Steiner-Khamsi for valuable discussions during her stay as a visiting scholar at the National Center for the Study of Privatization in Education, Teachers College, Columbia University, over the academic year 2004-2005. The work conducted during that period inspired the present paper. The author would also like to thank the participants to the Francophone Symposium of the XXII CESE conference, Granada, July 3-6, 2006, for their valuable comments and feedback on a preliminary version of this paper.
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<figure><img src="image_8.png" /><figcaption>Figure 1
Conceptual framework</figcaption></figure>

Note: See Figure 2 for further details
<figure><img src="image_9.png" /><figcaption>Figure 2
Path towards the adoption of a LiE policy</figcaption></figure>

Note: The environmental settings (E.S.) are composed of diffusion variables (e.g., inter-country communication), setting variables (e.g., historical settings, institutional settings, behavioral settings, external settings, and community-type settings), and mobility variables (e.g., nomadism vs. seasonal migration, and voluntary vs. involuntary migration). The nine types of language policies are derived from Leclerc (2006) and the LiE policies from Trueba (1979) and Skutnabb-Kangas & Garcia (1995).
<figure><img src="image_10.png" /><figcaption>Figure 3</figcaption></figure>

Partition of hypothetical population into native-language communities

(Source: Selten & Pool, 1991, 66)
<table><caption>Table 1
Variable values</caption><thead><tr><th></th><th>LiEp<sup>a</sup></th><th>L</th><th>B</th><th>E</th><th>C</th><th>I</th><th>H</th><th>D<sup>b</sup></th></tr></thead><tbody><tr><td>Angola</td><td>0</td><td>1</td><td>0</td><td>0.33</td><td>0</td><td>1</td><td>1</td><td>0.433</td></tr><tr><td>Benin</td><td>0</td><td>1</td><td>0</td><td>0.33</td><td>0</td><td>1</td><td>1</td><td>0.543</td></tr><tr><td>Botswana</td><td>0</td><td>2</td><td>0</td><td>1</td><td>1</td><td>1</td><td>0.5</td><td>0.703</td></tr><tr><td>Burkina Faso</td><td>0</td><td>4</td><td>0</td><td>0.67</td><td>0</td><td>1</td><td>1</td><td>0.557</td></tr><tr><td>Burundi</td><td>2</td><td>2</td><td>1</td><td>0.33</td><td>1</td><td>0.67</td><td>0.5</td><td>0.496</td></tr><tr><td>Cameroon</td><td>1</td><td>2</td><td>0</td><td>0.67</td><td>1</td><td>1</td><td>1</td><td>0.542</td></tr><tr><td>Central Africa</td><td>2</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0.5</td><td>1</td><td>0.548</td></tr><tr><td>Congo-Brazzaville</td><td>0</td><td>1</td><td>0</td><td>0.67</td><td>0</td><td>1</td><td>1</td><td>0.264<sup>c</sup></td></tr><tr><td>Congo-Kinshasa</td><td>0</td><td>1</td><td>0</td><td>0.33</td><td>0</td><td>0</td><td>1</td><td>0.436</td></tr><tr><td>Cote d'Ivoire</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td><td>1</td><td>0.568</td></tr><tr><td>Egypt</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0.5</td><td>0</td><td>0.522</td></tr><tr><td>Gabon</td><td>0</td><td>1</td><td>0</td><td>0.67</td><td>0</td><td>1</td><td>1</td><td>0.549</td></tr><tr><td>Gambia</td><td>0</td><td>1</td><td>0</td><td>0.33</td><td>0</td><td>1</td><td>1</td><td>0.579</td></tr><tr><td>Ghana</td><td>0</td><td>1</td><td>0</td><td>0.33</td><td>0</td><td>0</td><td>1</td><td>0.567</td></tr><tr><td>Guinea-Bissau</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0.471</td></tr><tr><td>Kenya</td><td>2</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0.5</td><td>1</td><td>0.60</td></tr><tr><td>Lesotho</td><td>2</td><td>2</td><td>1</td><td>1</td><td>1</td><td>1</td><td>0.5</td><td>0.57</td></tr><tr><td>Libya</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0.343</td></tr><tr><td>Mali</td><td>0</td><td>32</td><td>1</td><td>0.67</td><td>0</td><td>0.5</td><td>1</td><td>0.541</td></tr><tr><td>Mauritania</td><td>1</td><td>2</td><td>0</td><td>0.33</td><td>1</td><td>0.5</td><td>0.5</td><td>0.556</td></tr><tr><td>Morocco</td><td>0</td><td>2</td><td>0</td><td>0</td><td>0</td><td>0.33</td><td>0.5</td><td>0.53</td></tr><tr><td>Mozambique</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0.551</td></tr><tr><td>Namibia</td><td>2</td><td>13</td><td>1</td><td>0.67</td><td>1</td><td>0.33</td><td>0.5</td><td>0.609</td></tr><tr><td>Niger</td><td>0</td><td>21</td><td>1</td><td>1</td><td>1</td><td>1</td><td>0.33</td><td>0.536</td></tr><tr><td>Nigeria</td><td>0</td><td>4</td><td>0</td><td>0.67</td><td>1</td><td>1</td><td>0.5</td><td>0.488</td></tr><tr><td>Rwanda</td><td>3</td><td>3</td><td>1</td><td>0.67</td><td>1</td><td>1</td><td>0.33</td><td>0.543</td></tr><tr><td>Senegal</td><td>0</td><td>7</td><td>1</td><td>0.67</td><td>1</td><td>1</td><td>0.33</td><td>0.574</td></tr><tr><td>Sierra Leona</td><td>0</td><td>1</td><td>0</td><td>0.33</td><td>0</td><td>0.25</td><td>1</td><td>0.467</td></tr><tr><td>South Africa</td><td>2</td><td>11</td><td>1</td><td>0.67</td><td>1</td><td>1</td><td>0.67</td><td>0.663</td></tr><tr><td>Swaziland</td><td>2</td><td>2</td><td>0</td><td>0.67</td><td>1</td><td>1</td><td>0.5</td><td>0.622</td></tr><tr><td>Tanzania</td><td>2</td><td>2</td><td>0</td><td>0.67</td><td>1</td><td>1</td><td>0.5</td><td>0.593</td></tr><tr><td>Togo</td><td>0</td><td>3</td><td>0</td><td>0.67</td><td>0</td><td>1</td><td>1</td><td>0.485</td></tr><tr><td>Tunisia</td><td>0</td><td>2</td><td>0</td><td>0</td><td>1</td><td>0.33</td><td>0.5</td><td>0.592</td></tr><tr><td>Zambia</td><td>0</td><td>8</td><td>0</td><td>1</td><td>1</td><td>1</td><td>0.5</td><td>0.591</td></tr><tr><td>Zimbabwe</td><td>3</td><td>9</td><td>1</td><td>1</td><td>1</td><td>1</td><td>0.33</td><td>0.34</td></tr></tbody></table>

Notes: (a) LiEp: 0. Unilingual; 1. Bilingual (excl. Mother-tongue); 2. Bilingual (incl. Mother-tongue); 3. Trilingual. (b). All values of *D* (Index of Economic Freedom) are computed for the year 2006 except for Congo-Brazille (c), for which the latest valid data is from year 2000.
<table><caption>Table 2</caption><thead><tr><th>Variable</th><th>Obs</th><th>Mean</th><th>Std. Dev.</th><th>Min</th><th>Max</th></tr></thead><tbody><tr><td>LiEp</td><td>35</td><td>.6857143</td><td>1.022437</td><td>0</td><td>3</td></tr><tr><td>L</td><td>35</td><td>4.228571</td><td>6.472047</td><td>1</td><td>32</td></tr><tr><td>E</td><td>35</td><td>.5528572</td><td>.3433877</td><td>0</td><td>1</td></tr><tr><td>C</td><td>35</td><td>.4571429</td><td>.5054327</td><td>0</td><td>1</td></tr><tr><td>I</td><td>35</td><td>.7545714</td><td>.3497843</td><td>0</td><td>1</td></tr><tr><td>H</td><td>35</td><td>.6997143</td><td>.3207756</td><td>0</td><td>1</td></tr><tr><td>D</td><td>35</td><td>.5306286</td><td>.0879826</td><td>.264</td><td>.703</td></tr></tbody></table>

<caption>Summary statistics</caption>
Table 3

Results Ordered logistic regression

a. Complete model

Ordered logistic regression

Log likelihood = -23.071533

Number of obs = 35

LR chi2(6) = 19.68

Prob > chi2 = 0.0032

Pseudo R2 = 0.2990

<table><thead><tr><th>liep</th><th>Coef.</th><th>Std. Err.</th><th>z</th><th>P>|z|</th><th colspan="2">[95% Conf. Interval]</th></tr></thead><tbody><tr><td>l</td><td>-.1735128</td><td>.1150151</td><td>-1.51</td><td>0.131</td><td>-.3989383</td><td>.0519127</td></tr><tr><td>e</td><td>6.068395*</td><td>2.514478</td><td>2.41</td><td>0.016</td><td>1.140108</td><td>10.99668</td></tr><tr><td>c</td><td>4.419177**</td><td>1.90489</td><td>2.32</td><td>0.020</td><td>.6856611</td><td>8.152693</td></tr><tr><td>i</td><td>-3.910656</td><td>2.251928</td><td>-1.74</td><td>0.082</td><td>-8.324354</td><td>.5030427</td></tr><tr><td>h</td><td>-.008578</td><td>2.381896</td><td>-0.00</td><td>0.997</td><td>-4.677007</td><td>4.659851</td></tr><tr><td>d</td><td>-6.350042</td><td>5.947425</td><td>-1.07</td><td>0.286</td><td>-18.00678</td><td>5.306697</td></tr><tr><td>/cut1</td><td>.0610169</td><td>3.377253</td><td></td><td></td><td>-6.558277</td><td>6.680311</td></tr><tr><td>/cut2</td><td>.4983525</td><td>3.390367</td><td></td><td></td><td>-6.146645</td><td>7.14335</td></tr><tr><td>/cut3</td><td>3.072046</td><td>3.317035</td><td></td><td></td><td>-3.429223</td><td>9.573314</td></tr></tbody></table>

legend: * p<0.05; ** p<0.01; *** p<0.001

b. Multicollinearity test

(obs=35)

<table><thead><tr><th></th><th>l</th><th>e</th><th>c</th><th>i</th><th>h</th><th>d</th></tr></thead><tbody><tr><td>l</td><td>1.0000</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>e</td><td>0.3100</td><td>1.0000</td><td></td><td></td><td></td><td></td></tr><tr><td>c</td><td>0.2189</td><td>0.3685</td><td>1.0000</td><td></td><td></td><td></td></tr><tr><td>i</td><td>0.0263</td><td>0.4368</td><td>0.2923</td><td>1.0000</td><td></td><td></td></tr><tr><td>h</td><td>-0.1202</td><td>0.0485</td><td><strong>-0.5815</strong></td><td>0.0893</td><td>1.0000</td><td></td></tr><tr><td>d</td><td>0.1118</td><td>0.2374</td><td>0.3492</td><td>0.1480</td><td>-0.0179</td><td>1.0000</td></tr></tbody></table>

c. Reduced model

Ordered logistic regression

Log likelihood = -23.071539

Number of obs = 35

LR chi2(5) = 19.68

Prob > chi2 = 0.0014

Pseudo R2 = 0.2990

<table><thead><tr><th>liep</th><th>Coef.</th><th>Std. Err.</th><th>z</th><th>P>|z|</th><th colspan="2">[95% Conf. Interval]</th></tr></thead><tbody><tr><td>l</td><td>-.1733908</td><td>.1098959</td><td>-1.58</td><td>0.115</td><td>-.3887829</td><td>.0420012</td></tr><tr><td>e</td><td>6.067499*</td><td>2.501969</td><td>2.43</td><td>0.015</td><td>1.16373</td><td>10.97127</td></tr><tr><td>c</td><td>4.422515**</td><td>1.664344</td><td>2.66</td><td>0.008</td><td>1.160461</td><td>7.684569</td></tr><tr><td>i</td><td>-3.911179</td><td>2.247007</td><td>-1.74</td><td>0.082</td><td>-8.315232</td><td>.4928752</td></tr><tr><td>d</td><td>-6.353552</td><td>5.866549</td><td>-1.08</td><td>0.279</td><td>-17.85178</td><td>5.144673</td></tr><tr><td>/cut1</td><td>.0666254</td><td>2.99782</td><td></td><td></td><td>-5.808993</td><td>5.942244</td></tr><tr><td>/cut2</td><td>.5039706</td><td>3.01121</td><td></td><td></td><td>-5.397893</td><td>6.405835</td></tr><tr><td>/cut3</td><td>3.077235</td><td>2.988813</td><td></td><td></td><td>-2.780731</td><td>8.935201</td></tr></tbody></table>

legend: * p<0.05; ** p<0.01; *** p<0.001
STUDY II
<figure><img src="image_11.png" /></figure>
# The Role of Language in Learning Achievement:
## A Namibian Case study*

Christelle Garrouste⁺

### Abstract

This study investigates the role played by home language and language proficiency on learning achievement. It compares characteristics of 5048 Grade-6 learners in 275 Namibian schools. The outcome variable is the standardized SACMEQ mathematics achievement score collected in year 2000. Hierarchical linear modeling is used to partition the total variance in mathematics achievement into its within- and between-school components. The social distribution of achievement in each school is represented by a within-school model regressing mathematics achievement on home language, gender, social class (SES), grade repetition and reading test scores. The between-school model serves in turn at explaining heterogeneities as a function of school characteristics. An explanatory model is developed to identify specific features of school's academic organization and normative environment that are expected to contribute to the distribution of achievement. The results of the analysis show that although home language plays a limited role in explaining within-school variations in mathematics achievement and no significant role at the between-school level, language proficiency appears to play a much stronger role in explaining both within- and between-school heterogeneity of scores in Namibia, which confirms the role of language skills in learning achievement.

**Keywords:** Learning achievement, language skills, multilevel analysis, HLM, Namibia.

**JEL Codes:** I2, C13, C3.

<footnote>* Reproduced with permission from Working Paper Series, No.20 (October 2007).
http://www.interped.su.se/publaineWorking.asp. Copyright 2007 by the Institute of International Education, Stockholm University.</footnote>

<footnote>+ Christelle Garrouste is Doctoral Candidate at IIE, Stockholm University and Marie Curie Research Fellow at the Department of Economics “Marco Fanno”, Padua University (garrouste.norelius@interped.su.se / christelle.garrouste@unipd.it). The author would like to address her gratitude to all the Government Officers, NEPRU and UNAM Researchers, SIDA Officers, School Headmasters, School Inspectors and Students met during her fieldtrips to Namibia in December 2003 and April-May 2004, for their availability and cooperation in providing her with free access to all school databases, official documents and school facilities. Moreover, the author would also like to thank the SACMEQ Coordinating Center of Harare for granting her access to the SACMEQ I and II datasets, as well as the participants to her final research seminar at IIE, Stockholm University, September 25, 2007, and internal seminar at the Department of Economics “Marco Fanno”, Padua University, October 16, 2007, for their comments and suggestions on preliminary versions of this paper.</footnote>
Introduction

The need for reconstruction after the Second World War has rapidly led to a world-
wide growth of interest in the application of large-scale scientific survey research
techniques to the study of issues related to improving the productivity of workers through
an increase of the number of literate people, among which Husén's (1969) work and the
international research ran by the Association for the Evaluation of Education and
Achievement (IEA) in the early 1970s which encompassed twenty-three countries (see
Elley, 1992, 1994; Lundberg & Linnakyla, 1993; Postlethwaite & Ross, 1992). This trend
spread progressively to developing countries. In the 1980s the focus of these surveys
slowly moved from an increase of quantity of education to an improvement of quality of
education. Most occidental countries and an increasing number of developing countries are
now applying such techniques to undertake systematic studies of the conditions of
schooling and student achievement levels.

Summarizing the results of the IEA and other studies for developing countries,
Alexander & Simmons (1975) note the lack of consistency across studies and the
conflicting nature of the results. For instance, school-related variables, such as class size,
school size, and teacher characteristics, appear to be significant in some countries and non-
significant (or negatively significant) in others. Finally, although non-school variables
appear of high importance in all the studies, home background seems to have less influence
on pupils' performance in developing than in developed countries.

In 1983, Heyman & Loxley examined the effects of socioeconomic status and
school factors on students' science achievement in primary school in sixteen low-income
countries and thirteen high-income countries. They observed that the influence of family
background varies significantly with national economic development between countries,
and that the percentage of achievement variance explained by school and teacher variables
is negatively correlated with the level of a country's development. This result is confirmed
by Saha (1983) and Fuller (1987) who examined the effects of school factors on student
achievement in the Third World. Fuller concluded that "much of this empirical work
suggests that the school institution exerts a greater influence on achievement within
developing countries compared to industrialized nations, after accounting for the effect of
pupil background" (pp. 255-6; italics in original).
Further studies have highlighted the role of language proficiency on academic achievement. For instance, Geary, Bew-Thomas, Liu & Stigler (1996) found that the language structure of Asian number names assisted Chinese children in developing meaningful early number concepts. Valverde (1984) noted that differences in English and Spanish contributed to Hispanic Americans' poor performance and involvement in mathematics (see also Bush, 2002, for similar conclusions).

More recent international survey data have attempted to improve the quality of sampling methods to enable the run of more valid and sophisticated forms of statistical analyses. One example of such effort is the cooperative project launched in 1991 by the International Institute for Educational Planning (IIEP) together with a number of Ministries of Education in the Southern Africa Sub-region for the establishment of long-term strategies for building the capacity of educational planners to monitor and evaluate basic education systems. In 1993, an association was created to extend the reach and formal status of that work, namely the Southern Africa Consortium for Monitoring Educational Quality (SACMEQ), and in 1995 the first SACMEQ survey project was launched in six Southern African countries. The SACMEQ I project was completed in 1998 followed by the SACMEQ II project launched in 2000 in fourteen Southern and Eastern African countries.

By 2005, all fourteen national reports presenting the results from SACMEQ II had been released. What emerged from these results was the fact that most countries were still demonstrating large between- and within-school variations. Within-school variation is an indication of differences in abilities among learners within each school, and between-school variations, an indication of equity problems within the education system. South Africa, followed by Uganda and Namibia, demonstrated then the highest percentage of between-school variation.

More specifically, the Namibian results display very poor learners and teachers reading and mathematics scores, a definite decline in reading scores between the first SACMEQ study of 1995 and the second one of 2000 and considerable variation among regions (Makuwa, 2005). These results deserve further investigation in view of the high resource allocation efforts made by the Namibian authorities to launch substantial education reforms since independence in 1990, including the adoption of a bilingual language-in-education policy aiming primarily at facilitating the cognitive development
and, hence, the learning process of pupils, and with regard to the ambitious National Plans formulated since 1999.

Hence, after a short review of the status of Namibian schools and political agenda at the time the SACMEQ II was conducted (i.e. year 2000), this paper attempts to investigate the main factors explaining the poor scores of Namibian Grade-6 learners. More specifically, the objective is to see whether the home language and language proficiency constitute a significant discrimination factor in mathematics achievement to explain the within-school and between-school variations. The method used is an adaptation of the Hierarchical Linear Modeling (HLM). This paper follows the theoretical steps enounced by Bryk & Raudenbush (1988) and Hox (1995) for the use of the HLM method for education analyses.

## Namibia's School Structure and Policy Agenda at the Time of the Study

The Republic of Namibia is situated on the south west coast of Africa and is bordered by the Atlantic Ocean to the west, the republics of Angola and Zambia to the north and north-east respectively and the republics of Botswana and South Africa to the east and south respectively. It obtained national independence from former apartheid South African government on March 21, 1990, after many years of political, diplomatic and armed, national liberation struggle. Even if the country is well endowed with good deposits of uranium, diamonds, and other minerals as well as rich fishing grounds, there are wide disparities in the distribution of incomes. With a per capita income of US$2,000 Namibia may be regarded as a middle income country. Yet, the richest 10 percent of the society still receives 65 percent of the incomes. As a consequence, the ratio of per capita income between the top 5 percent and the bottom 50 percent is about 50:1 (Makuwa, 2005). This provides a brief understanding of the socio-economic context under which the education system has to develop in Namibia.

Since independence, Namibia has made strides in the provision of basic education, which by 2001 had resulted in a primary education net enrolment of 94 percent of all children aged 7-13 (in Grades 1-7), and by 2006 Namibia ranked among the top eight African countries in term of primary completion rate ( > 80 percent) (Vespoor, 2006). While much seems to have been achieved in terms of access to schooling, the quality of
education, efficiency and equity issues are since the late 1990s at the center of political preoccupations.

Because Article 20 of the Constitution of the Republic of Namibia provides for free and compulsory education for all learners between the ages of 6 and 16 or learners from Grade 1 up to the end of Grade 7; and because the government has declared education to be a priority among all other priorities in Namibia, education has received since independence the largest share of the national recurrent budget. For instance, out of the estimated total government current expenditure of N$8.35 billion for the 2001/2002 financial year, N$1.86 billion, i.e. about 20 percent of the budget, was earn-marked for basic education only. Of the total amount allocated for basic education, N$986.56 million was earn-marked for primary education and the rest for secondary education. Yet, almost 90 percent of the money allocated for primary education was spent on personnel costs (e.g., salaries and/or subsidies to teachers in a number of private schools), leaving only about 10 percent for all the other services and school supplies (Makuwa, 2005). As a consequence, the financial allocation per learner ratio is more favorable to regions with more qualified staff and fewer learners than to rural regions with more unqualified teachers and large pupil-teacher ratios. Finally, the authorized practice of collect by schools of school development funds from parents is again more favorable to schools in urban areas where parents have an income than to schools in more remote areas.

In addition to these obvious resource allocation issues, it is also important to highlight the many changes that took place in the education sector between 1995 and 2000. As explained in Makuwa's (2005) report, there were for instance more learners and more schools in 2000 than in 1995; the department of Sport was added to the Ministry of Basic Education and Culture; and, more important, the HIV/AIDS pandemic became a national problem affecting infected administrators, teachers, learners and/or parents. In view of these new contextual settings, the Ministry of Basic Education, sports and Culture (MBESC) defined eight new national priority areas in its “Strategic Plan” for the period 2001-2006: equitable access; education quality; teacher education and support; physical facilities; efficiency and effectiveness; HIV/AIDS; lifelong learning; and sports, arts and cultural heritage.

Finally, to understand the context framing the data used in this study, it is also essential to give an overview of the structure of the Namibian primary school system. The primary phase consists of the Lower Primary (Grades 1-4), during which mother tongue is
used as medium of instruction, and Upper Primary (Grades 5-7), during which English becomes the medium of instruction up to Grade 12. By the year 2000, there were 998 primary schools hosting a total of 406,623 learners, of which 952 were government schools and the rest were private schools. Nearly two thirds of all primary schools were located in the six most populated northern regions namely, Caprivi, Kavango, Ohangwena, Oshikoto, Oshana and Omusati.

It is in the above milieu that the second SACMEQ survey used in the present paper was conducted and it is therefore in that frame that the results of the analysis should be interpreted.

## Data and method

The sampling procedure for the SACMEQ II survey was geared by methodological recommendations to all participating countries, but with certain flexibility to take into account contextual differences. Hence, as for all other participating countries, the desired target population in Namibia was all learners enrolled in Grade 6 in the ninth month of the school year (i.e. in September 2000). The net enrolment ratio for the age group 7-13 years old who were enrolled in Grades 1 to 7 in Namibia in 2000 was 91.3 percent. However, in Namibia it was decided to exclude certain learners namely, learners in schools with less than fifteen Grade 6 learners, learners in "inaccessible" schools, and learners in special schools. A two-stage cluster sampling was employed using approximately equal size clusters stratified into the 13 educational regions, which led to a final sample of 5048 learners and 275 schools (Makuwa, 2005).

The HLM6.0 program is used in this study to partition the total variance in mathematics scores into its within- and between-school components. The HLM framework was developed during the 1980s by Aitkin & Longford (1986), DeLeeuw & Kreft (1986), Goldstein (1987), Mason et al. (1983) and Raudenbusk & Bryk (1986). As explained by Raudenbush & Bryk (1995), these procedures share two core features. First, they enable researchers to formulate and test explicit statistical models for processes occurring within and between educational units, thereby resolving the problem of aggregation bias under appropriate assumptions. Second, these methods enable specification of appropriate error structures, including random intercepts and random coefficients, which can solve the
problem of misestimated precision that characterized previous conventional linear models
and hindered their capacity to test hypotheses<fnref n="1" />.

Among the empirical works using this approach on international survey data is the study by Lamb & Fullarton (2002) which compared mathematics achievement in Australia and the U.S. using the HLM on TIMSS data. The results found that classroom differences accounted for about one-third of the variation in student achievement in the U.S. and over one-quart in Australia. Most of the classroom variation in both countries was due to compositional and organizational factors, very little due to differences between teachers. Moreover, Howie (2002, 2005) and Gustafsson (2007) used HLM on TIMSS and SACMEQ data, respectively, to understand school production in South Africa. Howie (2002, 2005) applied multilevel analysis (2002, 2005) on TIMSS data to show that significant predictors of between-school variations include pupils' performance in the English test, pupils' SES (to a lesser extent), pupils' self concept, pupils' perception of the importance of mathematics, their exposure to English, how pupils' math teachers perceive their professional status, pupils' math teachers beliefs about mathematics, the location of the school, the extent to which English is used in the classroom, the amount of time teachers spend working and the amount of time teachers spend in lesson planning. More recently, Gustafsson (2007) applied HLM to South Africa's SACMEQ II data and found that physical infrastructure, textbooks, nutrition budgets, correct allocation of teaching and management time in schools, less learner repetition, and better teaching methodologies are important factors of variations in mathematics scores within and between South African schools. This last study respects the theoretical steps of multilevel analysis more reliably than Howie's works but does not include any language related variable.

The theoretical framework of HLM modeling applied in the present study is the one derived from Bryk & Raudenbush (1988) and defined by Hox (1995) consisting in 5 steps: (1) the Null Model; (2) the estimation of the fixed effects of the within-school model; (3) the estimation of the variance components of the within-school model; (4) the exploration of between-school effects; and (5) the estimation of the cross-level interactions between the within- and between-school variables. Note that relevance to the Namibian context, correlations with test scores and correlations between input variables were taken into

<footnote n="1">¹ Lynch, Sabol, Planty & Shelly (2002) confirm the strength of HLM models compared to other multilevel models to produce superior unbiased estimates of coefficients and robust standard errors even when the assumptions required by OLS are violated.</footnote>
account in the selection of all the parameters retained for this model. Table 1 displays the descriptive statistics relative to each parameter.

## Results

### The Null Model

The first step in fitting an HLM model is to analyze a model with no explanatory variables. The output variable is pupil's total raw score in mathematics at the SACMEQ test (MATOTP). The SACMEQ II Mathematics test is composed of three domains, namely (1) number (i.e. operations and number line, square roots, rounding and place value, significant figures, fractions, percentages, and rations); (2) measurement (i.e. measurements related to distance, length, area, capacity, money, and time); and (3) space-data (i.e. geometric shapes, charts and data tables)<fnref n="2" />.

This intercept-only model is defined by:

$$ egin{cases} y_{ij} = \beta_{0j} + R_{ij} \\ \beta_{0j} = \mu_{00} + U_{0j} \end{cases} \qquad (1) $$

Hence,

$$ y_{ij} = \mu_{00} + U_{0j} + R_{ij}. \qquad (2) $$

In this intercept-only model, which is the null model of our analysis, the base coefficient $\beta_{0j}$ is defined as the mean mathematics score in school j. It is a standard one-way random effects ANOVA model where schools are a random factor with varying numbers of students in each school sample (Bryk & Raudenbush, 1988, p.75).

Whereas the within-school variance $var(R_{ij})$, i.e. the variability in student mathematics scores around their respective school means, is estimated to 25.556, the between-school variance $var(U_{0j}) = var(\beta_{0j})$, i.e. the variability among school means, is

<footnote n="2">² For a detailed overview of the levels and items composing the SACMEQ II Mathematics test, see the blueprint in Makuwa (2005, p. 31).</footnote>
estimated to 36.020. Consequently, the intra-school correlation $\rho$, i.e. the ratio of the between-school variance over the sum of the between- and within-school variances, is .585, which implies that approximately 58.5 percent of the variance in mathematics scores occurs between schools. This result confirms the proportion of between-school variations estimated by Makuwa (2005) in Namibian mathematics and reading scores, namely approximately 60 percent between-school variation against 40 percent within-school variation. What remains to be done is to explain these variations by fitting a model with the highest explanatory propension.

The Full Maximum Likelihood (FML) estimation method is used to calculate the value of deviance of this intercept-only model, which is a measure of the degree of misfit of the model (McCullagh & Nelder, 1989; Hox, 1995). We get a deviance of 31575.86 (number of estimated parameters = 3). Each of the following steps of this HLM analysis will now aim at fitting a model with a lower deviance value.

## The Within-School Model: Unconditional Model

The next phase is to analyze a model with pupil-level (within-school) explanatory variables fixed. This implies that the corresponding variance components of the slopes are fixed to zero. This fixed within-school model yields:

$$ 
\begin{aligned}
y_{ij} &= \beta_{0j} + \beta_{1j} X_{ij} + R_{ij} \\
&= \mu_{00} + \mu_{p0} X_{pij} + U_{0j} + R_{ij}
\end{aligned} 
\quad (3) $$

where the number of within-school explanatory variables is $p = 1,...,n$.

This model identifies five explanatory variables (i.e. six parameters when including the intercept namely, the base score):

ENGLISH is a dummy variable that takes the value of 1 if the pupil speaks English sometimes or always at home and the value of 0 if never. This variable aims at exploring the role played by the home language in achievement in a country applying a bilingual education policy based on mother-tongue instruction in the early phase of primary education before transiting to English in Grade 5 upwards. It is nevertheless important to highlight that because of the nature of the question – “How often do you speak English at home?” – inconsistency in the responses is plausible. For instance, the fact that 76.9
percent of the sampled pupils answered that they speak sometimes or all the time English at home does not mean that English is the mother-tongue of 76.9 percent of that population. In reality, English is the mother-tongue of only .56 percent of the Namibian population (Gordon, 2005). Moreover, no indication is provided about the nature and the level of communication in English that is occurring at home. Hence, this home language parameter should NOT be interpreted as a proxy of mother-tongue rather as a proxy of the linguistic home background of the pupil.

*FEMALE* takes the value of 1 if the pupil is a girl and the value of 0 if the pupil is a boy. Entering a gender parameter aims at addressing potential gender gaps in mathematics achievement. In the present case, although the mean mathematics score for boys (= 18.86) is very close to the one for girls (= 18.25) the existence of very high variance for each group (66.41 for boys and 56.45 for girls) justifies further exploration.

*SES* is a computed variable measuring the pupil's SES (in terms of parents' education, possessions at home, light, wall, roof, floor) that takes values between 1 and 15. Although the link between social background and achievement has been demonstrated to be less strong within-school in less developed countries than in industrial countries (see Heyman & Loxley, 1983; Saha, 1983; Fuller, 1987), it is still essential to include it in our analysis to avoid missing any explanation of between-school variations.

*RATOTP* is the pupil's total raw score in reading at the SACMEQ test. The reading test scores serve here as a proxy of English language proficiency (see Geary *et al.*, 1997; Valverde, 1984; Collier, 1992; Ehindero, 1980; Yip *et al.*, 2003; Clarkson & Galbraith, 1992). Note that the strong correlation expected between *RATOTP* and *ENGLISH* is present in our sample with a significance at the .01 level (2-tailed) and that the mean reading score of pupils who never speak English at home (= 29.86) is, again as expected, less than the mean score of pupils speaking sometimes or all the time English at home (= 35.00).

Finally, *REPEAT* is a dummy variable taking the value of 1 if the pupil has repeated at least one class and 0 if not. It provides information on the learning facilities/difficulties of the pupil and serves thereby as a proxy of the pupil's academic background when combined with *RATOTP* (Bryk & Raudenbush, 1988). In our sample the mean mathematics score of grade repeating pupils is 16.66 compared to 20.55 for pupils on-track with much larger variance among the first (= 87.95) than among the latter group (= 29.18).
The predictors SES and REPEAT are centered around their respective group mean. Figures 2.1-2.5 present the Stem & Leaf plots of Mathematics scores by each parameter. Each figure shows the existence of large variations between and/or within groups, which justify the conduct of the present HLM analysis on these parameters to investigate the source of this variance.

Replacing each parameter by its label-value in equation (3) we get:

$$MATOTP_{ij} = \mu_{00} + \mu_{10}ENGLISH_{ij} + \mu_{20}FEMALE_{ij} + \mu_{30}(SES_{ij} - \overline{SES}_{\bullet j}) + \mu_{40}(RATOTP_{ij} - \overline{RATOTP}_{\bullet j}) + \mu_{50}REPEAT_{ij} + U_{0j} + R_{ij} \quad (3')$$

The final estimation of these fixed effects with robust standard errors is displayed in Table 2. It appears that the most significant parameters are the pupil's mean mathematics score, gender and reading raw score. The slopes' signs show that, whereas being a girl has an overall negative impact on mathematics scores, a high mean mathematics score in the school attended and a high individual reading score have a positive impact on individual mathematics scores. The lack of statistical significance of the ENGLISH, SES and REPEAT parameters is however not strong enough to justify at this stage a removal from the model. So far, what the model shows is that speaking English at home and a high SES background have a positive impact on mathematics achievement, which confirms the theory. According to previous research on developing countries (Heyneman & Loxley, 1983; Saha, 1983; Fuller, 1987; etc.), it is expected that SES and REPEAT will remain non-significant.

Moreover, grade repetition has a negative impact on mathematics achievement, which confirms the conclusions reached by Verspoor (2006) in his report for ADEA. However, before claiming that this result either invalidates or confirms the assumption that repetition has a negative effect on pupil's achievement improvement, it is important to highlight that the SACMEQ dataset does not provide for any longitudinal data. This lack implies that it is impossible to know whether the pupil who repeated a grade did improve its mathematics score compared to the previous year or not. All we know from the present analysis is that, overall, pupils who have repeated a grade perform less well than their non-repeating peers. Hence, combined with the RATOTP parameter, this gives us an idea of the role of the educational background of the pupil on mathematics scores at a fixed date t,
with a higher mathematics achievement when the pupil is on school track (no repetition) and highly proficient in English.

The deviance of this model is 30002.99 (number of estimated parameters = 8) which means an improvement from the null model. This fixed model explains 61.7 percent of the total variance in mathematics scores.

The third step consists now in assessing whether the slope of any of the explanatory variables has a significant variance component between schools. The model considered is:

$$y_{ij} = \mu_{00} + \mu_{p0} X_{pij} + U_{pj} X_{pij} + U_{0j} + R_{ij}. \quad (4)$$

Replacing the parameters by their label name in equation (4) yields:

$$MATOTP_{ij} = \mu_{00} + \mu_{10} ENGLISH_{ij} + \mu_{20} FEMALE_{ij} + \mu_{30} (SES_{ij} - \overline{SES}_{\bullet j}) \\ + \mu_{40} (RATOTP_{ij} - \overline{RATOTP}_{\bullet j}) + \mu_{50} REPEAT_{ij} + U_{1j} ENGLISH_{ij} \\ + U_{2j} FEMALE_{ij} + U_{3j} (SES_{ij} - \overline{SES}_{\bullet j}) + U_{4j} (RATOTP_{ij} - \overline{RATOTP}_{\bullet j}) + U_{5j} REPEAT_{ij} + U_{0j} + R_{ij} \quad (4')$$

The testing of random slopes variations is done on a one-by-one basis. The deviance is now equal to 29663.63 (number of estimated parameters = 28), which implies a further improvement from to the null model. Table 2 presents all the results for the within-school explanatory model <u>unconditioned</u> by the between-school variables.

As explained by Raudenbush & Bryk (1987; 1988; 1992; 1995), the unconditional model is particularly valuable because it provides estimates of the total parameter variances and covariances among the $\beta_{pj}$. When expressed as correlations they describe the general structure among these within-school effects. Table 2 shows that a high base level of achievement is associated with less grade repetition ($r$ = .974), higher reading scores ($r$ = .915), higher SES ($r$ = .602), and male pupils ($r$ = .650) who do not have English as home language ($r$ = .192). There is also a substantial association between pupil high SES and academic achievement (with a high negative correlation between SES and grade repetition ($r$ = .624) and a positive correlation with reading achievement ($r$ = .278)).

Moreover, HLM derives an indicator of the reliabilities of the random effects by comparing the estimated parameter variance in each regression coefficient, $var(\beta_{ij})$, to the
total variance in the ordinary least square estimates. These results are also displayed in Table 2. As expected, the base score is rather reliable, .788, and the regression coefficients are less reliable ranging from a low of .036 for pupils' SES to a high .315 for reading raw score. This relatively low reliability may express the fact that much of the observed variability among schools in regression slopes is due to sampling error that can not be explained by within-school factors.

Finally, the results of the homogeneity-of-variance tests provide statistical evidence of significant variation within schools in each of the six random regression coefficients with a very high Chi-square statistic (417.13) with 233 d.f.. The probability of the observed variability in these coefficients, under a homogeneity hypothesis, is less than .001 for $\beta_0$, and $\beta_4$ and less than .20 for $\beta_5$. Hence, it appears that schools vary significantly in the degree to which achievement in mathematics depends on the child's reading score and repetition status, i.e. on the child's academic background, which confirms the findings by Raudenbush & Bryk (1988). Despite marginal significance, the pupil's gender, SES and home language status, are still retained as random parameters because of previously reported school effects (i.e. between-school variability) on each of them.

## The Between-School Model: Conditional Model

Next, the higher level explanatory variables $Z_{qj}$ (i.e., school-level factors) are added to equation (4) to examine whether these variables explain between-school variation in the dependent variable. This addition yields:

$$y_{ij} = \mu_{00} + \mu_{p0}X_{pij} + \mu_{0q}Z_{qj} + U_{pj}X_{pij} + U_{Oj} + R_{ij}, \quad (5)$$

with $q$ between-school explanatory variables $Z$, $q = 1,...,m$.

The between-school variables add information about the quality of teaching and the learning environment. In this model $q = 11$ and the $Z_{qj}$ include the following class-room and school parameters:

* TOTENROL which measures the size of the school in term of total enrolment;

* PTRATIO providing the pupil-teacher ratio in each mathematics class;

* STYPE, a dummy variable taking the value of 1 when the school is governmental and 0 when private;
SLOC, a dummy variable taking the value of 1 when the school is situated in an urban area and 0 when in a rural or isolated area;

PRACAD, a measure of the proportion of pupils on track (no grade repetition) in each school j;

DISCLIM which measures the overall discipline climate of the school. It is computed as the average value of the following dummy variables: pupil arrive late, pupil absenteeism, pupil skip class, pupil dropout, pupil classroom disturbance, pupil cheating, pupil language, pupil vandalism, pupil theft, pupil bullying pupils, pupil bullying staff, pupil injure staff, pupil sexually harass pupils, pupil sexually harass teachers, pupil drug abuse, pupil alcohol abuse, pupil fights, teacher arrive late, teacher absenteeism, teacher skip classes, teacher bully pupils, teacher harass sexually teachers, teacher harass sexually pupils, teacher language, teacher drug abuse, and teacher alcohol abuse. Each variable takes the value of 1 if the answer is “never”; and 0 if the answer is “sometimes/often”.

LGMNTY, a dummy variable taking the value of 1 when 40 percent or more of the pupils speak English at home in school j and the value of 0 when less than 40 percent never speak English at home. This computation follows Raudenbush & Bryk's (1988) computation of racial minority in the U.S. context.

MSES, the mean SES in school j;

TSEX taking the value of 1 when the mathematics teacher is a female and the value of 0 when a male;

TSATPLRN taking the value of 1 when the mathematics teacher considers the pupils' learning as very important and 0 when not important or of some importance; and

MATOTT, the mathematics raw score of the teacher, which serves as a proxy of the teacher's qualifications based on its mastery of the subject.

The predictors TOTENROL, PTRATIO, MSES and MATOTT are centered around their respective grand mean.

Replacing these variable labels into equation (5) yields the following model:
$$
\begin{align}
MATOTP_{ij} ={}& \mu_{00} + \mu_{10} \text{ENGLISH}_{ij} + \mu_{20} \text{FEMALE}_{ij} + \mu_{30} (\text{SES}_{ij} - \overline{\text{SES}}_{\bullet j}) \nonumber \\
& + \mu_{40} (\text{RATOTP}_{ij} - \overline{\text{RATOTP}}_{\bullet j}) + \mu_{50} \text{REPEAT}_{ij} + \nonumber \\
& \mu_{01} (\text{TOTENROL}_{j} - \overline{\text{TOTENROL}}_{\bullet}) + \mu_{02} (\text{PTRATIO}_{j} - \overline{\text{PTRATIO}}_{\bullet}) \nonumber \\
& + \mu_{03} \text{TYPE}_{j} + \mu_{04} \text{SLOC}_{j} + \mu_{05} \text{PRACAD}_{j} + \mu_{06} \text{DISCLIM}_{j} \nonumber \\
& + \mu_{07} \text{LGMNTY}_{j} + \mu_{08} (\text{MSES}_{j} - \overline{\text{MSES}}_{\bullet}) + \mu_{09} \text{TSEX}_{j} \nonumber \\
& + \mu_{010} \text{TSATPLRN}_{j} + \mu_{011} (\text{MATOTT}_{j} - \overline{\text{MATOTT}}_{\bullet}) + U_{1j} \text{ENGLISH}_{ij} \nonumber \\
& + U_{2j} \text{FEMALE}_{ij} + U_{3j} (\text{SES}_{ij} - \overline{\text{SES}}_{\bullet j}) + U_{4j} (\text{RATOTP}_{ij} - \overline{\text{RATOTP}}_{\bullet j}) \nonumber \\
& + U_{5j} \text{REPEAT}_{ij} + U_{0j} + R_{ij} \tag{5'}
\end{align}
$$

The FML estimation method is again used to test (with the global chi-square test)
the improvement of fit of the new model. After adding the between-school explanatory
parameters, the deviance is 29495.19 (degree of freedom = 39), which improves again the
null model. Table 3 presents the results for this conditional model. What appears from that
analysis is that the proportion of students on track, the mean pupil's SES and the level of
mathematics of the math teacher explain very significantly (significant at the .001 level)
variations in the individual mathematics scores. At a lesser level, the school's overall
disciplinary climate and the type of school also play a significant role, with t-values of
1.812 and -1.281 respectively. The negative slope of the type of school indicates that
private schools perform on average better than governmental schools.

The Final Model: Cross-Level Interaction Model

Finally, cross-level interactions between explanatory school-level variables and
those pupil-level explanatory variables that had significant slopes variation in equation (4)
are added. This last addition leads to the full model formulated in equation (6):

$$
y_{ij} = \mu_{00} + \mu_{p0} X_{pij} + \mu_{0q} Z_{qj} + \mu_{pq} Z_{qj} X_{pij} + U_{pj} X_{pij} + U_{Oj} + R_{ij}, \quad (6)
$$

which yields equation (6'):
$$
\begin{align*}
MATOTP_{ij} ={}& \mu_{00} + \mu_{01} \text{TYPE}_j + \mu_{02} \text{SLOC}_j + \mu_{03} \text{PRACAD}_j + \mu_{04} (\text{MSES}_j - \overline{\text{MSES}}_{\bullet j}) \\
& + \mu_{05} (\text{MATOTT}_j - \overline{\text{MATOTT}}_{\bullet j}) + \mu_{10} \text{ENGLISH}_{ij} + \mu_{11} \text{TYPE}_j \text{ENGLISH}_{ij} \\
& + \mu_{12} \text{DISCLIM}_j \text{ENGLISH}_{ij} + \mu_{20} \text{FEMALE}_{ij} \\
& + \mu_{21} (\text{MSES}_j - \overline{\text{MSES}}_{\bullet j}) \text{FEMALE}_{ij} + \mu_{30} (\text{SES}_{ij} - \overline{\text{SES}}_{\bullet j}) \\
& + \mu_{31} \text{DISCLIM}_j (\text{SES}_{ij} - \overline{\text{SES}}_{\bullet j}) + \mu_{40} (\text{RATOTP}_{ij} - \overline{\text{RATOTP}}_{\bullet j}) \\
& + \mu_{41} (\text{TOTENROL}_j - \overline{\text{TOTENROL}}_{\bullet j}) (\text{RATOTP}_{ij} - \overline{\text{RATOTP}}_{\bullet j}) \\
& + \mu_{42} \text{TYPE}_{1j} (\text{RATOTP}_{ij} - \overline{\text{RATOTP}}_{\bullet j}) + \mu_{43} \text{PRACAD}_j (\text{RATOTP}_{ij} - \overline{\text{RATOTP}}_{\bullet j}) \\
& + \mu_{44} (\text{MSES}_j - \overline{\text{MSES}}_{\bullet j}) (\text{RATOTP}_{ij} - \overline{\text{RATOTP}}_{\bullet j}) \\
& + \mu_{45} (\text{MATOTT}_j - \overline{\text{MATOTT}}_{\bullet j}) (\text{RATOTP}_{ij} - \overline{\text{RATOTP}}_{\bullet j}) + \mu_{50} \text{REPEAT}_{ij} \\
& + \mu_{51} \text{TYPE}_j \text{REPEAT}_{ij} + \mu_{52} (\text{MSES}_j - \overline{\text{MSES}}_{\bullet j}) \text{REPEAT}_{ij} + U_{1j} \text{ENGLISH}_{ij} \\
& + U_{2j} \text{FEMALE}_{ij} + U_{3j} (\text{SES}_{ij} - \overline{\text{SES}}_{\bullet j}) + U_{4j} (\text{RATOTP}_{ij} - \overline{\text{RATOTP}}_{\bullet j}) \\
& + U_{5j} \text{REPEAT}_{ij} + U_{0j} + R_{ij}
\end{align*}
$$

Here again, the FML estimation method is used to derive the global chi-square test to formally test the improvement of fit. The deviance is now 29354.015 (number of estimated parameters = 44), which means a 7.57 percent improvement compared to the null model. The OLS regression of the full explanatory model improves the capacity of explanation of the variations in mathematics scores by almost 2 percent ($R^2$ = .635 percent). The results of the final explanatory model are displayed in Table 4.

Table 4 shows that the base score differences between private and public schools (*TYPE*) disappear once the school location (*SLOC*), the portion of pupils on track (*PRACAD*), the mean SES (*MSES*) of the school and the mathematics score of the math teacher (*MATOTT*) are taken into account. The negative slope of the school type means that greater mathematics achievement is associated with private schools situated in urban areas, with a high proportion of pupils on track, a high average SES and a good mastery of mathematics by the teacher. The effect of the school type (public or private) on the attraction of home English speaking pupils disappears once the disciplinary climate (*DISCLIM*) is taken into account. Home-English speaking pupils tend to attend private schools where the disciplinary climate is safer. Furthermore, low average school SES tends to be more associated with boys than with girls (*FEMALE*), and pupil's SES is associated to important disciplinary problems. Greater reading scores are associated with public schools if they are of small size (*TOTENROL*), if the proportion of pupils on track is high and the school average SES is not too low. In addition, great reading scores are also
associated with a good mastery of mathematics by the math teacher. Finally, there seems to be less grade repetition in public schools and in schools with a lower average SES.

The last panel of Table 4 compares the residual parameter variances from the explanatory model with the total parameter variances estimated in the unconditional model. The proportion reduction in these parameter variances can be interpreted as an indicator of the power of the explanatory model. The fitted model accounts for a substantial percentage of the variance (percent of R²) of each within-school parameters ranging from 33.94 percent for ENGLISH to 72.72 percent for RATOTP.

Finally, the most rigorous test of the explanation power of the final model involves acceptance of the homogeneity of residual variance hypotheses, i.e. “after modeling each $\beta_{jk}$ as a function of some school-level variables, is there evidence of residual parameter variation in the $\beta_{jk}$ that remains unaccounted?” (Bryk & Raudenbush, 1988, p. 79). Table 4 shows evidence of significant residual variation (high Chi-square) in base achievement score and academic background (RATOTP and REPEAT). Moreover, the homogeneity hypothesis for the home language ($p > .500$), gender ($p > .500$) and social differentiation ($p > .500$) are still not sustained<fnref n="3" />. This means that the remaining variance in $\beta_{pj}$ might be due to sampling variance arising because $\hat{\beta}_{pj}$ measures $\beta_{pj}$ with error (i.e. $\hat{\beta}_{pj} = \beta_{pj} + R_{pj}$) and because of the existence of correlation between $X_{pij}$ and $U_{pj}$ (i.e. $E\{U_{pij} | X_{pij} \neq 0\} > 0$) (see Pedhazur, 1982, for a comprehensive discussion of measurement errors, specification errors, and multicollinearity). In microeconomics modeling, the existence of a “non-zero” correlation between $X_{pij}$ and $U_{pj}$ violates one of the basic validity conditions. It is however a very common issue in most empirical applications and especially in multilevel linear models (Billy, 2001). Indeed, it implies that pupils’ performance and school quality can be positively correlated, which means that the residual variability across schools with respect to $U_{pij}$, remaining after accounting for the observable heterogeneity $X_{pij}$, understates the true variability of $U_{pij}$. For instance, pupils with better than average characteristics might be better informed and thus more able to choose the best school (“pupils self-selection”), and schools that attract better pupils (because of a better location, better status – private vs. public – or better organizational characteristics) also tend to attract better teachers (“teachers self-selection”). Moreover, schools with better teachers and management are in

<footnote n="3">³ The test of homogeneity of level-1 variance gives a Chi-square statistic of 417.13 for 233 d.f. and a P-value = .000.</footnote>
a position to recruit better students and “weed out” less promising cases (“creaming”), as it is the case for Namibian private schools (see Grilli & Rampichini, 2007; Fielding & Steele, 2007; Peng, 2007; Frank, 2005; Rettore & Martini, 2001; Mason, 2001; and Willms & Raudenbush, 1989; for methodological discussions and statistical proposals or attempts to solve this endogeneity bias).

In the case of this paper, the existence of potential endogeneity bias has partially been accounted for by the computation of the indicator of the reliabilities of random effects. This indicator examines the reliability of the ordinary least squares (OLS) estimate and the correlation among the model’s parameters at the pupil and school levels. The reliability of the level-2 outcome variables (which are the input variables of level-1) is expected to ensure that the data can detect systematic relations between within- and between-school variables (Raudenbush & Bryk, 1992). The reliabilities depend on two factors: first, the degree to which the true underlying pupil parameters vary from school to school; and, second, the precision with which each school regression equation is estimated. For each school at Level-2,

$$ \text{reliability}(\hat{\beta}_{pj}) = \frac{\tau_{\beta}}{\tau_{\beta}/[\tau_{\beta} + \sigma^2/t_{jk}]} \quad (7) $$

is the reliability of the schools’ sample mean as an estimate of its true mean. The average of these reliabilities across schools presented in Tables 2-4 provide summary measures of the reliability of the school means (Xiao, 2001).

This indicator demonstrates weak reliability of all regression coefficients, except $\hat{\beta}_{0j}$, and a decrease of overall reliability between the final model (Table 4) and the unconditional model (Table 2), which confirms the presence of potential underestimation bias of the size of the random effects on the outcome variable. However, it is worth noticing that the bias is small when the number of Level-1 observations is large and the number of Level-2 groups is small (Miller & Phillips, 2002), which is exactly the case in our study (5048 pupils in Level-1 and 275 schools in Level-2).

Hence, although the sampling error and endogeneity bias should be accounted for when interpreting the results presented in this paper, it is reasonable to assume that the bias size is not problematic in this application.
Conclusions

In sum, this HLM analysis provides empirical support for the contention that
academic organization and normative environment of schools have a substantial impact on
the social distribution of achievement within them. At the individual level, the base
mathematics score of the school, followed by the academic background of the pupil
(RATOTP and REPEAT), its gender as well as its home language play a statistically
significant role in the individual mathematics achievement. The only non-significant
parameter is the SES of the pupil. At the school level, the analysis shows that, overall,
individual mathematics achievement is facilitated in schools with a higher proportion of
students on-track (RATOTP), a higher average SES and a strong mastery of the subject by
the mathematics teacher (MATOTT). Pupils also tend to perform better in private schools
than in governmental schools (STYPE) which confirms the observed tendency for higher
achievement in schools with less disciplinary problems (DISCLIM). The home language
parameter loses of its significance when comparing between-school variations which
could be due to the specification problems of the variable ENGLISH as explained earlier.
However, the language proficiency parameter (RATOTP) increases even more its
explanatory capacity at the between-school level which makes it one of the most
significant explanatory variables of this model and confirms the role played by language
skills in learning achievement.

The policy implications of these results are a necessary improvement of the quality
of resource allocations in teacher training to improve the subject mastery of teachers and,
more generally, in the development of better supervision structures to improve the
disciplinary climate in governmental schools. Moreover, it is important to investigate
further the potential negative direct (on the targeted pupil) and indirect (via peer-effect)
role played by high repetition rates in primary education. Lastly, the positive results
reached by this study on the role played by linguistic parameters on learning achievement
should guide decision makers in their search for optimal solutions for school effectiveness.
Hence, this study wants to underscore the need for more and better information about
pupils' and teachers' home language and mother-tongue in further international surveys in
Africa to investigate deeper the actual efficiency of bilingual and multilingual education
programs on overall learning achievement.
Finally, although assumed to have a potential positive effect on the fit of the final model in view of the HIV/AIDS pandemic affecting the whole country, the health status of the pupils could not be accounted for by this study. Because less than half<fnref n="4" /> of the pupils sampled (N=2199 out of 5048) answered the question related to the reasons of their absenteeism (illness, work, family or fee not paid), and because of the very unspecific nature of the question, this parameter could not be included in this analysis. Moreover, in absence of information about the type of illness or the duration of absenteeism in the SACMEQ II dataset, the choice of this parameter as a proxy of the potential role of HIV/AIDS on learning achievement would have been highly questionable. Further research should therefore attempt, first of all, to collect appropriate data on this phenomenon in the frame of larger international surveys such as SACMEQ and, second, to include this parameter in an HLM analysis to respond to the concerns raised by many African Governments about the negative effects of the HIV/AIDS pandemic on school effectiveness.

<footnote n="4">⁴ The parameters retained in this HLM analysis suffered no missing data, except for the outcome variable. In the case of the total raw mathematics scores of the pupils, 58 cases (1.1 percent) were missing because of non-completion of the test but these data could be recomputed by estimating a probabilistic value from the school mean and the grand mean.</footnote>
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<table><caption>Table 1
Sample Descriptive Statistics</caption><thead><tr><th>Variables</th><th>N</th><th>Minimum</th><th>Maximum</th><th>Mean</th><th>Sid.</th><th>Skewness</th><th>Kurtosis</th></tr></thead><tbody><tr><td>MATOTP</td><td>5048</td><td>4.00</td><td>57.00</td><td>18.54</td><td>7.835</td><td>1.706 (.034)</td><td>3.649 (.069)</td></tr><tr><td>ENGLISH</td><td>5048</td><td>.00</td><td>1.00</td><td>.77</td><td>.421</td><td>-1.280 (.034)</td><td>-3.63 (.069)</td></tr><tr><td>FEMALE</td><td>5048</td><td>.00</td><td>1.00</td><td>.51</td><td>.500</td><td>-.049 (.034)</td><td>-1.998 (.069)</td></tr><tr><td>SES</td><td>5048</td><td>1.00</td><td>15.00</td><td>6.85</td><td>3.39</td><td>.315 (.034)</td><td>-.896 (.069)</td></tr><tr><td>RATOTP</td><td>5048</td><td>4.00</td><td>78.00</td><td>33.81</td><td>13.617</td><td>1.258 (.034)</td><td>.922 (.069)</td></tr><tr><td>REPEAT</td><td>5048</td><td>.00</td><td>1.00</td><td>.52</td><td>.500</td><td>-.063 (.034)</td><td>-1.997 (.069)</td></tr><tr><td>TOTENROL</td><td>5048</td><td>112.00</td><td>1510.00</td><td>594.61</td><td>297.186</td><td>.705 (.034)</td><td>-.074 (.069)</td></tr><tr><td>PTRATIO</td><td>5048</td><td>8.05</td><td>53.93</td><td>30.20</td><td>6.797</td><td>.239 (.034)</td><td>1.061 (.069)</td></tr><tr><td>TYPE</td><td>5048</td><td>.00</td><td>1.00</td><td>.95</td><td>.209</td><td>-4.338 (.034)</td><td>16.825 (.069)</td></tr><tr><td>SLOC</td><td>5048</td><td>.00</td><td>1.00</td><td>.44</td><td>.496</td><td>.257 (.034)</td><td>-1.935 (.069)</td></tr><tr><td>PRACAD</td><td>5048</td><td>.00</td><td>1.00</td><td>.48</td><td>.190</td><td>.150 (.034)</td><td>-.239 (.069)</td></tr><tr><td>DISCLIM</td><td>5048</td><td>.00</td><td>.92</td><td>.49</td><td>.180</td><td>.151 (.034)</td><td>-.427 (.069)</td></tr><tr><td>LGMNTY</td><td>5048</td><td>.00</td><td>1.00</td><td>.05</td><td>.226</td><td>.3953 (.034)</td><td>13.630 (.069)</td></tr><tr><td>MSES</td><td>5048</td><td>1.89</td><td>13.58</td><td>6.85</td><td>2.722</td><td>.527 (.034)</td><td>-.731 (.069)</td></tr><tr><td>TSEX</td><td>5048</td><td>.00</td><td>1.00</td><td>.46</td><td>.499</td><td>.154 (.034)</td><td>-1.977 (.069)</td></tr><tr><td>TSATPLRN</td><td>5048</td><td>.00</td><td>1.00</td><td>.94</td><td>.231</td><td>-3.845 (.034)</td><td>12.786 (.069)</td></tr><tr><td>MATOTT</td><td>5048</td><td>7.00</td><td>41.00</td><td>23.24</td><td>.343</td><td>.343 (.034)</td><td>-.439 (.069)</td></tr><tr><td>Valid N (Listwise)</td><td>5048</td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

Note: The skewness and kurtosis' Standard Errors are displayed in brackets.
<caption>Table 2</caption>

Unconditional Model

<table><thead><tr><th>Fixed Effects</th><th>Estimated<br>Coefficient</th><th>Robust<br>Standard<br>Error</th><th>t-Ratio</th></tr></thead><tbody><tr><td>Base score, μ<sub>0</sub></td><td>18.578</td><td>.433</td><td>42.875</td></tr><tr><td>ENGLISH, μ<sub>1</sub></td><td>.397</td><td>.163</td><td>2.441</td></tr><tr><td>FEMALE, μ<sub>2</sub></td><td>-.673</td><td>.125</td><td>-5.349</td></tr><tr><td>SES, μ<sub>3</sub></td><td>.045</td><td>.029</td><td>1.541</td></tr><tr><td>RATOTP, μ<sub>4</sub></td><td>.252</td><td>.010</td><td>22.562</td></tr><tr><td>REPEAT, μ<sub>5</sub></td><td>-.381</td><td>.139</td><td>-2.742</td></tr><tr><th>Random Parameter</th><th>Estimated<br>Parameter<br>Variance</th><th>Degrees of<br>Freedom</th><th>Chi-square</th><th>P-Value</th></tr><tr><td>Base score, β<sub>0</sub></td><td>43.570</td><td>233</td><td>1335.669</td><td>.000</td></tr><tr><td>ENGLISH, β<sub>1</sub></td><td>.439</td><td>233</td><td>216.276</td><td>&gt;.500</td></tr><tr><td>FEMALE, β<sub>2</sub></td><td>.682</td><td>233</td><td>242.089</td><td>.327</td></tr><tr><td>SES, β<sub>3</sub></td><td>.012</td><td>233</td><td>215.688</td><td>&gt;.500</td></tr><tr><td>RATOTP, β<sub>4</sub></td><td>.011</td><td>233</td><td>409.413</td><td>.000</td></tr><tr><td>REPEAT β<sub>5</sub></td><td>.880</td><td>233</td><td>252.234</td><td>.185</td></tr><tr><th>Correlation Matrix<br>of Random Effects</th><th>β<sub>0</sub></th><th>β<sub>1</sub></th><th>β<sub>2</sub></th><th>β<sub>3</sub></th><th>β<sub>4</sub></th></tr><tr><td>Base score, β<sub>0</sub></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>ENGLISH, β<sub>1</sub></td><td>-.192</td><td></td><td></td><td></td><td></td></tr><tr><td>FEMALE, β<sub>2</sub></td><td>-.650</td><td>-.540</td><td></td><td></td><td></td></tr><tr><td>SES, β<sub>3</sub></td><td>.602</td><td>-.601</td><td>.092</td><td></td><td></td></tr><tr><td>RATOTP, β<sub>4</sub></td><td>.915</td><td>.118</td><td>-.864</td><td>.278</td><td></td></tr><tr><td>REPEAT β<sub>5</sub></td><td>-.974</td><td>.193</td><td>.617</td><td>-.624</td><td>-.866</td></tr><tr><th>Reliability of Within-School Random Effects</th><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Base score, β<sub>0</sub></td><td></td><td></td><td></td><td>.788</td><td></td></tr><tr><td>ENGLISH, β<sub>1</sub></td><td></td><td></td><td></td><td>.050</td><td></td></tr><tr><td>FEMALE, β<sub>2</sub></td><td></td><td></td><td></td><td>.119</td><td></td></tr><tr><td>SES, β<sub>3</sub></td><td></td><td></td><td></td><td>.036</td><td></td></tr><tr><td>RATOTP, β<sub>4</sub></td><td></td><td></td><td></td><td>.315</td><td></td></tr><tr><td>REPEAT β<sub>5</sub></td><td></td><td></td><td></td><td>.127</td><td></td></tr></tbody></table>

Notes: All estimates for two-level models reported in this article were computed using the HLM6.0 program.

The reliability estimates reported above are based on only 234 of 270 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
Table 3

Between-School Effects: Conditional Model

<table><thead><tr><th>Fixed Effects</th><th>Estimated<br>Coefficient</th><th>Robust<br>Standard<br>Error</th><th>t-Ratio</th></tr></thead><tbody><tr><td>Base score, β<sub>0</sub></td><td></td><td></td><td></td></tr><tr><td>INTERCEPT(*)</td><td>17.5982</td><td>1.977</td><td>8.901</td></tr><tr><td>TOTENROL</td><td>-.0004</td><td>.001</td><td>-.464</td></tr><tr><td>PTRATIO</td><td>.0207</td><td>.0325</td><td>.594</td></tr><tr><td>TYPE</td><td>-2.4568</td><td>1.918</td><td>-1.281</td></tr><tr><td>SLOC</td><td>.4107</td><td>.511</td><td>.804</td></tr><tr><td>PRACAD</td><td>5.0594</td><td>.966</td><td>5.239</td></tr><tr><td>DISCLIM</td><td>2.0183</td><td>1.114</td><td>1.812</td></tr><tr><td>LGMNTY</td><td>-.2038</td><td>.667</td><td>-.306</td></tr><tr><td>MSES</td><td>.8508</td><td>.127</td><td>6.668</td></tr><tr><td>TSEX</td><td>.3916</td><td>.375</td><td>1.043</td></tr><tr><td>TSATPLRN</td><td>-.4477</td><td>.569</td><td>-.787</td></tr><tr><td>MATOTT</td><td>.1051</td><td>.030</td><td>3.548</td></tr><tr><td>ENGLISH, β<sub>1</sub></td><td></td><td></td><td></td></tr><tr><td>INTERCEPT(*)</td><td>.3433</td><td>.162</td><td>2.123</td></tr><tr><td>FEMALE, β<sub>2</sub></td><td></td><td></td><td></td></tr><tr><td>INTERCEPT(*)</td><td>-.6484</td><td>.127</td><td>-5.106</td></tr><tr><td>SES, β<sub>3</sub></td><td></td><td></td><td></td></tr><tr><td>INTERCEPT(*)</td><td>.0527</td><td>.030</td><td>1.758</td></tr><tr><td>RATOTP, β<sub>4</sub></td><td></td><td></td><td></td></tr><tr><td>INTERCEPT(*)</td><td>.2695</td><td>.011</td><td>24.184</td></tr><tr><td>REPEAT β<sub>5</sub></td><td></td><td></td><td></td></tr><tr><td>INTERCEPT(*)</td><td>-.3063</td><td>.133</td><td>-2.299</td></tr></tbody></table><table><thead><tr><th>Random Parameter</th><th>Estimated<br>Parameter<br>Variance</th><th>Degrees of<br>Freedom</th><th>Chi-square</th><th>P-Value</th></tr></thead><tbody><tr><td>Base score, β<sub>0</sub></td><td>17.300</td><td>222</td><td>651.016</td><td>.000</td></tr><tr><td>ENGLISH, β<sub>1</sub></td><td>.383</td><td>233</td><td>216.635</td><td>&gt;.500</td></tr><tr><td>FEMALE, β<sub>2</sub></td><td>.740</td><td>233</td><td>242.144</td><td>.326</td></tr><tr><td>SES, β<sub>3</sub></td><td>.012</td><td>233</td><td>216.462</td><td>&gt;.500</td></tr><tr><td>RATOTP, β<sub>4</sub></td><td>.011</td><td>233</td><td>397.302</td><td>.000</td></tr><tr><td>REPEAT, β<sub>5</sub></td><td>.716</td><td>233</td><td>252.032</td><td>.187</td></tr></tbody></table><table><thead><tr><th colspan="5">Reliability of Within-School Random Effects</th></tr></thead><tbody><tr><td>Base score, β<sub>0</sub></td><td></td><td></td><td></td><td>.615</td></tr><tr><td>ENGLISH, β<sub>1</sub></td><td></td><td></td><td></td><td>.044</td></tr><tr><td>FEMALE, β<sub>2</sub></td><td></td><td></td><td></td><td>.128</td></tr><tr><td>SES, β<sub>3</sub></td><td></td><td></td><td></td><td>.037</td></tr><tr><td>RATOTP, β<sub>4</sub></td><td></td><td></td><td></td><td>.318</td></tr><tr><td>REPEAT, β<sub>5</sub></td><td></td><td></td><td></td><td>.106</td></tr></tbody></table>

Notes: (*) INTERCEPT corresponds to the base score.

The reliability estimates reported above are based on only 234 of 270 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
<caption>Table 4 (1/2)</caption>

Final Explanatory Model of Mathematics Achievement

<table><thead><tr><th>Fixed Effects</th><th>Estimated<br>Coefficient</th><th>Robust<br>Standard Error</th><th>t-Ratio</th></tr></thead><tbody><tr><td>Base score, β<sub>0</sub></td><td></td><td></td><td></td></tr><tr><td>INTERCEPT</td><td>19.799</td><td>2.639</td><td>7.501</td></tr><tr><td>STYPE</td><td>-4.568</td><td>2.704</td><td>-1.689</td></tr><tr><td>SLOC</td><td>.210</td><td>.519</td><td>.405</td></tr><tr><td>PRACAD</td><td>6.405</td><td>1.088</td><td>5.884</td></tr><tr><td>MSES</td><td>1.392</td><td>.145</td><td>9.568</td></tr><tr><td>MATOTT</td><td>.147</td><td>.032</td><td>4.585</td></tr><tr><td>ENGLISH, β<sub>1</sub></td><td></td><td></td><td></td></tr><tr><td>INTERCEPT</td><td>-1.786</td><td>1.352</td><td>-1.321</td></tr><tr><td>STYPE</td><td>2.247</td><td>1.333</td><td>1.686</td></tr><tr><td>DISCLIM</td><td>-.029</td><td>.651</td><td>-.045</td></tr><tr><td>FEMALE, β<sub>2</sub></td><td></td><td></td><td></td></tr><tr><td>INTERCEPT</td><td>-.675</td><td>.119</td><td>-5.673</td></tr><tr><td>MSES</td><td>-.237</td><td>.053</td><td>-4.442</td></tr><tr><td>SES, β<sub>3</sub></td><td></td><td></td><td></td></tr><tr><td>INTERCEPT</td><td>-.169</td><td>.082</td><td>-2.054</td></tr><tr><td>DISCLIM</td><td>.436</td><td>.165</td><td>2.636</td></tr><tr><td>RATOTP, β<sub>4</sub></td><td></td><td></td><td></td></tr><tr><td>INTERCEPT</td><td>.091</td><td>.044</td><td>2.037</td></tr><tr><td>TOTENROL</td><td>-.000029</td><td>.000024</td><td>-1.215</td></tr><tr><td>STYPE</td><td>.061</td><td>.039</td><td>1.553</td></tr><tr><td>PRACAD</td><td>.213</td><td>.049</td><td>4.326</td></tr><tr><td>MSES</td><td>.018</td><td>.004</td><td>4.390</td></tr><tr><td>MATOTT</td><td>.004</td><td>.001</td><td>3.552</td></tr><tr><td>REPEAT β<sub>5</sub></td><td></td><td></td><td></td></tr><tr><td>INTERCEPT</td><td>-1.706</td><td>.814</td><td>-2.095</td></tr><tr><td>STYPE</td><td>1.423</td><td>.833</td><td>1.707</td></tr><tr><td>MSES</td><td>-.256</td><td>.059</td><td>-4.359</td></tr></tbody><tbody><tr><td colspan="4">Reliability of Within-School Random Effects</td></tr><tr><td>Base score, β<sub>0</sub></td><td></td><td>.576</td><td></td></tr><tr><td>ENGLISH, β<sub>1</sub></td><td></td><td>.034</td><td></td></tr><tr><td>FEMALE, β<sub>2</sub></td><td></td><td>.061</td><td></td></tr><tr><td>SES, β<sub>3</sub></td><td></td><td>.021</td><td></td></tr><tr><td>RATOTP, β<sub>4</sub></td><td></td><td>.133</td><td></td></tr><tr><td>REPEAT β<sub>5</sub></td><td></td><td>.051</td><td></td></tr></tbody></table>
<table><caption>**Table 4 (2/2)**
**Final Explanatory Model of Mathematics Achievement**</caption><thead><tr><th rowspan="2">Random Effects</th><th colspan="2">Estimated</th><th rowspan="2">Degrees of Freedom</th><th rowspan="2">Chi-square</th><th rowspan="2">P-Value</th></tr><tr><th>Parameter Variance</th><th>Parameter Variance</th></tr></thead><tbody><tr><td>Base score, β₀</td><td>14.494</td><td></td><td>228</td><td>554.245</td><td>.000</td></tr><tr><td>ENGLISH, β₁</td><td>.290</td><td></td><td>231</td><td>213.203</td><td>&gt;.500</td></tr><tr><td>FEMALE, β₂</td><td>.323</td><td></td><td>232</td><td>230.790</td><td>&gt;.500</td></tr><tr><td>SES, β₃</td><td>.007</td><td></td><td>232</td><td>214.036</td><td>&gt;.500</td></tr><tr><td>RATOTP, β₄</td><td>.003</td><td></td><td>228</td><td>275.374</td><td>.017</td></tr><tr><td>REPEAT, β₅</td><td>.321</td><td></td><td>231</td><td>241.338</td><td>.307</td></tr><tr><th rowspan="2">MODEL</th><th colspan="2">Base score</th><th colspan="2">ENGLISH</th><th colspan="2">Percentage of Variance Explained</th><th colspan="2">REPEAT</th></tr><tr><th>var(β₀)</th><th>%R²</th><th>var(β₁)</th><th>%R²</th><th>var(β₂)</th><th>%R²</th><th>var(β₃)</th><th>%R²</th><th>var(β₄)</th><th>%R²</th><th>var(β₅)</th><th>%R²</th></tr><tr><td>Unconditional</td><td>43.570</td><td>...</td><td>.439</td><td>...</td><td>.682</td><td>...</td><td>.012</td><td>...</td><td>.011</td><td>...</td><td>.880</td><td>...</td></tr><tr><td>Explanatory</td><td>14.494</td><td>66.73</td><td>.290</td><td>33.94</td><td>.323</td><td>52.64</td><td>.007</td><td>41.67</td><td>.003</td><td>72.72</td><td>.321</td><td>63.52</td></tr></tbody></table>

Notes: (*) INTERCEPT corresponds to the base score.

The reliability estimates reported above are based on only 234 of 270 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
<figure><img src="image_12.png" /><figcaption>Figure 1. English Proficiency by Home Language Stem-and-Leaf Plots</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Figure 2.1 Mathematics Achievement by Home Language Stem-and-Leaf Plots</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>Figure 2.2 Mathematics Achievement by Pupil's Gender Stem-and-Leaf Plots</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Figure 2.3 Mathematics Achievement by Pupil's SES Stem-and-Leaf Plots</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>Figure 2.4 Mathematics Achievement by English Proficiency Stem-and-Leaf Plots</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>Figure 2.5 Mathematics Achievement by Grade Repetition Stem-and-Leaf Plots</figcaption></figure>
# STUDY III
<figure><img src="image_18.png" /></figure>
# Language Skills and Economic Returns*

Christelle Garrouste⁺

Institute of International Education (IIE), Department of Education, Stockholm University,
10691 Stockholm, Sweden

## Abstract

This paper focuses on the contributions from the positivist epistemological approach, endorsed by the economics of language and the economics of education, to study the returns to language skills, assuming that language competencies constitute key components of human capital. It presents results on economic returns to language skills in eight countries enrolled in the International Adult Literacy Survey (IALS) – Chile, Czech Republic, Denmark, Finland, Hungary, Italy, Norway and Italian-speaking Switzerland. The study shows commonalities between countries in terms of language skills valuing, beyond the type of language policy applied at the national level. In each of the eight countries compared, skills in a second language are estimated to be a major factor constraining positively wage opportunities.

<footnote>* Reproduced with permission from *Policy Futures in Education*, 6(3) (in print). Copyright 2008 by Symposium Journals.</footnote>

<footnote>⁺ The author would like to acknowledge Statistics Canada for providing her with formal authorization to access and use the IALS data in the frame of this study. An earlier version of this paper was presented at the CIES conference, Honolulu, HI, March 14-18, 2006.</footnote>